[Logarithmic, Trigonometric, and Mathematical Tables for Artillery]
[From the U.S. Government Publishing Office, www.gpo.gov]
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WAR DEPARTMENT TECHNICAL MANUAL
NON-CIRCULATING
LOGARITHMIC, TRIGONOMETRIC, AND MATHEMATICAL TABLES FOR ARTILLERY
WAR DEPARTMENT
OCTOBER 1944
NTSU LIBRARY
WAR DEPARTMENT TECHNICAL MANUAL
TM 20-230
LOGARITHMIC, TRIGONOMETRIC, AND MATHEMATICAL TABLES FOR ARTILLERY
WAR DEPARTMENT
OCTOBER 1944
United States Government Printing Office
Washington : 1944
WAR DEPARTMENT, Washington 25, D. C., 28 October 1944.
TM 20-230, Logarithmic, Trigonometric, and Mathematical Tables for Artillery, is published for the information and guidance of all concerned.
[A. G. 300.7 (26 Aug 44).]
By order of the Secretary of War:
G. C. MARSHALL,
Chief of Staff. Official:
J. A. ULIO,
Major General,
The Adjutant General.
Distribution:
As prescribed in paragraph 9a, FM 21-6: Armies (10); Corps (10); Depts (10); D (2); R&H 4, 6, 44 (5); Bn 4, 6 (10) 18 (4); IBn 44 (10); Arm & Sv Boards (2); ROTC Units (1).
IBn 44: T/O & E 44-15; 44-115.
For explanation of symbols, see F M21-6.
(ii)
QUICK INDEX
CONTENTS
Table Page
I. Common logarithms of numbers_____________________________________ 1
II. Common logarithms of functions of angles in mils_________________ 23 I
III. Common logarithms of functions of angles in degrees and minutes. 40
IV. Stadia reductions_______________________________________________ 86
V. Horizontal distances for given slope distances and gradients from HiHIMBHI 0° to 30°__________________________________________________________ 95
VI. Horizontal distances for given slope distances and gradients from HHMI 0 mils to 500 mils___________________________________________________ 96 BflBlKai
VII. Conversion of degrees to mils; and mils to degrees______________ 97
VIII. Map scales in English measure and metric units_________________ 100
IX. Useful constants and formulae__________________________________ 101
X. Greek alphabet_______________________________________________ 103 | ‘
XI. Standard time signals________________________________________ 104 |
XII. Azimuths of Polaris at elongation, for the years 1944-54------ 106
XIII. Mean astronomic refraction, with corrections----------------- 107 r‘J?
XIV. Parallax and altitude of the sun----------------------------- 109
XV. Curvature and refraction_____________________________________ 110 KgQBHIj]
XVI. Natural sines and cosines of angles in mils__________________ 111
XVII. Natural tangents and cotangents of angles in mils_____________ 116 ggHHKlgJHr
XVIII. Natural sines and cosines of angles in degrees and minutes--- 121 I ‘ C'
XIX. Natural tangents and cotangents of angles in degrees and minutes. 131
XX. Corrections to Ay for magnification of scale_________________ 144
(ni)
Purpose and scope. This manual provides artillery units with tables and data for survey and other mathematical computations.
Table I.—Common Logarithms of Numbers
1. Mantissa.—The mantissa or decimal part of a logarithm is always positive, and depends only upon the digits of a number. It remains unchanged as long as the sequence of the digits remains unchanged.
2. Characteristic.—a. For numbers greater than unity, the characteristic or integral part of the logarithm is one less than the number of integral digits and is always positive. Thus:
Log 1359 = 3.13322
Log 135.9 = 2.13322
Log 13.59 = 1.13322
Log 1.359 = 0.13322
6. For numbers less than unity, the characteristic is negative. It is one more than the number of ciphers between the decimal point and the first significant figure. Since the mantissa is positive, the negative sign is placed above the characteristic to show that it only is negative. Thus:
Log 0.1359 =7.13322 or 9.13322-10
Log 0.01359 =2.13322 or 8.13322-10
Log 0.001359 = 3.13322 or 7.13322-10
Log 0.0001359 = 4.13322 or 6.13322-10
3. Multiplication and division of numbers by logarithms.—Since logarithms are exponents, the logarithm of a product is the sum of the logarithm of the factors. Thus:
Log 20=log (10X2) =log 10+log 2 = 0.30103 + 1.00000=1.30103
Log 2000=log (2X1000)=log 2+log 1000=0.30103 + 3.00000=3.301Q3
Log 0.2=log (2X0.1) =log2+log 0.1 = 0.30103+7.00000=7.30103 = 9.30103-10
Log 0.02 = log (2X0.01) =log 2+log 0.01=0.30103
2.00000=2.30103 = 8.30103 —10
For division, the logarithms of the two numbers are substracted, the divisor being subtracted from the dividend.
4. Powers and roots.—The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power. The logarithm of the root of a number is equal to the logarithm of the number divided by the index of the root.
5. Proportional parts.—Suppose it is required to find the logarithm of 2245.7. First find the mantissa for 2245. This is 35122. Next find the mantissa of the next greater number, or 2246. This is 35141. The difference is:
35141
35122
19
1
Table I.—Common Logarithms of Numbers
Under the column head “Proportional parts,” find that group headed by 19. Since 2245.7 is seven-tenths greater than 2245, find the number opposite 7 in this group or 13.3. Add this to the mantissa of 2245 or
35122
13,3
35135.3 = mantissa of 22457.
The logarithm of 2245.7 is, therefore, 3.351353.
If it is required to find a number, given a logarithm, the method is reversed. Thus, suppose it is required to find the number whose logarithm is 3.35135. This mantissa cannot be found in the table. Therefore, find the two mantissas between which the given mantissa lies. They are 35122 and 35141. The difference between them is 19. The difference between the smaller mantissa and that given is—
35135
35122
13
Then find what number is opposite 13 in the group of proportional parts headed by 19. This is found to be 7. The number required is therefore 2245.7.
Had the given logarithm above been 35136, the difference would have been 14 instead of 13. Since 14 does not appear in the column of proportional parts, take the number closest thereto. In this case 13.3 is closer to 14 than is 15.2, so that line would be used giving the number 2245.7, same as above.
2
Table I.—Common Logarithms of Numbers
N. L. 0 1 2 3 4 5 6 7 8 9
0 00 000 30 103 47 712 60 206 69 897 77 815 84 510 90 309 95 424
1 00 000 04 139 07 918 11 394 14 613 17 609 20 412 23 045 25 527 27 875
2 30 103 32 222 34 242 36 173 38 021 39 794 41 497 43 136 44 716 46 240
3 47 712 49 136 50 515 51 851 53 148 54 407 55 630 56 820 57 978 59 106
4 60 206 61 278 62 325 63 347 64 345 65 321 66 276 67 210 68 124 69 020
3 69 897 70 757 71 600 72 428 73 239 74 036 74 819 75 587 76 343 77 085
6 77 815 78 533 79 239 79 934 80 618 81 291 81 954 82 607 83 251 83 885
7 84 510 85 126 85 733 86 332 86 923 87 506 88 081 88 649 89 209 89 763
8 90 309 90 849 91 381 91 908 92 428 92 942 93 450 93 952 94 448 94 939
0 95 424 95 904 96 379 96 848 97 313 97 772 98 227 98 677 99 123 99 564
10 00 000 00 432 00 860 01 284 01 703 02 119 02 531 02 938 03 342 03 743
11 04 139 04 532 04 922 05 308 05 690 06 070 06 446 06 819 07 188 07 555
12 07 918 08 279 08 636 08 991 09 342 09 691 10 037 10 380 10 721 11 059
13 11 394 11 727 12 057 12 385 12 710 13 033 13 354 13 672 13 988 14 301
14 14 613 14 922 15 229 15 534 15 836 16 137 16 435 16 732 17 026 17 319
15 17 609 17 898 18 184 18 469 18 752 19 033 19 312 19 590 19 866 20 140
16 20 412 20 683 20 952 21 219 21 484 21 748 22 011 22 272 22 531 22 789
17 23 045 23 300 23 553 23 805 24 055 24 304 24 551 24 797 25 042 25 285
18 25 527 25 768 26 007 26 245 26 482 26 717 26 951 27 184 27 416 27 646
19 27 875 28 103 28 330 28 556 28 780 29 003 29 226 29 447 29 667 29 885
20 30 103 30 320 30 535 30 750 30 963 31 175 31 387 31 597 31 806 32 015
21 32 222 32 428 32 634 32 838 33 041 33 244 33 445 33 646 33 846 34 044
22 34 242 34 439 34 635 34 830 35 025 35 218 35 411 35 603 35 793 35 984
23 36 173 36 361 36 549 36 736 36 922 37 107 37 291 37 475 37 658 37 840
24 38 021 38 202 38 382 38 561 38 739 38 917 39 094 39 270 39 445 39 620
25 39 794 39 967 40 140 40 312 40 483 40 654 40 824 40 993 41 162 41 330
26 41 497 41 664 41 830 41 996 42 160 42 325 42 488 42 651 42 813 42 975
27 43 136 43 297 43 457 43 616 43 775 43 933 44 091 44 248 44 404 44 560
28 44 716 44 871 45 025 45 179 45 332 45 484 45 637 45 788 45 939 46 090
29 46 240 46 389 46 538 46 687 46 835 46 982 47 129 47 276 47 422 47 567
30 47 712 47 857 48 001 48 144 48 287 48 430 48 572 48 714 48 855 48 996
31 49 136 49 276 49 415 49 554 49 693 49 831 49 969 50 106 50 243 50 379
32 50 515 50 651 50 786 50 920 51 055 51 188 51 322 51 455 51 587 51 720
33 51 851 51 983 52 114 52 244 52 375 52 504 52 634 52 763 52 892 53 020
34 53 148 53 275 53 403 53 529 53 656 53 782 53 908 54 033 54 158 54 283
35 54 407 54 531 54 654 54.777 54 900 55 023 55 145 55 267 55 388 55 509
36 55 630 55 751 55 871 55 991 56 110 56 229 56 348 56 467 56 585 56 703
37 56 820 56 937 57 054 57 171 57 287 57 403 57 519 57 634 57 749 57 864
38 57 978 58 092 58 206 58 320 58 433 58 546 58 659 58 771 58 883 58 995
39 59 106 59 218 59 329 59 439 59 550 59 660 59 770 59 879 59 988 60 097
40 60 206 60 314 60 423 60 531 60 638 60 746 60 853 60 959 61 066 61 172
41 61 278 61 384 61 490 61 595 61 700 61 805 61 909 62 014 62 118 62 221
42 62 325 62 428 62 531 62 634 62 737 62 839 62 941 63 043 63 144 63 246
43 63 347 63 448 63 548 63 649 63 749 63 849 63 949 64 048 64 147 64 246
44 64 345 64 444 64 542 64 640 64 738 64 836 64 933 65 031 65 128 65 225
45 65 321 65 418 65 514 65 610 65 706 65 801 65 896 65 992 66 087 66 181
46 66 276 66 370 66 464 66 558 66 652 66 745 66 839 66 932 67 025 67 117
47 67 210 67 302 67 394 67 486 67 578 67 669 67 761 67 852 67 943 68 034
48 68 124 68 215 68 305 68 395 68 485 68 574 68 664 68 753 68 842 68 931
49 69 020 69 108 69 197 69 285 69 373 69 461 69 548 69 636 69 723 69 810
50 69 897 69 984 70 070 70 157 70 243 70 329 70 415 70 501 70 586 70 672
N. L. 0 1 2 3 4 5 0 7 8 9
3
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9
50 69 897 69 984 70 070 70 157 70 243 70 329 70 415 70 501 70 586 70 672
51 70 757 70 842 70 927 71 012 71 096 71,181 71 265 71 349 71 433 71 517
52 71 600 71 684 71 767 71 850 71 933 72 016 72 099 72 181 72 263 72 346
53 72 428 72 509 72 591 72 673 72 754 72 835 72 916 72 997 73 078 73 159
54 73 239 73 320 73 400 73 480 73 560 73 640 73 719 73 799 73 878 73 957
55 74 036 74 115 74 194 74 273 74 351 74 429 74 507 74 586 74 663 74 741
56 74 819 74 896 74 974 75 051 75 128 75 205 75 282 75 358 75 435 75 511
57 75 587 75 664 75 740 75 815 75 891 75 967 76 042 76 118 76 193 76 268
58 76 343 76 418 76 492 76 567 76 641 76 716 76 790 76 864 76 938 77 012
59 77 085 77 159 77 232 77 305 77 379 77 452 77 525 77 597 77 670 77 743
60 77 815 77 887 77 960 78 032 78 104 78 176 78 247 78 319 78 390 78 462
61 78 533 78 604 78 675 78 746 78 817 78 888 78 958 79 029 79 099 79 169
62 79 239 79 309 79 379 79 449 79 518 79 588 79 657 79 727 79 796 79 865
63 79 934 80 003 80 072 80 140 80 209 80 277 80 346 80 414 80 482 80 550
64 80 618 80 686 80 754 80 821 80 889 80 956 81 023 81 090 81 158 81 224
65 81 291 81 358 81 425 81 491 81 558 81 624 81 690 81 757 81 823 81 889
66 81 954 82 020 82 086 82 151 82 217 82 282 82 347 82 413 82 478 82 543
67 82 607 82 672 82 737 82 802 82 866 82 930 82 995 83 059 83 123 83 187
68 83 251 83 315 83 378 83 442 83 506 83 569 83 632 83 696 83 759 83 822
69 83 885 83 948 84 011 84 073 84 136 84 198 84 261 84 323 84 386 84 448
70 84 510 84 572 84 634 84 696 84 757 84 819 84 880 84 942 85 003 85 065
71 85 126 85 187 85 248 85 309 85 370 85 431 85 491 85 552 85 612 85 673
72 85 733 85 794 85 854 85 914 85 974 86 034 86 094 86 153 86 213 86 273
73 86 332 86 392 86 451 86 510 86 570 86 629 86 688 86 747 86 806 86 864
74 86 923 86 982 87 040 87 099 87"157 87 216 87 274 87 332 87 390 87 448
75 87 506 87 564 87 622 87 679 87 737 87 795 87 852 87 910 87 967 88 024
76 88 081 88 138 88 195 88 252 88 309 88 366 88 423 88 480 88 536 88 593
77 88 649 88 705 88 762 88 818 88 874 88 930 88 986 89 042 89 098 89 154
78 89 209 89 265 89 321 89 376 89 432 89 487 89 542 89 597 89 653 89 708
79 89 763 89 818 89 873 89 927 89 982 90 037 90 091 90 146 90 200 90 255
80 90 309 90 363 90 417 90 472 90 526 90 580 90 634 90 687 90 741 90 795
81 90 849 90 902 90 956 91 009 91 062 91 116 91 169 91 222 91 275 91 328
82 91 381 91 434 91 487 91 540 91 593 91 645 91 698 91 751 91 803 91 855
83 91 908 91 960 92 012 92 065 92 117 92 169 92 221 92 273 92 324 92 376
84 92 428 92 480 92 531 92 583 92'634 92 686 92 737 92 788 92 840 92 891
85 92 942 92 993 93 044 93 095 93 146 93 197 93 247 93 298 93 349 93 399
86 93 450 93 500 93 551 93 601 93 651 93 702 93 752 93 802 93 852 93 902
87 93 952 94 002 94 052 94 161 * 94*151 94 201 94 250 94 300 94 349 94 399
88 94 448 94 498 94 547 94 596 94 645 94 694 94 743 94 792 94 841 94 890
89 94 939 94 988 95 036 95 085 95 134 95 182 95 231 95 279 95 328 95 376
90 95 424 95 472 95 521 95 569 95 617 95 665 95 713 95 761 95 809 95 856
91 95 904 95 952 95 999 96 047 96 095 96 142 96 190 96 237 96 284 96 332
92 96 379 96 426 96 473 96 520 96 567 96 614 96 661 96 708 96 755 96 802
93 96 848 96 895 96 942 96 988 97 035 97 081 97 128 97 174 97 220 97 267
94 97 313 97 359 97 405 97 451 97 497 97 543 97 589 97 635 97 681 97 727
95 97 772 97 818 97 864 97 909 97 955 98 000 98 046 98 091 98 137 98 182
96 98 227 98 272 98 318 98 363 98 408 98 453 98 498 98 543 98 588 98 632
97 98 677 98 722 98 767 98 811 98 856 98 900 98 945 98 989 99 034 99 078
98 99 123 99 167 99 211 99 255 99 300 99 344 99 388 99 432 99 476 99 520
99 99 564 99 607 99 651 99 695 99 739 99 782 99 826 99 870 99 913 99 957
100 00 000 00 043 00 087 00 130 00 173 00 217 00 260 00 303 00 346 00 389
N. L. 0 1 2 3 4 5 6 7 8 9
4
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
100 00 000 043 087 130 173 217 260 303 346 389
101 432 475 518 561 604 647 689 732 775 817 44 43 42
102 860 903 945 988 ,030 ,072 ,115 ,157 ,199 ,242 1 4,4 4,3 4,2
103 01 284 326 368 410 452 494 536 578 620 662 2 8,8 8,6 8,4
3 13,2 12,9 12,6
104 703 745 787 828 870 912 953 995 ,036 .078 4 17,6 17,2 16,8
105 02 119 160 202 243 284 325 366 407 449 490 5 22,0 21,5 21,0
106 531 572 612 653 694 735 776 816 857 898 6 26,4 25,8 25,2
7 30,8 30,1 29,4
107 938 979 ,019 ,060 ,100 .141 .181 ,222 .262 ,302 8 35,2 34,4 33,6
108 03 342 383 423 463 503 543 583 623 663 703 9 39,6 38,7 37,8
109 743 782 822 862 902 941 981 ,021 ,060 ,100
110 04 139 179 218 258 297 336 376 415 454 493
111 532 571 610 650 689 727 766 805 844 883 41 40 39
112 922 961 999 .038 ,077 .115 ,154 .192 .231 .269 i x 1 4 o a q
113 05 308 346 385 423 461 500 538 576 614 652 2 8,2 8,0 7,8
114 690 729 767 805 843 881 918 956 994 .032 3 12/3 12/0 11/7 4 16/4 16z0 15z6
115 06 070 108 145 183 221 258 296 333 371 408 5 20 5 20 0 19/5
116 446 483 521 558 595 633 670 707 744 781 6 24,6 24,0 23,4
117 819 856 893 930 967 ,004 ,041 .078 .115 ,151 7 28/7 28/0 27/3 . 8 32/8 32/0 31 z2
118 07 188 225 262 298 335 372 408 445 482 518 9 36/9 36/0 35/1
119 555 591 628 664 700 737 773 809 846 882
120 918 954 990 ,027 .063 ,099 ,135 .171 ,207 ,243
121 08 279 314 350 386 422 458 493 529 565 600 38 37 36
122 636 672 707 743 778 814 849 884 920 955
123 991 ,026 ,061 ,096 *132 ,167 ,202 .237 ,272 ,307 2 7,6 7,4 7,2
124 09 342 377 412 447 482 517 552 587 621 656 3 11/4 11/1 10/8 4 15 9. 148 144
125 691 726 760 795 830 864 899 934 968 ,003 5 19 0 18/5 18/0
126 10 037 072 106 140 175 209 243 278 312 346 6 22,8 22,2 21,6
127 380 415 449 483 517 551 585 619 653 687 7 26/6 25/9 25/2 8 30/4 29/6 28/8
128 721 755 789 823 857 890 924 958 992 .025 9 34^2 334 324
129 11 059 093 126 160 193 227 261 294 327 361
130 394 428 461 494 528 561 594 628 661 694
131 727 760 793 826 860 893 926 959 992 ,024 35 34 33
132 12 057 090 123 156 189 222 254 287 320 352 1 2 5 2 4 2,2
133 385 418 450 483 516 548 581 613 646 678 2 7,0 6,8 6,6
134 710 743 775 808 840 872 905 937 969 ,001 3 10/5 10/2 9/9 4 14/0 13/6 13/2
135 13 033 066 098 130 162 194 226 258 290 322 5 17/5 17/0 16/5
136 354 386 418 450 481 513 545 577 609 640 6 21,0 204 19,8
137 672 704 735 767 799 830 862 893 925 956 7 24/5 23/8 23/1 8 28/0 27/2 26z4
138 988 ,019 ,051 ,082 ,114 ,145 ,176 .208 ,239 ,270 9 31,5 30,6 29,7
139 14 301 333 364 395 426 457 489 520 551 582
140 613 644 675 706 737 768 799 829 860 891
141 922 953 983 ,014 ,045 ,076 ,106 .137 ,168 .198 32 31 30
142 15 229 259 290 320 351 381 412 442 473 503 1 2 2 2.1 3,0
143 534 564 594 625 655 685 715 746 776 806 2 64 6,2 6,0
144 836 866 897 927 957 987 ,017 .047 .077 .107 3 9,6 9,3 9,0 4 12,8 12,4 12,0
145 16 137 167 197 227 256 286 316 346 376 406 5 16/0 15/5 15/0
146 435 465 495 524 554 584 613 643 673 702 6 19,2 18,6 18,0
147 732 761 791 820 850 879 909 938 967 997 7 22,4 21,7 21,0 8 25,6 24,8 24,0
148 17 026 056 085 114 143 173 202 231 260 289 9 28,8 27,9 27,0
149 319 348 377 406 435 464 493 522 551 580
150 609 638 667 696 725 754 782 811 840 869
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
5
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop Pts.
150 17 609 638 667 696 725 754 782 811 840 869
151 898 926 955 984 ,013 ,041 ,070 ,099 ,127 ,156 29 28
152 18 184 213 241 270 298 327 355 384 412 441
153 469 498 526 554 583 611 639 667 696 724 1 2,9 2 5,8 2,8 5,6
154 752 780 808 837 865 893 921 949 977 ,005 3 8,7 8,4
155 19 033 061 089 117 145 173 201 229 257 285 4 11,6 11/2
156 312 340 368 396 424 451 479 507 535 562 5 14,5 6 17,4 14,0 16,8
157 590 618 645 673 700 728 756 783 811 838 7 20,3 19,6
158 866 893 921 948 976 ,003 ,030 ,058 ,085 ,112 8 23,2 22,4
159 20 140 167 194 222 249 276 303 330 358 385 9 26,1 25,2
160 412 439 466 493 520 548 575 602 629 656
161 683 710 737 763 790 817 844 871 898 925 27 26
162 952 978 ,005 ,032 ,059 *085 ,112 ,139 ,165 ,192
163 21 219 245 272 299 325 352 378 405 431 458 1 2,7 2 5,4 2,6 5,2
164 484 511 537 564 590 617 643 669 696 722 3 8,1 7,8
165 748 775 801 827 854 880 906 932 958 985 4 10/8 10,4
166 22 011 037 063 089 115 141 167 194 220 246 5 13,5 6 16,2 13,0 15,6
167 272 298 324 350 376 401 427 453 479 505 7 18,9 18,2
168 531 557 583 608 634 660 686 712 737 763 8 21,6 20,8
169 789 814 840 866 891 917 943 968 994 ,019 9 24/3 23,4
170 23 045 070 096 121 147 172 198 223 249 274
171 300 325 350 376 401 426 452 477 502 528 25 '
172 553 578 603 629 654 679 704 729 754 779
173 805 830 855 880 905 930 955 980 ,005 ,030 1 2 2,5 5,0
174 24 055 080 105 130 155 180 204 229 254 279 3 7,5
175 304 329 353 378 403 428 452 477 502 527 * 1U/U
176 551 576 601 625 650 674 699 724 748 773 5 12/5 6 15/0
177 797 822 846 871 895 920 944 969 993 ,018 7 17,5
178 25 042 066 091 115 139 164 188 212 237 261 8 20,0
179 285 310 334 358 382 406 431 455 479 503 9 22,5
180 527 551 575 600 624 648 672 696 720 744
181 768 792 816 *840 864 888 912 935 959 983 24 23
182 26 007 031 055 079 102 126 150 174 198 221
183 245 269 293 316 340 364 387 411 435 458 1 2/4 2 4/8 2,3 4,6
184 482 505 529 553 576 600 623 647 670 694 3 7,2 6,9
185 717 741 764 788 811 834 858 881 905 928 4 9,6 9,2
186 951 975 998 ,021 ,045 ,068 ,091 ,114 ,138 ,161 5 12/0 6 14/4 11,5 13,8
187 27 184 207 231 254 277 300 323 346 370 393 7 16,8 16,1
188 416 439 462 485 508 531 554 577 600 623 8 19,2 18,4
189 646 669 692 715 738 761 784 807 830 852 9 21,6 20,7
ISO 875 898 921 944 967 989 ,012 ,035 ,058 ,081
191 28 103 123 149 171 194 217 240 262 285 307 22 21
192 330 353 375 398 421 443 466 488 511 533
193 556 578 601 623 646 668 691 713 735 758 1 2,2 2,1
2 4,4 4,2
194 780 803 825 847 870 892 914 937 959 981 3 6,6 6,3
195 29 003 026 048 070 092 115 137 159 181 203 4 8,8 8/4
196 226 248 270 292 314 336 358 380 403 425 5 11,0 6 13,2 10,5 12,6
197 447 469 491 513 535 557 5?9 601 623 645 7 15,4 14,7
198 667 688 710 732 754 776 798 820 842 863 8 17,6 16,8
199 885 907 929 951 973 994 016 038 060 ,081 9 19,8 18,9
200 30 103 125 146 168 190 211 233 255 276 298
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
6
Table I.-—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
200 30 103 125 146 168 190 211 233 255 276 298
201 320 341 363 384 406 428 449 471 492 514 22 21
202 535 557 578 600 621 643 664 685 707 728
203 750 771 792 814 835 856 878 899 920 942 2 4,4 4,2
204 963 984 *006 *027 *048 *069 .091 ,112 .133 ,154 3 6Z6 6/3
205 31 175 197 218 239 260 281 302 323 34b 366
206 387 408 429 450 471 492 513 534 555 576 6 13,2 12/6
207 597 618 639 660 681 702 723 744 765 785 7 15/4 14/7 R 17z6 16/8
208 806 827 848 869 890 911 931 952 973 994 9 19/8 18/9
209 32 015 035 056 077 098 118 139 160 181 201
210 222 243 263 284 305 325 346 366 387 408
211 428 449 469 490 510 531 552 572 593 613 20
212 634 654 675 695 715 736 756 777 797 818
213 838 858 879 899 919 940 960 980 ,001 ,021 2 4/0
214 33 041 062 082 102 122 143 163 183 203 224 3 6/0
215 244 264 284 304 325 345 365 385 405 425
216 445 465 486 506 526 546 566 586 606 626 6 12/0
217 646 666 686 706 726 746 766 786 806 826 7 14/0 8 16/0
218 846 866 885 905 925 945 965 985 ,005 .025 9 18/0
219 34 044 064 084 104 124 143 163 183 203 223
220 242 262 282 301 321 341 361 380 400 420
221 439 459 479 498 518 537 557 577 596 616 IS
222 635 655 674 694 713 733 753 772 792 811 1 19
223 830 850 869 889 908 928 947 967 986 ,005 2 3,8
224 35 025 044 064 083 102 122 141 160 180 199 3 5/7 4 7/6
225 218 238 257 276 295 315 334 353 372 392
226 411 430 449 468 488 507 526 545 564 583 6 11,4
227 603 622 641 660 679 698 717 736 755 774 7 13/3 8 15/2
228 793 813 832 851 870 889 908 927 946 965 9 17/1
229 984 *003 *021 *040 *059 ,078 *097 ,116 ,135 ,154
230 36 173 192 211 229 248 267 286 305 324 342
231 361 380 399 418 436 455 474 493 511 530 18
232 549 568 586 605 624 642 6C1 680 698 717 1 1/8
233 736 754 773 791 810 829 847 866 884 903 2 3,6
234 922 940 959 977 996 *014 *033 ,051 ,070 ,088 3 5/4 4 7/2
235 37 107 125 144 162 181 199 218 236 254 273 5 9/0
236 291 310 328 346 365 383 401 420 438 457 6 10,8
237 475 493 511 530 548 566 585 603 621 639 7 12/6 8 14/4
238 658 676 694 712 731 749 767 785 803 822 9 16,2
239 840 858 876 894 912 931 949 967 985 ,003
240 38 021 039 057 075 093 112 130 148 166 184
241 202 220 238 256 274 292 310 328 346 364 17
242 382 399 417 435 453 471 489 507 525 543 1 1/7
243 561 578 596 614 632 650 668 686 703 721 2 3/4
244 739 757 775 792 810 828 846 863 881 899 3 5,1 4 6,8
245 917 934 952 970 987 *005 ,023 ,041 ,058 *076 5 8/5
246 39 094 111 129 146 164 182 199 217 23b 252 6 10,2
247 270 287 305 322 340 3.58 375 393 410 428 7 11,9 8 13,6
248 445 463 480 498 515 533 550 568 585 602 9 15,3
249 620 637 655 672 690 707 724 742 759 777
250 794 811 829 846 863 881 898 915 933 950
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
7
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
250 39 794 811 829 846 863 881 898 915 933 950
251 967 985 ♦002 ♦019 ♦037 ♦054 *071 ♦088 .106 *123 18
252 40 140 157 175 192 209 226 243 261 278 295
253 312 329 346 364 381 398 415 432 449 466 1 1,8 2 3,6
254 483 500 518 535 552 569 586 603 620 637 3 5,4
255 654 671 688 705 722 739 756 773 790 807 4 7,2
256 824 841 858 875 892 909 926 943 960 976 5 9,0 6 10,8
257 993 ♦010 ♦027 ♦044 ♦061 *078 *095 *111 *128 ♦145 7 12,6
258 41 162 179 196 212 229 246 263 280 296 313 8 14z4
259 330 347 363 380 397 414 430 447 464 481 9 16,2
260 497 514 531 547 564 581 597 614 631 647
261 664 681 697 714 731 747 764 780 797 814 17
262 830 847 863 880 896 913 929 946 963 979
263 996 ♦012 ♦029 *045 ♦062 *078 ♦095 *111 .127 ♦144 1 1,7 2 3,4
264 42 160 177 193 210 226 243 259 275 292 308 3 5,1
265 325 341 357 374 390 406 423 439 455 472 4 6,8
266 488 504 521 537 553 570 586 602 619 635 5 8,5
6 10,2
267 651 667 684 700 716 732 749 765 781 797 7 11,9
268 813 830 846 862 878 894 911 927 943 959 8 13,6
269 975 991 *008 *024 *040 ,056 *072 *088 .104 .120 9 15,3
270 43 136 152 169 185 201 217 233 249 265 281
271 297 313 329 345 361 377 393 409 425 441 16
272 457 473 489 505 521 537 553 569 584 600
273 616 632 648 664 680 696 712 727 743 759 1 1,6
2 3,2
274 775 791 807 823 838 854 870 886 902 917 3 4,8
275 933 949 965 981 996 *012 *028 *044 *059 ♦075 4 6,4
276 44 091 107 122 138 154 170 185 201 217 232 5 8,0
6 9,6
277 248 264 279 295 311 326 342 358 373 389 7 11,2
278 404 420 436 451 467 483 498 514 529 545 8 12,8
279 560 576 592 607 623 638 654 669 685 700 9 14,4
280 716 731 747 762 778 793 809 824 840 855
281 871 886 902 917 932 948 963 979 994 ♦010 15
282 45 025 040 056 071 086 102 117 133 148 163
283 179 194 209 225 240 255 271 286 301 317 1 1,5
2 3,0
284 332 347 362 378 393 408 423 439 454 469 3 4,5
285 484 500 515 530 545 561 576 591 606 621 4 6,0
286 637 652 667 682 697 712 728 743 758 773 5 7,5 6 9,0
287 788 803 818 834 849 864 879 894 909 924 7 10,5
288 939 954 969 984 ♦000 .015 *030 .045 .060 ♦075 8 12,0
289 46 090 105 120 135 150 165 180 195 210 225 9 13z5
290 240 255 270 285 300 315 330 345 359 374
291 389 404 419 434 449 464 479 494 509 523 14
292 538 553 568 583 598 613 627 642 657 672
293 687 702 716 731 746 761 776 790 805 820 1 1,4
2 2,8
294 835 850 864 879 894 909 923 938 953 967 3 4,2
295 982 997 ♦012 ♦026 ♦041 .056 ♦070 ,085 ♦100 .114 4 5,6
296 47 129 144 159 173 188 202 217 232 246 261 5 7,0 6 8,4
297 276 290 305 319 334 349 363 378 392 407 7 9,8
298 422 436 451 465 480 494 509 524 538 553 8 11/2
299 567 582 596 611 625 640 654 669 683 698 9 12,6
300 712 727 741 756 770 784 799 813 828 842
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
8
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
300 47 712 727 741 756 770 784 799 813 828 842
301 857 871 885 9Q0 914 929 943 958 972 986
302 48 001 015 029 044 058 073 087 101 116 130
303 144 159 173 187 202 216 230 244 259 273
304 287 302 316 330 344 359 373 387 401 416 15
305 430 444 458 473 487 501 515 530 544 558 1 1,5
300 572 586 601 615 629 643 657 671 686 700 2 3,0
3 4,5
307 714 728 742 756 770 785 799 813 827 841 4 6,0
308 855 869 883 897 911 926 940 954 968 982 5 7,5
309 996 ,010 ,024 ,038 ,052 ,066 ,080 ,094 ,108 ,122 6 9,0
310 49 136 150 164 178 192 206 220 234 248 262 8 12,0
9 1.3 5
311 276 290 304 318 332 346 360 374 388 402
312 415 429 443 457 471 485 499 513 527 541
313 554 568 582 596 610 624 638 651 665 679
314 693 707 721 734 748 762 776 790 803 817
315 831 845 859 872 886 900 914 927 941 955
316 969 982 996 ,010 ,024 ,037 ,051 ,065 ,079 ,092
1 1,4
317 50 1 06 120 133 147 161 174 188 202 215 229 2 2,8
318 243 256 270 284 297 311 325 338 352 365 3 4,2
319 379 393 406 420 433 447 461 474 488 501 4 5,6
5 7 0
320 515 529 542 556 569 583 596 610 623 637 6 8,4
7 9 8
321 651 664 678 691 705 718 732 745 759 772 8 11'2
322 786 799 813 826 840 853 866 880 893 907 9 12,6
323 920 934 947 961 974 987 ,001 ,014 ,028 ,041
324 51 055 068 081 095 108 121 135 148 162 175
325 188 202 215 228 242 255 268 282 295 308'
326 322 335 348 362 375 388 402 415 428 441
327 455 468 481 495 508 521 534 548 561 574 13
328 587 601 614 627 640 654 667 680 693 706 1 1/3
329 720 733 746 759 772 786 799 812 825 838 2 2/6
330 851 865 878 891 904 917 930 943 957 970 4 5/2
6 5
331 983 996 ,009 ,022 ,035 ,048 ,061 ,075 ,088 ,101 6 7'8
332 52 114 127 140 153 166 179 192 205 218 231 7 9/1
333 244 257 270 284 297 310 323 336 349 362 8 10,4
9 H/7
334 375 388 401 414 427 440 453 466 479 492
335 504 517 530 543 556 569 582 595 608 621
336 634 647 660 673 686 699 711 724 737 750
337 763 776 789 802 815 827 840 853 866 879
338 892 905 917 930 943 956 969 982 994 ,007
339 53 020 033 046 058 071 084 097 110 122 135 12
340 148 161 173 186 199 212 224 237 250 263 1 1/2
2
341 275 288 301 314 326 339 352 364 377 390 3 3,6
342 403 415 428 441 453 466 479 491 504 517 4 4,8
343 529 542 555 567 580 593 605 618 631 643 5 6,0
6 7,2
344 656 668 681 694 706 719 732 744 757 769 7 8,4
345 782 794 807 820 832 845 857 870 882 895 8 9,6
346 908 920 933 945 958 970 983 995 ,008 ,020 9 10,8
347 54 033 045 058 070 083 095 108 120 133 145
348 158 170 183 195 208 220 233 245 258 270
349 283 295 307 320 332 345 357 370 382 394
350 407 419 432 444 456 469 481 494 506 518
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
9
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
350 54 407 419 432 444 456 469 481 494 506 518
351 531 543 555 568 580 593 605 617 630 642
352 654 667 679 691 704 716 728 741 753 765
353 777 790 802 814 827 839 851 864 876 888 13
354 900 913 925 937 949 962 974 986 998 .011 1 1,3
355 55 023 035 047 060 072 084 096 108 121 133 2 2,6
356 145 157 169 182 194 206 218 230 242 255 3 3,9
357 267 279 291 303 315 328 340 352 364 376 4 5 5Z2 6,5
358 388 400 413 425 437 449 461 473 485 497 6 7,8
359 509 522 534 546 558 570 582 594 606 618 7 9,1
360 630 642 654 666 678 691 703 715 727 739 9 11,7
361 751 763 775 787 799 811 823 835 847 859
362 871 883 895 907 919 931 943 955 967 979
363 991 ,003 ,015 ,027 ,038 ,050 ,062 ,074 ,086 ,098
364 56 110 122 134 146 158 170 182 194 205 217
365 229 241 253 265 277 289 301 312 324 336
366 348 360 372 384 396 407 419 431 443 455 12
367 467 478 490 502 514 526 538 549 561 573 1 2 lz2 2/4
368 585 597 608 620 632 644 656 667 679 691 3 3,6
369 703 714 726 738 750 761 773 785 797 808 4 4,8
370 820 832 844 855 867 879 891 902 914 926 6 7,2
371 937 949 961 972 984 996 ,008 ,019 ,031 ,043 8 9Z6
372 57 054 066 078 089 101 113 124 136 148 159 9 10,8
373 171 183 194 206 217 229 241 252 264 276
374 287 299 310 322 334 345 357 368 380 392
375 403 415 426 438 449 461 473 484 496 507
376 519 530 542 553 565 576 588 600 611 623
377 634 646 657 669 680 692 703 715 726 738 LI
378 749 761 772 784 795 807 818 830 841 852 1 1,1
379 864 875 887 898 910 921 933 944 955 967 2 2,2
3,3
380 978 990 ,001 ,013 ,024 ,035 ,047 ,058 ,070 ,081 4 4,4
381 58 092 104 115 127 138 149 161 172 184 195 6 6,6
382 206 218 229 240 252 263 274 286 297 309 7 7,7
383 320 331 343 354 365 377 388 399 410 422 8 8,8
9 9,9
384 433 444 456 467 478 490 501 512 524 535
385 546 557 569 580 591 602 614 625 636 647
386 659 670 681 692 704 715 726 737 749 760
387 771 782 794 805 816 827 838 850 861 872
388 883 894 906 917 928 939 950 961 973 984
389 995 ,006 ,017 ,028 ,040 ,051 ,062 ,073 ,084 ,095 10
390 59 106 118 129 140 151 162 173 184 195 207 1 1,0
391 218 229 240 251 262 273 284 295 306 318 3 3/0
392 329 340 351 362 373 384 395 406 417 428 4 4,0
393 439 450 461 472 483 494 506 517 528 539 5 5,0
6 6,0
394 550 561 572 583 594 605 616 627 638 649 7 7,0
395 660 671 682 693 704 715 726 737 748 759 8 8,0
396 770 780 791 802 813 824 835 846 857 868 9 9,0
397 879 890 901 912 923 934 945 956 966 977
398 988 999 ,010 ,021 ,032 ,043 ,054 .065 ,076 ,086
399 60 097 108 119 130 141 152 163 173 184 195
400 206 217 228 239 249 260 271 282 293 304
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
10
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
400 60 206 217 228 239 249 260 271 282 293 304
401 314 325 336 347 358 369 379 390 401 412
402 423 433 444 455 466 477 487 498 509 520
403 531 541 552 563 574 584 595 606 617 627
404 638 649 660 670 681 692 703 713 724 735
405 746 756 767 778 788 799 810 821 831 842
406 853 863 874 885 895 906 917 927 938 949 11
407 959 970 981 991 *002 .013 .023 .034 .045 ,055 1 1/1
408 61 066 077 087 098 109 119 130 140 151 162 2 2,2
409 172 183 194 204 215 225 236 247 257 268 3 3,3
410 278 289 300 310 321 331 342 352 363 374 5 5,5
411 384 395 405 416 426 437 448 458 469 479 7 7/7
412 490 500 511 521 532 542 553 563 574 584 8 8,8
413 595 606 616 627 637 648 658 669 679 690 9 9,9
414 700 711 721 731 742 752 763 773 784 794
415 805 815 826 836 847 857 868 878 888 899
416 909 920 930 941 951 962 972 982 993 .003
417 62 014 024 034 045 055 066 076 086 097 107
418 118 128 138 149 159 170 180 190 201 211
419 221 232 242 252 263 273 284 294 304 315
420 325 335 346 356 366 377 387 397 408 418
421 428 439 449 459 469 480 490 500 511 521 10
422 531 542 552 562 572 583 593 603 613 624 1 1/0
423 634 644 655 665 675 685 696 706 716 726 2 2/0
3 3/0
424 737 747 757 767 778 788 798 808 818 829 4 4/0
425 839 849 859 870 880 890 900 910 921 931 5 5,0
426 941 951 961 972 982 992 .002 ,012 .022 ,033 6 6,0
7 7,0
427 63 043 053 063 073 083 094 104 114 124 134 8 8,0
428 144 155 165 175 185 195 205 215 225 236 9 9,0
429 246 256 266 276 286 296 306 317 327 337
430 347 357 367 377 387 397 407 417 428 438
431 448 458 468 478 488 498 508 518 528 538
432 548 558 568 579 589 599 609 619 629 639
433 649 659 669 679 689 699 709 719 729 739
434 749 759 769 779 789 799 809 819 829 839
435 849 859 869 879 889 899 909 919 929 939
436 949 959 969 979 988 998 ,008 ,018 .028 .038 9
437 64 048 058 068 078 088 098 108 118 128 137 1 0,9
438 147 157 167 177 187 197 207 217 227 237 2 1,8
439 246 256 266 276 286 296 306 316 326 335 3 2,7
4 3/6
440 345 355 365 375 385 395 404 414 424 434 5 4,5
5/4
441 444 454 464 473 483 493 503 513 523 532 7 6,3
442 542 552 562 572 582 591 601 611 621 631 8 7,2
443 640 650 660 670 680 689 699 709 719 729 9 8,1
444 738 748 758 768 777 787 797 807 816 826
445 836 846 856 865 875 885 895 904 914 924
446 933 943 953 963 972 982 992 .002 .011 ,021
447 65 031 040 050 060 070 079 089 099 108 118
448 128 137 147 157 167 176 186 196 205 215
449 225 234 244 254 263 273 283 292 302 312
450 321 331 341 350 360 369 379 389 398 408
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
11
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts. —
450 65 321 331 341 350 360 369 379 389 398 408
451 418 427 437 447 456 466 475 485 495 504
452 514 523 533 543 552 562 571 581 591 600
453 610 619 629 639 648 658 667 677 686 696
454 706 715 725 734 744 753 763 772 782 792
455 801 811 820 830 839 849 858 868 877 887
456 896 906 916 925 935 944 954 963 973 982 10
457 992 ,001 .011 *020 *030 *039 *049 *058 .068 .077 1 1,0
458 66 087 096 106 115 124 134 143 153 162 172 2 2,0
459 181 191 200 210 219 229 238 247 257 266 3 3,0
460 276 285 295 304 314 323 332 342 351 361 5 5,0
461 370 380 389 398 408 417 427 436 445 455 7 6,0 7/0
462 464 474 483 492 502 511 521 530 539 549 8 8,0
463 558 567 577 586 596 605 614 624 633 642 9 9,0
464 652 661 671 680 689 699 708 717 727 736
465 745 753 764 773 783 792 801 811 820 829
466 839 848 857 867 876 885 894 904 913 922
467 932 941 950 960 969 978 987 997 *006 *015
468 67 025 034 043 052 062 071 080 089 099 '108
469 117 127 136 145 154 164 173 182 191 ^01
470 210 219 228 237 247 256 265 274 284 293
471 302 311 321 330 339 348 357 367 376 385 8
472 394 403 413 422 431 440 449 459 468 477 1 0,9
473 486 495 504 514 523 532 541 550 560 569 2 1,8
474 578 587 596' 605 614 624 633 642 651 660 3 4 2,7 3,6
475 669 679 688 697 706 715 724 733 742 752 5 4,5
476 761 770 779 788 797 806 815 825 834 843 6 5,4
477 852 861 870 879 888 897 906 916 925 934 7 8 6,3 7,2
478 943 952 961 970 979 988 997 .006 ,015 *024 9 8,1
479 68 034 043 052 061 070 079 088 097 106 115
480 124 133 142 151 160 169 178 187 196 205
481 215 224 233 242 251 260 269 278 287 296
482 305 314 323 332 341 350 359 368 377 386
483 395 404 413 422 431 440 449 458 467 476
484 485 494 502 511 520 529 538 547 556 565
485 574 583 592 601 610 619 628 637 646 655
486 664 673 681 690 699 708 717 726 735 744 8
487 753 762 771 780 789 797 806 815 824 833 1 0,8
488 842 851 860 869 878 886 895 904 913 922 2 1,6
489 931 940 949 958 966 975 984 993 *002 *011 3 2,4
490 69 020 028 037 046 055 064 073 082 090 099 5 4,0
491 108 117 126 135 144 152 161 170 179 188 7 5,6
492 197 205 214 223 232 241 249 258 267 276 8 6,4
493 285 294 302 311 320 329 338 346 355 364 9 7,2
494 373 381 390 399 408 417 425 434 443 452
495 461 469 478 487 496 504 513 522 531 539
496 548 557 566 574 583 592 601 609 618 627
497 636 644 653 662 671 679 688 697 705 714
498 723 732 740 749 758 767 775 784 793 801
499 810 819 827 836 845 854 862 871 880 888
500 897 906 914 923 932 940 949 958 966 975
N. L, 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
12
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
509 69 897 906 914 923 932 940 949 958 966 975
501 984 992 *001 *010 ,018 *027 ,036 ,044 ,053 ,062
502 70 070 079 088 096 105 114 122 131 140 148
503 157 165 174 183 191 200 209 217 226 234
504 243 252 260 269 278 286 295 303 312 321
505 329 338 346 355 364 372 381 389 398 406
506 415 424 432 441 449 458 467 475 484 492
507 501 509 518 526 535 544 552 561 569 578
508 586 595 603 612 621 629 638 646 655 663
509 672 680 689 697 706 714 723 731 740 749 1 0,9
510 757 766 774 783 791 800 808 817 825 834 3 2,7
511 842 851 859 868 876 885 893 902 910 919 5 4,5
512 927 935 944 952 961 969 978 986 995 ,003 6 5,4
513 71 012 020 029 037 046 054 063 071 079 088 7 6,3
8 7,2
514 096 105 113 122 130 139 147 155 164 172 9 8,1
515 181 189 198 206 214 223 231 240 248 257
516 265 273 282 290 299 307 315 324 332 341
517 349 357 366 374 383 391 399 408 416 425
518 433 441 450 458 466 475 483 492 500 508
519 517 525 533 542 550 559 567 575 584 592
520 600 609 617 625 634 642 650 659 667 675
521 684 692 700 709 717 725 734 742 750 759 8
522 767 775 784 792 800 809 817 825 834 842 1 0,8
523 850 858 867 875 883 892 900 908 917 925 2 1,6
3 2,4
524 933 941 950 958 966 975 983 991 999 ,008 4 3,2
525 72 016 024 032 041 049 057 066 074 082 090 5 4,0
526 099 107 115 123 132 140 148 156 165 173 6 4,8
7 5,6
527 181 189 198 206 214 222 230 239 247 255 8 6,4
528 263 272 280 288 296 304 313 321 329 337 0 7,2
529 346 354 362 370 378 387 395 403 411 419
530 428 436 444 452 460 469 477 485 493 501
531 509 518 526 534 542 550 558 567 575 583
532 591 599 607 616 624 632 640 648 656 665
533 673 681 689 697 705 713 722 730 738, 746
534 754 762 770 779 787 795 803 811 819 827
535 835 843 852 860 868 876 884 892 900 908
536 916 925 933 941 949 957 965 973 981 989 1
537 997 *006 *014 *022 *030 *038 ,046 ,054 ,062 ,070 1 0,7
538 73 078 086 094 102 111 119 127 135 143 151 2 1,4
539 159 167 175 183 191 199 207 215 223 231 3 2,1
549 239 247 255 263 272 230 288 296 304 312 5 3,5
541 320 328 336 344 352 360 368 376 384 392 7 4,9
542 400 408 416 424 432 440 448 456 464 472 8 5,6
543 480 488 496 504 512 520 528 536 544 552 9 6,3
544 560 568 576 584 592 600 608 616 624 632
545 640 648 656 664 672 679 687 695 703 711
546 719 727 735 743 751 759 767 775 783 791
547 799 807 815 823 830 838 846 854 862 870
548 878 886 894 902 910 918 926 933 941 949
549 957 965 973 981 989 997 ,005 ,013 ,020 ,028
550 74 036 044 052 060 068 076 084 092 099 107
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
609025°— 44--2
13
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
550 74 036 044 052 060 068 076 084 092 099 107
551 115 123 131 139 147 155 162 170 178 186
552 194 202 210 218 225 233 241 249 257 265
553 273 280 288 296 304 312 320 327 335 343
554 351 359 367 374 382 390 398 406 414 421
555 429 437 445 453 461 468 476 484 492 500
556 507 515 523 531 539 547 554 562 570 578
557 586 593 601 609 617 624 632 640 648 656
558 663 671 679 687 695 702 710 718 726 733
559 741 749 757 764 772 780 788 796 803 811
560 819 827 834 842 850 858 865 873 881 889
561 896 904 912 920 927 935 943 950 958 966
562 974 981 989 997 *005 ,012 *020 .028 .035 .043 8
563 75 051 059 066 074 082 089 097 105 113 120 1 0,8
564 128 136 143 151 159 166 174 182 189 197 2 1,6 3 2,4
565 205 213 220 228 236 243 251 259 266 274 4 3^2
566 282 289 297 305 312 320 328 335 343 •351 5 4,0
567 358 366 374 381 389 397 404 412 420 427 6 4,8 7 5,6
568 435 442 450 458 465 473 481 488 496 504 8 6,4
569 511 519 526 534 542 549 557 565 572 580 9 7,2
570 587 595 603 610 618 626 633 641 648 656
571 664 671 679 686 694 702 709 717 724 732
572 740 747 755 762 770 778 785 793 800 808
573 815 823 831 838 846 853 861 868 876 884
574 891 899 906 914 921 929 937 944 952 959
575 967 974 982 989 997 *005 ,012 .020 .027 *035
576 76 042 050 057 065 072 080 087 095 103 110
577 118 125 133 140 148 155 163 170 178 185
578 193 200 208 215 223 230 238 245 253 260
579 268 275 283 290 298 305 313 320 328 335
580 343 350 358 365 373 380 388 395 403 410
581 418 425 433 440 448 455 462 470 477 485
582 492 500 507 515 522 530 537 545 552 559 7
583 567 574 582 589 597 604 612 619 626 634 1 0,7
584 641 649 656 664 671 678 686 693 701 708 2 1/4 3 2/1
585 716 723 730 738 745 753 760 768 775 782 4 2,8
586 790 797 805 812 819 827 834 842 849 856 5 3,5
6 4,2.
587 864 871 879 886 893 901 908 916 923 930 7 4,9
588 938 945 953 960 967 975 982 989 997 ,004 8 5,6
589 77 012 019 026 034 041 048 056 063 070 078 9 6,3
590 085 093 100 107 115 122 129 137 144 151
591 159 166 173 181 188 195 203 210 217 225
592 232 240 247 254 262 269 276 283 291 298
593 305 313 320 327 335 342 349 357 364 371
594 379 386 393 401 408 415 422 430 437 444
595 452 459 466 474 481 488 495 503 510 517
596 525 532 539 546 554 561 568 576 583 590
597 597 605 612 619 627 634 641 648 656 663
598 670 677 685 692 699 706 714 721 728 735
599 743 750 757 764 772 779 786 793 801 808
600 815 822 830 837 844 851 859 866 873 880
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
14
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
600 77 815 822 830 837 844 851 859 866 873 880
601 887 895 902 909 916 924 931 938 945 952
602 960 967 974 981 988 996 *003 *010 *017 .025
603 78 032 039 046 053 061 068 075 082 089 097
604 104 111 118 125 132 140 147 154 161 168
605 176 183 190 197 204 211 219 226 233 240
606 247 254 262 269 276 283 290 297 305 312 8
607 319 326 333 340 347 355 362 369 376 383 0,8 1/6 2,4
608 390 398 405 412 419 426 433 440 447 455 1
609 462 469 476 483 490 497 504 512 519 526 2 3
610 533 540 547 554 561 569 576 583 590 597 4 5 3,2 4,0
611 604 611 618 625 633 640 647 654 661 668 6 4,8 5,6 6,4 7,2
612 675 682 689 696 704 711 718 725 732 739
613 746 753 760 767 774 781 789 796 803 810 o 9
614 817 824 831 838 845 852 859 866 873 880
615 888 895 902 909 916 923 930 937 944 951
616 958 965 972 979 986 993 *000 *007 *014 *021
617 79 029 036 043 050 057 064 071 078 085 092
618 099 106 113 120 127 134 141 148 155 162
619 169 176 183 190 197 204 211 218 225 232
620 239 246 253 260 267 274 281 288 295 302
621' 309 316 323 330 337 344 351 358 365 372 7
622 379 386 393 400 407 414 421 428 435 442 0,7 1/4
623 449 456 463 470 477 484 491 498 505 511 1 2
624 618 525 532 539 546 553 560 567 574 581 3 2,1 2,8 3,5 4,2
625 588 595 602 609 616 623 630 637 644 650
626 657 664 671 678 685 692 699 706 713 720 0 6
627 727 734 741 748 754 761 768 775 782 789 7 4,9 5,6 6,3
628 796 803 810 8x7 824 831 837 844 851 858 Q
629 865 872 879 886 893 900 906 913 920 927
630 934 941 948 955 962 969 975 982 989 996
631 80 003 010 017 024 030 037 044 051 058 065
632 072 079 085 092 099 106 113 120 127 134
633 140 147 154 161 168 175 182 188 195 202
634 209 216 223 229 236 243 250 257 264 271
635 277 284 291 298 305 312 318 325 332 339
636 346 353 359 366 373 380 387 393 400 407 6
637 414 421 428 434 441 448 455 462 468 475 0,6 1/2 1,8
638 482 489 496 502 509 516 523 530 536 543 1
639 550 557 564 570 577 584 591 598 604 611 2 3
640 618 625 632 638 645 652 659 665 672 679 4 5 2,4 3,0
641 686 693 699 706 713 720 726 733 740 747 6 7 3,6 4,2 4,8 5,4
642 754 760 767 774 781 787 794 801 808 814 ft
643 821 828 835 841 848 855 862 868 875 882 9
644 889 895 902 909 916 922 929 936 943 949
645 956 963 969 976 983 990 996 *003 *010 *017
646 81 023 030 037 043 050 057 064 070 077 084
647 090 097 104 111 117 124 131 137 144 151
648 158 164 171 178 184 191 198 204 211 218
649 224 231 238 245 251 258 265 271 278 285
650 291 298 305 311 318 325 331 338 345 351
N, L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
15
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
650 81 291 298 305 311 318 325 331 338 345 351
651 358 365 371 378 385 391 398 405 411 418
652 425 431 438 445 451 458 465 471 478 485
653 491 498 505 511 518 525 531 538 544 551
654 558 564 571 578 584 591 598 604 611 617
1 655 624 631 637 644 651 657 664 671 677 684
656 690 697 704 710 717 723 730 737 743 750
657 757 763 770 776 783 790 796 803 809 816
658 823 829 836 842 849 856 862 869 875 882
659 889 895 902 908 915 921 928 935 941 948
660 954 961 968 974 981 987 994 ,000 ,007 ,014
661 82 020 027 033 040 046 053 060 066 073 079 7
662 086 092 099 105 112 119 125 132 138 145
663 151 158 164 171 178 184 191 197 204 210 1 0,7 2 1,4
664 217 223 230 236 243 249 256 263 269 276 3 2,1
665 282 289 295 302 308 315 321 328 334 341 4 2/8
666 347 354 360 367 373 380 387 393 400 406 5 3/5 6 4/2
667 413 419 426 432 439 445 452 458 465 471 7 4,9
668 478 484 491 497 504 510 517 523 530 536 8 5/6
669 543 549 556 562 569 575 582 588 595 601 9 6,3
670 607 614 620 627 633 640 646 653 659 666
671 672 679 685 692 698 705 711 718 724 730
672 737 743 750 756 763 769 776 782 789 795
673 802 808 814 821 827 834 840 847 853 860
674 866 872 879 885 892 898 905 911 918 924
675 930 937 943 950 956 963 969 975 982 988
676 995 ,001 *008 ,014 ,020 ,027 ,033 ,040 ,046 ,052
677 83 059 065 072 078 085 091 097 104 110 117
678 123 129 136 142 149 155 161 168 174 181
679 187 193 200 206 213 219 225 232 238 245
680 251 257 264 270 276 283 289 296 302 308
681 315 321 327 334 340 347 353 359 366 372
682 378 385 391 398 404 410 417 423 429 436 6
683 442 448 455 461 467 474 480 487 493 499 1 0,6
684 506 512 518 525 531 537 544 550 556 563 2 1,2 3 1,8
685 569 575 582 588 594 601 607 613 620 626 4 2,4
686 632 639 645 651 658 664 670 677 683 689 5 3,0
687 696 702 708 715 721 727 734 740 746 753 6 3,6 7 4,2
688 759 765 771 778 784 790 797 803 809 816 8 4,8
689 822 828 835 841 847 853 860 866 872 879 9 5,4
690 885 891 897 904 910 916 923 929 935 942
691 948 954 960 967 973 979 985 992 998 ,004
692 84 011 017 023 029 036 042 048 055 061 067
693 073 080 086 092 098 105 111 117 123 130
694 136 142 148 155 161 167 173 180 186 192
695 198 205 211 217 223 230 236 242 248 255
696 261 267 273 280 286 292 298 305 311 317
697 323 330 336 342 348 354 361 367 373 379
698 386 392 398 404 410 417 423 429 435 442
699 448 454 460 466 473 479 485 491 497 504
700 510 516 522 528 535 541 547 553 559 566
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
16
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
7oe 84 510 516 522 528 535 541 547 553 559 566
701 572 578 584 590 597 603 609 615 621 628
702 634 640 646 652 658 665 671 677 683 689
703 696 702 708 714 720 726 733 739 745 751
704 757 763 770 776 782 788 794 800 807 813
705 819 825 831 837 844 850 856 862 868 874
706 880 887 893 899 905 911 917 924 930 936 7
707 942 948 954 960 967 973 979 985 991 997 1 0,7
708 85 003 009 016 022 028 034 040 046 052 058 2 1,4
709 065 071 077 083 089 095 101 107 114 120 3 2,1
710 126 132 138 144 150 156 163 169 175 181 5 2,8 3,5 4,2
711 187 193 199 205 211 217 224 230 236 242 7 4,9
712 248 254 260 266 272 278 285 291 297 303 8 5,6
713 309 315 321 327 333 339 345 352 358 364 9 6,3
714 370 376 382 388 394 400 406 412 418 425
715 431 437 443 449 455 461 467 473 479 485
716 491 497 503 509 516 522 528 534 540 546
717 552 558 564 570 576 582 588 594 600 606
718 612 618 625 631 637 643 649 655 661 667
719 673 679 685 691 697 703 709 715 721 727
720 733 739 745 751 757 763 769 775 781 788
721 794 800 806 812 818 824 830 836 842 848
722 854 860 866 872 878 884 890 896 902 908
723 914 920 926 932 938 944 950 956 962 968 1 0,6
2 1,2
724 974 980 986 992 998 ,004 ,010 ,016 ,022 ,028 3 1,8
725 86 034 040 046 052 058 064 070 076 082 088 4 2,4
726 094 100 106 112 118 124 130 136 141 147 5 3,0
6 3,6
727 153 159 165 171 177 183 189 195 201 207 7 4,2
728 213 219 225 231 237 243 249 255 261 267 8 4,8
729 273 279 285 291 297 303 308 314 320 326 9 5,4
730 332 338 344 350 356 362 368 374 380 386
731 392 398 404 410 415 421 427 433 439 445
732 451 457 463 469 475 481 487 493 499 504
733 510 516 522 528 434 540 546 552 558 564
734 570 576 581 587 593 599 605 611 617 623
735 629 635 641 646 652 658 664 670 676 682
736 688 694 700 705 711 717 723 729 735 741 5
737 747 753 759 764 770 776 782 788 794 800 1 0,5
738 806 812 817 823 829 835 841 847 853 859 2 1,0
739 864 870 876 882 888 894 900 906 911 917 3 1,5
740 923 929 935 941 947 953 958 964 970 976 5 2,5
741 982 988 994 999 ,005 ,011 ,017 ,023 ,029 ,035 7 3,5
742 87 040 046 052 058 064 070 075 081 087 093 8 4/)
743 099 105 111 116 122 128 134 140 146 151 9 4,5
744 157 163 169 175 181 186 192 198 204 210
745 216 221 227 233 239 245 251 256 262 268
746 274 280 286 291 297 303 309 315 320 326
747 332 338 344 349 355 361 367 373 379 384
748 390 396 402 408 413 419 425 431 437 442
749 448 454 460 466 471 477 483 489 495 500
750 506 512 518 523 529 535 541 547 552 558 •
N. L 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
17
Table I.—Common Logarithms of Numbers—Continued
N. . L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
750 87 506 512 518 523 529 535 541 547 552 558
751 564 570 576 581 587 593 599 604 610 616
752 622 628 633 639 645 651 656 662 668 674
753 679 685 691 697 703 708 714 720 726 731
754 737 743 749 754 760 766 772 777 783 789
755 795 800 806 812 818 823 829 835 841 846
756 852 858 864 869 875 881 887 892 898 904
757 910 915 921 927 933 938 944 950 955 961
758 967 973 978 984 990 996 ,001 .007 *013 .018
759 88 024 030 036 041 047 053 058 064 070 076
760 081 087 093 098 104 110 116 121 127 133
761 138 144 150 156 161 167 173 178 184 190
762 195 201 207 213 218 224 230 235 241 247 6
763 252 258 264 270 275 281 287 292 298 304 1 0,6
764 309 315 321 326 332 338 343 349 355 360 2 1,2 3 1,8
765 366 372 377 383 389 395 400 406 412 417 4 2,4
766 423 429 434 440 446 451 457 463 468 474 5 3,0
767 480 485 491 497 502 508 513 519 525 530 6 3,6 7 4,2
768 536 542 547 553 559 564 570 576 581 587 8 4,8
769 593 598 604 610 615 621 627 632 638 643 9 54
770 649 655 660 666 672 677 683 689 694 700
771 705 711 717 722 728 734 739 745 750 756
772 762 767 773 779 784 790 795 801 807 812
773 818 824 829 835 840 846 852 857 863 868
774 874 880 885 891 897 902 908 913 919 925
775 930 936 941 947 953 958 964 969 975 981
776 986 992 997 *003 *009 *014 ,020 .025 ,031 ,037
777 89 042 048 053 059 064 070 076 081 087 092
778 098 104 109 115 120 126 131 137 143 148
779 154 159 165 170 176 182 187 193 198 204
780 209 215 221 226 232 237 243 248 254 260
781 265 271 276 282 287 293 298 304 310 315 5
782 321 326 332 337 343 348 354 360 365 371 1 0,5
783 376 382 387 393 398 404 409 415 421 426 2 1/)
784 432 437 443 448 454 459 465 470 476 481 3 1,5 4 2,0
785 487 492 498 504 509 515 520 526 531 537 5 2,5
786 542 548 553 559 564 570 575 581 586 592 6 3,0
787 597 603 609 614 620 625 631 636 642 647 7 3,5 8 4,0
788 653 658 664 669 675 680 686 691 697 702 9 4,5
789 708 713 719 724 730 735 741 746 752 757
790 763 768 774 779 785 790 796 801 807 812
791 818 823 829 834 840 845 851 856 862 867
792 873 878 883 889 894 900 905 911 916 922
793 927 933 938 944 949 955 960 966 971 977
794 982 988 993 998 ,004 ,009 *015 *020 *026 *031
795 90 037 042 048 053 059 064 069 075 080 086
796 091 097 102 108 113 119 124 129 135 140
797 146 151 157 162 168 173 179 184 189 195
798 200 206 211 217 222 227 233 238 244 249
799 255 260 266 271 276 282 287 293 298 304
80(F 309 314 320 325 331 336 342 347 352 358
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
18
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
800 90 309 314 320 325 331 336 342 347 352 358
801 363 369 374 380 385 390 396 401 407 412
802 417 423 428 434 439 445 450 455 461 466
803 472 477 482 488 493 499 504 509 515 520
804 526 531 536 542 547 553 558 563 569 574
805 580 585 590 596 601 607 612 617 623 628
806 634 639 644 650 655 660 666 671 677 682
807 687 693 698 703 709 714 720 725 730 736
808 741 747 752 757 763 768 773 779 784 789
809 795 800 806 811 816 822 827 832 838 843
810 849 854 859 865 870 875 881 886 891 897
811 902 907 813 918 924 929 934 940 945 950 e
812 956 961 966 972 977 982 988 993 998 ,004 1 0,6
813 91 009 014 020 025 030 036 041 046 052 057 2 1,2
3 1,8
814 062 068 073 078 084 089 094 100 105 110 4 2,4
815 116 121 126 132 137 142 148 153 158 164 5 3,0
816 169 174 180 185 190 196 201 206 212 217 6 3,6
7 4,2
817 222 228 233 238 243 249 254 259 265 270 8 4,8
818 275 281 286 291 297 302 307 312 318 323 9 54
819 328 334 339 344 350 355 360 365 371 376
820 381 387 392 397 403 408 413 418 424 429
821 434 440 445 450 455 461 466 471 477 482
822 487 492 498 503 508 514 519 524 529 535
823 540 545 551 556 561 566 572 577 582 587
824 593 598 603 609 614 619 624 630 635 640
825 645 651 656 661 666 672 677 682 687 693
826 698 703 709 714 719 724 730 735 740 745
827 751 756 761 766 772 777 782 787 793 798
828 803 808 814 819 824 829 834 840 845 850
829 855 861 866 871 876 882 887 892 897 903
830 908 913 918 924 929 934 939 944 950 955
831 960 965 971 976 981 986 991 997 .002 .007 5
832 92 012 018 023 028 033 038 044 049 054 059 1, 0,5
833 065 070 075 080 085 091 096 101 106 111 2 1,0
3 1,5
834 117 122 127 132 137 143 148 153 158 163 4 2,0
835 169 174 179 184 189 195 200 205 210 215 5 2,5
836 221 226 231 236 241 247 252 257 262 267 6 3,0
7 3,5
837 273 278 283 288 293 298 304 309 314 319 8 4/)
838 324 330 335 340 345 350 355 361 366 371 9 4,5
839 376 381 387 392 397 402 407 412 418 423
840 428 433 438 443 449 454 459 464 469 474
841 480 485 490 495 500 505 511 516 521 526
842 531 536 542 547 552 557 562 567 572 578
843 583 588 593 598 603 609 614 619 624 629
844 634 639 645 650 655 660 665 670 675 681
845 686 691 696 701 706 711 716 722 727 732
846 737 742 747 752 758 763 768 773 778 783
847 788 793 799 804 809 814 819 824 829 834
848 840 845 850 855 860 865 870 875 881 886
849 891 896 901 906 911 916 921 927 932 937
850 942 947 952 957 962 967 973 978 983 988
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
19
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
850 92 942 947 952 957 962 967 973 978 983 988
851 993 998 ,003 .008 ,013 ,018 .024 ,029 ,034 ,039
852 93 044 049 054 059 064 069 075 080 085 090
853 095 100 105 110 115 120 125 131 136 141
854 146 151 156 161 166 171 176 181 186 192
855 197 202 207 212 217 222 227 232 237 242
856 247 252 258 263 268 273 278 283 288 293 6
857 298 303 308 313 318 323 328 334 339 344 1 0,6
858 349 354 359 364 369 374 379 384 389 394 2 1,2
859 399 404 409 414 420 425 430 435 440 445 3 i;s
860 450 455 460 465 470 475 480 485 490 495 4 2,4 5 3,0
861 500 505 510 515 520 526 531 536 541 546 6 3,6 7 4,2
862 551 556 561 566 571 576 581 586 591 596 |8 4,8
863 601 606 611 616 621 626 631 636 641 646 9 5,4
864 651 656 661 666 671 676 682 687 692 697
865 702 707 712 717 722 727 732 737 742 747
866 752 757 762 767 772 777 782 787 792 797
867 802 807 812 817 822 827 832 837 842 847
868 852 857 862 867 872 877 882 887 892 897
869 902 907 912 917 922 927 932 937 942 947
870 952 957 962 967 972 977 982 987 992 997
871 94 002 007 012 017 022 027 032 037 042 047 5
872 052 057 062 067 072 077 082 086 091 096 1 0,5
873 101 106 111 116 121 126 131 136 141 146 2 1,0
874 151 156 161 166 171 176 181 186 191 196 3 1,5 4 2,0
875 201 206 211 216 221 226 231 236 240 245 5 2,5
876 250 255 260 265 270 275 280 285 290 295 6 3,0
877 300 305 310 315 320 325 330 335 340 345 7 3,5 8 4,0
878 349 354 359 364 369 374 379 384 389 394 9 4,5
879 399 404 409 414 419 424 429 433 438 443
880 448 453 458 463 468 473 478 483 488 493
881 498 503 507 512 517 522 527 532 537 542
882 547 552 557 562 567 571 576 581 586 591
883 596 601 606 611 616 621 626 630 635 640
884 645 650 655 660 665 670 675 680 685 689
885 694 699 704 709 714 719 724 729 734 738
886 743 748 753 758 763 768 773 778 783 787 4
887 792 797 802 807 812 817 822 827 832 836 1 0,4
888 841 846 851 856 861 866 871 876 880 885 2 0,8
889 890 895 900 905 910 915 919 924 929 934 3 1,2
890 939 944 949 954 959 963 968 973 978 983 4 1,6 5 2,0
891 988 993 998 ,002 ,007 ,012 ,017 ,022 ,027 ,032 7 2,8.
892 95 036 041 046 051 056 061 066 071 075 080 8 3,2
893 085 090 095 100 105 109 114 119 124 129 9 3,6
894 134 139 143 148 153 158 163 168 173 177
895 182 187 192 197 202 207 211 216 221 226
896 231 236 240 245 250 255 260 265 270 274
897 279 284 289 294 299 303 308 313 318 323
898 328 332 337 342 347 352 357 361 366 371
899 376 381 386 390 395 400 405 410 415 419
900 424 429 434 439 444 448 453 458 463 468
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
20
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
900 95 424 429 434 439 444 448 453 458 463 468
901 472 477 482 487 492 497 501 506 511 516
902 521 525 530 535 540 545 550 554 559 564
903 569 574 578 583 588 593 598 602 607 612
904 617 622 626 631 636 641 646 650 655 660
905 665 670 674 679 684 689 694 698 703 708
906 713 718 722 727 732 737 742 746 751 756
907 761 766 770 775 780 785 789 794 799 804
908 809 813 818 823 828 832 837 842 847 852
909 856 861 866 871 875 880 885 890 895 899
910 904 909 914 918 923 928 933 938 942 947
911 952 957 961 966 971 976 980 985 990 995
912 999 .004 ,009 ,014 ,019 *023 ,028 .033 ,038 ,042
913 96 047 052 057 061 066 071 076 080 085 090 1 0,5
2 1/0
914 095 099 104 109 114 118 123 128 133 137 3 1/5
915 142 147 152 156 161 166 171 175 180 185 4 2,0
916 190 194 199 204 209 213 218 223 227 232 5 2,5
6 3,0
917 237 242 246 251 256 261 265 270 275 280 7 3,5
918 284 289 294 298 303 308 313 317 322 327 8 4,0
919 332 336 341 346 350 355 360 365 369 374 9 4,5
920 379 384 388 393 398 402 407 412 417 421
921 426 431 435 440 445 450 454 459 464 468
922 473 478 483 487 492 497 501 506 511 515
923 520 525 530 534 539 544 548 553 558 562
924 567 572 577 581 586 591 595 600 605 609
925 614 619 624 628 633 638 642 647 652 656
926 661 666 670 675 680 685 689 694 699 703
927 708 713 717 722 727 731 736 741 745 750
928 755 759 764 769 774 778 783 788 792 797
929 802 806 811 816 820 825 830 834 839 844
930 848 853 858 862 867 872 876 881 886 890
931 895 900 904 909 914 918 923 928 932 937
932 942 946 951 956 960 965 970 974 979 984
933 988 993 997 *002 ,007 *011 ,016 *021 ,025 .030
1 0,4
934 97 035 039 044 049 053 058 063 067 072 077 2 0,8
935 081 086 090 095 100 104 109 114 118 123 3 1,2
936 128 132 137 142 146 151 155 160 165 169 4 1,6
5 2,0
937 174 179 183 188 192 197 202 206 211 216 6 2,4
938 220 225 230 234 239 243 248 253 257 262 7 2,8
939 267 271 276 280 285 290 204 299 304 308 8 3,2
940 313 317 322 327 331 336 340 345 350 354
941 359 364 368 373 377 382 387 391 396 400
942 405 410 414 419 424 428 433 437 442 447
943 451 456 460 465 470 474 479 483 488 493
944 497 502 506 511 516 520 525 529 534 539
945 543 548 552 557 562 566 571 575 580 585
946 589 594 598 603 607 612 617 621 626 630
947 635 640 644 649 653 658 663 667 672 676
948 681 685 690 695 699 704 708 713 717 722
949 727 731 736 740 745 749 754 759 763 768
950 772 777 782 786 791 795 800 804 809 813
N. L. 0 1 2 3 4 5 6 7 8 9 Prop . Pts.
21
Table I.—Common Logarithms of Numbers—Continued
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
#50 97 772 777 782 786 791 795 800 804 809 813
951 818 823 827 832 836 841 845 850 855 859
952 864 868 873 877 882 886 891 896 900 905
953 909 914 918 923 928 932 937 941 946 950
954 055 959 964 968 973 978 982 987 991 996
955 98 000 005 009 014 019 023 028 032 037 041
956 046 050 055 059 064 068 073 078 082 087
957 091 096 100 105 109 114 118 123 127 132
958 137 141 146 150 155 159 164 168 173 177
959 182 186 191 195 200 204 209 214 218 223
960 227 232 236 241 245 250 254 259 263 268 5
961 272 277 281 286 290 295 299 304 308 313 1 0,5
962 318 322 327 331 336 340 345 349 354 358 2 1,0
963 363 367 372 376 381 385 390 394 399 403 3 1,5
964 408 412 417 421 426 430 435 439 444 448 4 2,0
965 453 457 462 466 471 475 480 484 489 493 5 2,5
966 498 502 507 511 516 520 525 529 534 538 6 3,0
967 543 547 552 556 561 565 570 574 579 583 8 4,0
968 588 592 597 601 605 610 614 619 623 628 9 4,5
969 632 637 641 646 650 655 659 664 668 673
970 677 682 686 691 695 700 704 709 713 717
971 722 726 731 735 740 744 749 753 758 762
972 767 771 776 780 784 789 793 798 802 807
973 811 816 820 825 829 834 838 843 847 851
974 856 860 865 869 874 878 883 887 892 896
975 900 905 909 914 918 923 927 932 936 941
976 945 949 954 958 963 967 972 976 981 985
977 989 994 998 *003 *007 ,012 ,016 *021 *025 ,029
978 99 034 038 043 047 052 056 061 065 069 074
979 078 083 087 092 096 100 105 109 114 118
980 123 127 131 136 140 145 149 154 158 162 4
981 167 171 176 180 185 189 193 198 202 207 1 ox
982 211 216 220 224 229 233 238 242 247 251 2 0,8
983 255 260 264 269 273 277 282 286 291 295 3 1,2
984 300 304 308 313 317 322 326 330 335 339 4 1,6
985 344 348 352 357 361 3C6 370 374 379 383 5 2,0
986 388 392 396 401 405 410 414 419 423 427 6 2,4
987 432 436 441 445 449 454 458 463 467 471 8 3/2
988 476 480 484 489 493 498 502 506 511 515 9 3,6
989 520 524 528 533 537 542 546 550 555 559
990 564 568 572 577 581 585 590 594 599 603
991 607 612 616 621 625 629 634 638 642 647
992 651 656 660 664 669 673 677 682 686 691
993 695 699 704 708 712 717 721 726 730 734
994 739 743 747 752 756 760 765 769 774 778
995 782 787 791 795 800 804 808 813 817 822
996 826 830 835 839 843 848 852 856 861 865
997 870 874 878 883 887 891 896 900 904 909
998 913 917 922 926 930 935 939 944 948 952
999 957 961 965 970 974 978 983 987 991 996
1000 00 000 004 009 013 017 022 026 030 035 039
N. L. 0 1 2 3 4 5 6 7 8 9 Prop. Pts.
22
Table II.—Common Logarithms of Functions of Angles in Mils
Logarithms of the functions are given for each mil from 0 mils to 6,400 mils,
The quantity —10 is to be appended to all logarithms of the sine and cosine, to logarithms of the tangent from 0 to 800 mils, and to logarithms of the cotangent from 800 to 1,600 mils.
With hundreds of mils indicated on the first line at the top of the page, use the column headings on the first line at the top. With hundreds of mils indicated on the second line at the top of the page, use the column headings on the second line
With hundreds of mils indicated on the last line at the bottom of the page, use the column designations on the last line at the bottom. With hundreds of mils indicated on the next to the last line at the bottom of the page, use the column designations on the next to the last line at the bottom.
With hundreds of mils indicated at the top of the page (first or second line), use the unit mil column at the left. With hundreds of mils indicated at the bottom of the page (last or next to the last line), use the unit mil column at the right.
The values of angles of the first quadrant and the corresponding column headings are set in bold-face type.
Corresponding values in degrees, minutes, and seconds are given for each angle in mils.
Examples:
1. To find the azimuth of the line A-B, given the following coordinates: Point A 24.560- 96.895
Points 25.342-100.637
+ .782. +3.742
782
Tangent of the angle at A =
Log Tan of the angle at x4 = ^°g = 12.89321 —10
10g O /
-3.57310
9.32011-10
Enter the Tan column of table II with the log 9.32011 in order to find the number of mils corresponding to this log:
Log Tan of 209 mils=9.31830
Log Tan of 210 mils = 9.32043
Log Tan 9.320L1 lies eight-tenths of the way from 9.31830 to 9.32043; therefore the value of the angle is 209.8 mils, and the azimuth of the line (first quadrant) is 209.8 or 210 mils.
2. Given the coordinates of point X as 855.792—1298.057, the azimuth of the line X-Y as 3,968 mils, and the distance from X to Y as 1,054 yards.
Required: The coordinates of point Y.
DX=Sine of azimuth X distance
DY= Cosine of azimuth X distance
DX DY
From table I, log 1,054 3.02284 3.02284
17 x ui TT 1 a- O nno •! 9.83540—10, ~ 9.86271 — 10
From table II, log Sm 3,968 mils 12.85824-10 og Cos 12.88555-10
From table I, antilog (to nearest 722 768
yard)
Coordinates of point X 855.792—1298.057
DX, DY (third quadrant) —.722 —.768
Coordinates of point Y 855.070—1297.289
2
23
Table II.—Common Logarithms of Functions of Angles in Mils
0-, 32- O f // L Sin L Cos L Tan L Cot Mils
16-, 48- L Cos L Sin L Cot L Tan
00 000000 — 10.00000 — a 100
01 0 03 22. 5 6. 99200 10. 00000 6. 99200 3.00800 99
02 0 06 45.0 7. 29303 10. 00000 7. 29303 2. 70697 98
03 0 10 07. 5 7. 46912 10. 00000 7. 46912 2. 53088 97
04 0 13 30. 0 7. 59406 10. 00000 7. 59406 2. 40594 96
05 0 16 52. 5 7. 69097 10.00000 7. 69097 2. 30903 95
06 0 20 15.0 7. 77015 9. 99999 7. 77016 2. 22984 94
07 0 23 37. 5 7.83709 9. 99999 7. 83710 2. 16290 93
08 0 27 00.0 7.89509 9. 99999 7. 89510 2.10490 92
09 0 30 22. 5 7. 94624 9. 99998 7. 94625 2. 05375 91
10 0 33 45.0 7. 99199 9. 99998 7. 99201 2. 00799 90
11 0 37 07. 5 8. 03338 9. 99997 8 03340 1. 96660 89
12 0 40 30. 0 8. 07117 9. 99997 8. 07120 1.92880 88
13 0 43 52. 5 8.10593 9. 99996 8.10597 1. 89403 87
14 0 47 15. 0 8.13811 9. 99996 8.13816 1. 86184 86
15 0 50 37. 5 8. 16808 9.99995 8.16812 1.83188 85
16 0 54 00.0 8.19610 9.99995 8.19616 1. 80384 84
17 0 57 22. 5 8. 22243 9. 99994 8. 22249 1. 77751 83
18 1 00 45. 0 8. 24725 9.99993 8. 24732 1. 75268 82
19 1 04 07. 5 8. 27073 9. 99992 8. 27080 1. 72920 81
20 1 07 30. 0 8. 29300 9. 99992 8. 29309 1. 70691 80
21 1 10 52. 5 8. 31419 9.99991 8. 31428 1. 68572 79
22 1 14 15. 0 8. 33439 9. 99990 8. 33449 1. 66551 78
23 1 17 37. 5 8. 35369 9. 99989 8. 35380 1. 64620 77
24 1 21 00. 0 8. 37217 9.99988 8. 37229 1. 62771 76
25 1 24 22. 5 8. 38990 9. 99987 8. 39003 1. 60997 75
26 1 27 45. 0 8. 40693 9.99986 8.40707 1. 59293 74
27 1 31 07. 5 8. 42331 9.99985 8. 42347 1. 57653 73
28 1 34 30. 0 8. 43910 9. 99984 8. 43927 1. 56073 72
29 1 37 52. 5 8. 45434 9. 99982 8. 45452 1. 54548 71
30 1 41 15. 0 8. 46906 9. 99981 8.46925 1. 53075 70
31 1 44 37. 5 8. 48329 9. 99980 8. 48350 1. 51650 69
32 1 48 00. 0 8. 49708 9.99979 8. 49729 1. 50271 68
33 1 51 22. 5 8. 51043 9. 99977 8. 51067 1. 48933 67
34 1 54 45.0 8. 52340 9.99976 8. 52364 1. 47636 66
35 1 58 07. 5 8. 53598 9. 99974 8.53623 1.46376 65
36 2 01 30.0 8. 54821 9. 99973 8. 54848 1.45152 64
37 2 04 52. 5 8. 56011 9.99971 8. 56039 1. 43961 63
38 2 08 15.0 8. 57168 9. 99970 8. 57199 1. 42801 62
39 2 11 37. 5 8. 58296 9.99968 8. 58328 1. 41672 61
40 2 15 00. 0 8. 59395 9. 99967 8. 59428 1. 40572 60
41 2 18 22. 5 8. 60467 9.99965 8. 60502 1. 39498 59
42 2 21 45. 0 8. 61513 9. 99963 8. 61550 1. 38450 58
43 2 25 07. 5 8. 62533 9.99961 8. 62573 1. 37427 57
44 2 28 30. 0 8. 63532 9. 99959 8. 63572 1. 36428 56
45 2 31 52. 5 8. 64507 9.99958 8.64550 1.35450 55
46 2 35 15. 0 8. 65461 9.99956 8. 65505 1. 34495 54
47 2 38 37. 5 8. 66394 9. 99954 8. 66441 1. 33559 53
48 2 42 00. 0 8. 67308 9.99952 8. 67356 1. 32644 52
49 2 45 22. 5 8. 68203 9. 99950 8. 68253 1. 31747 51
50 2 48 45. 0 8. 69080 9. 99948 8. 69132 1. 30868 50
L Sin L Cos L Tan L Cot 63-, 31-
Mils o / // L Cos L Sin L Cot L Tan 47-, 15-
24
Table II.—Common Logarithms of Functions of Angles in Mils—Continued
0—, 32- ° / // L Sin L Cos L Tan L Cot Mils
16-,48- L Cos L Sin L Cot L Tan
50 2 48 45.0 8. 69080 9.99948 8.69132 1.30868 50
51 2 52 07.5 8.69939 9.99946 8.69993 1. 30007 49
52 2 55 30.0 8. 70781 9. 99943 8. 70838 1. 29162 48
53 2 58 52. 5 8. 71608 9.99941 8. 71667 1.28333 47
54 3 02 15.0 8. 72419 9.99939 8.72480 1.27520 46
55 3 05 37.5 8.73215 9. 99937 8.73278 1.26722 45
56 3 09 00.0 8.73997 9.99934 8. 74063 1. 25937 44
57 3 12 22.5 8. 74765 9.99932 8.74833 1.25167 43
58 3 15 45.0 8.75519 9.99930 8.75590 1.24410 42
59 3 19 07. 5 8. 76261 9. 99927 8. 76334 1. 23666 41
60 3 22 30.0 8. 76990 9.99925 8. 77065 1.22935 40
61 3 25 52. 5 8. 77707 9.99922 8.77785 1. 22215 39
62 3 29 15.0 8. 78412 9.99919 8. 78493 1.21507 38
63 3 32 37. 5 8. 79106 9.99917 8. 79189 1. 20811 37
64 3 36 00.0 8. 79789 9.99914 8. 79875 1.20125 36
65 3 39 22.5 8.80462 9. 99912 8.80550 1.19450 35
66 3 42 45.0 8.81124 9.99909 8.81215 1.18785 34
67 3 46 07. 5 8. 81776 9.99906 8. 81870 1.18130 33
68 3 49 30.0 8.82419 9. 99903 8.82515 1.17485 32
69 3 52 52.5 8.83052 9. 99900 8.83151 1.16849 31
70 3 56 15.0 8.83676 9.99897 8.83778 1.16222 30
71 3 59 37. 5 8. 84291 9.99894 8. 84396 1.15604 29
72 4 03 00.0 8. 84897 9.99891 8.85006 1.14994 28
73 4 06 22.5 8. 85495 9.99888 8.85607 1.14393 27
74 4 09 45.0 8. 86085 9.99885 8.86200 1.13800 26
75 4 13 07.5 8.86667 9 99882 8.86785 1.13215 25
76 4 16 30.0 8. 87241 9.99879 8.87362 1.12638 24
77 4 19 52. 5 8.87808 9.99876 8.87932 1.12068 23
78 4 23 15.0 8.88367 9. 99873 8.88494 1.11506 22
79 4 26 37.5 8.88919 9. 99869 8.89050 1.10950 21
80 4 30 00.0 8. 89464 9. 99866 8.89598 1.10402 20
81 4 33 22. 5 8. 90003 9.99863 8.90140 1.09860 19
82 4 36 45. 0 8. 90534 9. 99859 8.90675 1.09325 18
83 4 40 07. 5 8.91060 9. 99856 8.91204 1.08796 17
84 4 43 30.0 8. 91579 9.99852 8.91727 1.08273 16
85 4 46 52.5 8.92091 9.99849 8.92243 1.07757 15
86 4 50 15.0 8.92598 9.99845 8.92753 1.07247 14
87 4 53 37. 5 8.93099 9.99841 8.93258 1.06742 13
88 4 57 00.0 8.93594 9.99838 8. 93757 1.06244 12
89 5 00 22. 5 8.94084 9.99834 8. 94250 1.05750 11
90 5 03 45.0 8.94568 9. 99830 8.94737 1.05263 10
91 5 07 07.5 8.95046 9. 99826 8.95220 1.04780 09
92 5 10 30.0 8.95520 9. 99823 8.95697 1.04303 08
93 5 13 52. 5 8.95988 9.99819 8.96169 1.03831 07
94 5 17 15.0 8.96451 9.99815 8.96636 1. 03364 06
95 5 20 37.5 8.96909 9.99811 8.97099 1.02901 05
96 5 24 00.0 8.97363 9.99807 8.97556 1.02444 04
97 5 27 22.5 8.97812 9.99803 8. 98009 1.01991 03
98 5 30 45.0 8. 98256 9. 99799 8.98457 1.01543 02
99 5 34 07. 5 8. 98695 9.99795 8.98901 1.01099 01
100 5 37 30.0 8.99130 9. 99790 8. 99340 1.00660 00
L Sin L Cos L Tan L Cot 63-, 31-
Mils o / //
L Cos L Sin | L Cot L Tan 47-, 15-
25
Table II.—Common Logarithms of Functions of Angles in Mils—Continued
1-, 33- o / // L Sin L Cos L Tan L Cot - Mils
17-, 49- L Cos LSin L Cot L Tan
00 5 37 30.0 8. 99130 9. 99790 8. 99340 1.00660 100
01 5 40 52.5 8. 99561 9. 99786 8. 99775 1.00225 99
02 5 44 15.0 8. 99987 9. 99782 9. 00206 0. 99794 98
03 5 47 37. 5 9.00410 9. 99778 9.00632 0. 99368 97
04 5 51 00. 0 9. 00828 9. 99773 9. 01055 0.98945 96
05 5 54 22. 5 9. 01242 9. 99769 9.01473 0. 98527 95
06 5 57 45.0 9.01652 9. 99764 9.01888 0. 98112 94
07 6 01 07. 5 9. 02058 9. 99760 9. 02299 0. 97701 93
08 6 04 30. 0 9. 02461 9. 99755 9. 02706 0. 97294 92
09 6 07 52. 5 9.02860 9. 99751 9. 03109 0. 96891 91
10 6 11 15.0 9. 03255 9. 99746 9. 03509 0. 96491 90
11 6 14 37. 5 9. 03646 9. 99742 9. 03905 0. 96095 89
12 6 18 00. 0 9. 04034 9. 99737 9. 04297 0. 95703 88
13 6 21 22. 5 9. 04419 9. 99732 9.04687 0. 95313 87
14 6 24 45.0 9.04800 9. 99727 9.05072 0. 94928 86
15 6 28 07. 5 9. 05177 9. 99723 9.05455 0. 94545 85
16 6 31 30.0 9.05552 9. 99718 9. 05834 0. 94166 84
17 6 34 52. 5 9. 05923 9. 99713 9. 06210 0. 93790 83
18 6 38 15. 0 9. 06291 9.99708 9. 06583 0. 93417 82
19 6 41 37. 5 9.06656 9. 99703 9.06953 0.93047 81
20 6 45 00. 0 9.07018 9. 99698 9.07320 0. 92680 80
21 6 48 22. 5 9.07376 9.99693 9.07683 0. 92317 79 |
22 6 51 45.0 9. 07732 9. 99688 9.08044 0. 91956 78
23 6 55 07. 5 9. 08085 9. 99683 9.08402 0. 91598 77
24 6 58 30.0 9. 08435 9. 99677 9. 08757 0. 91243 76
25 7 01 52.5 9.08782 9. 99672 9. 09110 0. 90890 75
26 7 05 15.0 9.09126 9. 99667 9.09459 0. 90541 74
27 7 08 37. 5 9.09468 9.99662 9.09806 0. 90194 73
28 7 12 00.0 9. 09807 9. 99656 9.10150 0. 89850 72
29 7 15 22. 5 9.10143 9. 99651 9.10492 0. 89508 71
30 7 18 45.0 9.10476 9. 99645 9.10831 0.89169 70
31 7 22 07. 5 9.10807 9. 99640 9.11168 0.88832 69
32 7 25 30.0 9.11136 9.99634 9.11501 0.88499 68
33 7 28 52. 5 9.11462 9. 99629 9.11833 0.88167 67
34 7 32 15. 0 9.11785 9. 99623 9.12162 0. 87838 66
35 7 35 37.5 9.12106 9. 99617 9.12489 0.87511 65
36 7 39 00.0 9.12425 9. 99612 9. 12813 0. 87187 64
37 7 42 22. 5 9.12741 9. 99606 9.13135 0. 86865 63
38 7 45 45.0 9.13055 9. 99600 9.13455 0.86545 62
39 7 49 07. 5 9.13367 9. 99594 9.13772 0.86228 61
40 7 52 30.0 9.13676 9.99588 9.14087 0. 85913 60
41 7 55 52. 5 9.13983 9.99583 9.14401 0.85599 59
42 7 59 15.0 9.14288 9.99577 9.14711 0.85289 58
43 8 02 37.5 9.14591 9. 99571 9.15020 0.84980 57
44 8 06 00.0 9.14891 9. 99565 9.15327 0. 84673 56
45 8 09 22.5 9.15190 9.99558 9.15632 0.84368 55
46 8 12 45.0 9.15486 9.99552 9.15934 0. 84066 54
47 8 16 07.5 9.15781 9.99546 9.16235 0.83765 53
48 8 19 30.0 9.16073 9. 99540 9.16533 0.83467 52
49 8 22 52. 5 9.16364 9.99534 9.16830 0.83170 51
50 8 26 15.0 9.16652 9.99527 9.17125 0.82875 50
LSin L Cos L Tan L Cot 62-, 30-
Mils o / //
L Cos L Sin L Cot L Tan 16-, 14-
26
Table II.—Common Logarithms of Functions of Angles in Mils—Continued
1-, 33- o / n 1 L Sin L Cos L Tan L Cot Mils
17-, 49- L Cos L Sin L Cot L Tan
50 8 26 15.0 9.16652 9.99527 9.17125 0.82875 50
51 8 29 37. 5 9.16938 9.99521 9.17417 0.82583 49
52 8 33 00.0 9.17223 9.99515 9.17708 0.82292 48
53 8 36 22. 5 9.17506 9. 99508 9.17997 0.82003 47
54 8 39 45.0 9.17786 9.99502 9.18285 0.81715 46
55 8 43 07. 5 9.18065 9.99495 9.18570 0.81430 45
56 8 46 30.0 9.18343 9. 99489 9.18854 0. 81146 44
57 8 49 52. 5 9.18618 9.99482 9.19136 0. 80864 43
58 8 53 15. 0 9.18891 9.99475 9.19416 0. 80584 42
59 8 56 37. 5 9.19163 9. 99469 9.19694 0.80306 41
60 9 00 00.0 9.19433 9.99462 9.19971 9.80029 40
61 9 03 22. 5 9.19702 9.99455 9. 20246 0. 79754 39
62 9 06 45.0 9.19968 9. 99448 9. 20520 0.79489 38
63 9 10 07. 5 9. 20233 9.99442 9. 20792 0. 79208 37
64 9 13 30. 0 9. 20497 9. 99435 9. 21062 0. 78938 36
65 9 16 52. 5 9 20758 9.99428 9. 21331 0. 78669 35
66 9 20 15. 0 9. 21018 9.99421 9. 21598 0.78402 34
67 9 23 37. 5 9. 21277 9. 99414 9. 21863 0.78137 33
68 9 27 00. 0 9. 21534 9.99407 9. 22127 0. 77873 32
69 9 30 22. 5 9. 21789 9. 99399 9. 22390 0. 77610 31
70 9 33 45.0 9.22043 9.99392 9. 22651 0. 77349 30
71 9 37 07. 5 9. 22295 9.99385 9. 22910 0. 77090 29
72 9 40 30.0 9. 22546 9.99378 9.23168 0. 76832 28
73 9 43 52. 5 9. 22796 9.99371 9. 23425 0. 76575 27
74 9 47 15.0 9. 23043 9. 99363 9. 23680 0. 76320 26
75 9 50 37. 5 9. 23290 9.99356 9. 23934 0. 76066 25
76 9 54 00.0 9. 23535 9.99348 9. 24186 0. 75814 24
77 9 57 22. 5 9. 23779 9.99341 9. 24438 0. 75562 23
78 10 00 45.0 9. 24021 9.99333 9. 24687 0.75313 22
79 10 04 07. 5 9. 24262 9.99326 9. 24936 0. 75064 21
80 10 07 30.0 9. 24501 9.99318 9. 25183 0.74817 20
81 10 10 52.5 9 24739 9.99311 9. 25428 0. 74572 19
82 10 14 15.0 9. 24976 9.99303 9. 25673 0. 74327 18
83 10 17 37. 5 9. 25211 9. 99295 9.25916 0. 74084 17
84 10 21 00. 0 9. 25445 9. 99288 9. 26158 0. 73842 16
85 10 24 22. 5 9. 25678 9.99280 9. 26398 0. 73602 15
86 10 27 45.0 9. 25910 9. 99272 9. 26638 0.73362 14
87 10 31 07.5 9. 26140 9.99264 9. 26876 0. 73124 13
88 10 34 30.0 9.26369 9.99256 9. 27113 0. 72887 12
89 10 37 52. 5 9. 26597 9.99248 9. 27349 0. 72651 11
90 10 41 15.0 9. 26823 9.99240 9. 27583 0. 72417 10
91 10 44 37. 5 9. 27049 9.99232 9. 27817 0. 72183 09
92 10 48 00. 0 9. 27273 9.99224 9. 28049 0. 71951 08
93 10 51 22.5 9. 27496 9.99216 9. 28280 0. 71720 07
94 10 54 45.0 9. 27717 9.99207 9. 28510 0. 71490 06
95 10 58 07. 5 9.27938 9. 99199 9. 28739 0. 71261 05
96 11 01 30.0 9. 28157 9. 99191 9. 28966 0. 71034 04
97 11 04 52.5 9. 28376 9.99183 9. 29193 0.70807 03
98 11 08 15.0 9. 28593 9.99174 9. 29418 0. 70582 02
99 11 11 37.5 9. 28809 9.99166 9. 29643 0. 70357 01
100 11 15 00.0 9. 29024 9.99157 9. 29866 0. 70134 00
L Sin L Cos L Tan L Cot 62-, 30-
Mils o / //
L Cos L Sin L Cot L Tan 46-, 14-
27
Table II.—Common Logarithms of Functions of Angles in Mils—Continued
2-, 34- - O/// L Sin L Cos L Tan L Cot Mils
18-, 50- L Cos L Sin L Cot L Tan
00 11 15 00.0 9.29024 9.99157 9. 29866 0. 70134 100
01 11 18 22. 5 9. 29237 9. 99149 9. 30088 0. 69912 99
02 11 21 45.0 9. 29450 9.99140 9. 30310 0 69690 98
03 11 25 07.5 9. 29662 9. 99132 9. 30530 0. 69470 97
04 11 28 30.0 9. 29872 9. 99123 9. 30749 0. 69251 96
05 11 31 52. 5 9.30082 9.99114 9.30967 0. 69033 95
06 11 35 15.0 9.30290 9.99106 9.31185 0.68815 94
07 08 11 38 37. 5 11 42 00.0 9. 30498 9. 30704 9. 99097 9. 99088 9. 31401 9.31616 0.68599 0. 68384 93 92
09 11 45 22. 5 9. 30909 9. 99079 9. 31830 0. 68170 91
10 11 48 45.0 9. 31114 9.99070 9. 32043 0. 67957 90
11 11 52 07.5 9.31317 9.99061 9.32256 0. 67744 89
12 11 55 30. 0 9. 31520 9.99052 9.32467 0. 67533 88
13 11 58 52. 5 9.31721 9. 99043 9.32678 0.67322 87
14 12 02 15. 0 9.31921 9.99034 9.32887 0. 67113 86
15 12 05 37. 5 9.32121 9.99025 9.33096 0.66904 85
16 12 09 00.0 9. 32319 9.99016 9. 33303 0. 66697 84
17 12 12 22. 5 9. 32517 9. 99007 9.33510 0. 66490 83
18 12 15 45. 0 9.32714 9. 98998 9. 33716 0. 66284 82
19 12 19 07. 5 9. 32909 9. 98988 9.33921 0. 66079 81
20 12 22 30. 0 9.33104 9.98979 9. 34125 0. 65875 80
21 12 25 52. 5 9. 33298 9. 98970 9. 34328 0. 65672 79
22 12 29 15. 0 9. 33491 9.98960 9.34531 0. 65469 78
23 12 32 37. 5 9. 33683 9. 98951 9. 34732 0. 65268 77
24 12 36 00. 0 9. 33874 9. 98941 9. 34933 0. 65067 76
25 12 39 22. 5 9. 34064 9.98932 9.35133 0. 64867 75
26 12 42 45. 0 9. 34254 9.98922 9.35332 0. 64668 74
27 12 4o 0Z. 5 9.34442 9. 98912 9.35530 0. 64470 73
28 12 49 30. 0 9.34630 9. 98903 9. 35727 0. 64273 72
29 12 52 52. 5 9.34817 9. 98893 9.35924 0. 64076 71
30 12 56 15.0 9.35003 9.98883 9.36120 0.63880 70
31 12 59 37. 5 9. 35188 9.98873 9.36315 0. 63685 69
32 13 03 00.0 9. 35373 9. 98864 9. 36509 0.63491 68
33 13 06 22. 5 9.35556 9. 98854 9. 36702 0. 63298 67
34 13 09 45.0 9. 35739 9. 98844 9.36895 0. 63105 66
35 13 13 07. 5 9.35921 9. 98834 9.37087 0. 62913 65
36 13 16 30.0 9. 36102 9. 98824 9.37278 0. 62722 64
37 13 19 52.5 9.36282 9.98814 9. 37469 0. 62531 63
38 13 23 15.0 9.36462 9. 98804 9. 37658 0. 62342 62
39 13 26 37. 5 9.36641 9.98793 9.37847 0. 62153 61
40 13 30 00.0 9.36819 9.98783 9.38035 0.61965 60
41 13 33 22. 5 9. 36996 9.98773 9.38223 0. 61777 59
42 13 36 45.0 9.37172 9. 98763 9.38410 0. 61590 58
43 13 40 07.5 9.37348 9.98752 9.38596 0. 61404 57
44 13 43 30.0 9.37523 9. 98742 9.38781 0. 61219 56
45 13 46 52. 5 9.37697 9.98731 9.38966 0.61034 55
46 13 50 15.0 9.37870 9.98721 9.39150 0.60850 54
47 13 53 3/. 5 9. 38043 9.98710 9.39333 0. 60667 53
48 13 57 00.0 9.38215 9.98700 9.39515 0. 60485 52
49 14 00 22. 5 9.38387 9. 98689 9.39697 0. 60303 51
50 14 03 45.0 9.38557 9.98679 9.39879 0. 60121 50
L Sin L Cos L Tan L Cot 1-, 29-
Mils O / //
L Cos L Sin L Cot | L Tan 5-, 13-
28
Table II.—Common Logarithms of Functions of Angles in Mils—Continued
2-, 34- o / // L Sin L Cos L Tan L Cot Mils
18-, 50- L Oos L Sin L Cot L Tan
50 14 03 45.0 9.38557 9.98679 9.39879 0.60121 50
51 14 07 07.5 9.38727 9.98668 9.40059 0. 59941 49
52 14 10 30.0 9. 38896 9.98657 9.40239 0.59761 48
53 14 13 52.5 9.39065 9. 98646 9. 40418 0. 59582 47
54 14 17 15.0 9. 39232 9.98635 9.40597 0.59403 46
55 14 20 37.5 9.39399 9.98625 9.40775 0.59225 45
56 14 24 00.0 9. 39566 9.98614 9.40952 0. 59048 44
57 14 27 22.5 9.39732 9.98603 9.41129 0. 58871 43
58 14 30 45. 0 9.39897 9.98592 9.41305 0.58695 42
59 14 34 07.5 9.40061 9. 98581 9.41480 0. 58520 41
60 14 37 30.0 9.40225 9.98570 9. 41655 0.58345 40
61 14 40 52.5 9. 40388 9. 98558 9.41829 0.58171 39
62 14 44 15. 0 9.40551 9.98547 9.42003 0.57997 38
63 14 47 37. 5 9.40712 9. 98536 9.42176 0. 57824 37
64 14 51 00. 0 9.40873 9. 98525 9.42348 0.57652 36
65 14 54 22. 5 9.41034 9.98513 9.42520 0.57480 35
66 14 57 45.0 9.41193 9.98502 9.42691 0. 57309 34
67 15 01 07.5 9.41353 9.98491 9.42862 0. 57138 33
68 15 04 30.0 9.41511 9.98479 9. 43032 0. 56968 32
69 15 07 52. 5 9.41669 9. 98468 9.43202 0. 56798 31
70 15 11 15.0 9.41827 9.98456 9. 43371 0.56629 30
71 15 14 37.5 9. 41983 9.98444 9.43539 0.56461 29
72 15 18 00.0 9.42140 9.98433 9.43707 0.56293 28
73 15 21 22.5 9. 42295 9. 98421 9.43874 0. 56126 27
74 15 24 45.0 9.42450 9.98409 9. 44041 0.55959 26
75 15 28 07.5 9.42604 9.98398 9.44207 0.55793 25
76 15 31 30.0 9.42758 9.98386 9.44372 0.55628 24
77 15 34 52. 5 9.42911 9.98374 9. 44537 0.55463 23
78 15 38 15.0 9.43064 9. 98362 9. 44702 0. 55298 22
79 15 41 37. 5 9.43216 9.98350 9.44866 0. 55134 21
80 15 45 00.0 9.43367 9.98338 9.45029 0. 54971 20
81 15 48 22.5 9.43518 9.98326 9.45192 0. 54808 19
82 15 51 45.0 9.43669 9.98314 9.45355 0.54645 18
83 15 55 07. 5 9.43818 9.98302 9. 45517 0. 54483 17
84 15 58 30.0 9.43968 9. 98290 9.45678 0. 54322 16
85 16 01 52.5 9.44116 9. 98277 9.45839 0.54161 15
86 16 05 15.0 9.44264 9.98265 9.45999 0. 54001 14
87 16 08 37. 5 9.44412 9.98253 9.46159 0.53841 13
88 16 12 00.0 9.44559 9.98240 9. 46319 0. 53681 12
89 16 15 22.5 9.44706 9.98228 9. 46478 0.53522 11
90 16 18 45.0 9.44851 9.98216 9.46636 0.53364 10
91 16 22 07.5 9.44997 9.98203 9. 46794 0.53206 09
92 16 25 30.0 9.45142 9. 98190 9.46951 0.53049 08
93 16 28 52. 5 9.45286 9.98178 9.47108 0.52892 07
94 16 32 15.0 9.45430 9.98165 9.47265 0.52735 06
95 16 35 37.5 9.45573 9.98153 9.47421 0.52579 05
96 16 39 00.0 9.45716 9.98140 9.47576 0. 52424 04
97 16 42 22.5 9.45858 9.98127 9.47731 0. 52269 03
98 16 45 45.0 9.46000 9.98114 9.47886 0. 52114 02
99 16 49 07.5 9.46142 9. 98101 9.48040 0.51960 01
100 16 52 30.0 9.46282 9.98088 9.48194 0.51806 00
L Sin L Cos L Tan L Cot 61-, 29-
Mils o / //
L Cos L Sin L Cot L Tan 45-, 13-
609023°—44----3
29
Table II.—Common Logarithms of Functions of Angles in Mils—Continued
3-, 35- L Sin L Cos L Tan L Cot
Mils
19-, 51- L Cos L Sin L Cot L Tan
00 16 52 30.0 9. 46282 9.98088 9. 48194 0.51806 100
01 16 55 52.5 9.46423 9.98076 9.48347 0.51653 9Q
02 16 59 15.0 9.46563 9.98063 9.48500 0.51500 98
03 17 02 37. 5 9.46702 9.98050 9.48652 0. 51348 97
04 17 06 00.0 9.46841 9.98036 9. 48804 0. 51196 96
05 17 09 22.5 9.46979 9.98023 9.48956 0.51044 95
06 17 12 45.0 9.47117 9.98010 9.49107 0. 50893 94
07 17 16 07.5 9.47254 9. 97997 9.49257 0. 50743 98
08 17 19 30.0 9.47391 9. 97984 9.49408 0. 50592 92
09 17 22 52.5 9.47528 9.97970 9.49557 0. 50443 91
10 17 26 15.0 9.47664 9.97957 9.49707 0. 50293 90
11 17 29 37.5 9.47799 9.97943 9.49856 0.50144 89
12 17 33 00.0 9.47934 9.97930 9. 50004 0.49996 88
13 17 36 22.5 9. 48069 9. 97916 9. 50152 0.49848 87
14 17 39 45.0 9. 48203 9.97903 9. 50300 0.49700 86
15 17 43 07.5 9.48337 9.97889 9.50447 0.49553 85
16 17 46 30.0 9.48470 9.97876 9.50594 0.49406 84
17 17 49 52.5 9. 48603 9.97862 9.50741 0.49259 83
18 1/53 15.0 9.48735 9.97848 9.50887 0.49113 82
19 17 56 37.5 9.48867 9. 97834 9.51032 0.48968 81
20 18 00 00.0 9.48998 9.97821 9.51178 0.48822 80
21 18 03 22.5 9. 49129 9.97807 9.51322 0.48678 79
22 18 06 45.0 9.49260 9. 97793 9. 51467 0.48533 78
23 18 10 07.5 9.49390 9.97779 9. 51611 0.48389 77
24 18 13 30.0 9.49520 9. 97765 9. 51755 0.48245 76
25 18 16 52.5 9.49649 9. 97751 9. 51898 6.48102 75
26 18 20 15.0 9. 49778 9. 97737 9. 52041 0.47959 74
27 18 23 37.5 9.49906 9.97722 9.52184 0. 47816 73
28 18 27 00.0 9. 50034 9.97708 9.52326 0.47674 72
29 18 30 22. 5 9. 50162 9. 97694 9.52468 0. 47532 71
30 18 33 45.0 9.50289 9.97680 9.52609 0.47391 70
31 18 37 07. 5 9.50416 9. 97665 9. 52750 0.47250 69
32 18 40 30.0 9.50542 9.97651 9.52891 0.47109 68
33 18 43 52. 5 9.50668 9.97637 9.53031 0.46969 67
34 18 47 15.0 9. 50794 9.97622 9.53171 0.46829 66
35 18 50 37. 5 9.50919 9. 97608 9.53311 0.46689 65
36 18 54 00.0 9.51043 9. 97593 9. 53450 0.46550 64
37 18 5/ 22. 5 9.51168 9.97578 9. 53589 0. 46411 63
38 19 00 45.0 9. 51292 9.97564 9.53728 0.46272 62
39 19 04 07.5 9. 51415 9.97549 9.53866 0.46134 61
40 19 07 30.0 9.51538 9. 97534 9.54004 0.45996 60
41 19 10 52. 5 9.51661 9.97519 9. 54142 0.45858 59
42 19 14 15.0 9.51784 9.97505 9.54279 0.45721 58
43 19 17 37.5 9.51906 9.97490 9.54416 0.45584 57
44 19 21 00.0 9.52027 9.97475 9. 54552 0.45448 56
45 19 24 22.5 9. 52148 9.97460 9.54689 0.45311 55
46 19 27 45.0 fi. 52269 9.97445 9. 54824 0.45176 54
47 19 31 07.5 9.52390 9.97430 9.54960 0.45040 53
48 19 34 30.0 9. 52510 9.97414 9.55095 0.44905 52
49 19 3/ 52. 5 9.52629 9.97399 9.55230 0. 44770 51
50 19 41 15.0 9.52749 9.97384 9.55365 0.44635 50
L Sin L Cos L Tan L Cot 0-, 28-
Mils
I. Cos L Sin L Cot L Tan 4-, 12-
30
Table II.—Common Logarithms of Functions of Angles in Mils—Continued
3-, 35- o / // L Sin L Cos L Tan L Cot Mils
19-, 51- L Cos L Sin L Cot L Tan
50 19 41 15.0 9.52749 9.97384 9.55365 0.44635 50
51 19 44 37.5 9.52868 9.97369 9.55499 0.44501 49
52 19 48 00.0 9.52986 9.97353 9.55633 0.44367 48
53 19 51 22.5 9. 53105 9.97338 9.55767 0.44233 47
54 19 54 45.0 9.53223 9.97323 9.55900 0. 44100 46
55 19 58 07.5 9.53340 9.97307 9.56033 0.43967 45
56 20 01 30.0 9 53457 9.97292 9.56166 0.43834 44
57 20 04 52.5 9.53574 9.97276 9. 56298 0.43702 43
58 20 08 15.0 9.53690 9.97261 9.56430 0.43570 42
59 20 11 37.5 9.53807 9.97245 9. 56562 0.43438 41
60 20 15 00. 0 9.53922 9.97229 9. 56693 0.43307 40
61 20 18 22.5 9.54038 9.97213 9.56824 0.43176 39
62 20 21 45.0 9.54153 9.97198 9. 56955 0.43045 38
63 20 25 07.5 9.54267 9.97182 9.57086 0.42914 37
64 20 28 30.0 9. 54382 9.97166 9.57216 0.42784 36
65 20 31 52.5 9.54496 9.97150 9.57346 0.42654 35
66 20 35 15.0 9.54610 9.97134 9.57476 0.42524 34
67 20 38 37.5 9. 54723 9.97118 9.57605 0.42395 33
_ 68 20 42 00.0 9.54836 9.97102 9.57734 0.42266 32
69 20 45 22.5 9. 54949 9.97086 9.57863 0.42137 31
70 20 48 45.0 9.55061 9.97069 9.57991 0.42009 30
71 20 52 07.5 9.55173 9.97053 9.58120 0.41880 29
72 20 55 30.0 9.55285 9.97037 9.58248 0.41752 28
73 20 58 52. 5 9.55396 9.97021 9.58375 0.41625 27
74 21 02 15. 0 9.55507 9.97004 9.58503 0.41497 26
75 21 05 37.5 9.55618 9.96988 9.58630 0.41370 25
76 21 09 00.0 9.55728 9.96971 9.58757 0.41243 24
77 21 12 22.5 9.55838 9.96955 9.58883 0.41117 23
78 21 15 45.0 9. 55948 9.96938 9.59009 0.40991 22
79 21 19 07.5 9.56057 9.96922 9. 59135 0.40865 21
80 21 22 30.0 9.56166 9.96905 9.59261 0.40739 20
81 21 25 52. 5 9.56275 9.96888 9. 59387 0.40613 19
82 21 29 15. 0 9.56383 9.96872 9.59512 0.40488 18
83 21 32 37.5 9.56492 9.96855 9.59637 0.40363 17
84 21 36 00. 0 9. 56599 9.96838 9.59762 0.40238 16
85 21 39 22.5 9.56707 9.96821 9.59886 0.40114 15
86 21 42 45.0 9. 56814 9.96804 9.60010 0.39990 14
87 21 46 07.5 9. 56921 9.96787 9.60134 0.39866 13
88 21 49 30.0 9. 57028 9.96770 9.60258 0.39742 12
89 21 52 52.5 9.57134 9.96753 9.60381 0.39619 11
90 21 56 15.0 9.57240 9.96736 9.60504 0.39496 10
91 21 59 37.5 9. 57346 9.96719 9.60627 0. 39373 09
92 22 03 00.0 9.57451 9.96701 9. 60750 0.39250 08
93 22 06 22.5 9.57556 9.96684 9.60872 0.39128 07
94 22 09 45.0 9.57661 9.96667 9.60995 0.39005 06
95 22 13 07.5 9.57766 9.96649 9.61116 0.38884 05
96 22 16 30.0 9.57870 9.96632 9.61238 0.38762 04
97 22 19 52.5 9.57974 9.96614 9.61360 0.38640 03
98 22 23 15.0 9.58078 9.96597 9.61481 0.38519 02
99 22 26 37.5 9. 58181 9.96579 9.61602 0.38398 01
100 22 30 00.0 9. 58284 9.96562 9.61722 0.38278 00
Mils L Sin L Cos L Tan L Cot 60-, 28-
L Cos LSin L Cot L Tan 44-, 12-
31
Table II.—Common Logarithms of Functions of Angles in Mils—Continued
4-, 36- o / // L Sin L Cos L Tan L Cot Mils
20-, 52- L Cos L Sin L Cot L Tan
00 22 30 00.0 9. 58284 9.96562 9.61722 0. 38278 100
01 22 33 22.5 9. 58387 9.96544 9. 61843 0.38157 99
02 22 36 45.0 9. 58489 9. 96526 9.61963 0. 38037 98
03 22 40 07.5 9.58591 9. 96508 9. 62083 0.37917 97
04 22 43 30. 0 9. 58693 9. 96490 9.62203 0. 37797 96
05 22 46 52.5 9.58795 9.96473 9.62322 0. 37678 95
06 22 50 15.0 9. 58896 9. 96455 9. 62442 0. 37559 94
07 22 53 37. 5 9. 58998 9. 96437 9. 62561 0. 37439 93
08 22 57 00.0 9.59098 9. 96419 9. 62680 0. 37320 92
09 23 00 22. 5 9. 59199 9. 96401 9. 62798 0. 37202 91
10 23 03 45. 0 9.59299 9. 96382 9. 62917 0.37083 90
11 23 07 07. 5 9. 59399 9. 96364 9. 63035 0. 36965 89
12 23 10 30.0 9. 59499 9. 96346 9. 63153 0. 36847 88
13 23 13 52. 5 9. 59598 9. 96328 9. 63271 0. 36729 87
14 23 17 15. 0 9. 59698 9. 96310 9. 63388 0. 36612 86
15 23 20 37. 5 9.59797 9. 96291 9. 63505 0. 36495 85
16 23 24 00.0 9.59895 9.96273 9. 63623 0.36377 84
17 23 27 22. 5 9. 59994 9. 96254 9. 63739 0. 36261 83
18 23 30 45.0 9. 60092 9. 96236 9. 63856 0. 36144 82
19 23 34 07. 5 9. 60190 9. 96217 9. 63973 0. 36027 81
20 23 37 30. 0 9. 60287 9. 96198 9. 64089 0. 35911 80
21 23 40 52. 5 9. 60385 9.96180 9. 64205 0. 35795 79
22 23 44 15. 0 9. 60482 9. 96161 9. 64321 0. 35679 78
23 23 47 3 /. 5 9. 60578 9. 96142 9.64436 0. 35564 77
24 23 51 00.0 9. 60675 9. 96123 9. 64552 0. 35448 76
25 23 54 22. 5 9.60771 9. 96105 9. 64667 0. 35333 75
26 23 57 45. 0 9. 60867 9. 96086 9. 64782 0. 35218 74
27 24 01 07. 5 9. 60963 9. 96067 9. 64897 0. 35103 73
28 24 04 30. 0 9. 61059 9. 96048 9. 65011 0. 34989 72
29 24 07 52. 5 9. 61154 9. 96029 9. 65126 0. 34875 71
30 24 11 15.0 9. 61249 9. 96009 9. 65240 0.34760 70
31 24 14 37. 5 9.61344 9. 95990 9. 65354 0. 34646 69
32 24 18 00. 0 9. 61438 9.95971 9. 65467 0. 34533 68
33 24 21 22. 5 9. 61533 9. 95952 9. 65581 0. 34419 67
34 24 24 45. 0 9. 61627 9. 95932 9. 65694 0.34306 66
35 24 28 07. 5 9. 61721 9.95913 9.65808 0.34192 65
36 24 31 30.0 9.61814 9. 95894 9. 65921 0. 34079 64
37 24 34 52. 5 9. 61908 9. 95874 9.66033 0.33967 63
38 24 38 15. 0 9. 62001 9.95855 9.66146 0. 33854 62
39 24 41 37. 5 9.62094 9. 95835 9.66258 0. 33742 61
40 24 45 00. 0 9.62186 9. 95815 9.66371 0.33629 60
41 24 48 22. 5 9.62278 9. 95796 9. 66483 0. 33517 59
42 24 51 45. 0 9. 62371 9. 95776 9.66595 0. 33405 58
43 24 55 07. 5 9. 62463 9. 95756 9. 66706 0.33294 57
44 24 58 30.0 9.62554 9. 95736 9. 66818 0.33182 56
45 25 01 52. 5 9.62646 9. 95717 9.66929 0.33071 55
46 25 05 15.0 9. 62737 9.95697 9.67040 0.32960 54
47 25 08 37. 5 9.62828 9. 95677 9. 67151 0.32849 53
48 25 12 00.0 9.62918 9. 95657 9.67262 0. 32738 52
49 25 15 22.5 9.63009 9. 95636 9. 67372 0.32628 51
50 25 18 45.0 9.63099 9. 95616 9.67483 0.32517 50
L Sin L Cos L Tan L Cot 59-, 27-
Mils O f ft
L Cos L Sin | L Cot L Tan 13-, 11-
32
Table II.—Common Logarithms of Functions of Angles in Mils—Continued
4-, 36- o / // L Sin L Cos L Tan L Cot Mils
20-, 52- L Cos L Sin L Cot L Tan
50 25 18 45.0 9. 63099 9.95616 9. 67483 0.32517 50
51 25 22 07. 5 9.63189 9.95596 9. 67593 0. 32407 49
52 25 25 30.0 9. 63279 9.95576 9. 67703 0.32297 48
53 25 28 52. 5 9. 63369 9.95556 9. 67813 0. 32187 47
54 25 32 15.0 9. 63458 9.95535 9. 67923 0. 32077 46
55 25 35 37. 5 9.63547 9.95515 9. 68032 0. 31968 45
56 25 39 00.0 9.63636 9.95494 9.68142 0.31858 44
57 25 42 22.5 9.63725 9.95474 9.68251 0. 31749 43
58 25 45 45.0 9. 63813 9.95453 9. 68360 0. 31640 42
59 25 49 07.5 9. 63901 9.95433 9.68469 0. 31531 41
60 25 52 30.0 9. 63989 9.95412 9.68577 0. 31423 40
61 25 55 52. 5 9.64077 9.95391 9. 68686 0. 31314 39
62 25 59 15.0 9. 64165 9.95371 9. 68794 0. 31206 38
63 26 02 37. 5 9. 64252 9.95350 9. 68902 0. 31098 37
64 26 06 00. 0 9. 64339 9.95329 9. 69010 0. 30990 36
65 26 09 22.5 9.64426 9.95308 9. 69118 0.30882 35
66 26 12 45.0 9. 64513 9.95287 9. 69226 0. 30774 34
67 26 16 07. 5 9. 64599 9.95266 9.69333 0. 30667 33
68 26 19 30.0 9. 64686 9.95245 9. 69441 0. 30559 32
69 26 22 52. 5 9.64772 9.95224 9. 69548 0. 30452 31
70 26 26 15.0 9. 64858 9.95203 9.69655 0.30345 30
71 26 29 37. 5 9. 64943 9.95181 9. 69762 0. 30238 29
72 26 33 00. 0 9. 65029 9.95160 9. 69868 0. 30132 28
73 26 36 22. 5 9.65114 9.95139 9. 69975 0. 30025 27
74 26 39 45.0 9.65199 9. 95117 9. 70081 0. 29919 26
75 26 43 07. 5 9.65284 9.95096 9. 70188 0. 29812 25
76 26 46 30.0 9. 65368 9.95075 9. 70294 0. 29706 24
77 26 49 52. 5 9.65453 9. 95053 9. 70400 0.29600 23
78 26 53 15. 0 9. 65537 9.95031 9.70505 0. 29495 22
79 26 56 37.5 9. 65621 9.95010 9. 70611 0. 29389 21
80 27 00 00.0 9.65705 9.94988 9.70717 0.29283 20
81 27 03 22. 5 9. 65788 9.94966 9. 70822 0. 29178 19
82 27 06 45.0 9. 65872 9.94945 9. 70927 0. 29073 18
83 27 10 07. 5 9. 65955 9.94923 9. 71032 0. 28968 17
84 27 13 30.0 9. 66038 9.94901 9. 71137 0. 28863 16
85 27 16 52.5 9. 66121 9.94879 9. 71242 0. 28758 15
86 27 20 15.0 9. 66203 9.94857 9.71346 0.28654 14
87 27 23 37. 5 9. 66286 9.94835 9. 71451 0. 28549 13
88 27 27 00.0 9. 66368 9.94813 9.71555 0. 28445 12
89 27 30 22. 5 9. 66450 9.94790 9.71659 0. 28341 11
90 27 33 45.0 9. 66531 9.94768 9. 71763 0. 28237 10
91 27 37 07. 5 9. 66613 9.94746 9.71867 0. 28133 09
92 27 40 30.0 9. 66694 9.94724 9.71971 0. 28029 08
93 27 43 52. 5 9.66776 9.94701 9.72074 0. 27926 07
94 27 47 15.0 9. 66857 9.94679 9.72178 0.27822 06
95 27 50 37.5 9.66937 9.94656 9.72281 0.27719 05
96 27 54 00.0 9. 67018 9.94634 9. 72384 0. 27616 04
97 27 57 22. 5 9. 67099 9.94611 9. 72487 0. 27513 03
98 28 00 45.0 9. 67179 9.94588 9. 72590 0. 27410 02
99 28 04 07. 5 9. 67259 9.94566 9. 72693 0. 27307 01
100 28 07 30.0 9. 67339 9.94543 9. 72796 0.27204 00
L Sin L Cos L Tan L Cot 59-, 27-
Mils O / ff
L Cos L Sin L Cot L Tan 43-, 11-
33
Table II — Common Logarithms of Functions of Angles in Mils—Continued
5-, 37- O ' " L Sin L Cos L Tan L Cot Mils
21-, 53- L Cos L Sin L Cot L Tan
00 28 07 30.0 9.67339 9. 94543 9.72796 0.27204 100
01 28 10 52.5 9.67418 9.94520 9. 72898 0. 27102 99
02 28 14 15.0 9.67498 9. 94497 9. 73001 0. 26999 98
03 28 17 37. 5 9.67577 9.94474 9. 73103 0. 26897 97
04 28 21 00. 0 9.67656 9. 94451 9. 73205 0. 26795 96
05 28 24 22. 5 9.67735 9.94428 9. 73307 0.26693 95
06 28 27 45.0 9.67814 9.94405 9. 73409 0. 26591 94
07 28 31 07. 5 9.67892 9.94382 9. 73510 0. 26490 93
08 28 34 30. 0 9.67971 9. 94359 9. 73612 0.26388 92
09 28 37 52. 5 9. 68049 9. 94336 9. 73713 0. 26287 91
10 28 41 15. 0 9.68127 9. 94312 9. 73815 0. 26185 90
11 28 44 37. 5 9. 68205 9. 94289 9. 73916 0. 26084 89
12 28 48 00. 0 9. 68283 9. 94266 9. 74017 0. 25983 88
13 28 51 22. 5 9.68360 9. 94242 9. 74118 0.25882 87
14 28 54 45. 0 9. 68437 9. 94219 9. 74219 0. 25781 86
15 28 58 07. 5 9.68514 9.94195 9.74319 0.25681 85
16 29 01 30.0 9.68591 9.94171 9.74420 0. 25580 84
17 29 04 52. 5 9.68668 9.94148 9. 74520 0. 25480 83
18 29 08 15.0 9.68745 9. 94124 9. 74621 0. 25379 82
19 29 11 37. 5 9.68821 9. 94100 9. 74721 0. 25279 81
20 29 15 00. 0 9.68897 9.94076 9. 74821 0. 25179 80
21 29 18 22. 5 9.68973 9.94052 9. 74921 0. 25079 79
22 29 21 45.0 9.69049 9. 94028 9. 75021 0.24979 78
23 29 25 07. 5 9. 69125 9. 94004 9. 75120 0. 24880 77
24 29 28 30.0 9.69200 9.93980 9. 75220 0. 24780 76
25 29 31 52. 5 9.69276 9.93956 9. 75320 0.24680 75
26 29 35 15.0 9.69351 9. 93932 9. 75419 0. 24581 74
27 29 38 37.5 9.69426 9.93908 9. 75518 0.24482 73
28 29 42 00.0 9.69501 9.93884 9. 75617 0. 24383 72
29 29 45 22. 5 9. 69575 9.93859 9. 75716 0. 24284 71
30 29 48 45. 0 9.69650 9.93835 9. 75815 0. 24185 70
31 29 52 07. 5 9.69724 9.93810 9. 75914 0. 24086 69
32 29 55 30.0 9.69798 9. 93786 9. 76013 0. 23987 68
33 29 58 52. 5 9.69872 9. 93761 9. 76111 0.23889 67
34 30 02 15. 0 9.69946 9. 93737 9. 76210 0. 23790 66
35 30 05 37.5 9.70020 9.93712 9. 76308 0.23692 65
36 30 09 00.0 9.70093 9.93687 9. 76406 0. 23594 64
37 30 12 22. 5 9. 70167 9. 93662 9. 76504 0.23496 63
38 30 15 45. 0 9. 70240 9.93638 9. 76602 0.23398 62
39 30 19 07. 5 9. 70313 9.93613 9. 76700 0. 23300 61
40 30 22 30. 0 9. 70386 9.93588 9. 76798 0.23202 60
41 30 25 52. 5 9. 70458 9. 93563 9. 76896 0.23104 59
42 30 29 15. 0 9. 70531 9.93538 9. 76993 0.23007 58
43 30 32 37. 5 9. 70603 9. 93512 9. 77091 0.22909 57
44 30 36 00. 0 9. 70675 9. 93487 9. 77188 0.22812 56
45 30 39 22. 5 9. 70747 9.93462 9. 77285 0.22715 55
46 30 42 45.0 9.70819 9.93437 9. 77382 0. 22618 54
47 30 46 07. 5 9. 70891 9. 93411 9. 77479 0.22521 53
48 30 49 30.0 9. 70962 9.93386 9. 77576 0.22424 52
49 30 52 52.5 9. 71034 9. 93361 9. 77673 0. 22327 51
50 30 56 15.0 9. 71105 9.93335 9. 77770 0.22230 50
L Sin L Cos L Tan L Cot 58-, 26-
Mils 0 / //
L Cos L Sin L Cot L Tan 12-,10-
34
Table II.—Common Logarithms of Functions of Angles in Mils—Continued
5-, 37- O / tt L Sin L Cos L Tan L Cot MAS
21-, 53- L Cos L Sin L Cot L Tan
50 30 56 15.0 9. 71105 9.93335 9. 77770 0.22230 50
51 30 59 37. 5 9. 71176 9.93309 9. 77867 0. 22133 49
52 31 03 00. 0 9. 71247 9. 93284 9. 77963 0.22037 48
53 31 06 22.5 9. 71318 9. 93258 9. 78060 0. 21940 47
54 31 09 45.0 9. 71388 9. 93232 9. 78156 0. 21844 46
55 31 13 07. 5 9. 71459 9.93206 9. 78252 0. 21748 45
56 31 16 30.0 9. 71529 9. 93181 9. 78348 0. 21652 44
57 31 19 52.5 9. 71599 9. 93155 9. 78444 0. 21556 43
58 31 23 15.0 9. 71669 9. 93129 9. 78540 0. 21460 42
59 31 26 37. 5 9. 71739 9. 93103 9. 78636 0. 21364 41
60 31 30 00. 0 9. 71809 9. 93077 9. 78732 0. 21268 40
61 31 33 22. 5 9. 71878 9.93050 9. 78828 0. 21172 39
62 31 36 45. 0 9. 71947 9. 93024 9. 78923 0. 21077 38
63 31 40 07. 5 9. 72017 9. 92998 9. 79019 0. 20981 37
64 31 43 30.0 9.72086 9. 92972 9. 79114 0. 20886 36
65 31 46 52. 5 9.72154 9.92945 9.79209 0. 20791 35
66 31 50 15. 0 9. 72223 9.92919 9. 79304 0. 20696 34
67 31 53 37. 5 9. 72292 9. 92892 9. 79400 0.20600 33
68 31 57 00. 0 9. 72360 9.92866 9. 79495 0. 20505 32
69 32 00 22. 5 9.72429 9.92839 9. 79589 0. 20411 31
70 32 03 45.0 9. 72497 9.92812 9. 79684 0. 20316 30
71 32 07 07.5 9. 72565 9.92786 9. 79779 0. 20221 29
72 32 10 30. 0 9. 72633 9.92759 9. 79874 0. 20126 28
73 32 13 52. 5 9. 72700 9.92732 9. 79968 0.20032 27
74 32 17 15.0 9. 72768 9.92705 9.80063 0.19937 26
75 32 20 37. 5 9.72835 9.92678 9. 80157 0.19843 25
76 32 24 00. 0 9.72902 9.92651 9. 80251 0.19749 24
77 32 27 22. 5 9.72970 9.92624 9. 80346 0.19654 23
78 32 30 45. 0 9. 73037 9.92597 9. 80440 0.19560 22
79 32 34 07. 5 9. 73103 9.92570 9. 80534 0.19466 21
80 32 37 30.0 9. 73170 9.92542 9.80628 0.19372 20
81 32 40 52. 5 9. 73237 9.92515 9. 80721 0.19279 19
82 32 44 15.0 9. 73303 9. 92488 9.80815 0.19185 18
83 32 47 37. 5 9. 73369 9. 92460 9. 80909 0.19091 17
84 32 51 00.0 9. 73435 9. 92433 9. 81003 0.18997 16
85 32 54 22.5 9. 73501 9.92405 9.81096 0.18904 15
86 32 57 45. 0 9. 73567 9.92378 9. 81189 0.18811 14
87 33 01 07. 5 9. 73633 9. 92350 9. 81283 0.18717 13
88 33 04 30. 0 9. 73698 9. 92322 9. 81376 0.18624 12
89 33 07 52. 5 9. 73764 9.92294 9. 81469 0.18531 11
90 33 11 15.0 9. 73829 9.92267 9.81562 0.18438 10
91 33 14 37. 5 9. 73894 9.92239 9. 81655 0.18345 09
92 33 18 00.0 9. 73959 9.92211 9.81748 0.18252 08
93 33 21 22. 5 9. 74024 9. 92183 9. 81841 0.18159 07
94 33 24 45. 0 9. 74089 9. 92154 9. 81934 0.18066 06
95 33 28 07. 5 9. 74153 9.92126 9.82027 0.17973 05
96 33 31 30.0 9. 74218 9.92098 9.82119 0. 17881 04
97 33 34 52.5 9.74282 9. 92070 9.82212 0.17788 03
98 33 38 15. 0 9. 74346 9. 92041 9. 82305 0.17695 02
99 33 41 37. 5 9.74410 9. 92013 9.82397 0. 17603 01
100 33 45 00. 0 9. 74474 9. 91985 9.82489 0.17511 00
L Sin L Cos L Tan L Cot 58-, 26-
Mils ox //
L Cos L Sin | L Cot L Tan 42-, 10-1
35
Table II— Common Logarithms of Functions of Angles in Mils— Continued
6-, 38- O / // L Sin L Cos L Tan L Cot Mils
22- 54- L Cos L Sin L Cot L Tan
00 33 45 00.0 9. 74474 9.91985 9.82489 0.17511 100
01 33 48 22. 5 9. 74538 9.91956 9. 82582 0.17418 99
02 33 51 45.0 9.74601 9.91928 9.82674 0.17326 98
03 33 55 07. 5 9. 74665 9.91899 9.82766 0.17234 97
04 33 58 30. 0 9. 74728 9.91870 9.82858 0.17142 96
05 34 01 52. 5 9. 74791 9.91841 9.82950 0.17050 95
06 34 05 15.0 9.74854 9.91813 9.83041 0.16959 94
07 34 08 37. 5 9. 74917 9.91784 9.83134 0.16866 93
08 34 12 00. 0 9.74980 9.91755 9.83225 0.16775 92
09 34 15 22. 5 . 9. 75043 9.91726 9.83317 0.16683 91
10 34 18 45. 0 9.75105 9.91697 9.83409 0.16591 90
11 34 22 07. 5 9. 75168 9.91668 9.83500 0.16500 89
12 34 25 30. 0 9. 75230 9.91638 9.83592 0.16408 88
13 34 28 52. 5 9.75292 9.91609 9.83683 0.16317 87
14 34 32 15. 0 9. 75354 9. 91580 9.83774 0.16226 86
15 34 35 37. 5 9.75416 9.91550 9.83866 0.16134 85
16 34 39 00. 0 9. 75478 9.91521 9. 83957 0.16043 84
17 34 42 22.5 9. 75539 9.91492 9.84048 0.15952 83
18 34 45 45.0 9. 75601 9. 91462 9.84139 0.15861 82
19 34 49 07. 5 9.75662 9.91432 9.84230 0.15770 81
20 34 52 30.0 9.75724 9.91403 9.84321 0.15679 80
21 34 55 52. 5 9. 75785 9.91373 9.84412 0.15588 79
22 34 59 15.0 9. 75846 9. 91343 9.84503 0.15497 78
23 35 02 37. 5 9. 75906 9. 91313 9.84593 0.15407 77
24 35 06 00. 0 9. 75967 9. 91283 9.84684 0.15316 76
25 35 09 22. 5 9. 76028 9.91253 9. 84775 0.15225 75
26 35 12 45. 0 9. 76088 9.91223 9.84865 0.15135 74
27 35 16 07. 5 9. 76149 9. 91193 9.84956 0.15044 73
28 35 19 30.0 9.76209 9.91163 9.85046 0.14954 72
29 35 22 52. 5 9.76269 9. 91133 9. 85136 0.14864 71
30 35 26 15.0 9.76329 9.91102 9.85227 0:14773 70
31 35 29 37. 5 9. 76389 9.91072 9.85317 0.14683 69
32 35 33 00. 0 9.76448 9.91042 9.85407 0.14593 68
33 35 36 22. 5 9.76508 9.91011 9. 85497 0.14503 67
34 35 39 45. 0 9.76568 9.90980 9.85587 0.14413 66
35 35 43 07. 5 9. 76627 9.90950 9.85677 0.14323 65
36 35 46 30. 0 9.76686 9.90919 9.85767 0.14233 64
37 35 49 52. 5 9.76745 9. 90888 9.85857 0.14143 63
38 35 53 15.0 9. 76804 9. 90858 9.85947 0.14053 62
39 35 56 37. 5 9. 76863 9.90827 9. 86036 0.13964 61
40 36 00 00. 0 9. 76922 9. 90796 9.86126 0.13874 60
41 36 03 22. 5 9. 76980 9.90765 9.86216 0.13784 59
42 36 06 45. 0 9.77039 9.90734 9.86305 0.13695 58
43 36 10 07. 5 9. 77097 9. 90703 9.86395 0.13605 57
44 36 13 30. 0 9.77156 9. 90671 9.86484 0.13516 56
45 36 16 52. 5 9.77214 9.90640 9.86574 0.13426 55
46 36 20 15.0 9. 77272 9.90609 9.86663 0.13337 54
47 36 23 37. 5 9.77330 9. 90577 9.86752 0.13248 53
48 36 27 00.0 9. 77387 9.90546 9.86842 0.13158 52
49 36 30 22. 5 9.77445 9.90514 9.86931 0.13069 51
50 36 33 45.0 9. 77503 9.90483 9.87020 0.12980 50
■ - *
L Sin L Cos L Tan L Cot 57-, 25-
Mils 0 / // — — —
1 L Cos L Sin L Cot L Tan 41-, 9-
36
Table II. Common Logarithms of Functions of Angles in Mils—Continued
6-, 38- o / // L Sin L Cos L Tan L Cot Mils
22-, 54- L Cos L Sin L Cot L Tan
50 36 33 45.0 9. 77503 9.90483 9.87020 0.12980 50
51 36 37 07. 5 9. 77560 9.90451 9.87109 0.12891 49
52 36 40 30.0 9. 77617 9. 90419 9. 87198 0.12802 48
53 36 43 52. 5 9. 77675 9.90388 9.87287 0.12713 47
54 36 47 15.0 9. 77732 9.90356 9.87376 0.12624 46
55 36 50 37.5 9. 77789 9.90324 9.87465 0.12535 45
56 36 54 00.0 9.77846 9.90292 9.87554 0.12446 44
57 36 57 22.5 9. 77902 9. 90260 9.87642 0.12358 43
58 37 00 45. 0 9. 77959 9. 90228 9.87731 0.12269 42
59 37 04 07. 5 9. 78015 9. 90196 9.87820 0.12180 41
60 27 07 30.0 9.78072 9.90163 9.87908 0.12092 40
61 37 10 52.5 9. 78128 9.90131 9.87997 0.12003 39
62 37 14 15.0 9.78184 9.90099 9.88086 0.11914 38
63 37 17 37. 5 9. 78240 9. 90066 9.88174 0.11826 37
64 37 21 00.0 9. 78296 9.90034 9.88262 0.11738 36
65 37 24 22.5 9. 78352 9. 90001 9.88351 0.11649 35
66 37 27 45.0 9. 78408 9.89968 9.88439 0.11561 34
67 37 31 07.5 9. 78463 9.89936 9.88527 0.11473 33
68 37 34 30.0 9.78519 9.89903 9.88616 0.11384 32
69 37 37 52.5 9. 78574 9.89870 9.88704 0.11296 31
70 37 41 15.0 9. 78629 9.89837 9.88792 0.11208 30
71 37 44 37.5 9. 78684 9.89804 9. 88880 0.11120 29 ~
72 37 48 00.0 9. 78739 9.89771 9.88968 0.11032 28
73 37 51 22. 5 9. 78794 9.89738 9.89056 0.10944 27
74 37 54 45.0 9. 78849 9.89705 9.89144 0.10856 26
75 37 58 07. 5 9. 78904 9.89672 9.89232 0.10768 25
76 38 01 30.0 9. 78958 9.89638 9.89320 0.10680 24
77 38 04 52. 5 9. 79013 9.89605 9.89408 0.10592 23
78 38 08 15.0 9. 79067 9.89572 9.89496 0.10504 22
79 38 11 37. 5 9. 79122 9.89538 9.89583 0.10417 21
80 38 15 00.0 9.79176 9.89504 9.89671 0.10329 20
81 38 18 22. 5 9. 79230 9.89471 9.89759 0.10241 19
82 38 21 45.0 9. 79284 9.89437 9.89846 0.10154 18
83 38 25 07. 5 9. 79337 9.89403 9.89934 0.10066 17
84 38 28 30.0 9. 79391 9.89370 9. 90022 0.09978 16
85 38 31 52. 5 9. 79445 9.89336 9.90109 0.09891 15
86 38 35 15. 0 9.79498 9.89302 9.90197 0.09803 14
87 38 38 37.5 9. 79552 9.89268 9.90284 0. 09716 13
88 38 42 00.0 9. 79605 9.89233 9. 90371 0. 09629 12
89 38 45 22. 5 9. 79658 9. 89199 9.90459 0.09541 11
90 38 48 45. 0 9. 79711 9.89165 9.90546 0.09454 10
91 38 52 07. 5 9. 79764 9.89131 9.90633 0.09367 09
92 38 55 30.0 9.79817 9. 89096 9. 90721 0.09279 08
93 38 58 52. 5 9. 79870 9.89062 9.90808 0.09192 07
94 39 02 15.0 9. 79922 9.89027 9. 90895 0. 09105 06
95 39 05 37. 5 9. 79975 9.88993 9.90982 0.09018 05
96 39 09 00.0 9.80027 9. 88958 9. 91069 0. 08931 04
97 39 12 22. 5 9.80080 9. 88923 9. 91156 0. 08844 03
98 39 15 45. 0 9.80132 9.88888 9. 91243 0.08757 02
99 39 19 07. 5 9. 80184 9. 88853 9. 91330 0. 08670 01
100 39 22 30.0 9.80236 9.88819 9. 91417 0.08583 00
L Sin L Cos L Tan L Cot 57-, 25-
Mils o t tt
L Cos L Sin L Cot L Tan 41-9-
37
Table II.—Common Logarithms of Functions of Angles in Mils—-‘Continued
7-, 39- o / n L Sin L Cos L Tan L Cot Mils
23-, 55- L Cos L Sin L Cot L Tan
00 39 22 30.0 9.80236 9.88819 9. 91417 0.08583 100
01 39 25 52. 5 9.80288 9.88784 9.91504 0.08496 99
02 39 29 15.0 9.80340 9.88748 9.91591 0.08409 98
03 39 32 37.5 9.80391 9.88713 9. 91678 0.08322 97
04 39 36 00.0 9.80443 9.88678 9. 91765 0.08235 96
05 39 39 22.5 9.80494 9.88643 9.91852 0.08148 95
06 39 42 45.0 9.80546 9.88607 9.91938 0.08062 94
07 39 46 07. 5 9.80597 9.88572 9.92025 0.07975 93
08 39 49 30.0 9.80648 9.88536 9.92112 0. 07888 92
09 39 52 52. 5 9.80699 9.88501 9. 92198 0.07802 91
10 39 56 15.0 9.80750 9.88465 9.92285 0.07715 90
11 39 59 37.5 9.80801 9.88429 9.92372 0.07628 89
12 40 03 00.0 9.80852 9.88394 9.92458 0.07542 88
13 40 06 22. 5 9.80903 9.88358 9.92545 0.07455 87
14 40 09 45.0 9.80953 9.88322 9. 92631 0.07369 86
15 40 13 07.5 9.81004 9.88286 9.92718 0.07282 85
16 40 16 30.0 9.81054 9.88250 9.92804 0.07196 84
17 40 19 52. 5 9.81104 9.88213 9.92891 0.07109 83
18 40 23 15.0 9.81154 9.88177 9.92977 0.07023 82
19 40 26 37. 5 9.81204 9.88141 9.93064 0.06936 81
20 40 30 00.0 9.81254 9.88105 9.93150 0.06850 80
21 40 33 22. 5 9.81304 9.88068 9.93236 0.06764 79
22 40 36 45.0 9.81354 9.88032 9.93323 0.06677 78
23 40 40 07.5 9.81404 9.87995 9.93409 0.06591 77
24 40 43 30.0 9.81453 9.87958 9.93495 0.06505 76
25 40 46 52.5 9.81503 9.87922 9.93581 0.06419 75
26 40 50 15.0 9.81552 9.87885 9.93667 0.06333 74
27 40 53 37. 5 9.81601 9.87848 9. 93754 0.06246 73
28 40 57 00.0 9. 81651 9.87811 9.93840 0.06160 72
29 41 00 22.5 9. 81700 9.87774 9.93926 0.06074 71
30 41 03 45.0 9. 81749 9.87737 9.94012 0.05988 70
31 41 07 07.5 9.81798 9.87700 9. 94098 0.05902 69
32 41 10 30.0 9.81846 9.87662 9.94184 0.05816 68
33 41 13 52. b 9.81895 9. 87625 9. 94270 0.05730 67
34 41 17 15.0 9.81944 9.87588 9.94356 0.05644 66
35 41 20 37.5 9.81992 9.87550 9.94442 0.05558 65
36 41 24 00.0 9.82041 9.87513 9.94528 0.05472 64
37 41 27 22. 5 9.82089 9.87475 9. 94614 0.05386 63
38 41 30 45.0 9.82137 9.87437 9.94700 0.05300 62
39 41 34 07.5 9.82185 9.87399 9. 94786 0.05214 61
40 41 37 30.0 9.82233 9.87362 9.94872 0.05128 60
41 41 40 52. 5 9.82281 9.87324 9. 94958 0.05042 59
42 41 44 15.0 9.82329 9.87286 9.95043 0.04957 58
43 41 47 37. 5 9. 82377 9.87248 9.95129 0.04871 57
44 41 51 00.0 9.82424 9.87209 9.95215 0.04785 56
45 41 54 22.5 9.82472 9.87171 9.95301 0.04699 55
46 41 57 45.0 9.82520 9.87133 9.95387 0.04613 54
47 42 01 07.5 9.82567 9.87095 9.95472 0.04528 53
48 42 04 30.0 9.82614 9.87056 9. 95558 0.04442 52
49 42 07 52.5 9.82661 9.87018 9. 95644 0.04356 51
50 42 11 15.0 9.82708 9.86979 9. 95729 0.04271 50
L Sin L Cos L Tan L Cot 56-, 24-
Mils O/ //
L Cos j L Sin L Cot L Tan 40-, 8-
38
Table II.—Common Logarithms of Functions of Angles in Mils—Continued
7-, 39- o , n L Sin L Cos L Tan L Cot Mils
23-,55- L Cos L Sin L Cot L Tan
50 42 11 15.0 9. 82708 9. 86979 9. 95729 0.04271 50
51 42 14 37. 5 9.82755 9. 86940 9. 95815 0.04185 49
52 42 18 00.0 9. 82802 9. 86902 9. 95901 0. 04099 48
53 42 21 22. 5 9. 82849 9.86863 9.95986 0. 04014 47
54 42 24 45.0 9. 82896 9. 86824 9. 96072 0.03928 46
55 42 28 07.5 9. 82942 9.86785 9. 96158 0.03842 45
56 42 31 30.0 9.82989 9. 86746 9.96243 0.03757 44
57 42 34 52. 5 9.83035 9. 86707 9. 96329 0. 03671 43
58 42 38 15.0 9.83082 9.86667 9.96414 0. 03586 42
59 42 41 37. 5 9.83128 9.86628 9. 96500 0.03500 41
60 42 45 00. 0 9.83174 9.86589 9. 96586 0.03414 40
61 42 48 22. 5 9.83220 9. 86549 9. 96671 0.03329 39
62 42 51 45. 0 9.83266 9. 86510 9. 96757 0.03243 38
63 42 55 07. 5 9.83312 9.86470 9. 96842 0. 03158 37
64 42 58 30.0 9.83358 9. 86430 9.96928 0.03072 36
65 43 01 52.5 9.83404 9.86391 9.97013 0.02987 35
66 43 05 15. 0 9. 83449 9. 86351 9. 97099 0.02901 34
67 43 08 37. 5 9. 83495 9. 86311 9. 97184 0. 02816 33
68 43 12 00. 0 9. 83540 9. 86271 9. 97269 0.02731 32
69 43 15 22. 5 9. 83586 9. 86231 9. 97355 0. 02645 31
70 43 18 45.0 9.83631 9.86191 9. 97440 0. 02560 30
71 43 22 07. 5 9. 83676 9. 86150 9.97526 0.02474 29
72 43 25 30. 0 9. 83721 9. 86110 9. 97611 0. 02389 28
73 43 28 52. 5 9. 83766 9.86070 9. 97697 0.02303 27
74 43 32 15. 0 9. 83811 9. 86029 9.97782 0.02218 26
75 43 35 37. 5 9.83856 9.85989 9.97867 0. 02133 25
76 43 39 00.0 9. 83901 9.85948 9. 97953 0.02047 24
77 43 42 22. 5 9. 83945 9.85907 9. 98038 0.01962 23
78 43 45 45. 0 9.83990 9.85867 9. 98123 0.01877 22
79 43 49 07. 5 9.84034 9.85826 9. 98209 0. 01791 21
80 43 52 30. 0 9.84079 9.85785 9. 98294 0. 01706 20
81 43 55 52. 5 9. 84123 9. 85744 9. 98379 0.01621 19
82 43 59 15. 0 9.84167 9.85703 9.98465 0.01535 18
83 44 02 37. 5 9. 84211 9.85661 9. 98550 0. 01450 17
84 44 06 00. 0 9. 84255 9. 85620 9. 98635 0.01365 16
85 44 09 22. 5 9.84299 9. 85579 9.98721 0.01279 15
86 44 12 45.0 9. 84343 9.85537 9.98806 0.01194 14
87 44 16 07. 5 9.84387 9. 85496 9. 98891 0.01109 13
88 44 19 30. 0 9.84431 9.85454 9.98977 0.01023 12
89 44 22 52. 5 9. 84474 9. 85412 9. 99062 0.00938 11
90 44 26 15.0 9.84518 9. 85371 9. 99147 0.00853 10
91 44 29 37. 5 9. 84561 9.85329 9.99232 0. 00768 09
92 44 33 00. 0 9.84605 9. 85287 9.99318 0. 00682 08
93 44 36 22. 5 9.84648 9.85245 9. 99403 0. 00597 07
94 44 39 45.0 9. 84691 9. 85203 9. 99488 0. 00512 06
95 44 43 07. 5 9.84734 9.85161 9.99574 0. 00426 05
96 44 46 30.0 9. 84777 9.85118 9.99659 0. 00341 04
97 44 49 52. 5 9.84820 9. 85076 9. 99744 0.00256 03
98 44 53 15.0 9.84863 9.85034 9. 99829 0. 00171 02
99 44 56 37. 5 9.84906 9. 84991 9. 99915 0. 00085 01
100 45 00 00.0 9.84949 9.84949 0.00000 0.00000 00
L Sin L Cos L Tan L Cot 56-, 24-
0 / ft
L Cos LSin L Cot L Tan 40-, 8-
39
Table IIICommon Logarithms of Functions of Angles in Degrees and Minutes
Logarithms of the functions are given for each minute from 0° to 360°.
The quantity —10 is to be appended to all logarithms of the sine and cosine, to logarithms of the tangent from 0° to 45° and to logarithms of the cotangent from 45° to 90°.
With degrees indicated on the first line at the top of the page, use the column headings on the first line at the top. With degrees indicated on the second line at the top of the page, use the column headings on the second line at the top.
With degrees indicated on the last line at the bottom of the page, use the column designations on the last line at the bottom. With degrees indicated on the next to the last line at the bottom of the page, use the column designations on the next to the last line at the bottom.
With degrees indicated at the top of the page (first or second lines), use the minute column at the left. With degrees indicated at the bottom of the page (last or next to the last line), use the minute column at the right.
The values of angles of the first quadrant and the corresponding column headings are set in bold-face type.
Examples:
1. To find the azimuth of the line A-B, given the following coordinates-Point A —24.560— 96.895
Point B—25.342-100.637
+ .782 +3.742
Tangent of the angle at A= 782;
3742
Log Tan of the angle at M=log 782 =12.89321-10 log 3742
-3.57310
9.32011-10
Enter the Tan column of table III with the log 9.32011 in order to find the number of degrees corresponding to this log:
Log Tan of 11°48' = 9.31996
Log Tan of 11°49' = 9.32059
Log Tan 9.32011 lies (using table of proportional parts) two-tenths of the way from 9.31996 to 9.32059; therefore the value of the angle is 11°48.2', and the azimuth of the line (first quadrant) is 11°48.2'.
2. Given the coordinates of point X as 855.792-1298.057, the azimuth of the line X-Y as 223°12', and the distance from X to Y as 1,054 yards.
Required: The coordinates of point Y.
DX = Sine of azimuth X distance
DY= Cosine of azimuthXdistance
DX DY
From table I, log 1054 3.02284 3.02284
From table III, log Sin 223°12' 9.83540-10 log Cos 9.86271-10
12.85824-10 12.88555 — 10
From table I, antilog (to nearest 722 768
yard)
Coordinates of point X 855.792—1298.057
DX, DY (third quadrant) —.722 —.768
Coordinates of point Y 855.070—1297.289
40
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes
:—
0°-, 180°- L Sin L Tan L Cot L Cos
rrop. pts.
90°-,270°- L Cos L Cot L Tan L Sin
0 — 0. 00 000 60
1 6.46 373 30103 6.46 373 30103 3.53 627 0.00 000 59 3476 3218 2997
2 3 4 6. 76 476 6.94 085 7. 06 579 17609 12494 9691 6. 76 476 6.94 085 7.06 579 17609 12494 9691 3.23 524 3.05 915 2.93 421 0.00 000 0. 00 000 0.00 000 58 57 56 1 2 3 348 695 1043 322 644 965 300 599 899
5 6 7.16 270 7.24 188 7918 6694 7.16 270 7. 24 188 7918 6694 5800 5115 4576 2.83 730 2.75 812 0. 00 000 0.00 000 55 54 4 5 1390 1738 1287 1609 1199 1498
7 7. 30 882 5800 7.30 882 2.69 118 0. 00 000 53
8 7.36 682 5115 7. 36 682 2.63 318 0. 00 000 52 2802 2633 2483
9 7.41 797 4576 7.41 797 2.58 203 0. 00 000 51 1 280 263 248
10 11 12 13 7.46 373 7. 50 512 7.54 291 7.57 767 4139 3779 3476 3218 7. 46 373 7. 50 512 7. 54 291 7.57 767 4139 3779 3476 3219 2996 2.53 627 2.49 488 2.45 709 2. 42 233 0. 00 000 0.00 000 0. 00 000 0.00 000 50 49 48 47 2 3 4 5 560 841 1121 1401 527 790 1053 1316 497 745 993 1242
14 7.60 985 2997 7.60 986 2.39 014 0.00 000 46 2227 2021 1848
J5 16 17 18 19 7.63 982 7. 66 784 7.69 417 7.71 900 7.74 248 2802 2633 2483 2348 2227 7.63 982 7. 66 785 7. 69 418 7. 71 900 7.74 248 2803 2633 2482 2348 2228 2.36 018 2.33 215 2. 30 582 2. 28 100 2. 25 752 0. 00 000 0. 00 000 9.99 999 9.99 999 9.99 999 45 44 43 42 41 1 2 3 4 5 223 445 668 891 1113 202 404 606 808 1010 185 370 554 739 924
20 7.76 475 2119 7. 76 476 2119 2020 1931 1848 1773 2. 23 524 9.99 999 40
21 7.78 594 2021 7.78 595 2. 21 405 9. 99 999 39 1704 1579 1472
22 23 24 7.80 615 7.82 545 7.84 393 1930 1848 1773 7.80 615 7.82 546 7.84 394 2.19 385 2.17 454 2.15 606 9.99 999 9.99 999 9.99 999 38 37 36 1 2 3 170 341 511 158 316 474 147 294 442
25 26 7.86 166 7.87 870 1704 1639 7.86 167 7.87 871 1704 2.13 833 2.12 129 9.99 999 9.99 999 35 34 4 5 682 852 632 789 589 736
27 7.89 509 1579 7.89 510 1579 1524 1473 2.10 490 9.99 999 33
28 7.91 088 1524 7.91 089 2.08 911 9.99 999 32 1379 1297 1223
29 7.92 612 1472 7.92 613 2.07 387 9.99 998 31 1 138 130 122
30 31 32 33 7.94 084 7.95 508 7.96 887 7.98 223 1424 1379 1336 1297 7.94 086 7.95 510 7.96 889 7.98 225 1424 1379 1336 1297 1259 2.05 914 2. 04 490 2.03 111 2.01 775 9.99 998 9.99 998 9.99 998 9.99 998 30 29 28 27 2 3 4 5 276 414 552 690 259 389 519 649 245 367 489 612
34 7.99 520 1259 7.99 522 2. 00 478 9.99 998 26
1158 1100 1046
35 36 37 38 39 8.00 779 8. 02 002 8. 03 192 8. 04 350 8.05 478 1223 1190 1158 1128 1100 8.00 781 8.02 004 8. 03 194 8.04 353 8. 05 481 1223 1190 1159 1128 1100 1.99 219 1.97 996 1.96 806 1.95 647 1.94 519 9.99 998 9.99 998 9.99 997 9.99 997 9.99 997 25 24 23 22 21 1 2 3 4 5 116 232 347 463 579 110 220 330 440 550 105 209 314 418 523
40 8.06 578 1072 8.06 581 1072 1047 1022 998 976 1. 93 419 9.99 997 20
41 8. 07 650 8.07 653 1.92 347 9.99 997 19 999 954 914
42 43 44 8. 08 696 8. 09 718 8.10 717 1022 999 976 8. 08 700 8.09 722 8.10 720 1.91 300 1.90 278 1.89 280 9.99 997 9.99 997 9.99 996 18 17 16 1 2 3 100 200 300 95 191 286 91 183 274
45 46 8.11 693 8.12 647 954 8.11 696 8.12 651 955 1.88 304 1.87 349 9.99 996 9.99 996 15 14 4 5 400 500 382 477 366 457
47 8.13 581 914 8.13 585 915 895 878 1.86 415 9.99 996 13
48 8.14 495 8.14 500 1.85 500 9.99 996 12 877 843 812
49 8.15 391 877 8.15 395 1.84 605 9.99 996 11 1 88 84 81
50 51 52 53 8.16 268 8.17 128 8.17 971 8.18 798 860 843 827 812 797 8.16 273 8.17 133 8.17 976 8.18 804 860 843 828 812 797 1.83 727 1.82 867 1. 82 024 1.81 196 9.99 995 9.99 995 9.99 995 9.99 995 10 9 8 7 2 3 4 5 175 263 351 438 169 253 337 422 162 244 325 406
54 8.19 610 8.19 616 1.80 384 9.99 995 6
782 755 730
55 56 57 58 59 8. 20 407 8.21 189 8.21 958 8. 22 713 8. 23 456 782 769 755 743 730 8.20 413 8. 21 195 8. 21 964 8.22 720 8.23 462 782 769 756 742 730 1.79 587 1.78 805 1.78 036 1. 77 280 1. 76 538 9.99 994 9.99 994 9.99 994 9.99 994 9.99 994 5 4 3 2 1 1 2 3 4 5 78 156 235 313 391 75 151 226 302 377 73 146 219 292 365
60 8.24 186 8.24 192 1.75 808 9.99 993 0
L Sin L Tan L Cot L Cos 359° 179°-
d cd
L Cos L Cot L Tan L Sin 269° 89°-
3
41
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
1°-,181°- / L Sin L Tan L Cot L Cos
91°-, L Cos cd Prop. pts.
271°- L Cot L Tan L Sin
0 8. 24 186 717 8. 24 192 718 706 696 1.75 808 9. 99 993 60 717 695
1 8.24 903 706 8. 24 910 1. 75 090 9. 99 993 59 673
2 8. 25 609 695 8. 25 616 1. 74 384 9.99 993 58 1 71.7 69.5 67.3
3 8. 2b 304 684 8. 26 312 684 1. 73 688 9.99 993 57 2 143.4 139.0 134.6
4 8.26 988 673 8. 26 996 673 1.73 004 9.99 992 56 3 215.1 286.8 358.5 208.5 201.9
5 6 8.27 661 8. 28 324 663 653 8. 27 669 8. 28 332 663 1.72 331 1.71 668 9.99 992 9.99 992 55 54 4 5 278.0 347.5 269.2 336.5
7 8 8. 28 977 8.29 621 644 634 8. 28 986 8.29 629 643 1.71 014 1.70 371 9. 99 992 9.99 992 53 52 653 634 616
9 8.30 255 624 8.30 263 625 1.69 737 9.99 991 51 1 65.3 63.4 61.6
10 8. 30 879 8.31 495 616 8. 30 888 617 1.69 112 9.99 991 50 2 3 130.6 195.9 126.8 190.2 123.2 184.8
608 8.31 505 607 1.68 495 9.99 991 49 4 261.2 253.6 246.4
13 8.32 103 8.32 702 599 590 8.32 112 8.32 711 599 1.67 888 1.67 289 9.99 990 9.99 990 48 47 5 326.5 317.0 308.0
14 8.33 292 583 8. 33 302 584 1.66 698 9.99 990 46 599 583 56R
15 8.33 875 8.34 450 8.35 018 575 8.33 886 575 1.66 114 9. 99 990 45 1 59.9 58.3 56.8
568 8.34 461 568 1.65 539 9.99 989 44 2 119.8 116.6 113.6
560 8. 35 029 561 1.64 971 9. 99 989 43 3 179.7 174.9 170.4
8.35 578 8.36 131 553 8. 35 590 553 1.64 410 9. 99 989 42 4 239.6 233.2 227.2
547 8. 36 143 546 1.63 857 9.99 989 41 5 299.5 291.5 284.0
20 21 8.36 678 8.37 217 539 533 8.36 689 8. 37 229 540 533 527 1.63 311 1.62 771 9.99 988 9. 99 988 40 39 553 539 526
22 8.37 750 526 8. 37 762 1.62 238 9. 99 988 38 1 55.3 53.9 52.6
8. 38 276 8.38 796 520 8.38 289 520 1.61 711 9.99 987 37 2 110.6 107.8 105.2
514 8.38 809 514 1.61 191 9.99 987 36 3 165.9 221.2 276.5 161.7 157.8
25 26 8.39 310 8.39 818 508 502 8.39 323 8.39 832 509 502 1.60.677 1.60 168 9.99 987 9.99 986 35 34 4 5 215. G 269.5 210.4 263.0
27 28 8.40 320 8.40 816 496 491 8.40 334 8.40 830 496 4Q1 1. 59 666 1. 59 170 9.99 986 9. 99 986 33 32 514 502 490
29 8.41 307 485 8.41 321 486 1.58 679 9.99 985 31 1 51.4 102.8 154.2 50.2 49
30 8.41 792 480 8.41 807 480 1.58 193 9.99 985 30 3 100.4 150.6 98 147
8.42 272 474 8.42 287 475 1.57 713 9.99 985 29 4 205.6 200.8 196
33 8.42 746 8.43 216 470 464 8.42 762 8.43 232 470 1.57 238 1. 56 768 9.99 984 9.99 984 28 27 5 257.0 251.0 245
34 8.43 680 459 8.43 696 460 1.56 304 9.99 984 26 480 470 47 460 46
35 8.44 139 455 8.44 156 455 1.55 844 9.99 983 25 1 48
36 8.44 594 450 8.44 611 450 1. 55 389 9. 99 983 24 2 96 94 92
37 8.45 044 445 8.45 061 446 1. 54 939 9. 99 983 23 3 144 141 138
38 8.45 489 441 8.45 507 441 1. 54 493 9. 99 982 22 4 192 188 184
39 8.45 930 436 8.45 948 437 1.54 052 9.99 982 21 5 240 | 235 230
40 8.46 366 433 8.46 385 432 1. 53 615 9. 99 982 20 450
41 8.46 799 427 8.46 817 1. 53 183 9. 99 981 19 440 430
42 8.47 226 424 8.47 245 424 1. 52 755 9. 99 981 18 1 45 44 43
43 8.47 650 419 8.47 669 420 1. 52 331 9. 99 981 17 2 90 88 86
44 8.48 069 416 8.48 089 416 1.51 911 9.99 980 16 3 135 132 129
45 46 8.48 485 8.48 896 411 408 8.48 505 8.48 917 412 408 404 401 397 1.51 495 1. 51 083 9.99 980 9. 99 979 15 14 4 5 180 225 176 220 172 215
47 48 8.49 304 8.49 708 404 400 8.49 325 8.49 729 1. 50 675 1. 50 271 9.99 979 9.99 979 13 12 420 410 400
49 8. 50 108 396 8. 50 130 1.49 870 9. 99 978 11 1 42 41 40
50 8. 50 504 393 8. 50 527 393 1.49 473 9.99 978 10 2 3 84 126 82 123 80 120
51 8. 50 897 390 8. 50 920 390 1.49 080 9. 99 977 9 4 168 164 160
52 53 8.51 287 8. 51 673 386 382 8.51 310 8. 51 696 386 383 1.48 690 1.48 304 9. 99 977 9.99 977 8 7 5 210 205 200
54 8.52 055 379 8.52 079 380 1.47 921 9.99 976 6 390 380 370 37
55 8.52 434 376 8.52 459 376 373 1.47 541 9. 99 976 5 1 39 38
56 8. 52 810 373 8.52 835 1.47 165 9. 99 975 4 2 78 76 74
57 8.53 183 369 8.53 208 370 1.46 792 9. 99 975 3 3 117 114 111
58 8. 53 552 367 8. 53 578 367 1.46 422 9. 99 974 2 4 156 152 148
59 8. 53 919 363 8. 53 945 363 1.46 055 9.99 974 1 5 195 190 185
60 8.54 282 8.54 308 1.45 692 9.99 974 0
L Sin L Tan L Cot L Cos 358°- , 178°-
d
L Cos | L Cot L Tan L Sin 268°- -, 88°-
42
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
2°-,182°- / L Sin d L Tan cd L Cot L Cos Prop. pts.
92°-, 272°- L Cos L Cot L Tan L Sin
0 8. 54 282 360 357 355 351 8. 54 308 361 1.45 692 9.99 974 60 360 350
1 8. 54 642 8. 54 669 1.45 331 9.99 973 59 340
2 8. 54 999 9. 55 027 355 352 349 1.44 973 9. 99 973 58 1 36 35 34
3 8. 55 354 8.55 382 1.44 618 9.99 972 57 2 72 70 68
4 8. 55 705 349 8. 55 734 1. 44 266 9.99 972 56 3 4 108 144 105 140 102 136
8.56 054
5 346 343 341 337 336 8. 56 083 346 344 341 338 336 1.43 917 9.99 971 55 5 180 175 170
6 8. 56 400 8. 56 429 1.43 571 9. 99 971 54 6 216 210 204
7 8.56 743 8. 56 773 1.43 227 9.99 970 53 7 252 245 238
8 8. 57 084 8. 57 114 1.42 886 9.99 970 52 8 288 280 272
9 8. 57 421 8.57 452 1.42 548 9.99 969 51 9 324 315 306
10 8. 57 757 8. 57 788 333 330 1.42 212 9. 99 969 50 330 310
11 8. 58 089 330 328 8. 58 121 1.41 879 9.99 968 49 320
12 8. 58 419 8. 58 451 1.41 549 9.99 968 48 1 33 32 31
13 8. 58 747 8. 58 779 1.41 221 9.99 967 47 2 66 64 62
14 8. 59 072 323 8.59 105 323 1.40 895 9.99 967 46 3 99 132 96 128 93 124
8.59 395
15 320 318 316 313 311 8.59 428 321 319 316 314 311 1.40 572 9.99 967 45 5 165 160 155
16 8. 59 715 8. 59 749 1.40 251 9.99 966 44 6 198 192 186
17 8.60 033 8.60 068 1.39 932 9.99 966 43 7 231 224 217
18 8. 60 349 8.60 384 1.39 616 9.99 965 42 8 264 256 248
19 8. 60 662 8.60 698 1.39 302 9.99 964 41 9 297 288 279
20 8. 60 973 309 307 305 302 301 8.61 009 310 307 305 303 301 1.38 991 9.99 964 40 300
21 8.61 282 8.61 319 1. 38 681 9.99 963 39 290 285
22 8.61 589 8.61 626 1. 38 374 9.99 963 38 1 30 29 28.5
23 8.61 894 8.61 931 1.38 069 9.99 962 37 2 60 58 57.0
24 8.62 196 8.62 234 1.37 766 9.99 962 36 3 4 90 120 87 116 85.5 114.0
2b 8.62 497 298 8.62 535 1. 37 465 9.99 961 35 5 150 145 142.5
26 8. 62 795 2^6 8. 62 834 1.37 166 9. 99 961 34 6 180 174 171.0
27 8.63 091 204 8.63 131 1. 36 869 9.99 960 33 7 210 203 199.5
28 8.63 385 293 8.63 426 1.36 574 9.99 960 32 8 240 232 228.0
29 8.63 678 290 8.63 718 291 1.36 282 9. 99 959 31 9 270 261 256.5
30 8.63 968 8.64 009 1.35 991 9. 99 959 30 275 270
31 8. 64 256 8.64 298 1.35 702 9. 99 958 29 280
32 8.64 543 284 8.64 585 2^5 1.35 415 9.99 958 28 1 28.0 27.5 27.0
33 8. 64 827 283 8.64 870 1.35 130 9. 99 957 27 2 56.0 55.0 54.0
34 8.65 110 281 8.65 154 281 1.34 846 9.99 956 26 3 84.0 82.5 81.0
112.0 110.0 108.0
35 8.65 391 279 8.65 435 280 278 276 274 273 1. 34 565 9.99 956 25 5 140.0 137.5 135.0
36 8. 65 670 277 276 8.65 715 1. 34 285 9.99 955 24 6 168.0 165.0 162.0
37 8.65 947 8.65 993 1. 34 007 9.99 955 23 7 196.0 192.5 189.0
38 8. 66 223 274 272 8.66 269 1. 33 731 9. 99 954 22 8 224.0 220.0 216.0
39 8. 66 497 8.66 543 1.33 457 9.99 954 21 9 252.0 247.5 243.0
40 8.66 769 270 8.66 816 271 1.33 184 9. 99 953 20 260
41 8.67 039 8. 67 087 1.32 913 9.99 952 19 265 255
42 8.67 308 8.67 356 1.32 644 9. 99 952 18 1 26.5 26.0 25.5
43 8.67 575 8. 67 624 266 264 1. 32 376 9. 99 951 17 2 53.0 52.0 51.0
44 8. 67 841 263 8.67 890 1.32 110 9.99 951 16 3 79.5 78.0 76.5
4 106.0 104.0 102.0
4b 8.68 104 8.68 154 1.31 846 9. 99 950 15 5 132.5 130.0 127.5
46 8.68 367 260 8.68 417 261 260 1.31 583 9.99 949 14 6 159.0 156.0 153.0
47 8.68 627 8. 68 678 1. 31 322 9. 99 949 13 7 185. 5 182.0 178.5
48 8.68 886 8.68 938 1. 31 062 9. 99 948 12 8 212.0 208.0 204.0
49 8.69 144 256 8.69 196 257 1. 30 804 9.99 948 11 9 23». 5 234.0 229.5
50 51 8.69 400 8. 69 654 254 8.69 453 8.69 708 255 254 1.30 547 1. 30 292 9. 99 947 9.99 946 10 9 250 245 240
52 8. 69 907 252 250 249 8.69 962 1.30 038 9. 99 946 8 1 25.0 24.5 24.0
53 8. 70 159 8. 70 214 251 249 1. 29 786 9.99 945 7 2 50.0 49.0 48.0
54 8. 70 409 8. 70 465 1. 29 535 9.99 944 6 3 75.0 73.5 72.0
4 100.0 198.0 96.0
55 8. 70 658 247 246 8. 70 714 248 246 245 244 243 1.29 286 9.99 944 5 5 125.0 122.5 120.0
56 8. 70 905 8. 70 962 1.29 038 9.99 943 4 6 150.0 147.0 144.0
57 8.71 151 244 243 8.71 208 1. 28 792 9. 99 942 3 7 175.0 171.5 168.0
58 8. 71 395 8 71. 453 1.28 547 9. 99 942 2 8 200.0 196.0 192.0
59 8.71 638 242 8.71 967 1. 28 303 9. 99 941 1 9 225.0 220.5 216.0
60 8. 71 880 8. 71 940 1.28 060 9.99 940 0
L Sin L Tan L Cot L Cos 357° 177°-
cd
L Cos L Cot L Tan L Sin d 267° 87°-
43
Table III—Common Logarithms of Functions of Angles in Degrees and Minutes— T.
Continued
3°-,183° _ / L Sin - d L Tan ed L Cot L Cos Prop. pts.
93°-, 273°- L Cos L Cot L Tan L Sin
0 1 2 3 4 8.71 880 8. 72 120 8. 72 359 8.72 597 8. 72 834 240 239 238 237 235 8.71 940 8. 72 181 8. 72 420 8. 72 659 8. 72 896 241 239 239 237 236 1. 28 060 1. 27 819 1.27 580 1. 27 341 1.27 104 9.99 940 9.99 940 9.99 939 9.99 938 9.99 938 60 59 58 57 56 1 2 3 238 23.8 47.6 71.4 234 23.4 46.8 70.2 229 22.9 45.8 68.7
5 6 7 8 9 8. 73 069 8.73 303 8.73 535 8. 73 767 8. 73 997 234 232 232 230 229 8.73 132 8. 73 366 8. 73 600 8. 73 832 8.74 063 234 234 232 231 229 1. 26 868 1.26 634 1.26 400 1. 26 168 1.25 937 9.99 937 9.99 936 9. 99 936 9.99 935 9.99 934 55 54 53 52 51 4 5 6 7 8 9 95. 2 119.0 142.8 166.6 190.4 214.2 93.6 117.0 140.4 163.8 187.2 210.6 91.6 114.5 137.4 160.3 183.2 206.1
10 11 12 13 14 8. 74 226 8.74 454 8. 74 680 8.74 906 8. 75 130 228 226 226 224 223 8. 74 292 8. 74 521 8. 74 748 8. 74 974 8. 75 199 229 227 226 225 224 1.25 708 1.25 479 1.25 252 1.25 026 1.24 801 9.99 934 9.99 933 9. 99 932 9. 99 932 9.99 931 50 49 48 47 46 1 2 3 225 22.5 45.0 67.5 220 22.0 44.0 66.0 216 21.6 43.2 64.8
15 16 17 18 19 8. 75 353 8. 75 575 8.75 795 8. 76 015 8. 76 234 222 220 220 219 217 8. 75 423 8.75 645 8. 75 867 8. 76 087 8. 76 306 222 222 220 219 219 1. 24 577 1.24 355 1. 24 133 1.23 913 1.23 694 9. 99 930 9.99 929 9.99 929 9.99 928 9.99 927 45 44 43 42 41 4 5 6 7 8 9 90.0 112.5 135.0 157.5 180.0 202.5 88.0 110.0 132.0 154.0 176.0 198.0 86.4 108.0 129.6 151.2 172.8 194.4
20 21 22 23 24 8. 76 451 8. 76 667 8. 76 883 8. 77 097 8.77 310 216 216 214 213 212 8. 76 525 8. 76 742 8. 76 958 8. 77 173 8. 77 387 217 216 215 214 213 1. 23 475 1. 23 258 1.23 042 1.22 827 1. 22 613 9.99 926 9.99 926 9. 99 925 9.99 924 9.99 923 40 39 38 37 36 1 2 3 212 21.2 42.4 63.6 208 20.8 41.6 62.4 204 20.4 40.8 61.2
25 26 27 28 29 8.77 522 8. 77 733 8. 77 943 8. 78 152 8. 78 360 211 210 209 208 208 8. 77 600 8.77 811 8. 78 022 8. 78 232 8.78 441 211 211 210 209 208 1.22 400 1. 22 189 1.21 978 1.21 768 1.21 559 9. 99 923 9.99 922 9. 99 921 9. 99 920 9.99 920 35 34 33 32 31 4 5 6 7 8 9 84.8 106.0 127.2 148.4 169.6 190.8 83.2 104.0 124.8 145.6 166.4 187.2 81.6 102.0 122.4 142.8 163.2 183.6
30 31 32 33 34 8.78 568 8. 78 774 8. 78 979 8.79 183 8. 79 386 206 205 204 203 202 8. 78 649 8. 78 855 8. 79 061 8. 79 266 8.79 470 206 206 205 204 203 1.21 351 1.21 145 1. 20 939 1. 20 734 1.20 530 9.-99 919 9.99 918 9. 99 917 9.99 917 9.99 916 30. 29 28 27 26 1 2 3 201 20.1 40.2 60.3 197 19.7 39.4 59.1 193 19.3 38.6 57.9
35 36 37 38 39 8.79 588 8.79 789 8.79 990 8.80 189“ 8.80 388 201 201 199 199 197 8. 79 673 8. 79 875 8.80 076 8.80 277 8.80 476 202 201 201 199 198 1. 20 327 1. 20 125 1.19 924 1.19 723 1.19 524 9.99 915 9. 99 914 9. 99 913 9.99 913 9.99 912 25 24 23 22 21 4 5 6 7 8 9 80. 4 100.5 120.6 140.7 160.8 180.9 78.8 98.5 118.2 137.9 157.6 177.3 77.2 96.5 115.8 135.1 154.4 173.7
40 41 42 43 44 8.80 585 8. 80 782 8.80 978 8.81 173 8.81 367 197 196 195 194 193 8. 80 674 8.80 872 8.81 068 8.81 264 8.81 459 198 196 196 195 194 1.19 326 1.19 128 1.18 932 1.18 736 1.18 541 9.99 911 9. 99 910 9.99 909 9. 99 909 9.99 908 20 19 18 17 16 1 2 3 189 18.9 37.8 56.7 75.6 94.5 113.4 132.3 151.2 170.1 185 18.5 37.0 55.5 181 18.1 36.2 54.3
45 46 47 48 49 8.81 560 8.81 752 8.81 944 8.82 134 8. 82 324 192 192 190 190 189 8.81 653 8.81 846 8.82 038 8.82 230 8.82 420 193 192 192 190 190 1.18 347 1.18 154 1.17 962 1.17 770 1.17 580 9.99 907 9.99 906 9.99 905 9. 99 904 9.99 904 15 14 13 12 11 4 5 6 7 8 9 74.0 92.5 111.0 129.5 148.0 166.5 72.4 90.5 108.6 126.7 144.8 162.9
50 51 52 53 54 8. 82 513 8. 82 701 8.82 888 8. 83 075 8.83 261 188 187 187 186 185 8.82 610 8.82 799 8.82 987 8.83 175 8.83 361 189 188 188 186 186 1.17 390 1.17 201 1.17 013 1.16 825 1.16 639 9.99 903 9.99 902 9. 99 901 9. 99 900 9.99 899 10 9 8 7 6 1 2 3 4 0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2 3.6 3 0.3 0.6 0.9 2 0.2 0.4 0.6 1 0.1 0.2 0.3
55 56 57 58 59 8. 83 446 8. 83 630 8. 83 813 8. 83 996 8.84 177 184 183 183 181 181 8.83 547 8. 83 732 8.83 916 8.84 100 8.84 282 185 184 184 182 182 1.16 453 1.16 268 1.16 084 1.15 900 1.15 718 9.99 898 9.99 898 9. 99 897 9. 99 896 9. 99 895 5 4 3 2 1 4 5 6 7 8 9 1. 2 1.5 1.8 2.1 2.4 2.7 0.8 1.0 1.2 1.4 1.6 1.8 0.4 0.5 0.6 0.7 0.8 0.9
60 8.84 358 8.84 464 1.15 536 9.99 894 0
L Sin d L Tan L Cot L Cos 356°- , 176°-
L Cos L Cot L Tan L Sin 266°- 86°-
44
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
4°-,184°- / L Sin d L Tan cd L Cot L Cos Prop. pts.
94°-, 274°- L Cos L Cot L Tan L Sin
0 8.84 358 8. 84 464 1.15 536 9. 99 894 60
1 8.84 539 lol 170 8. 84 646 loJ ISA 1.15 354 9.99 893 59 181 179 177
2 8. 84 718 179 8.84 826 180 1.15 174 9.99 892 58 1 18.1 17.9 17.7
3 8.84 897 17R 8.85 006 17Q 1.14 994 9.99 891 57 2 36.2 35.8 35.4
4 8.85 075 177 8.85 185 178 1.14 815 9.99 891 56 3 54.3 53.7 53.1
b 8.85 252 177 8.85 363 177 1.14 637 9.99 890 55 5 90.5 89.5 88.5
6 8.85 429 176 8. 85 540 177 1.14 460 9.99 889 54 6 108.6 107.4 106.2
7 8.85 605 17.5 8.85 717 176 1.14 283 9. 99 888 53 7 126.7 125.3 123.9
8 8.85 780 175 8.85 893 176 1.14 107 9. 99 887 52 8 144.8 143.2 141.6
9 8.85 955 173 8.86 069 174 1.13 931 9.99 886 51 9 162.9 161.1 159.3
10 8.86 128 8.86 243 1.13 757 9.99 885 50
11 8.86 301 173 8.86 417 174 174 1.13 583 9.99 884 49 175 173 171
12 8.86 474 171 8.86 591 179 1.13 409 9.99 883 48 1 17.5 17.3 17.1
13 8.86 645 171 8.86 763 172 1.13 237 9.99 882 47 2 35.0 34.6 34.2
14 8.86 816 171 8.86 935 171 1.13 065 9.99 881 46 3 52.5 51.9 51.3
15 8.86 987 169 8. 87 106 171 1.12 894 9.99 880 45 5 87.5 86.5 85.5
16 8.87 156 169 8.87 277 170 1.12 723 9.99 879 44 6 105.0 103.8 102.6
17 8.87 325 16Q 8.87 447 1 fig 1.12 553 9. 99 879 43 7 122.5 121.1 119.7
18 8.87 494 167 8.87 616 169 1.12 384 9.99 878 42 8 140.0 138.4 136.8
19 8.87 661 168 8.87 785 168 1.12 215 9.99 877 41 9 157.5 155.7 153.9
20 8. 87 829 8.87 953 1.12 047 9. 99 876 40
21 8.87 995 166 8. 88 120 10/ 167 1.11 880 9.99 875 39 168 166 164
22 8. 88 161 165 8.88 287 166 1.11 713 9.99 874 38 1 16.8 16.6 16.4
23 8. 88 326 164 8. 88 453 165 1.11 547 9.99 873 37 2 33.6 33.2 32.8
24 8.88 490 164 8.88 618 165 1.11 382 9.99 872 36 3 50.4 49.8 49.2
25 8.88 654 162 8.88 783 165 1.11 217 9.99 871 35 5 84.0 83.0 82.0
26 8. 88 817 162 8.88 948 1^3 1.11 052 9.99 870 34 6 100.8 99.6 98.4
27 8. 88 980 162 8.89 111 1^3 1.10 889 9. 99 869 33 7 117.6 116.2 114.8
28 8.89 142 162 8.89 274 163 1.10 726 9.99 868 32 8 34.4 132.8 131.2
29 8.89 304 160 8.89 437 161 1.10 563 9.99 867 31 9 151.2 149.4 147.6
30 8.89 464 161 8.89 598 1.10 402 9.99 866 30 162 159 157
31 8.89 625 15Q 8.89 760 i^o 1.10 240 9.99 865 29
32 8.89 784 159 8.89 920 160 1.10 080 9.99 864 28 1 16.2 15.9 15.7
33 8. 89 943 159 8. 90 080 160 1.09 920 9. 99 863 27 2 32.4 31.8 31.4
34 8. 90 102 158 8.90 240 159 1.09 760 9. 99 862 26 3 48.6 47.7 47.1
35 8. 90 260 157 8.90 399 158 1.09 601 9.99 861 25 5 81.0 79.5 78.5
36 8.90 417 157 8. 90 557 158 1.09 443 9.99 860 24 6 97.2 95.4 94.2
37 8. 90 574 156 8.90 715 157 1.09 285 9. 99 859 23 7 113.4 111.3 109.9
38 8. 90 730 155 8.90 872 157 1.09 128 9.99 858 22 8 129.6 127.2 125.6
39 8. 90 885 155 8.91 029 156 1.08 971 9.99 857 21 9 145.8 143.1 141.3
40 8.91 040 155 8.91 185 1.08 815 9.99 856 20
41 8.91 195 154 8.91 340 155 1.08 660 9.99 855 19 155 153 151
42 8. 91 349 152 8. 91 495 155 1.08 505 9. 99 854 18 1 15.5 15.3 15.1
43 8.91 502 152 8. 91 650 153 1.08 350 9. 99 853 17 2 31.0 30.6 30.2
44 8. 91 655 152 8. 91 803 154 1.08 197 9.99 852 16 3 46.5 45.9 45.3
45 8. 91 807 152 8.91 957 153 1.08 043 9. 99 851 15 5 77.5 76.5 75.5
46 8. 91 959 151 8.92 110 152 1.07 890 9. 99 850 14 6 93.0 91.8 90.6
47 8. 92 110 151 8.92 262 152 1.07 738 9. 99 848 13 7 108.5 107.1 105.7
48 8. 92 261 1.50 8.92 414 151 1.07 586 9.99 847 12 8 124.0 122.4 120.8
49 8. 92 411 150 8.92 565 151 1.07 435 9.99 846 11 9 139.5 137.7 135.9
50 8.92 561 149 8.92 716 1.07 284 9.99 845 10
51 8.92 710 149 8. 92 866 1^0 1.07.134 9. 99 844 9 149 147 1
52 8.92 859 148 8.93 016 149 1.06 984 9.99 843 8 1 14.9 14.7 0.1
53 8. 93 077 147 8. 93 165 148 1.06. 835 9.99 842 7 2 29.8 29.4 0.2
54 8.93 154 147 8. 93 313 149 1.06 687 9.99 841 6 3 44.7 44.1 0.3
55 8. 93 301 147 8. 93 462 147 1.06 538 9. 99 840 5 5 74.5 73.5 0.5
56 8. 93 448 146 8. 93 609 147 1.06 391 9. 99 839 4 6 89.4 88.2 0.6
57 8. 93 594 146 8.93 756 147 1.06 244 9. 99 838 3 7 104.3 102.9 0.7
58 8.93 740 145 8. 93 903 146 1.06 097 9. 99 837 2 8 119.2 117.6 0.8
59 8. 93 885 145 8.94 049 146 1.05 951 9. 99 836 1 9 134.1 132.3 0.9
60 8.94 030 8.94 195 1.05 805 9.99 834 0
L Sin L Tan L Cot L Cos 355°-, 175°-
J •
L Cos L Cot L Tan L Sin 265°-, 85°-
609023°—44
45
Table III. Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
5°-185°- / L Sin d L Tan cd L Cot L Cos Prop. pts.
95°-, 275°- L Cos L Cot L Tan L Sin
0 8. 94 030 144 143 144 8. 94 195 145 145 145 143 144 1. 05 805 9. 99 834 60 145
1 8. 94 174 8. 94 340 1.05 660 9. 99 833 59 143 141
2 8.94 317 8.94 485 1.05 515 9. 99 832 58 •1 14.5 14.3 14.1
3 8.94 461 142 8.94 630 1.05 370 9. 99 831 57 2 29.0 28.6 28. 2
4 8.94 603 143 8. 94 773 1.05 227 9.99 830 56 3 43.5 58.0 72.5 42.9 42.3
5 8. 94 746 141 8.94 917 143 1.05 083 9. 99 829 55 4 5 57. 2 71.5 56.4 70.5
6 8. 94 887 142 8. 95 060 142 1. 04 940 9.99 828 54 6 87.0 85.8 84.6
7 8. 95 029 141 8. 95 202 142 1. 04 798 9. 99 827 53 7 101.5 100.1 98.7
8 8. 95 170 140 8. 95 344 142 1. 04 656 9. 99 825 52 8 116.0 114.4 112.8
9 •8. 95 310 140 8.95 486 141 1. 04 514 9. 99 824 51 9 130.5 128.7 126.9
10 11 8. 95 450 8. 95 589 139 139 8.95 627 8. 95 767 140 141 130 1. 04 373 1.04 233 9.99 823 9. 99 822 50 49 139 138 136
12 8. 95 728 139 8. 95 908 1.04 092 9. 99 821 48 1 13.9 13.8 13.6
13 8. 95 867 138 8.96 047 140 1. 03 953 9.99 820 47 2 27.8 27.6 27.2
14 8.96 005 138 8.96 187 138 1. 03 813 9.99 819 46 3 41.7 41.4 40.8
15 8.96 143 137 8. 96 325 139 1.03 675 9.99 817 45 4 5 55.6 69.5 55. 2 69.0 54. 4 68.0
16 8. 96 280 137 8.96 464 133 1.03 536 9. 99 816 44 6 83.4 82.8 81.6
17 8.96 417 136 8. 96 602 137 1.03 398 9.99 815 43 7 97.3 96.6 95.2
18 8. 96 553 136 8. 96 739 133 1. 03 261 9. 99 814 42 8 111.2 110.4 108.8
19 8.96 689 136 8.96 877 136 1.03 123 9. 99 813 41 9 125.1 124.2 122.4
20 8. 96 825 135 8. 97 013 137 135 136 1.02 987 9. 99 812 40 135 133
21 8. 96 960 8.97 150 1.02 850 9. 99 810 39 131
22 8.97 095 134 8.97 285 1. 02 715 9. 99 809 38 1 13.5 13.3 13.1
23 8.97 229 134 8. 97 421 135 1. 02 579 9.99 808 37 2 27.0 26.6 26. 2
24 8.97 363 133 8. 97 556 135 1.02 444 9. 99 807 36 3 40.5 39.9 39.3
25 8. 97 496 133 8. 97 691 134 1.02 309 9. 99 806 35 4 5 54.0 67.5 53.2 66.5 52.4 65. 5
26 8.97 629 133 8.97 825 134 1. 02 175 9. 99 804 34 6 81.0 79.8 78.6
27 8.97 762 132 8. 97 959 133 1.02 041 9. 99 803 33 7 94.5 93.1 91.7
28 8. 97 894 132 8. 98 092 133 1. 01 908 9. 99 802 32 8 108.0 106.4 104.8
29 8.98 026 131 8. 98 225 133 1.01 775 9. 99 801 31 9 121.5 119.7 117.9
30 31 8. 98 157 8. 98 288 131 131 8. 98 358 8. 98 490 132 132 131 1.01 642 1.01 510 9. 99 800 9. 99 798 30 29 129 128 126
32 8. 98 419 130 8. 98 622 1. 01 378 9. 99 797 28 1 12.9 12.8 12.6
33 8. 98 549 130 8. 98 753 131 1. 01 247 9. 99 796 27 2 25.8 25.6 25.2
34 8. 98 679 129 8. 98 884 131 1.01 116 9. 99 795 26 3 38.7 51.6 64.5 38.4 37.8
35 8.98 808 129 8. 99 015 130 1. 00 985 9. 99 793 25 4 5 51, 2 64.0 50.4 63.0
36 8. 98 937 129 8.99 145 130 1. 00 855 9. 99 792 24 6 77.4 76.8 75.6
37 8. 99 066 128 8. 99 275 130 1. 00 725 9. 99 791 23 7 90.3 89.6 88.2
38 8.99 194 128 8. 99 405 129 1. 00 595 9. 99 790 22 8 103.2 102.4 100.8
39 8. 99 322 128 8. 99 534 128 1. 00 466 9. 99 788 21- 9 116.1 115.2 113.4
40 41 8.99 450 8. 99 577 127 127 8.99 662 8.99 791 129 1. 00 338 1. 00 209 9. 99 787 9. 99 786 20 19 125 123 122
42 8.99 704 126 8. 99 919 127 1. 00 081 9.99 785 18 1 12.5 12.3 12.2
43 8. 99 830 126 9. 00 046 123 0. 99 954 9. 99 783 17 2 25.0 24.6 24.4
44 8. 99 956 126 9. 00 174 127 0. 99 826 9. 99 782 16 3 37.5 50.0 62.5 36.9 36.6
45 9. 00 082 125 9. 00 301 126 0. 99 699 9. 99 781 15 4 5 49. 2 61.5 48.8 61.0
46 9. 00 207 125 9. 00 427 126 0. 99 573 9. 99 780 14 6 75.0 73.8 73. 2
47 9. 00 332 124 9. 00 553 126 0.99 447 9.99 778 13 7 87.5 86.1 85.4
48 9. 00 456 125 9. 00 679 126 0. 99 321 9. 99 777 12 8 100.0 98.4 97.6
9. 00 581 123 9. 00 805 125 0.99 195 9. 99 776 11 9 112.5 110.7 109.8
50 51 9. 00 704 9. 00 828 124 123 9. 00 930 9. 01 055 125 124 124 0. 99 070 0.98 945 9. 99 775 9. 99 773 10 9 121 120 1
52 9. 00 951 123 9.01 179 0. 98 821 9. 99 772 8 1 12.1 12.0 0.1
53 9. 01 074 122 9. 01 303 124 0. 98 697 9. 99 771 7 2 24.2 24.0 0.2
54 9. 01 196 122 9.01 427 123 0. 98 573 9. 99 769 6 3 36.3 36.0 0.3
55 9. 01 318 9. 01 440 9. 01 561 9.01 682 9.01 803 122 9.01 550 123 0. 98 450 9. 99 768 5 4 5 48. 4 60.5 48. 0 60.0 0.4 0.5
57 58 59 121 121 121 120 9. 01 673 9. 01 796 9. 01 918 9.02 040 123 122 122 122 0. 98 327 0. 98 204 0. 98 082 0. 97 960 9. 99 767 9. 99 765 9. 99 764 9. 99 763 4 3 2 1 6 7 8 9 72.6 84.7 96.8 108.9 72.0 84.0 96.0 108.0 0.6 0.7 0.8 0.9
60 9. 01 923 9. 02 162 0. 97 838 9. 99 761 0
L Sin d L Tan L Cot L Cos 354°- 174°-
L Cos L Cot L Tan L Sin 264° 84°-
46
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
6°-, 186°- / L Sin L Tan L Cot L Cos Prop. pts.
96°-, 276°- L Cos L Cot L Tan L Sin
0 1 2 3 4 9. 01 923 9.02 043 9.02 163 9. 02 283 9.02 402 120 120 120 119 118 9.02 162 9.02 283 9.02 404 9. 02 525 9.02 645 121 121 121 120 121 0.97 838 0.97 717 0.97 596 0.97 475 0.97 355 9.99 761 9. 99 760 9. 99 759 9. 99 757 9.99 756 60 59 58 57 56 121 120 119 1 12.1 12.0 11.9 2 24.2 24.0 23.8 3 36.3 36.0 35.7
5 6 7 8 9 9.02 520 9.02 639 9.02 757 9.02 874 9.02 992 119 118 117 118 117 9.02 766 9. 02 885 9.03 005 9.03 124 9.03 242 119 120 119 118 119 0.97 234 0.97 115 0.96 995 0.96 876 0.96 758 9.99 755 9. 99 753 9.99 752 9.99 751 9.99 749 55 54 53 52 51 5 60.5 60.0 59.5 6 72.6 72.0 71.4 7 84.7 84.0 83.3 8 96.8 96.0 95.2 9 108.9 108.0 107.1
10 11 12 13 14 9.03 109 9. 03 226 9.03 342 9. 03 458 9. 03 574 117 116 116 116 116 9.03 361 9. 03 479 9. 03 597 9.03 714 9.03 832 118 118 117 118 116 0.96 639 0.96 521 0.96 403 0.96 286 0.96 168 9.99 748 9. 99 747 9.99 745 9. 99 744 9.99 742 50 49 48 47 46 118 117 116 1 11.8 11.7 11.6 2 23.6 23.4 23.2 3 35.4 35.1 34.8 4 47.2 46.8 46.4 5 59.0 58.5 58.0 6 70.8 70.2 69.6 7 82.6 81.9 81.2 8 94.4 93.6 92.8 9 106.2 105.3 104.4
15 16 17 18 19 9.03 690 9.03 805 9. 03 920 9. 04 034 9.04 149 115 115 114 115 113 9.03 948 9. 04 065 9. 04 181 9. 04 297 9.04 413 117 116 116 116 115 0.96 052 0.95 935 0.95 819 0.95 703 0.95 587 9.99 741 9.99 740 9. 99 738 9.99 737 9.99 736 45 44 43 42 41
20 21 22 23 24 9.04 262 9.04 376 9. 04 490 9. 04 603 9. 04 715 114 114 113 112 113 9.04 528 9.04 643 9.04 758 9.04 873 9.04 987 115 115 115 114 114 0.95 472 0.95 357 0.95 242 0.95 127 0.95 013 9.99 734 9.99 733 9.99 731 9. 99 730 9.99 728 40 39 38 37 36 115 114 113 1 11.5 11.4 11.3 2 23.0 22.8 22.6 3 34.5 34.2 33.9 4 46.0 45.6 45.2 5 57.5 57.0 56.5 6 69.0 68.4 67.8 7 80.5 79.8 79.1 8 92.0 91.2 90.4 9 103.5 102.6 101.7
25 26 27 28 29 9.04 828 9. 04 940 9. 05 052 9.05 164 9.05 275 112 112 112 111 111 9.05 101 9.05 214 9.05 328 9.05 441 9.05 553 113 114 113 112 113 0.94 899 0.94 786 0.94 672 0.94 559 0.94 447 9.99 727 9.99 726 9.99 724 9. 99 723 9.99 721 35 34 33 32 31
30 31 32 33 34 9.05 386 9. 05 497 9. 05 607 9. 05 717 9.05 827 111 110 110 110 110 9.05 666 9.05 778 9.05 890 9. 06 002 9.06 113 112 112 112 111 111 0.94 334 0. 94 222 0.94 110 0.93 998 0. 93 887 9. 99 720 9. 99 718 9. 99 717 9. 99 716 9. 99 714 30 29 28 27 26 112 111 110 1 11.2 11.1 11.0 2 22.4 22.2 22.0 3 33.6 33.3 33.0 4 44.8 44.4 44.0 5 56.0 55.5 55.0 6 67.2 66.6 66.0 7 78.4 77.7 77.0 8 89.6 88.8 88.0 9 100.8 99.9 99.0
35 36 37 38 39 9. 05 937 9.06 046 9.06 155 9. 06 264 9. 06 372 109 109 109 108 109 9. 06 224 9.06 335 9.06 445 9.06 556 9. 06 666 111 110 111 110 109 0. 93 776 0. 93 665 0. 93 555 0.93 444 0. 93 334 9. 99 713 9.99 711 9. 99 710 9.99 708 9.99 707 25 24 23 22 21
40 41 42 43 44 9. 06 481 9.06 589 9. 06 696 9. 06 804 9.06 911 108 107 . 108 107 107 9. 06 775 9. 06 885 9. 06 994 9.07 103 9. 07 211 110 109 109 108 109 0.93 225 0.93 115 0.93 006 0.92 897 0.92 789 9.99 705 9.99 704 9.99 702 9. 99 701 9.99 699 20 19 18 17 16 109 108 107 1 10.9 10.8 10.7 2 21.8 21.6 21.4 3 32.7 32.4 32.1 4 43.6 43.2 42.8 5 54.5 54.0 53.5 6 65.4 64.8 64.2 7 76.3 75.6 74.9 8 87.2 86.4 85.6 9 98.1 97.2 96.3
45 46 47 48 49 9.07 018 9. 07 124 9. 07 231 9. 07 337 9. 07 442 106 107 106 105 106 9.07 320 9. 07 428 9. 07 536 9. 07 643 9. 07 751 108 108 107 108 107 0.92 680 0. 92 572 0.92 464 0. 92 357 0.92 249 9.99 698 9. 99 696 9. 99 695 9. 99 693 9.99 692 15 14 13 12 11
50 51 52 53 54 9. 07 548 9. 07 653 9. 07 758 9.07 863 9.07 968 105 105 105 105 104 9.07 858 9. 07 964 9. 08 071 9.08 177 9.08 283 106 107 106 106 106 0.92 142 0.92 036 0.91 929 0. 91 823 0. 91 717 9. 99 690 9. 99 689 9. 99 687 9.99 686 9. 99 684 10 9 8 7 6 106 105 104 1 10.6 10.5 10.4 2 21.2 21.0 20.8 3 31.8 31.5 31.2 4 42.4 42.0 41.6 5 53.0 52.5 52.0 6 63.6 63.0 62.4 7 74.2 73.5 72.8 8 84.8 84.0 83.2 9 95.4 94.5 93.6
55 56 57 58 59 9. 08 072 9.08 176 9. 08 280 9. 08 383 9. 08 486 104 104 103 103 103 9.08 389 9. 08 495 9.08 600 9. 08 705 9. 08 810 106 105 105 105 104 0.91 611 0.91 505 0.91 400 0.91 295 0.91 190 9. 99 683 9.99 681 9.99 680 9.99 678 9. 99 677 5 4 3 2 1
60 9.08 589 9.08 914 0.91 086 9.99 675 0
L Sin d L Tan cd L Cot L Cos 353°-, 173°-
L Cos L Cot L Tan L Sin 263°-, 83°-
47
Table III. Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
7°-, 187°- 97°-, 277°- / L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9.08 589 9.08 692 9. 08 795 9. 08 897 9. 08 999 9.09 101 9. 09 202 9.09 304 9.09 405 9. 09 506 9. 09 606 9. 09 707 9. 09 807 9. 09 907 9.10 006 9.10 106 9.10 205 9. 10 304 9.10 402 9.10 501 9.10 599 9.10 697 9.10 795 9. 10 893 9.10 990 9.11 087 9.11 184 9.11 281 9. 11 377 9.11 474 9.11 570 9. 11 666 9. 11 761 9.11 857 9.11 952 9.12 047 9.12 142 9.12 236 9.12 331 9.12 425 9.12 519 9.12 612 9.12 706 9.12 799 9.12 892 9.12 985 9.13 078 9.13 171 9.13 263 9. 13 355 9.13 447 9.13 539 9. 13 630 9.13 722 9.13 813 9.13 904 9.13 994 9.14 085 9.14 175 9.14 266 9.14 356 103 103 102 102 102 101 102 101 101 100 101 100 100 99 100 99 99 98 99 98 98 98 98 97 97 97 97 96 97 96 96 95 96 95 95 95 94 95 94 94 93 94 93 93 93 93 93 92 92 92 92 91 92 91 91 90 91 90 91 90 9. 08 914 9. 09 019 9. 09 123 9.09 227 9. 09 330 9. 09 434 9.09 537 9. 09 640 9. 09 742 9. 09 845 9. 09 947 9.10 049 9.10 150 9. 10 252 9.10 353 9.10 454 9.10 555 9.10 656 9.10 756 9.10 856 9.10 956 9.11 056 9.11 155 9.11 254 9.11 353 9.11 452 9.11 551 9.11 649 9.11 747 9.11 845 9.11 943 9.12 040 9. 12 138 9.12 235 9.12 332 9.12 428 9.12 525 9.12 621 9.12 717 9.12 813 9.12 909 9.13 004 9.13 099 9.13.194 9.13 289 9.13 384 9.13 478 9.13 573 9.13 667 9.13 761 9.13 854 9.13 948 9.14 041 9. 14 134 9.14 227 9.14 320 9.14 412 9.14 504 9.14 597 9.14 688 9.14 780 105 104 104 103 104 103 103 102 103 102 102 101 102 101 101 101 101 100 100 100 100 99 99 99 99 99 98 98 98 98 97 98 97 97 96 97 96 96 96 96 95 95 95 95 95 94 95 94 94 93 94 93 93 93 93 92 92 93 91 92 0.91 086 0. 90 981 0. 90 877 0. 90 773 0. 90 670 0.90 566 0.90 463 0. 90 360 0.90 258 0.90 155 0.90 053 0. 89 951 0.89 850 0. 89 748 0.89 647 0.89 546 0.89 445 0.89 344 0.89 244 0.89 144 0. 89 044 0.88 944 0.88 845 0. 88 746 0.88 647 0. 88 548 0.88 449 0.88 351 0. 88 253 0.88 155 0.88 057 0.87 960 0.87 862 0. 87 765 0.87 668 0.87 572 0.87 475 0.87 379 0. 87 283 0.87 187 0.87 091 0. 86 996 0.86 901 0. 86 806 0.86 711 9. 99 675 9. 99 674 9. 99 672 9. 99 670 9. 99 669 9. 99 667 9. 99 666 9. 99 664 9. 99 663 9. 99 661 9. 99 659 9. 99 658 9. 99 656 9. 99 655 9. 99 653 9. 99 651 9. 99 650 9. 99 648 9. 99 647 9. 99 645 9. 99 643 9. 99 642 9.99 640 9. 99 638 9. 99 637 9. 99 635 9. 99 633 9. 99 632 9. 99 630 9.99 629 9. 99 627 9. 99 625 9. 99 624 9. 99 622 9. 99 620 9. 99 618 9. 99 617 9. 99 615 9.99 613 9. 99 612 9. 99 610 9. 99 608 9. 99 607 9. 99 605 9. 99 603 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 105 104 . 103 1 10.5 10.4 10.3 2 21.0 20.8 20.6 3 31.5 31.2 30.9 4 42.0 41.6 41.2 5 52.5 52.0 51.5 6 63.0 62.4 61.8 7 73.5 72.8 72.1 8 84.0 83.2 82.4 9 94.5 93.6 92.7 102 101 100 1 10.2 10.1 10.0 2 20.4 20.2 20.0 3 30.6 30.3 30.0 4 40.8 40.4 40.0 5 51.0 50.5 50.0 6 61.2 60.6 60.0 7 71.4 70.7 70.0 8 81.6 80.8 80.0 9 91.8 90.9 90.0 99 98 1 9.9 9.8 2 19.8 19.6 3 29.7 29.4 4 39.6 39.2 5 49.5 49.0 6 59.4 58.8 7 69.3 68.6 8 79.2 78.4 9 89.1 88.2 97 96 95 1 9.7 9.6 9.5 2 19.4 19.2 19.0 3 29.1 28.8 28.5 4 38.8 38.4 38.0 5 48.5 48.0 47.5 6 58.2 57.6 57.0 7 67.9 67.2 66.5 8 77.6 76.8 76.0 9 87.3 86.4 85.5 94 93 92 1 9.4 9.3 9.2 2 18.8 18.6 18.4 3 28.2 27.9 27.6 4 37.6 37.2 36.8 5 47.0 46.5 46.0 6 56.4 55.8 55.2 7 65.8 65.1 64.4 8 75.2 74.4 73.6 9 84.6 83.7 82.8 91 90 2 1 9.1 9.0 0.2 2 18.2 18.0 0.4 3 27.3 27.0 0.6 4 36.4 36.0 0.8 5 45.5 45.0 1.0 6 54.6 54.0 1.2 7 63.7 63.0 1.4 8 72.8 72.0 1.6 9 81.9 81.0 1.8
0.86 616 0.86 522 0.86 427 0.86 333 0.86 239 0. 86 146 0.86 052 0. 85 959 0. 85 866 0.85 773 0. 85 680 0.85 588 0. 85 496 0. 85 403 0.85 312 0. 85 220 9. 99 601 9. 99 600 9. 99 598 9. 99 596 9. 99 595 9. 99 593 9. 99 591 9. 99 589 9.99 588 9. 99 586 9. 99 584 9. 99 582 9. 99 581 9. 99 579 9.99 577 9. 99 575 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0
L Sin L Cos d - L Tan L Cot Cd L Cot L Cos / 352°-, 172°-
L Tan L Sin 262°-, 82°-
48
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
8°-, 188°- / L Sin d
98°-, 278°- L Cos
0 9.14 356 20
1 9.14 445 OU QQ
2 9.14 535 VU QQ
3 9.14 624 Off
4 9.14 714 yu 89
5 9.14 803 QQ
6 9.14 891 oo QQ
7 9.14 980 Oif QO
8 9.15 069 OU QQ
9 9.15 157 OO 88
10 9.15 245 QQ
11 9.15 333 OO QQ
12 9.15 421 OO Q7
13 9.15 508 ol
14 9.15 596 OO 87
15 9.15 683 07
16 9.15 770 ol Q7
17 9.15 857 ol Q7
18 9.15 944 ol
19 9.16 030 OU 86
20 9.16 116 Q7
21 9.16 203 ol
22 9.16 289 OO
23 9.16 374 OO
24 9.16 460 86 85
25 9.16 545 86
26 9.16 631
27 9.16 716 85 Q£
28 9.16 801 oo 85 84
29 9.16 886
30 9.16 970 QK
31 9.17 055 OO Qd
32 9.17 139 O'*
33 9. 17 223 o4 Q4
34 9.17 307 O'* 84
35 9.17 391
36 9.17 474 83
37 9.17 558 oT
38 9.17 641 83 QQ
39 9.17 724 OO 83
40 9.17 807 QQ
41 9.17 890 OO QQ
42 9.17 973 O«5 QO
43 9.18 055 oZ 82 83
44 9.18 137
45 9.18 220 QO
46 9.18 302 oZ
47 9.18 383 81 82
48 9.18 465
49 9.18 547 82 81
50 9.18 628 QI
51 9.18 709 ol QI
52 9.18 790 Ol Q1
53 9.18 871 ol QI
54 9. 18 952 ol 81
55 9.19 033 80 80 QQ
56 9.19 113
57 9.19 193
58 9.19 273 OU on
59 9.19 353 oU 80
60 9.19 433
L Sin
— d
L Cos J
L Tan cd L Cot L Cos
L Cot L Tan L Sin
9.14 780 OO 0.85 220 9.99 575
9.14 872 9.14 963 yz 91 Q1 0.85 128 0.85 037 9.99 9. 99 574 572
9.15 054 9.15 145 yi 91 91 0.84 946 0.84 855 9.99 9.99 570 568
9.15 236 91 0.84 764 9.99 566
9.15 327 on 0.84 673 9.99 565
9.15 417 01 0.84 583 9. 99 563
9.15 508 9.15 598 90 90 0.84 492 0. 84 402 9.99 9.99 561 559
9.15 688 QQ 0. 84 312 9.99 557
9.15 777 QQ 0.84 223 9. 99 556
9.15 867 QQ 0.84 133 9. 99 554
9.15 956 QQ 0.84 044 9.99 552
9.16 046 89 0.83 954 9.99 550
9.16 135 QQ 0.83 865 9.99 548
9.16 224 OU 0.83 776 9.99 546
9.16 312 oo QQ 0.83 6S8 9.99 545
9.16 401 QQ 0.83 599 9.99 543
9.16 489 88 0.83 511 9.99 541
9.16 577 88 QQ 0.83 423 9.99 539
9.16 665 0.83 335 9. 99 537
9.16 753 QQ 0. 83 247 9.99 535
9.16 841 Q7 0. 83 159 9.99 533
9.16 928 ol 88 0.83 072 9. 99 532
9.17 016 Q7 0. 82 984 9.99 530
9.17 103 Q7 0.82 897 9.99 528
9.17 190 ol Q7 0.82 810 9. 99 526
9.17 277 QA 0.82 723 9.99 524
9.17 363 87 0.82 637 9.99 522
9.17 450 86 QA 0.82 550 9.99 520
9.17 536 0.82 464 9. 99 518
9.17 622 QA 0.82 378 9.99 517
9.17 708 86 0.82 292 9.99 515
9.17 794 86 0.82 206 9. 99 513
9.17 880 85 0.82 120 9. 99 511
9.17 965 QQ 0.82 035 9.99 509
9.18 051 85 0.81 949 9. 99 507
9.18 136 85 85 0.81 864 9.99 505
9.18 221 0.81 779 9.99 503
— ■■■ * 1 ■ 1 «
9.18 306 85 0.81 694 9. 99 501
9.18 391 84 0.81 609 9.99 499
9.18 475 85 0.81 525 9.99 497
9.18 560 84 0.81 440 9. 99 495
9.18 644 84 0.81 356 9.99 494
9.18 728 QI 0.81 272 9. 99 492
9.18 812 o'* Q4 0.81 188 9. 99 490
9.18 896 83 84 0.81 104 9.99 488
9.18 979 0.81 021 9.99 486
9.19 063 83 0.80 937 9.99 484
9.19 146 83 QQ 0.80 854 9. 99 482
9.19 229 0.80 771 9.99 480
9.19 312 83 83 83 0.80 688 9.99 478
9.19 395 0.80 605 9.99 476
9.19 478 0.80 522 9. 99 474
9.19 561 82 0.80 439 9.99 472
9.19 643 82 0.80 357 9.99 470
9.19 725 82 0. 80 275 9.99 468
9.19 807 Q9 0.80 193 9. 99 466
9.19 889 82 0.80 111 9. 99 464
9.19 971 0.80 029 9.99 462
L Tan L Cot L Cos
— cd —
L Cot L Tan L Sin
Prop. pts.
60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 92 91 90 1 9.2 9.1 9.0 2 18.4 18.2 18.0 3 27.6 27.3 27.0 4 36.8 36.4 36.0 5 46.0 45.5 45.0 6 55.2 54.6 54.0 7 64.4 63.7 63.0 -8 73.6 72.8 72.0 9 82.8 81.9 81.0 89 88 1 8.9 8.8 2 17.8 17.6 3 26.7 26.4 4 35.6 35.2 5 44.5 44.0 6 53.4 52.8 7 62.3 61.6 8 71.2 70.4 9 80.1 79.2 87 86 1 8.7 8.6 2 17.4 17.2 3 26.1 25.8 4 34.8 34.4 5 43.5 43.0 6 52.2 51.6 7 60.9 60.2 8 69.6 68.8 9 78.3 77.4 85 84 1 8.5 8.4 2 17.0 16.8 3 25.5 25.2 4 34.0 33.6 5 42.5 42.0 6 51.0 50.4 7 59.5 58.8 8 68.0 67.2 9 76.5 75.6 83 82 1 8.3 8.2 2 16.6 16.4 3 24.9 24.6 4 33.2 32.8 5 41.5 41.0 6 49.8 49.2 7 58.1 57.4 8 66.4 65.6 9 74.7 73.8 81 80 2 1 8.1 8.0 0.2 2 16.2 16.0 0.4 3 24.3 24.0 0.6 4 32.4 32.0 0.8 5 40.5 40.0 1.0 6 48.6 48.0 1.2 7 56.7 56.0 1.4 8 64.8 64.0 1.6 9 72.9 72.0 1.8
/ 351°-, 171°-
261°-, 81°-
49
Table III—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
9°-, 189°
99°-, 279°-
t L Sin d L Tan cd L Cot L Cos Prop. pts.
L Cos L Cot L Tan L Sin
0 1 2 3 4 9.19 433 9.19 513 9.19 592 9.19 672 9.19 751 80 79 80 79 79 79 79 79 78 78 79 78 78 77 78 78 77 77 77 77 77 77 76 77 76 76 76 76 75 76 75 76 75 75 75 74 75 75 74 74 74 74 74 74 73 74 73 73 73 73 73 73 72 73 72 72 73 71 72 72 9.19 971 9. 20 053 9. 20 134 9. 20 216 9. 20 297 82 81 82 81 81 81 81 81 80 81 80 80 80 80 80 79 80 79 79 79 79 79 78 79 78 78 78 78 78 78 77 78 77 77 77 77 77 76 77 76 76 77 76 76 75 76 75 76 75 75 75 75 75 74 75 74 75 74 74 74 0.80 029 0.79 947 0. 79 866 0. 79 784 0. 79 703 9.99 462 9.99 460 9.99 458 9.99 456 9.99 454 60 59 58 57 56 82 81 80 1 8.2 8.1 8.0 2 16.4 16.2 16.0 3 24.6 24.3 24.0 4 32.8 32.4 32.0 5 41.0 40.5 40.0 6 49.2 48.6 48.0 7 57.4 56.7 56.0 8 65.6 64.8 64.0 9 73.8 72.9 72.0 79 78 1 7.9 7.8 2 15.8 15.6 3 23.7 23.4 4 31.6 31.2 5 39.5 39.0 6 47.4 46.8 7 55.3 54.6 8 63.2 62.4 9 71.1 70.2 77 76 1 7.7 7.6 2 15.4 15.2 3 23.1 22.8 4 30.8 30.4 5 38.5 38.0 6 46.2 45.6 7 53.9 53.2 8 61.6 60.8 9 69.3 68.4 75 74 1 7.5 7.4 2 15.0 14.8 3 22.5 22.2 4 30.0 29.6 5 37. 5 37.0 6 45.0 44.4 7 52.5 51.8 8 60.0 59. 2 9 67.5 66.6 73 72 1 7.3 7.2 2 14.6 14.4 3 21.9 21.6 4 29.2 28.8 5 36.5 36.0 6 43.8 43.2 7 51.1 50.4 8 58.4 57.6 9 65.7 64.8 71 3 2 1 7.1 0.3 0.2 2 14.2 0. 6 0.4 3 21.3 0.9 0.6 4 28.4 1.2 0.8 5 35. 5 1. 5 1.0 6 42.6 1.8 1.2 7 49.7 2.1 1.4 8 56. 8 2.4 1.6 9 63.9 2. 7 1.8
5 6 7 8 9 9.19 830 9.19 909 9.19 988 9. 20 067 9. 20 145 9. 20 378 9. 20 459 9.20 540 9. 20 621 9. 20 701 0.79 622 0. 79 541 0.79 460 0. 79 379 0. 79 299 9.99 452 9. 99 450 9. 99 448 9. 99 446 9.99 444 55 54 53 52 51
10 11 12 13 14 9. 20 223 9. 20 302 9. 20 380 9. 20 458 9. 20 535 9. 20 782 9. 20 862 9. 20 942 9.21 022 9.21 102 0. 79 218 0.79 138 0. 79 058 0. 78 978 0.78 898 9.99 442 9.99 440 9.99 438 9. 99 436 9. 99 434 50 49 48 47 46
15 16 17 18 19 9. 20 613 9. 20 691 9. 20 768 9. 20 845 9. 20 922 9.21 182 9.21 261 9 21 341 9. 21 420 9. 21 499 0.78 818 0. 78 739 0.78 659 0.78 580 0.78 501 9.99 432 9. 99 429 9.99 427 9.99 425 9.99 423 45 44 43 42 41
20 21 22 23 24 9. 20 999 9. 21 076 9.21 153 9.21 229 9. 21 306 9.21 578 9 21 657 9. 21 736 9. 21 814 9. 21 893 0.78 422 0. 78 343 0. 78 264 0.78 186 0. 78 107 9.99 421 9. 99 419 9. 99 417 9.99 415 9. 99 413 40 39 38 37 36
25 26 27 28 29 9. 21 382 9. 21 458 9.21 534 9. 21 610 9. 21 685 9.21 971 9. 22 049 9. 22 127 9. 22 205 9.22 283 0. 78 029 0. 77 951 0.77 873 0.77 795 0. 77 717 9. 99 411 9.99 409 9.99 407 9.99 404 9.99 402 35 34 33 32 31
30 31 32 33 34 9. 21 761 9. 21 836 9. 21 912 9. 21 987 9. 22 062 9. 22 361 9. 22 438 9. 22 516 9. 22 593 9. 22 670 0.77 639 0.77 562 0. 77 484 0. 77 407 0. 77 330 9.99 400 9.99 398 9.99 396 9.99 394 9.99 392 30 29 28 27 26
35 36 37 38 39 9. 22 137 9. 22 211 9.22 286 9.22 361 9. 22 435 9. 22 747 9. 22 824 9.22 901 9. 22 977 9. 23 054 0. 77 253 0. 77 176 0.77 099 0.77 023 0. 76 946 9.99 390 9.99 388 9. 99 385 9.99 383 9.99 381 25 24 23 22 21
40 41 42 43 44 9. 22 509 9. 22 583 9. 22 657 9. 22 731 9. 22 805 9.23 130 9. 23 206 9. 23 283 9. 23 359 9. 23 435 0. 76 870 0. 76 794 0. 76 717 0. 76 641 0. 76 565 9.99 379 9. 99 377 9.99 375 9. 99 372 9.99 370 20 19 18 17 16
45 46 47 48 49 9. 22 878 9. 22 952 9. 23 025 9. 23 098 9.23 171 9.23 510 9. 23 586 9. 23 661 9. 23 737 9. 23 812 0. 76 490 0. 76 414 0. 76 339 0. 76 263 0.76 188 9.99 368 9.99 366 9. 99 364 9.99 362 9.99 359 15 14 13 12 11
50 51 52 53 54 9. 23 244 9. 23 317 9. 23 390 9. 23 462 9. 23 535 9. 23 887 9. 23 962 9. 24 037 9.24 112 9.24 186 0.76 113 0. 76 038 0.75 963 0.75 888 0.75 814 9.99 357 9.99 355 9. 99 353 9.99 351 9.99 348 10 9 8 7 6
55 56 57 58 59 9. 23 607 9. 23 679 9. 23 752 9. 23 823 9. 23 895 9. 24 261 9. 24 335 9. 24 410 9.24 484 9.24 558 0. 75 739 0. 75 665 0. 75 590 0.75 516 0.75 442 9.99 346 9.99 344 9.99 342 9. 99 340 9. 99 337 5 4 3 2 1
60 9.23 967 9.24 632 0. 75 368 9.99 335 0
L Sin L Cos d L Tan cd L Cot L Cos / 350°-, 170°-
L Cot L Tan L Sin 260°-, 80°-
50
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes
Continued
10°-, 190°- 100°-, 280°- / L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin Prop. pts.
• 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9. 23 967 9. 24 039 9. 24 110 9. 24 181 9. 24 253 9. 24 324 9. 24 395 9. 24 466 9. 24 536 9. 24 607 9. 24 677 9. 24 748 9. 24 818 9.24 888 9. 24 958 9. 25 028 9. 25 098 9.25 168 9. 25 237 9. 25 307 9. 25 376 9. 25 445 9. 25 514 9. 25 583 9. 25 652 9. 25 721 9. 25 790 9. 25 858 9. 25 927 9. 25 995 9. 26 063 9. 26 131 9. 26 199 9. 26 267 9. 26 335 9. 26 403 9. 26 470 9. 26 538 9. 26 605 9. 26 672 9. 26 739 9. 26 806 9. 26 873 9. 26 940 9. 27 007 9. 27 073 9.27 140 9.27 206 9. 27 273 9. 27 339 9.27 405 9. 27 471 9. 27 537 9. 27 602 9. 27 668 9. 27 734 9. 27 799 9. 27 864 9. 27 930 9. 27 995 9. 28 060 72 71 71 72 71 71 71 70 71 70 71 70 70 70 70 70 70 69 70 69 69 69 69 69 69 69 68 69 68 68 68 68 68 68 68 67 68 67 67 67 67 67 67 67 66 67 66 67 66 66 66 66 65 66 66 65 65 66 65 65 9. 24 632 9. 24 706 9. 24 779 9. 24 853 9. 24 926 9. 25 000 9. 25 073 9. 25 146 9. 25 219 9. 25 292 9. 25 365 9. 25 437 9. 25 510 9. 25 582 9. 25 655 9. 25 727 9. 25 799 9. 25 871 9. 25 943 9. 26 015 9. 26 086 9. 26 158 9. 26 229 9. 26 301 9. 26 372 9. 26 443 9. 26 514 9. 26 585 9. 26 655 9. 26 726 9. 26 797 9. 26 867 9. 26 937 9. 27 008 9. 27 078 9. 27 148 9. 27 218 9. 27 288 9. 27 357 9. 27 427 9. 27 496 9. 27 566 9. 27 635 9. 27 704 9. 27 773 9. 27 842 9. 27 911 9. 27 980 9.28 049 9. 28 117 9. 28 186 9. 28 254 9. 28 323 9. 28 391 9. 28 459 9. 28 527 9. 28 595 9. 28 662 9. 28 730 9. 28 798 9.28 865 74 73 74 73 74 73 73 73 73 73 72 73 72 73 72 72 72 72 72 71 72 71 72 71 71 71 71 70 71 71 70 70 71 70 70 70 70 69 70 69 70 69 69 69 69 69 69 69 68 69 68 69 68 68 68 68 67 68 68 67 0. 75 368 0. 75 294 0. 75 221 0. 75 147 0. 75 074 0. 75 000 0. 74 927 0. 74 854 0. 74 781 0. 74 708 0. 74 635 0. 74 563 0. 74 490 0. 74 418 0. 74 345 0. 74 273 0. 74 201 0. 74 129 0. 74 057 -0.73 985 0. 73 914 0. 73 842 0. 73 771 0. 73 699 0. 73 628 0. 73 557 0. 73 486 0. 73 415 0. 73 345 0.73 274 0. 73 203 0. 73 133 0. 73 063 0. 72 992 0. 72 922 0.72 852 0. 72 782 0. 72 712 0. 72 643 0. 72 573 0. 72 504 0. 72 434 0.72 365 0. 72 296 0. 72 227 0. 72 158 0. 72 089 0.72 020 0. 71 951 0.71 883 0. 71 814 0. 71 746 0. 71 677 0. 71 609 0.71 541 0.71 473 0. 71 405 0. 71 338 0. 71 270 0.71 202 0.71 135 9.99 335 9. 99 333 9. 99 331 9. 99 328 9. 99 326 9.99 324 9. 99 322 9. 99 319 9. 99 317 9.99 315 9.99 313 9. 99 310 9.99 308 9.99 306 9. 99 304 9.99 301 9. 99 299 9. 99 297 9. 99 294 9.99 292 9. 99 290 9. 99 288 9.99 285 9. 99 283 9.99 281 9. 99 278 9. 99 276 9.99 274 9. 99 271 9.99 269 9.99 267 9. 99 264 9. 99 262 9. 99 260 9.99 257 9.99 255 9. 99 252 9. 99 250 9.99 248 9.99 245 9.99 243 9.99 241 9. 99 238 9. 99 236 9. 99 233 9. 99 231 9. 99 229 9. 99 226 9.99 224 9. 99 221 9. 99 219 9. 99 217 9. 99 214 9.99 212 9.99 209 9. 99 207 9 99 204 9. 99 202 9. 99 200 9.99 197 9.99 195 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 74 73 1 7.4 7.3 2 14.8 14.6 3 22.2 21.9 4 29.6 29.2 5 37.0 36.5 6 44.4 43.8 7 51.8 51.1 8 59.2 58.4 9 66.6 65.7 72 71 1 7.2 7.1 2 14.4 14.2 3 21.6 21.3 4 28. 8 28.4 5 36.0 35.5 6 43. 2 42.6 7 50. 4 49. 7 8 57.6 56.8 9 64.8 63.9 70 69 1 7.0 6.9 2 14.0 13.8 3 21.0 20.7 4 28.0 27.6 5 35.0 34. 5 6 42.0 41.4 7 49.0 48.3 8 56.0 55.2 9 63.0 62.1 68 67 1 6.8 6.7 2 13.6 13.4 3 20.4 20.1 4 27. 2 26.8 5 34.0 33.5 6 40.8 40. 2 7 47.6 46.9 8 54.4 53. 6 9 61.2 60.3 66 65 1 6.6 6.5 2 13.2 13.0 3 19.8 19. 5 4 26.4 26.0 5 33.0 32. 5 6 39.6 39.0 7 46. 2 45.5 8 52.8 52.0 9 59.4 58.5 3 2 1 0.3 0.2 2 0.6 0.4 3 0.9 0.6 4 1.2 0.8 5 1.5 1.0 6 1.8 1.2 7 2.1 1.4 8 2.4 1.6 9 2.7 1.8
L Sin I, Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin / 349°-, 169°- 259°-, 79°-
51
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
11°-, 191°- L Sin L Tan L Cot L Cos —
/ d
101°-, 281°- cd Prop. pts.
L Cos L Cot L Tan L Sin
0 9. 28 060 65 9. 28 865 68 0.71 135 9. 99 195 60
1 9. 28 125 65 9. 28 933 67 0. 71 067 9. 99 192 59 68 67
2 9.28 190 64 9. 29 000 67 0. 71 000 9. 99 190 58 1 6.8 6.7
3 9. 28 254 65 9. 29 067 67 0. 70 933 9.99 187 57 2 13.6 13.4
4 9. 28 319 65 9. 29 134 67 0.70 866 9.99 185 56 3 20.4 27.2 20.1
9.28 384
5 64 9. 29 201 67 0. 70 799 9.99 182 55 5 34.0 33.5
6 9. 28 448 64 9. 29 268 67 0. 70 732 9. 99 180 54 6 40.8 40.2
7 9.28 512 65 9. 29 335 67 0. 70 665 9. 99 177 53 7 47.6 46.9
8 9. 28 577 64 9. 29 402 66 0. 70 598 9. 99 175 52 8 54.4 53.6
9 9. 28 641 64 9. 29 468 67 0. 70 532 9. 99 172 51 9 61.2 60.3
10 9. 28 705 64 9. 29 535 66 A7 0. 70 465 9.99 170 50 66
11 9. 28 769 64 9. 29 601 0. 70 399 9. 99 167 49 65
12 9. 28 833 63 9. 29 668 66 66 0. 70 332 9.99 165 48 1 6.6 6.5
13 9. 28 896 64 9. 29 734 0. 70 266 9.99 162 47 2 13.2 13.0
14 9.28 960 64 9. 29 800 66 0. 70 200 9. 99 160 46 3 19.8 26.4 19.5 26.0
9.29 024
15 63 9. 29 866 aa 0. 70 134 9. 99 157 45 5 33.0 32.5
16 9. 29 087 63 9. 29 932 66 0. 70 068 9.99 155 44 6 39.6 39.0
17 9.29 150 64 9. 29 998 66 0. 70 002 9. 99 152 43 7 46.2 45.5
18 9. 29 214 63 9. 30 064 66 0. 69 936 9. 99 150 42 8 52.8 52.0
19 9. 29 277 63 9. 30 130 65 0. 69 870 9. 99 147 41 9 59.4 58.5
20 9. 29 340 63 9.30 195 0.69 805 9. 99 145 40
21 9. 29 403 63 9. 30 261 DO AK 0. 69 739 9.99 142 39 64 63
22 9. 29 466 63 9. 30 326 OO 65 0.69 674 9. 99 140 38 1 6.4 6.3
23 9. 29 529 62 9. 30 391 AA 0.69 609 9. 99 137 37 2 12.8 12.6
24 9. 29 591 63 9. 30 457 65 0. 69 543 9. 99 135 36 3 19.2 25.6 18.9 25.2
9. 29 654
25 62 9. 30 522 ak 0. 69 478 9. 99 132 35 5 32.0 31.5
26 9.29 716 63 9. 30 587 65 0. 69 413 9. 99 130 34 6 38.4 37.8
27 9.29 779 62 9.30 652 65 0.69 348 9. 99 127 33 7 44.8 44.1
28 9. 29 841 62 9. 30 717 ak 0. 69 283 9. 99 124 32 8 51.2 50.4
29 9.29 903 63 9. 30 782 64 0.69 218 9. 99 122 31 9 57.6 56.7
30 9.29 966 9. 30 846 0. 69 154 9.99 119 30
31 9.30 028 62 9. 30 911 65 A/1 0. 69 089 9.99 117 29 62 61
32 9. 30 090 61 9. 30 975 65 64 0.69 025 9. 99 114 28 1 6.2 6.1
33 9. 30 151 62 9. 31 040 0.68 960 9.99 112 27 2 12.4 12.2
34 9.30 213 62 9.31 104 64 0. 68 896 9. 99 109 26 3 4 18.6 24.8 18.3 24.4
9. 30 275
35 61 9.31 168 65 0. 68 832 9. 99 106 25 5 31.0 30.5
36 9. 30 336 62 9.31 233 64 0. 68 767 9. 99 104 24 6 37.2 36.6
37 9. 30 398 61 9. 31 297 64 0. 68 703 9. 99 101 23 7 43.4 42.7
38 9. 30 459 62 9. 31 361 64 0. 68 639 9. 99 099 22 8 49.6 48.8
39 9.30 521 61 9.31 425 64 0.68 575 9. 99 096 21 9 55.8 54.9
40 9. 30 582 61 9. 31 489 0. 68 511 9. 99 093 20 59
41 9. 30 643 61 9. 31 552 bo 0.68 448 9. 99 091 19 60
42 9. 30 704 61 9. 31 616 O'* 63 0. 68 384 9. 99 088 18 1 6.0 5.9
43 9.30 765 61 9.31 679 64 0. 68 321 9. 99 086 17 2 12.0 11.8
44 9. 30 826 61 9.31 743 63 0.68 257 9. 99 083 16 3 18.0 24.0 30.0 17.7 23.6 29.5
45 9. 30 887 60 9. 31 806 64 0. 68 194 9. 99 080 15 5
46 9. 30 947 61 9. 31 870 63 0. 68 130 9. 99 078 14 6 36.0 35.4
47 48 9. 31 008 9. 31 068 60 61 9.31 933 9.31 996 63 AQ 0. 68 067 0.68 004 9. 99 075 9. 99 072 13 12 7 8 42.0 48.0 41.3 47.2
49 9.31 129 60 9. 32 059 63 0.67 941 9. 99 070 11 9 54.0 53.1
50 9.31 189 61 9. 32 122 A2 0. 67 878 9. 99 067 10
51 9. 31 250 60 9. 32 185 63 0.67 815 9. 99 064 9 3 2
52 9.31 310 60 9. 32 248 63 0. 67 752 9. 99 062 8 1 0.3 0.2
53 9.31 370 60 9.32 311 62 0. 67 689 9. 99 059 7 2 0.6 0.4
54 9. 31 430 60 9. 32 373 63 0.67 627 9.99 056 6 3 4 5 0.9 1.2 1.5 0.6 0.8 1.0
55 9. 31 490 59 9. 32 436 A9 0. 67 564 9. 99 054 5
56 9. 31 549 60 9. 32 498 AQ 0.67 502 9. 99 051 4 6 1.8 1.2
57 9.31 609 60 9. 32 561 A9 0. 67 439 9. 99 048 3 7 2.1 1.4
58 9.31 669 59 9. 32 623 A9 0. 67 377 9. 99 046 2 8 2.4 1.6
59 9.31 728 60 9.32 685 62 0.67 315 9. 99 043 1 9 2.7 1.8
60 9. 31 788 9.32 747 0.67 253 9.99 040 0
L Sin L Tan L Cot L Cos 348°-, 168°-
d
L Cos L Cot L Tan L Sin 258°-, 78°-
52
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
12°-, 192°- 102°-, 282°- t LSin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9. 31 788 9. 31 847 9. 31 907 9. 31 966 9.32 025 9. 32 084 9. 32 143 9. 32 202 9. 32 261 9. 32 319 9. 32 378 9. 32 437 9. 32 495 9. 32 553 9. 32 612 9. 32 670 9. 32 728 9.32 786 9. 32 844 9. 32 902 9.32 960 9. 33 018 9.33 075 9. 33 133 9.33 190 9. 33 248 9. 33 305 9. 33 362 9.33 420 9. 33 477 9. 33 534 9. 33 591 9.33 647 9. 33 704 9. 33 761 9. 33 818 9. 33 874 9. 33 931 9. 33 987 9. 34 043 9. 34 100 9.34 156 9. 34 212 9. 34 268 9. 34 324 9.34 380 9. 34 436 9.34 491 9. 34 547 9. 34 602 9. 34 658 9. 34 713 9. 34 769 9. 34 824 9. 34 879 9.34 934 9. 34 989 9. 35 044 9. 35 099 9. 35 154 9.35 209 59 60 59 59 59 59 59 59 58 59 59 58 58 59 58 58 58 58 58 58 58 57 58 57 58 57 57 58 57 57 57 56 57 57 57 56 57 56 56 57 56 56 56 56 56 56 55 56 55 56 55 56 55 55 55 55 55 55 55 55 9.32 747 9. 32 810 9. 32 872 9.32 933 9.32 995 9. 33 057 9.33 119 9. 33 180 9. 33 242 9.33 303 9.33 365 9. 33 426 9. 33 487 9. 33 548 9. 33 609 9. 33 670 9.33 731 9. 33 792 9.33 853 9.33 913 9.33 974 9.34 034 9.34 095 9.34 155 9. 34 215 9.34 276 9.34 336 9. 34 396 9. 34 456 9. 34 516 9.34 576 9 34 635 9.34 695 9. 34 755 9.34 814 9. 34 874 9. 34 933 9. 34 992 9. 35 051 9.35 111 9.35 170 9.35 229 9. 35 288 9. 35 347 9.35 405 9.35 464 9.35 523 9.35 581 9. 35 640 9.35 698 9. 35 757 9. 35 815 9. 35 873 9.35 931 9.35 989 9. 36 047 9. 36 105 9. 36 163 9. 36 221 9.36 279 9. 36 336 63 62 61 62 62 62 61 62 61 62 61 61 61 61 61 61 61 61 60 61 60 61 60 60 61 60 60 60 60 60 59 60 60 59 60 59 59 59 60 59 59 59 59 58 59 59 58 59 58 59 58 58 58 58 58 58 58 58 58 57 0.67 253 0.67 190 0.67 128 0. 67 067 0.67 005 0.66 943 0.66 881 0. 66 820 0. 66 758 0. 66 697 0.66 635 0. 66 574 0.66 513 0. 66 452 0.66 391 0.66 330 0.66 269 0.66 208 0. 66 147 0.66 087 0.66 026 0.65 966 0. 65 905 0.65 845 0.65 785 0. 65 724 0. 65 664 0. 65 604 0.65 544 0.65 484 0.65 424 0.65 365 0.65 305 0.65 245 0.65 186 0.65 126 0.65 067 0.65 008 0. 64 949 0. 64 889 0.64 830 0. 64 771 0.64 712 0.64 653 0.64 595 0.64 536 0.64 477 0.64 419 0. 64 360 0.64 302 0.64 243 0.64 185 0. 64 127 0.64 069 0.64 011 0.63 953 0.63 895 0.63 837 0.63 779 0.63 721 0.63 664 9.99.040 9. 99 038 9.99 035 9.99 032 9.99 030 9.99 027 9.99 024 9.99 022 9.99 019 9.99 016 9.99 013 9.99 011 9.99 008 9.99 005 9.99 002 9.99 000 9.98 997 9.98 994 9.98 991 9.98 989 9.98 986 9.98 983 9.98 980 9. 98 978 9.98 975 9.98 972 9.98 969 9.98 967 9. 98 964 9.98 961 9.98 958 9.98 955 9.98 953 9.98 950 9.98 947 9.98 944 9. 98 941 9.98 938 9. 98 936 9.98 933 9.98 930 9.98 927 9.98 924 9. 98 921 9.98 919 9.98 916 9.98 913 9.98 910 9.98 907 9.98 904 9.98 901 9.98 898 9.98 896 9.98 893 9.98 890 9.98 887 9. 98 884 9.98 881 9.98 878 9.98 875 9.98 872 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 63 62 1 6.3 6.2 2 12.6 12.4 3 18.9 18.6 4 25.2 24.8 5 31.5 31.0 6 37.8 37.2 7 44.1 43.4 8 50.4 49.6 9 56.7 55.8 61 60 1 6.1 6.0 2 12.2 12.0 3 18.3 18.0 4 24.4 24.0 5 30.5 30.0 6 36.6 36.0 7 42.7 42.0 8 48.8 48.0 9 54.9 54.0 59 1 5.9 2 11.8 3 17.7 4 23.6 5 29.5 6 35.4 7 41.3 8 47.2 9 53.1 58 57 1 5.8 5.7 2 11.6 11.4 3 17.4 17.1 4 23.2 22.8 5 29.0 28.5 6 34.8 34.2 7 40.6 39.9 8 46.4 45.6 9 52.2 51.3 56 55 1 5.6 5.5 2 11.2 11.0 3 16.8 16.5 4 22.4 22.0 5 28.0 27.5 6 33.6 33.0 7 39.2 38.5 8 44.8 44.0 9 50.4 49.5 3 2 1 0.3 0.2 2 0.6 0.4 3 0.9 0.6 4 1.2 0.8 5 1. 5 1. 0 6 1.8 1.2 7 2.1 1.4 8 2.4 1.6 9 2.7 1.8
L Sin L Cos d *. L Tan L Cot cd L Cot L Tan L Cos L Sin / 347°-, 167°- 257°-, 77°-
53
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
13°-, 193°- 103°-, 283°- / L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9.35 209 9. 35 263 9.35 318 9. 35 373 9.35 427 9.35 481 9.35 536 9.35 590 9.35 644 9.35 698 9. 35 752 9.35 806 9. 35 860 9.35 914 9. 35 968 9.36 022 9.36 075 9.36 129 9. 36 182 9.36 236 9.36 289 9. 36 342 9.36 395 9. 36 449 9. 36 502 9. 36 555 9.36 608 9.36 660 9.36 713 9.36 766 9.36 819 9.36 871 9.36 924 9.36 976 9.37 028 9 37 081 9.37 133 9.37 185 9. 37 237 9.37 289 9. 37 341 9.37 393 9.37 445 9. 37 497 9.37 549 9.37 600 9.37 652 9.37 703 9.37 755 9. 37 806 9.37 858 9. 37 909 9. 37 960 9.38 011 9. 38 062 9.38 113 9.38 164 9. 38 215 9. 38 266 9. 38 317 9.38 368 54 55 55 54 54 55 54 54 54 54 54 54 54 54 54 53 54 53 54 53 53 53 54 53 53 53 52 53 53 53 52 53 52 52 53 52 52 52 52 52 52 52 52 52 51 52 51 52 51 52 51 51 51 51 51 51 51 51 51 51 9.36 336 9.36 394 9.36 452 9.36 509 9. 36 566 9.36 624 9.36 681 9. 36 738 9.36 795 9.36 852 9.36 909 9. 36 966 9.37 023 9. 37 080 9.37 137 9.37 193 9.37 250 9. 37 306 9. 37 363 9.37 419 9.37 476 9. 37 532 9.37 588 9. 37 644 9.37 700 9. 37 756 9. 37 812 9. 37 868 9.37 924 9.37 980 9.38 035 9. 38 091 9. 38 147 9.38 202 9.38 257 9. 38 313 9.38 368 9. 38 423 9. 38 479 9.38 534 9.38 589 9.38 644 9.38 699 9.38 754 9.38 808 9.38 863 9.38 918 9.38 972 9.39 027 9.39 082 9.39 136 9.39 190 9. 39 245 9. 39 299 9.39 353 9.39 407 9.39 461 9.39 515 9. 39 569 9. 39 623 9. 39 677 58 58 57 57 58 57 57 57 57 57 57 57 57 57 56 57 56 57 56 57 56 56 56 56 56 56 56 56 56 55 56 56 55 55 56 55 55 56 55 55 55 55 55 54 55 55 54 55 55 54 54 55 54 54 54 54 54 54 54 54 0.63 664 0.63 606 0. 63 548 0.63 491 0.63 434 0.63 376 0. 63 319 0.63 262 0.63 205 0.63 148 0.63 091 0.63 034 0.62 977 0.62 920 0.62 863 0.62 807 0. 62 750 0.62 694 0. 62 637 0.62 581 0.62 524 0.62 468 0. 62 412 0.62 356 0.62 300 0. 62 244 0. 62 188 0.62 132 0. 62 076 0.62 020 0.61 965 0.61 909 0.61 853 0. 61 798 0.61 743 0. 61 687 0. 61 632 0.61 577 0.61 521 0.61 466 0.61 411 0.61 356 0.61 301 0. 61 246 0.61 192 0.61 137 0.61 082 0.61 028 0. 60 973 0.60 918 0.60 864 0. 60 810 0. 60 755 0.60 701 0.60 647 0. 60 593 0. 60 539 0. 60 485 0.60 431 0. 60 377 0. 60 323 9.98 872 9.98 869 9.98 867 9. 98 864 9.98 861 9.98 858 9.98 855 9. 98 852 9. 98 849 9. 98 846 9.98 843 9. 98 840 9.98 837 9.98 834 9.98 831 9. 98 828 9.98 825 9.98 822 9.98 819 9.98 816 9. 98 813 9.98 810 9. 98 807 9. 98 804 9. 98 801 9. 98 798 9.98 795 9. 98 792 9. 98 789 9.98 786 9.98 783 9.98 780 9.98 777 9.98 774 9.98 771 9.98 768 9. 98 765 9. 98 762 9.98 759 9.98 756 9.98 753 9.98 750 9.98 746 9.98 743 9.98 740 9.98 737 9.98 734 9.98 731 9.98 728 9.98 725 9. 98 722 9.98 719 9.98 715 9. 98 712 9.98 709 9.98 706 9.98 703 9.98 700 9. 98 697 9. 98 694 9.98 690 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 58 57 1 5.8 5.7 2 11.6 11.4 3 17.4 17.1 4 23.2 22.8 5 29.0 28. 5 6 34.8 34.2 7 40.6 39.9 8 46.4 45.6 9 52.2 51.3 56 55 1 5.6 5.5 2 11.2 11.0 3 16.8 16.5 4 22.4 22.0 5 28.0 27.5 6 33.6 33.0 7 39.2 38.5 8 44.8 44.0 9 50.4 49.5 54 1 5.4 2 10.8 3 16.2 4 21.6 5 27.0 6 32.4 7 37.8 8 43.2 9 48.6 53 52 1 5.3 5.2 2 10.6 10.4 3 15.9 15.6 4 21.2 20.8 5 26.5 26.0 6 31.8 31.2 7 37.1 36.4 8 42.4 41.6 9 47.7 46.8 51 4 1 5.1 0.4 2 10.2 0.8 3 15.3 1.2 4 20.4 1.6 5 25.5 2.0 6 30.6 2.4 7 35.7 2.8 8 40.8 3.2 9 45.9 3.6 3 2 1 0.3 0.2 2 0.6 0.4 3 0.9 0.6 4 1.2 0.8 5 1.5 1.0 6 1.8 1.2 7 2.1 1.4 8 2.4 1.6 9 2.7 1.8
L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin / 346°-, 166°- 256°-, 76°-
54
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
14°-, 194°- L Sin d L Tan cd L Cot L Cos d
104°-, 284°- L Cos L Cot L Tan L Sin
0 9.38 368 KA 9. 39 677 KA 0.60 323 9. 98 690 Q 60 1
1 9. 38 418 OU 9.39 731 Ott KA 0. 60 269 9. 98 687 0 59
2 9. 38 469 01 KA 9. 39 785 K2 0. 60 215 9.98 684 3 Q 58
3 9. 38 519 OU KI 9. 39 838 00 KA 0.60 162 9.98 681 o Q 57 54 53
4 9. 38 570 01 50 9. 39 892 Ott 53 0.60 108 9.98 678 0 3 56 1 5.4 5.3
5 9. 38 620 50 KI 9. 39 945 KA 0.60 055 9.98 675 A 55 2 3 10.8 16.2 21.6 27.0 32.4 37.8 10.6 15.9 21.2 26.5 31.8 37.1
6 9. 38 670 9. 39 999 Ott KQ 0.60 001 9. 98 671 tt Q 54
7 9 38 721 01 KA 9. 40 052 00 KA 0. 59 948 9. 98 668 0 Q 53
8 9. 38 771 OU KA 9.40 106 KQ 0. 59 894 9. 98 665 0 Q 52 O
9 9. 38 821 OU 50 9.40 159 00 53 0. 59 841 9.98 662 0 3 51 6 7
10 9. 38 871 KA 9.40 212 KA 0. 59 788 9.98 659 Q 50 8 43.2 48.6 42.4 47.7
11 9. 38 921 OU KA 9.40 266 KQ 0. 59 734 9. 98 656 6 A 49 y
12 9. 38 971 OU KA 9. 40 319 00 KQ 0.59 681 9.98 652 Q 48
13 9. 39 021 OU KA 9. 40 372 Ou KQ 0. 59 628 9. 98 649 6 Q 47
14 9. 39 071 OU 50 9.40 425 00 53 0.59 575 9.98 646 0 3 46
15 9. 39 121 AQ 9. 40 478 KQ 0. 59 522 9.98 643 Q 45 52 51
16 9. 39 170 tty KA 9. 40 531 O0 KQ 0.59 469 9. 98 640 0 A 44 1 5.2 5.1
17 9. 39 220 OU KA 9.40 584 Ou KO 0. 59 416 9. 98 636 tt Q 43 2 10.4 10.2
18 9. 39 270 OU AQ 9.40 636 OZ KQ 0. 59 364 9. 98 633 0 Q 42 3 15.6 15.3
19 9.39 319 tty 50 9.40 689 00 53 0.59 311 9.98 630 0 3 41 4 K 20.8 26.0 20.4 25.5
20 9. 39 369 49 9. 40 742 53 0. 59 258 9.98 627 4 40 6 31.2 30.6
21 9. 39 418 AQ 9.40 795 K9 0. 59 205 9. 98 623 Q 39 7 36.4 35.7
22 9. 39 467 KA 9. 40 847 oz KQ 0.59 153 9. 98 620 0 Q 38 8 41.6 40.8
23 9. 39 517 OU AQ 9.40 900 OO KO 0. 59 100 9.98 617 0 Q 37 9 46.8 45.9
24 9.39 566 tty 49 9.40 952 OZ 53 0.59 048 9.98 614 0 4 36
25 9.39 615 AQ 9.41 005 KO 0. 58 995 9.98 610 Q 35
26 9. 39 664 AQ 9. 41 057 oz KO 0. 58 943 9.98 607 0 Q 34
27 9. 39 713 ^y AQ 9.41 109 OZ KO 0. 58 891 9.98 604 0 Q 33 50 49
28 9. 39 762 tty 49 9.41 161 OZ KQ 0. 58 839 9.98 601 0 4 32 5.0 10.0 4.9 9.8
29 9. 39 811 49 9.41 214 OO 52 0.58 786 9.98 597 3 31 1 2
30 9. 39 860 49 9. 41 266 52 KO 0.58 734 9.98 594 Q 30 3 A 15.0 20.0 25.0 30.0 35.0 40.0 14.7 19.6 24.5 29.4 34.3 39.2
31 9. 39 909 49 9.41 318 0. 58 682 9.98 591 0 Q 29
32 9. 39 958 48 49 9.41 370 OZ KO 0. 58 630 9.98 588 0 4 28 O
33 9. 40 006 9. 41 422 OZ KO 0. 58 578 9.98 584 Q 27 0 7
34 9.40 055 48 9.41 474 OZ 52 0.58 526 9. 98 581 0 3 26 I 8
35 9. 40 103 49 9.41 526 KO 0.58 474 9.98 578 A 25 9 45.0 44.1
36 9. 40 152 Aft 9.41 578 OZ K1 0.58 422 9.98 574 Q 24
37 9. 40 200 49 9.41 629 01 KO 0. 58 371 9.98 571 0 Q 23
38 9. 40 249 48 49 9. 41 681 OZ KO 0. 58 319 9. 98 568 0 Q 22
39 9. 40 297 9.41 733 OZ 51 0.58 267 9.98 565 0 4 21 48 47
40 9. 40 346 48 Aft 9.41 784 KO 0.58 216 9. 98 561 Q 20 1 o 4.8 9.6 14.4 19.2 24.0 28.8 4.7 9.4 14.1 18.8 23.5 28.2
41 9. 40 394 9.41 836 OZ K1 0. 58 164 9. 98 558 0 Q 19
42 9. 40 442 0.0 48 Aft 9. 41 887 01 KO 0. 58 113 9.98 555 0 A 18 0
43 9.40 490 9. 41 939 OZ K1 0. 58 061 9.98 551 tt Q 17 tt
44 9.40 538 tlo 48 9.41 990 01 51 0.58 010 9. 98 548 0 3 16 0 6
45 9.40 586 Aft 9.42 041 KO 0. 57 959 9.98 545 A 15 7 33.6 38.4 43.2 32.9 37.6 42.3
46 9. 40 634 tto 48 9. 42 093 OZ KI 0. 57 907 9.98 541 tt Q 14 o Q
47 9.40 682 AQ 9. 42 144 01 K1 0.57 856 9. 98 538 0 Q 13 y
48 9. 40 730 tto 48 9.42 195 01 51 0. 57 805 9. 98 535 0 4 12
49 9. 40 778 47 9.42 246 51 0.57 754 9.98 531 3 11
50 9.40 825 Aft 9.42 297 K1 0. 57 703 9. 98 528 3 10 4 3
51 9. 40 873 ttO Aft 9.42 348 01 K1 0. 57 652 9.98 525 4 9 1 0.4 0.8 1.2 1.6 0.3 0.6 0.9 1.2
52 9.40 921 oo A7 9.42 399 01 KI 0. 57 601 9. 98 521 Q 8 i o
53 9. 40 968 tt/ Aft 9. 42 450 01 K1 0. 57 550 9. 98 518 0 Q 7 Q
54 9.41 016 tto 47 9.42 501 01 51 0.57 499 9.98 515 0 4 6 0 4
55 9.41 063 Aft 9.42 552 KI 0. 57 448 9.98 511 Q 5 5 C 2.0 2.4 2.8 3.2 3.6 1.5 1.8 2.1 2.4
56 9.41 111 tio A7 9. 42 603 01 KA 0. 57 397 9. 98 508 0 Q 4 0 7
57 9.41 158 A7 9.42 653 OU KI 0. 57 347 9. 98 505 0 A 3 Q
58 9.41 205 tt/ A7 9.42 704 01 K1 0. 57 296 9. 98 501 tt Q 2 O Q
59 9.41 252 tt/ 48 9.42 755 01 50 0. 57 245 9. 98 498 0 4 1 y
60 9.41 300 9. 42 805 0.57 195 9.98 494 0
L Sin L Tan L Cot L Cos 345°-, 165°-
cd d
d
L Cos L Cot L Tan LSin 255°-, 75°-
55
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
15°-, 195°- f L Sin d L Tan cd L Cot L Cos d Prop. pts.
105°-, 285°- L Cos L Cot L Tan LSin
0 9.41 300 47 9.42 805 KI 0.57 195 9.98 494 60
1 9.41 347 47 9.42 856 01 KA 0.57 144 9.98 491 3 59
2 9.41 394 47 9. 42 906 OU 0.57 094 9.98 488 3 58
3 9.41 441 9.42 957 01 0. 57 043 9.98 484 4 3 4 57
4 9.41 488 47 9. 43 007 OU 50 0.56 993 9.98 481 56 51 5.1 10.2 50 5.0 10.0
5 9.41 535 47 9.43 057 51 0.56 943 9.98 477 55 2
6 9. 41 582 46 9. 43 108 KA 0. 56 892 9. 98 474 o 54 3 15.3 15.0
7 9.41 628 47 9.43 158 KA 0.56 842 9. 98 471 o 53 4 20.4 20.0
8 9. 41 675 47 9. 43 208 KA 0. 56 792 9.98 467 4 52 5 25.5 25.0
9 9.41 722 46 9.43 258 OU 50 0.56 742 9.98 464 3 4 51 6 30.6 35.7 40.8 30.0 35.0 40.0
10 9.41 768 47 9.43 308 50 0. 56 692 9.98 460 50 8
11 9.41 815 46 9.43 358 50 KA 0.56 642 9.98 457 o 49 9 45.9 45.0
12 9.41 861 47 9.43 408 0.56 592 9.98 453 4 48
13 9.41 908 46 9.43 458 OU KA 0.56 542 9.98 450 3 47
14 9.41 954 47 9.43 508 OU 50 0.56 492 9. 98 447 3 4 46
15 9.42 001 46 9. 43 558 0.56 442 9.98 443 45 49 48
16 9.42 047 46 9.43 607 KA 0. 56 393 9.98 440 3 44 1 4.9 4.8
17 9.42 093 47 9.43 657 50 0. 56 343 9. 98 436 4 43 2 9.8 9.6
18 9. 42 140 46 9. 43 707 49 0.56 293 9.98 433 o 42 3 14.7 14.4
19 9.42 186 46 9.43 756 50 0.56 244 9. 98 429 4 3 41 4 5 6 19.6 24.5 29.4 19.2 24.0 28.8
20 9.42 232 46 9.43 806 49 0.56 194 9. 98 426 40
21 9.42 278 46 9.43 855 50 49 0. 56 145 9. 98 422 4 39 7 34.3 33.6
22 9.42 324 46 9.43 905 0. 56 095 9. 98 419 3 38 8 39.2 38.4
23 9.42 370 46 9.43 954 KA 0.56 046 9.98 415 37 9 44.1 43.2
24 9.42 416 45 9.44 004 49 0.55 996 9. 98 412 6 3 36
25 9.42 461 46 9.44 053 0.55 947 9. 98 409 35
26 27 9.42 507 9.42 553 46 46 9.44 102 9.44 151 49 KA 0.55 898 0.55 849 9. 98 405 9.98 402 4 3 34 33 47 46
28 9.42 599 45 9.44 201 OU 49 0.55 799 9.98 398 4 32 1 4.7 4.6
29 9.42 644 46 9.44 250 49 0.55 750 9.98 395 3 4 31 2 3 4 9.4 14.1 18.8 9.2 13.8 18.4
30 9.42 690 45 9.44 299 49 0. 55 701 9.98 391 30
31 9.42 735 46 9.44 348 49 0.55 652 9. 98 388 3 29 5 23.5 23.0
32 9.42 781 45 9. 44 397 X.Q 0.55 603 9. 98 384 4 28 6 28.2 27.6
33 9.42 826 46 9. 44 446 49 0. 55 554 9.98 381 3 27 7 32.9 32.2
34 9.42 872 45 9.44 495 49 0.55 505 9.98 377 4 4 26 8 37.6 42.3 36.8 41.4
35 9.42 917 45 9.44 544 XQ 0.55 456 9.98 373 25
36 9. 42 962 46 9.44 592 XQ 0.55 408 9.98 370 3 24
37 9.43 008 45 9. 44 641 XQ 0.55 359 9. 98 366 4 3 4 3 23
38 39 9.43 053 9.43 098 45 45 9.44 690 9.44 738 48 49 0.55 310 0.55 262 9. 98 363 9. 98 359 22 21 1 2 45 4.5 9.0 44 4.4 8.8
40 9.43 143 45 9. 44 787 49 0.55 213 9. 98 356 20
41 9.43 188 45 9. 44 836 48 49 0.55 164 9. 98 352 4 19 3 13.5 13.2
42 9.43 233 45 9. 44 884 0.55 116 9. 98 349 3 18 4 18.0 17.6
43 9.43 278 45 9.44 933 48 0.55 067 9.98 345 4 17 5 22.5 22.0
44 9. 43 323 44 9.44 981 48 0.55 019 9.98 342 3 4 16 6 7 8 27.0 31.5 36.0 26.4 30.8 35.2
45 9.43 367 45 9.45 029 49 0.54 971 9. 98 338 15
46 47 9.43 412 9.43 457 45 45 9. 45 078 9.45 126 48 ' XQ 0.54 922 0.54 874 9.98 334 9. 98 331 4 3 14 13 9 40.5 39.6
48 9. 43 502 44 9.45 174 48 49 0.54 826 9.98 327 4 12
49 9.43 546 45 9. 45 222 0.54 778 9.98 324 3 4 11
50 9.43 591 44 9. 45 271 48 0. 54 729 9.98 320 10 4 3
51 9. 43 635 45 9. 45 319 0.54 681 9. 98 317 3 9 1 0.4 0.3
52 53 9.43 680 9.43 724 44 45 9. 45 367 9.45 415 48 48 48 0.54 633 0. 54 585 9.98 313 9. 98 309 4 4 8 7 2 3 0.8 1.2 0.6 0.9
54 9.43 769 44 9.45 463 0. 54 537 9. 98 306 3 4 6 4 1.6 2.0 2.4 1.2 1.5 1.8
55 9.43 813 44 9.45 511 4ft 0. 54 489 9.98 302 5 6
56 9.43 857 44 9.45 559 47 0. 54 441 9. 98 299 3 4 7 2.8 2.1
57 9.43 901 45 9.45 606 4ft 0. 54 394 9.98 295 4 3 8 3.2 2.4
58 9.43 946 44 9.45 654 4ft 0.54 346 9.98 291 4 2 9 3.6 2.7
59 9.43 990 44 9.45 702 48 0. 54 298 9.98 288 3 4 1
60 9.44 034 9.45 750 0.54 250 9.98 284 0
L Sin L Tan L Cot L Cos 344°-, 164°-
d
CQ d
L Cos L Cot L Tan LSin 254°-, 74°-
56
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes-
Continued
16°-, 196°- / L Sin d L Tan cd L Cot L Cos d Prop. pts.
106°-, 286°- L Cos L Cot L Tan L Sin
0 1 2 3 4 9.44 034 9.44 078 9. 44 122 9.44 166 9. 44 210 44 44 44 44 43 44 44 44 43 44 44 43 43 44 43 44 43 43 43 43 43 44 43 42 43 43 43 43 43 42 43 42 43 42 43 42 43 42 42 42 43 42 42 42 42 42 42 42 41 42 42 42 41 42 41 42 41 42 41 42 9.45 750 9.45 797 9.45 845 9. 45 892 9.45 940 47 48 47 48 47 48 47 48 47 47 47 48 47 47 47 47 47 47 47 46 47 47 47 46 47 47 46 47 46 46 47 46 46 47 46 46 46 46 46 46 46 46 46 46 46 45 46 46 46 45 46 45 46 45 45 46 45 45 46 45 0.54 250 0. 54 203 0.54 155 0.54 108 0.54 060 9.98 284 9.98 281 9.98 277 9. 98 273 9. 98 270 3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 4 3 4 4 4 3 4 4 4 3 4 4 4 3 4 4 4 3 4 4 4 4 3 4 4 4 4 4 3 4 4 4 4 4 4 3 60 59 58 57 56 48 47 1 4.8 4.7 2 9.6 9.4 3 14.4 14.1 4 19.2 18.8 5 24.0 23.5 6 28.8 28.2 7 33.6 32.9 8 38.4 37.6 9 43.2 42.3 46 45 1 4.6 4.5 2 9.2 9.0 3 13.8 13.5 4 18.4 18.0 5 23.0 22.5 6 27.6 27.0 7 32.2 31.5 8 36.8 36.0 9 41.4 40.5 44 43 1 4.4 4.3 2 8.8 8.6 3 13.2 12.9 4 17.6 17.2 5 22.0 21.5 6 26.4 25.8 7 30.8 30.1 8 35.2 34.4 9 39.6 38.7 42 41 1 4.2 4.1 2 8.4 8.2 3 12.6 12.3 4 16.8 16.4 5 21.0 20.5 6 25.2 24.6 7 29.4 28.7 8 33.6 32.8 9 37.8 36.9 4 3 1 0.4 0.3 2 0.8 0.6 3 1.2 0.9 4 1.6 1.2 5 2.0 1.5 6 2.4 1.8 7 2.8 2.1 8 3.2 2.4 9 3.6 2.7
5 6 7 8 9 9. 44 253 9. 44 297 9. 44 341 9. 44 385 9. 44 428 9.45 987 9.46 035 9.46 082 9. 46 130 9. 46 177 0. 54 013 0. 53 965 0. 53 918 0. 53 870 0.53 823 9.98 266 9.98 262 9.98 259 9. 98 255 9.98 251 55 54 53 52 51
10 11 12 13 14 9- 44 472 9. 44 516 9.44 559 9.44 602 9.44 646 9.46 224 9. 46 271 9. 46 319 9.46 366 9. 46 413 0.53 776 0.53 729 0. 53 681 0. 53 634 0.53 587 9.98 248 9.98 244 9. 98 240 9.98 237 9.98 233 50 49 48 47 46
15 16 17 18 19 9. 44 689 9.44 733 9.44 776 9. 44 819 9.44 862 9.46 460 9. 46 507 9. 46 554 9.46 601 9. 46 648 0.53 540 0.53 493 0. 53 446 0. 53 399 0. 53 352 9. 98 229 9. 98 226 9.98 222 9. 98 218 9. 98 215 45 44 43 42 41
20 21 22 23 24 9.44 905 9.44 948 9.44 992 9. 45 035 9.45 077 9.46 694 9. 46 741 9.46 788 9. 46 835 9.46 881 0.53 306 0.53 259 0. 53 212 0. 53 165 0. 53 119 9.98 211 9. 98 207 9. 98 204 9.98 200 9. 98 196 40 39 38 37 36
25 26 27 28 29 9. 45 120 9. 45 163 9. 45 206 9.45 249 9.45 292 9. 46 928 9. 46 975 9.47 021 9.47 068 9.47 114 0.53 072 0. 53 025 0. 52 979 0. 52 932 0. 52 886 9.98 192 9.98 189 9.98 185 9.98 181 9.98 177 35 34 33 32 31
30 31 32 33 34 9.45 334 9. 45 377 9.45 419 9.45 462 9.45 504 9.47 160 9.47 207 9.47 253 9. 47 299 9.47 346 0.52 840 0.52 793 0. 52 747 0. 52 701 0. 52 654 9.98 174 9.98 170 9.98 166 9.98 162 9.98 159 30 29 28 27 26
35 36 37 38 39 9.45 547 9. 45 589 9.45 632 9.45 674 9. 45 716 9.47 392 9.47 438 9.47 484 9.47 530 9.47 576 0. 52 608 0. 52 562 0. 52 516 0. 52 470 0.52 424 9.98 155 9.98 151 9. 98 147 9. 98 144 9.98 140 25 24 23 22 21
40 41 42 43 44 9.45 758 9.45 801 9. 45 843 9. 45 885 9.45 927 9.47 622 9. 47 668 9.47 714 9.47 760 9.47 806 0. 52 378 0. 52 332 0 52 286 0. 52 240 0. 52 194 9.98 136 9. 98 132 9.98 129 9. 98 125 9. 98 121 20 19 18 17 16
45 46 47 48 49 9.45 969 9.46 011 9.46 053 9.46 095 9. 46 136 9.47 852 9.47 897 9. 47 943 9. 47 989 9.48 035 0. 52 148 0. 52 103 0. 52 057 0. 52 011 0.51 965 9.98 117 9.98 113 9.98 110 9. 98 106 9.98 102 15 14 13 12 11
50 51 52 53 54 9 46 178 9.46 220 9.46 262 9.46 303 9.46 345 9.48 080 9. 48 126 9.48 171 9.48 217 9.48 262 0. 51 920 0.51 874 0. 51 829 0.51 783 0.51 738 9.98 098 9.98 094 9. 98 090 9. 98 087 9.98 083 10 9 8 7 6
55 56 57 58 59 9.46 386 9.46 428 9.46 469 9. 46 511 9.46 552 9.48 307 9.48 353 9.48 398 9.48 443 9.48 489 0.51 693 0.51 647 0.51 602 0.51 557 0.51 511 9.98 079 9.98 075 9. 98 071 9.98 067 9.98 063 5 4 3 2 1
60 9.46 594 9.48 534 0.51 466 9.98 060 0
L Sin d L Tan cd L Cot L Cos d / 343°-, 163°-
L Cos L Cot L Tan L Sin 253°-, 73°-
57
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
17°-, 197°- L Sin L Tan L Cot L Cos
— f — d — cd — d Prop. pts.
107°-, 287°- L Cos L Cot L Tan L Sin
0 9.46 594 41 9.48 534 45 0. 51 466 9.98 060 60
1 9. 46 635 41 9. 48 579 AR 0. 51 421 9. 98 056 4 59
2 9. 46 676 41 9. 48 624 0. 51 376 9. 98 052 4 58
3 9.46 717 41 9.48 669 A 0. 51 331 9. 98 048 4 57
4 9. 46 758 42 9. 48 714 45 0.51 286 9.98 044 4 4 56 45 44
9.46 800 ■ ■ — ■ — 1 4.5 4.4
b 41 9.48 759 45 0. 51 241 9. 98 040 A 55 2 9.0 8.8
6 9. 46 841 41 9. 48 804 45 0.51 196 9. 98 036 A 54 3 13.5 13.2
7 9.46 882 41 9.48 849 45 45 0.51 151 9. 98 032 4 Q 53 4 18.0 17.6
8 9.46 923 41 9.48 894 0.51 106 9. 98 029 o A 52 5 22.5 22.0
9 9.46 964 41 9.48 939 45 0. 51 061 9. 98 025 4 4 51 6 27.0 26.4
9.47 005 - - ———— 7 31.5 30.8
10 40 9. 48 984 45 0. 51 016 9. 98 021 A 50 8 36.0 35.2
11 9.47 045 41 9. 49 029 44 0. 50 971 9. 98 017 4 A 49 9 40.5 39.6
12 9.47 086 41 9.49 073 45 0. 50 927 9. 98 013 4 A 48
13 9.47 127 41 9.49 118 45 0. 50 882 9. 98 009 4 47
14 9. 47 168 41 9. 49 163 44 0.50 837 9. 98 005 4 4 46
15 9. 47 209 40 9. 49 207 45 0. 50 793 9. 98 001 A 45 43 42
16 9.47 249 41 9.49 252 44 0. 50 748 9. 97 997 4 A 44 1 4.3 4.2
17 9. 47 290 40 9. 49 296 45 0. 50 704 9. 97 993 4 A 43 2 8.6 8.4
18 9.47 330 41 9.49. 341 44 0. 50 659 9. 97 989 4 Q 42 3 12.9 12.6
19 9.47 371 40 9.49 385 45 0. 50 615 9. 97 986 O 4 41 4 17.2 16.8
9. 47 411 — • — 5 21.5 21.0
20 41 9.49 430 44 0. 50 570 9. 97 982 40 6 25.8 25.2
21 9.47 452 40 9.49 474 45 0. 50 526 9. 97 978 4 39 7 30.1 29.4
22 9.47 492 41 9. 49 519 44 0. 50 481 9. 97 974 4 A 38 8 34.4 33.6
23 9.47 533 40 9. 49 563 44 0. 50 437 9. 97 970 4 A 37 9 38.7 37.8
24 9. 47 573 40 9.49 607 45 0. 50 393 9.97 966 4 4 36
9.47 613 ■
25 41 9. 49 652 44. 0. 50 348 9. 97 962 A 35
• 26 9.47 654 40 9. 49 696 AA 0. 50 304 9. 97 958 4 34
27 9.47 694 40 9. 49 740 44 0. 50 260 9. 97 954 4 33 41 40
28 9.47 734 40 9. 49 784 44 0. 50 216 9. 97 950 4 A 32 1 4.1 4.0
29 9. 47 774 40 9.49 828 44 0.50 172 9. 97 946 4 4 31 2 8.2 8.0
30 9.47 814 3 12.3 12.0
40 9.49 872 44 0. 50 128 9. 97 942 A 30 4 16.4 16.0
31 9.47 854 40 9.49 916 44 0. 50 084 9. 97 938 4 A 29 5 20.5 20.0
32 9.47 894 40 9. 49 960 44 0. 50 040 9. 97 934 4 A 28 6 24.6 24.0
33 9. 47 934 40 9. 50 004 44 0.49 996 9. 97 930 4 A 27 7 28.7 28.0
34 9.47 974 40 9.50 048 44 0.49 952 9.97 926 4 4 26 8 32.8 32.0
9.48 014 —.— 9 36.9 36.0
3b 40 9. 50 092 44 0.49 908 9. 97 922 A 25
36 9.48 054 40 9. 50 136 44 0. 49 864 9. 97 918 4 A 24
37 9.48 094 39 9. 50 180 43 AA 0.49 820 9. 97 914 4 A 23
38 9.48 133 40 9. 50 223 0. 49 777 9.97 910 4 22 39
39 9.48 173 40 9. 50 267 Wk 44 0.49 733 9.97 906 4 4 21 5
9.48 213 . 1 3.9 0.5
40 39 9. 50 311 44 0. 49 689 9. 97 902 A 20 2 7.8 1.0
41 9.48 252 40 9. 50 355 43 44 0.49 645 9. 97 898 4 A 19 3 11.7 1.5
42 9. 48 292 40 9. 50 398 0.49 602 9. 97 894 4 A 18 4 15.6 2.0
43 9. 48 332 39 9. 50 442 43 44 0.49 558 9. 97 890 4 A 17 5 19.5 2.5
44 9. 48 371 40 9. 50 485 0.49 515 9. 97 886 4 4 16 6 23.4 3.0
9.48 411 7 27.3 3.5
45 39 9. 50 529 43 0.49 471 9. 97 882 A 15 8 31.2 4.0
46 9.48 450 40 9. 50 572 44 0.49 428 9. 97 878 4 A 14 9 35.1 4.5
47 9.48 490 39 9. 50 616 0.49 384 9. 97 874 4 13
48 9. 48 529 39 9. 50 659 44 0.49 341 9.97 870 4 12
49 9. 48 568 39 9. 50 703 43 0.49 297 9. 97 866 4 5 11
50 9. 48 607 40 9. 50 746 4Q 0.49 254 9. 97 861 10 4 3
51 9.48 647 39 9. 50 789 44 0.49 211 9. 97 857 4 A 9 1 0.4 0.3
52 9.48 686 39 9. 50 833 43 43 43 0.49 167 9. 97 853 4 A 8 2 0.8 0.6
53 9.48 725 39 9. 50 876 0.49 124 9. 97 849 4 A 7 3 1.2 0.9
54 9.48 764 39 9. 50 919 0.49 081 9.97 845 4 4 6 4 1.6 1.2
9.48 803 5 2.0 1.5
55 39 9. 50 962 4Q 0.49 038 9.97 841 5 6 2.4 1.8
56 9.48 842 39 39 9. 51 005 ,19 0. 48 995 9. 97 837 4 4 7 2.8 2.1
57 9.48 881 9.51 048 AA 0.48 952 9. 97 833 4 3 8 3.2 2.4
58 9.48 920 39 39 9. 51 092 44 AH 0.48 908 9.97 829 4 2 9 3.6 2.7
59 60 9.48 959 9.48 998 9.51 135 9.51 178 40 43 0.48 865 0.48 822 9.97 825 9.97 821 4 4 1 0
L Sin L Tan L Cot L Cos 342°-, 162°-
— d — cd — d / —
L Cos L Cot L Tan L Sin 252°-, 72°-
58
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—-
Continued
18°-, 198°- / L Sin d L Tan cd L Cot L Cos d Prop. pts.
108°-, 288°- L Cos L Cot L> Tan L Sin
0 9.48 998 39 39 QQ 9.51 178 43 0.48 822 9.97 821 A 60
1 9.49 037 9.51 221 0.48 779 9.97 817 d 59
2 9.49 076 9. 51 264 0.48 736 9.97 812 0 A 58 43 42
3 9.49 115 9Q 9. 51 306 43 0. 48 694 9.97 808 A 57 1 4.3 8.6 2.9 4.2 8.4 12.6 16.8 21.0 25.2 29.4 33.6 37.8
4 5 9.49 153 9. 49 192 39 39 qq 9.51 349 9.51 392 43 43 49 0.48 651 0.48 608 9.97 804 9. 97 800 d 4 A 56 55 1 2 3
6 9.49 231 9.51 435 0.48 565 9. 97 796 A 54 K 21.5 25.8 30.1 34.4 38.7
7 9.49 269 QQ 9.51 478 49 0.48 522 9.97 792 d: A 53
8 9.49 308 39 38 39 9.51 520 43 0.48 480 9.97 788 d A 52 D 7
9 10 9.49 347 9. 49 385 9.51 563 9. 51 606 43 42 43 43 49 0. 48 437 0.48 394 9. 97 784 9.97 779 d 5 A 51 50 8 9
11 9.49 424 38 38 on 9.51 648 0.48 352 9.97 775 A 49
12 9.49 462 9. 51 691 0.48 309 9.97 771 ek A 48
13 9. 49 500 9.51 734 0. 48 266 9.97 767 *1 A 47
14 9. 49 539 38 9.51 776 43 0.48 224 9.97 763 d 4 46 1 4.1
15 9. 49 577 38 39 9. 51 819 42 0.48 181 9.97 759 K 45 8.2
16 9.49 615 9.51 861 49 0.48 139 9.97 754 0 A 44 12.3
17 9.49 654 9. 51 903 4Q 0.48 097 9.97 750 d A 43 16.4
• 18 9.49 692 38 38 9. 51 946 42 43 0.48 054 9. 97 746 d A 42 20.5
19 9.49 730 9. 51 988 0.48 012 9.97 742 d 4 41 6 7 24.6 28.7
20 9.49 768 qo 9. 52 031 42 0.47 969 9.97 738 A 40 8 32.8
21 9.49 806 22 9. 52 073 0.47 927 9. 97 734 d K 39 9 36.9
22 9.49 844 oo 22 9.52 115 42 4Q 0. 47 885 9.97 729 O A 38
23 9.49 882 22 9.52 157 0.47 843 9.97 725 A 37
24 9. 49 920 38 9.52 200 42 0.47 800 9.97 721 d 4 36 39 38
25 9.49 958 22 9. 52 242 42 42 0. 47 758 9.97 717 A 35 3.9 3.8 7.6 11.4 15.2 19.0 22.8 26.6 30.4 34.2
26 9.49 996 OO 22 9.52 284 0.47 716 9.97 713 d 34
27 9. 50 034 22 9. 52 326 0.47 674 9. 97 708 O A 33 11.7 15.6 19.5 23.4 27.3
28 9.50 072 OO 22 9.52 368 49 0. 47 632 9.97 704 A 32 4
29 30 9. 50 110 9. 50 148 38 27 9.52 410 9.52 452 42 49 0.47 590 0.47 548 9. 97 700 9. 97 696 4 K 31 30 5 6 7
31 9.50 185 22 9. 52 494 0.47 506 9. 97 691 O A 29
32 9. 50 223 oo 22 9. 52 536 42 0.47 464 9.97 687 4 4 28 9 QK 1
33 9. 50 261 27 9.52 578 42 41 0.47 422 9.97 683 A 27
34 35 9. 50 298 9. 50 336 OZ 38 38 27 9.52 620 9.52 661 0.47 380 0.47 339 9.97 679 9.97 674 d 5 A 26 25
36 9.50 374 9. 52 703 42 42 42 41 0.47 297 9.97 670 4 A 24 07 36
37 9. 50 411 oZ 22 9.52 745 0.47 255 9.97 666 4 A 23 oi
38 ‘ 39 9. 50 449 9. 50 486 Oo 37 37 9. 52 787 9.52 829 0.47 213 0.47 171 9.97 662 9.97 657 4 5 4 22 21 1 2 3 3.7 7.4 11.1 3.6 7.2 10.8
40 9.50 523 22 9. 52 870 42 0. 47 130 9. 97 653 A 20 4 14.8 14.4
41 9. 50 561 OO 27 9.52 912 0.47 088 9.97 649 4 A 19 5 18.5 18.0
42 9. 50 598 OZ 27 9. 52 953 42 42 41 0. 47 047 9.97 645 4 18 6 22.2 21.6
43 44 9. 50 635 9.50 673 OZ 38 37 9.52 995 9. 53 037 0.47 005 0.46 963 9.97 640 9.97 636 O 4 4 17 16 7 8 9 25.9 29.6 33.3 25.2 28.8 32.4
45 9. 50 710 27 9. 53 078 0. 46 922 9.97 632 4 15
46 9. 50 747 OZ 27 9. 53 120 41 0.46 880 9.97 628 5 14
47 9. 50 784 OZ 27 9. 53 161 41 0.46 839 9.97 623 4 13
48 9. 50 821 OZ 27 9.53 202 42 41 0.46 798 9.97 619 4 12
49 9. 50 858 OZ 38 9.53 244 0. 46 756 9.97 615 5 11
50 9. 50 896 9. 53 285 0.46 715 9.97 610 A 10 0.5 1.0 1 5 0.4 0.8
51 9.50 933 OZ 27 9. 53 327 0.46 673 9.97 606 4 A 9
52 9. 50 970 OZ 27 9.53 368 41 0.46 632 9.97 602 4 § 8 3
53 9. 51 007 2A 9.53 409 41 0.46 591 9.97 597 4 7 4 2 0 1 fl
54 55 9.51 043 9. 51 080 37 27 9.53 450 9. 53 492 42 41 0.46 550 0.46 508 9.97 593 9.97 589 4 5 6 5 5 6 7 2.5 3.0 3 5 2.0 2.4 2 8
56 9.51 117 37 9.53 533 41 0. 46 467 9. 97 584 4 4 g 4 0 3 2
57 9.51 154 27 9.53 574 41 0.46 426 9.97 580 4 3 g 4.5 3.6
58 9.51 191 2A 9. 53 615 0.46 385 9.97 576 2
59 ' 60 9.51 227 9.51 264 00 37 9.53 656 9.53 697 41 0.46 344 0.46 303 9.97 571 9.97 567 O 4 1 0
L Sin L Tan L Cot L Cos 341°-, 161°-
— d — cd d / —
L Cos L Cot L Tan LSin 251°-, n°-
59
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
19°-, 199°- 109°-, 289°- / L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9. 51 264 9.51 301 9.51 338 9.51 374 9. 51 411 9.51 447 9. 51 484 9.51 520 9.51 557 9.51 593 9.51 629 9.51 666 9.51 702 9.51 738 9.51 774 9.51 811 9.51 847 9. 51 883 9. 51 919 9.51 955 9. 51 991 9. 52 027 9.52 063 9. 52 099 9.52 135 9.52 171 9.52 207 9. 52 242 9. 52 278 9. 52 314 9.52 350 9. 52 385 9. 52 421 9. 52 456 9.52 492 9.52 527 9. 52 563 9. 52 598 9.52 634 9.52 669 9. 52 705 9. 52 740 9.52 775 9. 52 811 9.52 846 9. 52 881 9. 52 916 9. 52 951 9.52 986 9.53 021 9. 53 056 9.53 092 9.53 126 9.53 161 9.53 196 9. 53 231 9.53 266 9. 53 301 9.53 336 9.53 370 9. 53 405 37 37 36 37 36 37 36 37 36 36 37 36 36 36 37 36 36 36 36 36 36 36 36 36 36 36 35 36 36 36 35 36 35 36 35 36 35 36 35 36 35 35 36 35 35 35 35 35 35 35 36 34 35 35 35 35 35 35 34 35 9. 53 697 9.53 738 9.53 779 9. 53 820 9.53 861 9. 53 902 9. 53 943 9. 53 984 9. 54 025 9. 54 065 9.54 106 9. 54 147 9.54 187 9. 54 228 9. 54 269 9. 54 309 9. 54 350 9.54 390 9.54 431 9. 54 471 9. 54 512 9. 54 552 9. 54 593 9.54 633 9.54 673 9.54 714 9. 54 754 9.54 794 9. 54 835 9.54 875 9. 54 915 9. 54 955 9.54 995 9.55 035 9.55 075 9.55 115 9. 55 155 9. 55 195 9. 55 235 9.'55 275 9. 55 315 9.55 355 9. 55 395 9.55 434 9.55 474 9. 55 514 9.55 554 9.55 593 9. 55 633 9.55 673 9.55 712 9. 55 752 9.55 791 9. 55 831 9.55 870 9.55 910 9. 55 949 9. 55 989 9. 56 028 9. 56 067 9. 56 107 41 41 41 41 41 41 41 41 40 41 41 40 41 41 40 41 40 41 40 41 40 41 40 40 41 40 40 41 40 40 40 40 40 40 40 40 40 40 40 40 40 40 39 40 40 40 39 40 40 39 40 39 40 39 40 39 40 39 39 40 0.46 303 0.46 262 0.46 221 0.46 180 0.46 139 0.46 098 0.46 057 0.46 016 0.45 975 0.45 935 0.45 894 0. 45 853 0.45 813 0.45 772 0.45 731 0.45 691 0.45 650 0.45 610 0. 45 569 0.45 529 0.45 488 0.45 448 0.45 407 0.45 367 0.45 327 0.45 286 0.45 246 0.45 206 0.45 165 0.45 125 0.45 085 0.45 045 0.45 005 0.44 965 0.44 925 0.44 885 0.44 845 0.44 805 0.44 765 0.44 725 0. 44 685 0.44 645 0.44 605 0.44 566 0.44 526 0.44 486 0.44 446 0.44 407 0.44 367 0.44 327 0.44 288 0.44 248 0. 44 209 0.44 169 0.44 130 0.44 090 0.44 051 0. 44 011 0.43 972 0.43 933 0.43 893 9. 97 567 9.97 563 9. 97 558 9.97 554 9. 97 550 9. 97 545 9. 97 541 9.97 536 9.97 532 9.97 528 9.97 523 9.97 519 9.97 515 9.97 510 9.97 506 9. 97 501 9.97 497 9.97 492 9. 97 488 9.97 484 9.97 479 9. 97 475 9. 97 470 9.97 466 9.97 461 9.97 457 9.97 453 9. 97 448 9. 97 444 9.97 439 9.97 435 9. 97 430 9.97 426 9. 97 421 9.97 417 9.97 412 9.97 408 9. 97 403 9. 97 399 9. 97 394 9. 97 390 9.97 385 9.97 381 9.97 376 9.97 372 9.97 367 9.97 363 9. 97 358 9.97 353 9.97 349 9.97 344 9.97 340 9.97 335 9.97 331 9.97 326 9.97 322 9.97 317 9.97 312 9.97 308 9. 97 303 9.97 299 4 5 4 4 5 4 5 4 4 5 4 4 5 4 5 4 5 4 4 5 4 5 4 5 4 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 4 5 5 4 5 4 5 4 5 4 5 5 4 5 4 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 41 40 1 4.1 4.0 2 8.2 8.0 3 12.3 12.0 4 16.4 16.0 5 20.5 20.8 6 24.6 24.0 7 28.7 28.0 8 32.8 32.0 9 36.9 36.0 39 1 3.9 2 7.8 3 11.7 4 15.6 5 19.5 6 23.4 7 27.3 8 31.2 9 35.1 37 36 1 3.7 3.6 2 7.4 7.2 3 11.1 10.8 4 14.8 14.4 5 18.5 18.0 6 22.2 21.6 7 25.9 25.2 8 29.6 28.8 9 33.3 32.4 35 34 1 3.5 3.4 2 7.0 6.8 3 10.5 10.2 4 14.0 13.6 5 17.5 17.0 6 21.0 20.4 7 24.5 23.8 8 28.0 27.2 9 31.5 30.6 5 4 1 0.5 0.4 2 1.0 0.8 3 1.5 1.2 4 2.0 1.6 5 2.5 2.0 6 3.0 2.4 7 3.5 2.8 8 4.0 3.2 9 4.5 3.6
L Sin L Cos d LTan L Cot < cd L Cot L Tan L Cos L Sin d / 340°-, 160°- 250°-, 70°-
60
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
20°-, 200°- 110°-, 290°- / L Sih L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9. 53 405 9. 53 440 9. 53 475 9. 53 509 9. 53 544 9. 53 578 9. 53 613 9. 53 647 9. 53 682 9.53 716 9. 53 751 9. 53 785 9. 53 819 9. 53 854 9. 53 888 9. 53 922 9. 53 957 9. 53 991 9. 54 025 9. 54 059 9. 54 093 9. 54 127 9. 54 161 9. 54 195 9. 54 229 9. 54 263 9. 54 297 9. 54 331 9. 54 365 9. 54 399 9. 54 433 9. 54 466 9. 54 500 9. 54 534 9. 54 567 9. 54 601 9. 54 635 9. 54 668 9. 54 702 9. 54 735 9. 54 769 9. 54 802 9. 54 836 9. 54 869 9. 54 903 9. 54 936 9. 54 969 9. 55 003 9. 55 036 9. 55 069 9. 55 102 9. 55 136 9.55 169 9. 55 202 9. 55 235 9. 55 268 9. 55 301 9. 55 334 9. 55 367 9. 55 400 9. 55 433 35 35 34 35 34 35 34 35 34 35 34 34 35 34 34 35 34 34 34 34 34 34 34 34 34 34 34 34 34 34 33 34 34 33 ' 34 34 33 34 33 34 33 34 33 34 33 33 34 33 33 33 34 33 33 33 33 33 33 33 33 33 9. 56 107 9. 56 146 9.56 185 9. 56 224 9. 56 264 9. 56 303 9. 56 342 9. 56 381 9. 56 420 9. 56 459 9. 56 498 9. 56 537 9. 56 576 9. 56 615 9. 56 654 9. 56 693 9. 56 732 9. 56 771 9. 56 810 9. 56 849 9. 56 887 9. 56 926 9. 56 965 9. 57 004 9. 57 042 9. 57 081 9. 57 120 9. 57 158 9. 57 197 9. 57 235 9. 57 274 9. 57 312 9. 57 351 9. 57 389 9. 57 428 9. 57 466 9. 57 504 9. 57 543 9. 57 581 9. 57 619 9. 57 658 9. 57 696 9. 57 734 9. 57 772 9. 57 810 9. 57 849 9. 57 887 9. 57 925 9. 57 963 9. 58 001 9. 58 039 9. 58 077 9. 58 115 9.58 153 9. 58 191 9. 58 229 9.58 267 9. 58 304 9. 58 342 9. 58 380 9.58 418 39 39 39 40 39 39 39 39 39 39 39 39 39 39 39 39 39 39 39 38 39 39 39 38 39 39 38 39 38 39 38 39 38 39 38 38 39 38 38 39 38 38 38 38 39 38 38 38 38 38 38 38 38 38 38 38 37 38 38 38 0.43 893 0.43 854 0.43 815 0.43 776 0.43 736 0. 43 697 0.43 658 0.43 619 0.43 580 0.43 541 0.43 502 0.43 463 0.43 424 0.43 385 0.43 346 0.43 307 0.43 268 0.43 229 0.43 190 0.43 151 0.43 113 0.43 074 0.43 035 0.42 996 0.42 958 0.42 919 0.42 880 0.42 842 0.42 803 0.42 765 0.42 726 0.42 688 0.42 649 0.42 611 0.42 572 0.42 534 0.42 496 0.42 457 0.42 419 0.42 381 0.42 342 0.42 304 0.42 266 0.42 228 0.42 190 0.42 151 0.42 113 0.42 075 0.42 037 0.41 999 0.41 961 0.41 923 0.41 885 0.41 847 0.41 809 0.41 771 0.41 733 0. 41 696 0.41 658 0. 41 620 0.41 582 9.97 299 9.97 294 9.97 289 9.97.285 9.97 280 9.97 276 9.97 271 9. 97 266 9. 97 262 9.97 257 9.97 252 9.97 248 9.97 243 9.97.238 9.97 234 9.97 229 9.97 224 9. 97 220 9.97 215 9.97 210 9.97 206 9. 97 201 9.97 196 9 97 192 9.97 187 9. 97 182 9.97 178 9.97 173 9.97 168 9.97 163 9.97 159 9.97 154 9.97 149 9. 97 145 9. 97 140 9.97 135 9.97 130 9.97 126 9.97 121 9. 97 116 9.97 111 9.97 107 9.97 102 9.97 097 9.97 092 9.97 087 9.97 083 9.97 078 9.97 073 9.97 068 9. 97 063 9.97 059 9.97 054 9.97 049 9.97 044 9.97 039 9.97 035 9. 97 030 9. 97 025 9.97 020 9.97 015 5 5 4 5 4 5 5 4 5 5 4 5 5 4 5 5 4 5 5 4 5 5 4 5 5 4 5 5 5 4 5 5 4 5 5 5 4 5 5 5 4 5 5 5 5 4 5 5 5 5 4 5 5 5 5 4 5 5 5 5 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 40 39 1 4.0 3.9 2 8.0 7.8 3 12.0 11.7 4 16.0 15.6 5 20.0 19.5 6 24.0 23.4 7 28.0 27.3 8 32.0 31.2 9 36.0 35.1 38 37 1 3.8 3.7 2 7.6 7.4 3 11.4 11.1 4 15.2 14.8 5 19.0 18.5 6 22.8 22.2 7 26.6 25.9 8 30.4 29.6 9 34.2 33.3 35 1 3.5 2 7.0 3 10.5 4 14.0 5 17.5 6 21.0 7 24.5 8 28.0 9 31.5 34 33 1 3.4 3.3 2 6.8 6.6 3 10.2 9.9 4 13.6 13.2 5 17.0 16.5 6 20.4 19.8 7 23.8 23.1 8 27.2 26.4 9 30.6 29.7 5 4 1 0.5 0.4 2 1.0 0.8 3 1.5 1.2 4 2.0 1.6 5 2.5 2.0 6 3.0 2.4 7 3.5 2.8 8 4.0 3.2 9 4.5 3.6
L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d / 339°-, 159°- 249°-, 69°-
609023°—44---5
61
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
21°-, 201°- 111°-, 291°- f L Sin L Cos - d L Tan L Cot cd L Cot L Tan L Cos L Sin - d Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9. 55 433 9. 55 466 9. 55 499 9. 55 532 9. 55 564 9. 55 597 9. 55 630 9. 55 663 9. 55 695 9. 55 728 9. 55 761 9. 55 793 9. 55 826 9. 55 858 9. 55 891 9. 55 923 9. 55 956 9. 55 988 9. 56 021 9. 56 053 9. 56 085 9. 56 118 9. 56 150 9. 56 182 9. 56 215 9. 56 247 9. 56 279 9. 56 311 9. 56 343 9. 56 375 9. 56 408 9. 56 440 9. 56 472 9. 56 504 9. 56 536 9. 56 568 9. 56 599 9. 56 631 9. 56 663 9. 56 695 9. 56 727 9. 56 759 9. 56 790 9. 56 822 9. 56 854 9. 56 886 9. 56 917 9. 56 949 9. 56 980 9. 57 012 9. 57 044 9. 57 075 9. 57 107 9. 57 138 9. 57 169 9. 57 201 9. 57 232 9. 57 264 9. 57 295 9. 57 326 9. 57 358 33 33 33 32 33 33 33 32 33 33 32 33 32 33 32 33 32 33 32 32 33 32 32 33 32 32 32 32 32 33 32 32 32 32 32 31 32 32 32 32 32 31 32 32 32 31 32 31 32 32 31 32 31 31 32 31 32 31 31 32 9. 58 418 9. 58 455 9. 58 493 9. 58 531 9. 58 569 9. 58 606 9. 58 644 9. 58 681 9. 58 719 9. 58 757 9. 58 794 9. 58 832 9. 58 869 9. 58 907 9. 58 944 9. 58 981 9. 59 019 9. 59 056 9. 59 094 9. 59 131 9. 59 168 9. 59 205 9. 59 243 9. 59 280 9. 59 317 9. 59 354 9. 59 391 9. 59 429 9. 59 466 9. 59 503 9. 59 540 9. 59 577 9. 59 614 9. 59 651 9. 59 688 9. 59 725 9. 59 762 9. 59 799 9. 59 835 9. 59 872 9. 59 909 9. 59 946 9. 59 983 9. 60 019 9. 60 056 9. 60 093 9. 60 130 9. 60 166 9. 60 203 9. 60 240 9. 60 276 9. 60 313 9. 60 349 9. 60 386 9. 60 422 9. 60 459 9.60 495 9. 60 532 9. 60 568 9. 60 605 9.60 641 37 38 38 38 37 38 37 38 38 37 38 37 38 37 37 38 37 38 37 37 37 38 37 37 37 37 38 37 37 37 37 37 37 37 37 37 37 36 37 37 37 37 36 37 37 37 36 37 37 36 37 36 37 36 37 36 37 36 37 36 0.41 582 0.41 545 0.41 507 0. 41 469 0.41 431 0.41 394 0.41 356 0.41 319 0.41 281 0.41 243 0. 41 206 0.41 168 0.41 131 0.41 093 0. 41 056 0.41 019 0. 40 981 0.40 944 0. 40 906 0. 40 869 0.40 832 0.40 795 0.40 757 0. 40 720 0. 40 683 0. 40 646 0. 40 609 0.40 571 0. 40 534 0.40 497 0.40 460 0. 40 423 0. 40 386 0. 40 349 0. 40 312 0.40 275 0.40 238 0.40 201 0.40 165 0.40 128 0.40 091 0. 40 054 0.40 0J7 0. 39 981 0.39 944 0.39 907 0. 39 870 0. 39 834 0. 39 797 0.39 760 0.39 724 0. 39 687 0. 39 651 0. 39 614 0. 39 578 0. 39 541 0. 39 505 0. 39 468 0. 39 432 0. 39 395 0. 39 359 9.97 015 9.97 010 9.97 005 9.97 001 9.96 996 9. 96 991 9. 96 986 9.96 981 9. 96 976 9. 96 971 9.96 966 9. 96 962 9. 96 957 9. 96 952 9.96 947 9.96 942 9. 96 937 9. 96 932 9. 96 927 9. 96 922 9. 96 917 9.96 912 9. 96 907 9. 96 903 9. 96 898 9. 96 893 9. 96 888 9. 96 883 9. 96 878 9. 96 873 9. 96 868 9. 96 863 9. 96 858 9. 96 853 9. 96 848 9. 96 843 9. 96 838 9.96 833 9. 96 828 9. 96 823 9.96 818 9. 96 813 9. 96 808 9. 96 803 9. 96 798 9. 96 793 9. 96 788 9. 96 783 9. 96 778 9. 96 772 9. 96 767 9. 96 762 9.96 757 9.96 752 9. 96 747 9. 96 742 9. 96 737 9. 96 732 9. 96 727 9. 96 722 9.96 717 5 5 4 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 38 37 1 3.8 3.7 2 7.6 7.4 3 11.4 11.1 4 15.2 14.8 5 19.0 18.5 6 22.8 22.2 7 26.6 25.9 8 30.4 29.6 9 34.2 33.3 36 33 1 3.6 3.3 2 7.2 6.6 3 10.8 9.9 4 14.4 13.2 5 18.0 16.5 6 21.6 19.8 7 25.2 23.1 8 28.8 26.4 9 32.4 29.7 32 1 3.2 2 6.4 3 9.6 4 12.8 5 16.0 6 19.2 7 22.4 8 25.6 9 28.8 31 6 1 3.1 0.6 2 6.2 1.2 3 9.3 1.8 4 12.4 2.4 5 15. 5 3.0 6 18.6 3.6 7 21. 7 4.2 8 24.8 4.8 9 27.9 5.4 5 4 1 0.5 0.4 2 1.0 0.8 3 1.5 1.2 4 2.0 1.6 5 2.5 2.0 6 3.0 2.4 7 3.5 2.8 8 4.0 3.2 9 4.5 | 3.6
L Sin L Cos d L Tan L Cot J cd L Cot L Cos d / 338°-, 158°-
L Tan L Sin 248°-, 68°-
62
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
22°-, 202°- t L Sin d L Tan ed L Cot L Cos d Prop. pts.
112°-, 292°- L Cos L Cot L Tan L Sin
0 1 2 3 4 9. 57 358 9. 57 389 9. 57 420 9. 57 451 9. 57 482 31 31 31 31 32 31 31 31 31 31 31 31 31 31 31 31 30 31 31 31 30 31 31 31 30 31 30 31 30 31 30 31 30 31 30 31 30 30 30 31 30 30 30 31 30 30 30 30 30 30 30 30 30 30 30 30 29 30 ' 30 30 9. 60 641 9.60 677 9.60 714 9 60 750 9.60 786 36 37 36 1 36 36 36 36 37 36 36 36 36 36 36 36 36 36 36 36 36 36 36 36 35 36 36 36 35 36 36 36 35 36 35 36 36 35 36 35 36 35 36 35 36 35 35 36 35 35 36 35 35 35 36 35 35 35 35 0.39 359 0.39 323 0.39 286 0.39 250 0.39 214 9. 96 717 9. 96 711 9.96 706 9.96 701 9.96 696 6 5 5 5 5 5 5 5 6 5 5 5 5 5 5 6 5 5 5 5 6 5 5 5 5 6 5 5 5 5 6 5 5 5 6 5 5 5 6 5 5 6 5 5 5 6 5 5 6 5 5 6 5 5 6 5 5 6 5 5 60 59 58 57 56 37 36 1 3.7 3.6 2 7.4 7.2 3 11.1 10.8 4 14.8 14.4 5 18.5 18.0 6 22.2 21.6 7 25.9 25.2 8 29.6 28.8 9 33.3 32.4 35 1 3.5 2 7.0 3 10.5 4 14.0 5 17.5 6 21.0 7 24.5 8 28.0 9 31.5 32 31 1 3.2 3.1 2 6.4 6.2 3 9.6 9.3 4 12.8 12.4 5 16.0 15.5 6 19.2 18.6 7 22.4 21.7 8 25.6 24.8 9 28.8 27.9 30 29 1 3.0 2.9 2. 6.0 5.8 3 9.0 8.7 4 12.0 11.6 5 15.0 14.5 6 18.0 17.4 7 21.0 20.3 8 24.0 23.2 9 27.0 26.1 6 5 1 0.6 0.5 2 1.2 1.0 3 1.8 1.5 4 2.4 2.0 5 3.0 2.5 6 3.6 3.0 7 4.2 3.5 8 4.8 4.0 9 5.4 4.5
5 6 7 8 9 9. 57 514 9. 57 545 9. 57 576 9. 57 607 9. 57 638 9. 60 823 9. 60 859 9.60 895 9.60 931 9.60 967 0.39 177 0.39 141 0.39 105 0.39 069 0.39 033 9.96 691 9. 96 686 9. 96 681 9.96 676 9. 96 670 55 54 53 52 51
10 11 12 13 14 9.57 669 9. 57 700 9. 57 731 9. 57 762 9. 57 793 9. 61 004 9. 61 040 9. 61 076 9.61 112 9.61 148 0.38 996 0.38 960 0.38 924 0.38 888 0.38 852 9.96 665 9. 96 660 9. 96 655 9.96 650 9. 96 645 50 49 48 47 46
15 16 17 18 19 9. 57 824 9. 57 855 9. 57 885 9. 57 916 9. 57 947 9.61 184 9.61 220 9.61 256 9. 61 292 9. 61 328 0.38 816 0.38 780 0.38 744 0.38 708 0.38 672 9.96 640 9. 96 634 9.96 629 9. 96 624 9.96 619 45 44 43 42 41
20 21 22 23 24 25 26 27 28 29 9. 57 978 9.58 008 9. 58 039 9. 58 070 9. 58 101 9. 58 131 9. 58 162 9.58 192 9. 58 223 9.58 253 9. 61 364 9. 61 400 9.61 436 9. 61 472 9. 61 508 9.61 544 9.61 579 9.61 615 9. 61 651 9. 61 687 0.38 636 0.38 600 0.38 564 0.38 528 0.38 492 0.38 456 0.38 421 0.38 385 0. 38 349 0.38 313 9. 96 614 9.96 608 9. 96 603 9. 96 598 9.96 593 9.96 588 9.96 582 9.96 577 9. 96 572 9.96 567 40 39 38 37 36 35 34 33 32 31
30 31 32 33 34 9.58 284 9.58 314 9.58 345 9.58 375 9. 58 406 9.61 722 9.61 758 9.61 794 9.61 830 9. 61 865 0.38 278 0. 38 242 0.38 206 0. 38 170 0.38 135 9.96 562 9. 96 556 9.96 551 9.96 546 9.96 541 30 29 28 27 26
35 36 37 38 39 9. 58 436 9. 58 467 9. 58 497 9. 58 527 9. 58 557 9.61 901 9.61 936 9. 61 972 9.62 008 9. 62 043 0.38 099 0.38 064 0.38 028 0.37 992 0.37 957 9.96 535 9.96 530 9.96 525 9. 96 520 9.96 514 25 24 23 22 21
40 41' 42 43 44 9. 58 588 9. 58 618 9. 58 648 9. 58 678 9. 58 709 9.62 079 9.62 114 9. 62 150 9. 62 185 9. 62 221 0.37 921 0. 37 886 0.37 850 0.37 815 0.37 779 9. 96 509 9. 96 504 9. 96 498 9.96 493 9. 96 488 20 19 18 17 16
45 46 47 48 49 9.58 739 9.58 769 9. 58 799 9. 58 829 9. 58 859 9. 62 256 9.62 292 9. 62 327 9.62 362 9.62 398 0. 37 744 0. 37 708 0.37 673 0.37 638 0.37 602 9.96 483 9.96 477 9. 96 472 9. 96 467 9.96 461 15 14 13 12 11
50 51 52 53 54 9. 58 889 9.58 919 9.58 949 9. 58 979 9. 59 009 9.62 433 9.62 468 9.62 504 9.62 539 9.62 574 0.37 567 0. 37 532 0.37 496 0.37 461 0.37 426 9.96 456 9.96 451 9.96 445 9.96 440 9.96 435 10 9 8 7 6
55 56 57 58 59 9.59 039 9. 59 069 9. 59 098 9. 59 128 9. 59 158 9. 62 609 9.62 645 9.62 680 9.62 715 9. 62 750 0.37 391 0.37 355 0.37 320 0.37 285 0.37 250 9.96 429 9.96 424 9.96 419 9.96 413 9.96 408 5 4 3 2 1
60 9. 59 188 9.62 785 0.37 215 9.96 403 0
L Sin d L Tan cd L Cot L Cos d / 337°-, 157°-
L Cos L Cot L Tan L Sin 247°-, 67°-
63
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
23°-, 203°- / L Sin d L Tan cd L Cot L Cos d Prop. pts.
113°-, 293°- L Cos L Cot L Tan L Sin
0 1 2 3 4 9. 59 188 9. 59 218 9. 59 247 9. 59 277 9. 59 307 30 29 30 30 29 9.62 785 9.62 820 9.62 855 9. 62 890 9. 62 926 35 35 35 36 35 0. 37 215 0. 37 180 0.37 145 0.37 110 0.37 074 9. 96 403 9.96 397 9. 96 392 9. 96 387 9. 96 381 6 5 5 6 5 60 59 58 57 56 1 36 3.6 35 3.5 7.0 10.5 14.0 17.5 21.0 24.5 28.0 31.5 14
5 6 7 8 9 9. 59 336 9. 59 366 9. 59 396 9. 59 425 9. 59 455 30 30 29 30 29 9.62 961 9. 62 996 9. 63 031 9. 63 066 9.63 101 35 35 35 35 34 0.37 039 0. 37 004 0.36 969 0.36 934 0.36 899 9.96 376 9.96 370 9.96 365 9.96 360 9.96 354 6 5 5 6 5 55 54 53 52 51 3 4 5 6 7 7. Z 10.8 14.4 18.0 21.6 25.2
10 11 12 13 14 9. 59 484 9. 59 514 9. 59 543 9. 59 573 9. 59 602 30 29 30 29 30 9.63 135 9. 63 170 9.63 205 9.63 240 9.63 275 35 35 35 35 35 0. 36 865 0. 36 830 0.36 795 0.36 760 0.36 725 9. 96 349 9.96 343 9. 96 338 9.96 333 9.96 327 6 5 5 6 5 50 49 48 47 46 9 3 2.4
15 16 17 18 19 9. 59 632 9. 59 661 9. 59 690 9. 59 720 9. 59 749 29 29 30 29 29 9. 63 310 9.63 345 9. 63 379 9. 63 414 9.63 449 35 34 35 35 35 0.36 690 0.36 655 0.36 621 0.36 586 0.36 551 9.96 322 9.96 316 9.96 311 9.96 305 9.96 300 6 5 6 5 6 45 44 43 42 41 1 2 3 4 5 3.4 6.8 10.2 13.6 17.0 20.4 23.8 27.2 30.6
20 21 22 23 24 9. 59 778 9. 59 808 9. 59 837 9. 59 866 9. 59 895 30 29 29 29 29 9.63 484 9. 63 519 9. 63 553 9. 63 588 9. 63 623 35 34 35 35 34 0.36 516 0. 36 481 0. 36 447 0.36 412 0.36 377 9.96 294 9. 96 289 9.96 284 9.96 278 9.96 273 5 5 6 5 6 40 39 38 37 36 6 7 8 9
25 26 27 28 29 9. 59 924 9. 59 954 9. 59 983 9.60 012 9. 60 041 30 29 29 29 29 9.63 657 9. 63 692 9.63 726 9. 63 761 9. 63 796 35 34 35 • 35 34 0.36 343 0.36 308 0. 36 274 0.36 239 0. 36 204 9.96 267 9.96 262 9.96 256 9 96 251 9.96 245 5 6 5 6 5 35 34 33 32 31 1 2 3 30 3.0 6.0 9.0 29 2.9 5.8 8.7
30 31 32 33 34 9.60 070 9. 60 099 9. 60 128 9. 60 157 9.60 186 29 29 29 29 29 9.63 830 9.63 865 9. 63 899 9. 63 934 9. 63 968 35 34 35 34 35 0.36 170 0.36 135 0.36 101 0.36 066 0. 36 032 9.96 240 9.96 234 9.96 229 9. 96 223 9.96 218 6 5 6 5 6 30 29 28 27 26 4 5 6 7 8 9 12.0 15.0 18.0 21.0 24.0 27.0 11.6 14.5 17.4 20.3 23.2 26.1
35 36 37 38 39. 9.60 215 9. 60 244 9. 60 273 9.60 302 9. 60 331 29 29 29 29 28 9.64 003 9. 64 037 9. 64 072 9. 64 106 9.64 140 34 35 34 34 35 0.35 997 0. 35 963 0.35 928 0. 35 894 0.35 860 9.96 212 9. 96 207 9.96 201 9.96 196 9.96 190 5 6 5 6 5 25 24 23 22 21 1 2 3 4 5 6 7 8 9 i 8
40 41 ' 42 43 44 9. 60 359 9. 60 388 9. 60 417 9. 60 446 9. 60 474 29 29 29 28 29 9.64 175 9. 64 209 9. 64 243 9. 64 278 9.64 312 34 34 35 34 34 0.35 825 9.35 791 0.35 757 0.35 722 0.35 688 9.96 185 9.96 179 9. 96 174 9.96 168 9.96 162 6 5 6 6 5 20 19 18 17 16 z. s 5.6 8.4 11.2 14.0 16.8 19.6 22.4 25.2
45 46 47 48 49 9. 60 503 9. 60 532 9.60 561 9. 60 589 9. 60 618 29 29 28 29 28 9. 64 346 9. 64 381 9.64 415 9. 64 449 9. 64 483 35 34 34 34 34 0. 35 654 0.35 619 0. 35 585 0.35 551 0.35 517 9.96 157 9.96 151 9.96 146 9.96 140 9.96 135 6 5 6 5 6 15 14 13 12 11
50 51 52 53 54 9. 60 646 9. 60 675 9. 60 704 9. 60 732 9. 60 761 29 29 28 29 28 9. 64 517 9. 64 552 9. 64 586 9. 64 620 9. 64 654 35 34 34 34 34 0.35 483 0.35 448 0. 35 414 0.35 380 0.35 346 9. 96 129 9.96 123 9.96 118 9. 96 112 9. 96 107 6 5 6 5 6 10 9 8 7 6 1 2 3 4 6 0.6 1.2 1.8 2.4 5 0.5 1.0 1.5 2.0
55 56 57 58 59 9. 60 789 9. 60 818 9. 60 846 9. 60 875 9. 60 903 29 28 29 28 28 9. 64 688 9. 64 722 9. 64 756 9.64 790 9. 64 824 34 34 34 34 34 0.35 312 0.35 278 0.35 244 0. 35 210 0.35 176 9. 96 101 9.96 095 9. 96 090 9. 96 084 9.96 079 6 5 6 5 6 5 4 3 2 1 5 6 7 8 9 3.0 3.6 4.2 4.8 5.4 2.5 3.0 3.5 4.0 4.5
60 9.60 931 9.64 858 0. 35 142 9.96 073 0
L Sin L Tan L Cot L Cos 336° -, 156°-
L Cos L Cot L Tan L Sin d 246c -, 66°-
64
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
24°-, 204°- 114°-, 294°- / L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d Prop. pts.
• 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9.60 931 9. 60 960 9. 60 988 9. 61 016 9. 61 045 9.61 073 9.61 101 9. 61 129 9. 61 158 9.61 186 9. 61 214 9. 61 242 9. 61 270 9. 61 298 9. 61 326 9.61 354 9. 61 382 9.61 411 9.61 438 9. 61 466 9. 61 494 9.61 522 9. 61 550 9. 61 578 9.61 606 9. 61 634 9.61 662 9. 61 689 9.61 717 9.61 745 9.61 773 9. 61 800 9. 61 828 9. 61 856 9. 61 883 9.61 911 9. 61 939 9. 61 966 9. 61 994 9. 62 021 9.62 049 9. 62 076 9.62 104 9.62 131 9. 62 159 9. 62 186 9. 62 214 9. 62 241 9. 62 268 9.62 296 9. 62 323 9. 62 350 9. 62 377 9. 62 405 9. 62 432 9 62 459 9. 62 486 9. 62 513 9.62 541 9.62 568 9.62 595 29 28 28 29 28 28 28 29 28 28 28 28 28 28 28 28 29 27 28 28 28 28 28 28 28 28 27 28 28 28 27 28 28 27 28 28 27 28 27 28 27 28 27 28 27 28 27 27 28 27 27 27 28 27 27 27 27 28 27 27 9. 64 858 9. 64 892 9. 64 926 9. 64 960 9.64 994 9.65 028 9. 65 062 9. 65 096 9. 65 130 9.65 164 9. 65 197 9. 65 231 9. 65 265 9. 65 299 9. 65 333 9. 65 366 9. 65 400 9. 65 434 9. 65 467 9. 65 501 9. 65 535 9. 65 568 9. 65 602 9. 65 636 9. 65 669 9.65 703 9. 65 736 9.65 770 9. 65 803 9.65 837 9. 65 870 9.65 904 9.65 937 9.65 971 9.66 004 9. 66 038 9. 66 071 9. 66 104 9. 66 138 9. 66 171 9. 66 204 9. 66 238 9. 66 271 9. 66 304 9.66 337 9. 66 371 9. 66 404 9. 66 437 9. 66 470 9. 66 503 9. 66 537 9. 66 570 9. 66 603 9. 66 636 9. 66 669 9. 66 702 9. 66 735 9. 66 768 9. 66 801 9.66 834 9.66 867 34 34 34 34 34 34 34 34 34 33 34 34 34 34 33 34 34 33 34 34 33 34 34 33 34 33 34 33 34 33 34 33 34 33 34 33 33 34 33 33 34 33 33 33 34 33 33 33 33 34 33 33 33 33 33 33 33 33 33 33 0.35 142 0.35 108 0.35 074 0.35 040 0.35 006 0.34 972 0. 34 938 0. 34 904 0. 34 870 0. 34 836 0. 34 803 0.34 769 0.34 735 0. 34 701 0.34 667 0. 34 634 0. 34 600 0. 34 566 0.34 533 0.34 499 0. 34 465 0.34 432 0. 34 398 0.34 364 0.34 331 0.34 297 0. 34 264 0. 34 230 0.34 197 0. 34 163 0. 34 130 0.34 096 0. 34 063 0.34 029 0.33 996 0. 33 962 0. 33 929 0. 33 896 0.33 862 0.33 829 0.33 796 0. 33 762 0. 33 729 0. 33 696 0.33 663 0.33 629 0. 33 596 0. 33 563 0. 33 530 0.33 497 0.33 463 .0.33 430 0. 33 397 0. 33 364 0.33 331 0. 33 298 0.33 265 0. 33 232 0.33 199 0.33 166 0.33 133 9. 96 073 9. 96 067 9. 96 062 9. 96 056 9. 96 050 9. 96 045 9. 96 039 9. 96 034 9. 96 028 9.96 022 9. 96 017 9.96 011 9. 96 005 9.96 000 9. 95 994 9. 95 988 9. 95 982 9.95 977 9.95 971 9. 95 965 9. 95 960 9. 95 954 9. 95 948 9. 95 942 9. 95 937 9.95 931 9. 95 925 9. 95 920 9.95 914 9. 95 908 9. 95 902 9. 95 897 9. 95 891 9. 95 885 9.95 879 9. 95 873 9.95 868 9. 95 862 9.95 856 9.95 850 9. 95 844 9. 95 839 9. 95 833 9. 95 827 9. 95 821 9. 95 815 9.95 810 9. 95 804 9.95 798 9.95 792 9. 95 786 9. 95 780 9. 95 775 9. 95 769 9.95 763 9. 95 757 9. 95. 751 9. 95 745 9. 95 739 9. 95 733 9.95 728 6 5 6 6 5 6 5 6 6 5 6 6 5 6 6 6 5 6 6 5 6 6 6 5 6 6 5 6 6 6 5 6 6 6 6 5 6 6 6 6 5 6 6 6 6 5 6 6 6 6 6 5 6 6 6 6 6 6 6 5 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 34 33 1 3.4 3.3 2 6.8 6.6 3 10.2 9.9 4 13.6 13.2 5 17.0 16.5 6 20.4 19.8 7 23.8 23.1 8 27.2 26.4 9 30.6 29.7 29 1 2.9 2 5.8 3 8.7 4 11.6 5 14.5 6 17.4 7 20.3 8 23.2 9 26.1 28 1 2.8 2 5.6 3 8.4 4 11.2 5 14.0 6 16.8 7 19.6 8 22.4 9 25.2 27 1 2.7 2 5.4 3 8.1 4 10.8 5 13.5 6 16.2 7 18.9 8 21.6 9 24.3 6 5 1 0.6 0.5 2 1.2 1.0 3 1.8 1.5 4 2.4 2.0 5 3.0 2.5 6 3.6 3.0 7 4.2 3.5 8 4.8 4.0 9 5.4 4.5
L Sin L Cos d \— L Tan L Cot cd L Cot L Tan L Cos L Sin d / 335°-, 155°- 245°-, 65°-
65
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
25°-, 205°-
115-°, 295°-
— / L Sin d L Tan cd L Cot L Cos d Prop. pts.
L Cos L Cot L Tan L Sin
0 1 2 3 4 9. 62 595 9.62 622 9.62 649 9.62 676 9. 62 703 27 27 27 27 27 27 27 27 27 27 27 26 27 27 27 27 26 27 27 27 26 27 27 26 27 26 27 26 27 26 27 26 27 26 27 26 26 27 26 26 27 26 26 26 27 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 9.66 867 9.66 900 9.66 933 9. 66 966 9.66 999 33 33 33 33 33 33 33 33 32 33 33 33 33 32 33 33 33 32 33 33 32 33 33 32 33 32 33 33 32 33 32 33 32 33 32 32 33 32 33 32 32 33 32 32 33 32 32 32 33 32 32 32 32 33 32 32 32 32 32 32 0. 33 133 0. 33 100 0. 33 067 0. 33 034 0.33 001 9.95 728 9.95 722 9. 95 716 9. 95 710 9.95 704 6 6 6 6 6 6 6 6 6 6 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 6 6 6 6 6 6 6 6 6 6 6 7 6 6 6 6 6 6 7 6 6 6 60 59 58 57 56 33 32 1 3.3 3.2 2 6.6 6.4 3 9.9 9.6 4 13.2 12.8 5 16.5 16.0 6 19.8 19.2 7 23.1 22.4 8 26.4 25.6 9 29.7 28.8 27 1 2.7 2 5.4 3 8.1 4 10.8 5 13.5 6 16.2 7 18.9 8 21.6 9 24.3 26 1 2.6 2 5.2 3 7.8 4 10.4 5 13.0 6 15.6 7 18.2 8 20.8 9 23.4 7 1 0.7 2 1.4 3 2.1 4 2.8 5 3.5 6 4.2 7 4.9 8 5.6 9 6.3 6 5 1 0.6 0.5 2 1.2 1.0 3 1.8 1.5 4 2.4 2.0 5 3.0 2.5 6 3.6 3.0 7 4.2 3.5 8 4.8 4.0 9 5.4 4.5
5 6 7 8 9 9.62 730 9. 62 757 9.62 784 9.62 811 9.62 838 9.67 032 9.67 065 9.67 098 9.67 131 9.67 163 0.32 968 0.32 935 0. 32 902 0.32 869 0.32 837 9.95 698 9.95 692 9.95 686 9.95 680 9.95 674 55 54 53 52 51
10 11 12 13 14 9.62 865 9.62 892 9.62 918 9. 62 945 9.62 972 9.67 196 9. 67 229 9.67 262 9.67 295 9. 67 327 0.32 804 0. 32 771 0.32 738 0. 32 705 0. 32 673 9.95 668 9.95 663 9.95 657 9.95 651 9.95 645 50 49 48 47 46
15 16 17 18 19 9.62 999 9.63 026 9.63 052 9.63 079 9.63 106 9. 67 360 9. 67 393 9. 67 426 9.67 458 9.67 491 0. 32 640 0. 32 607 0. 32 574 0.32 542 0.32 509 9.95 639 9.95 633 9. 95 627 9. 95 621 9.95 615 45 44 43 42 41 40 39 38 37 36
20 21 22 23 24 9.63 133 9.63 159 9.63 186 9. 63 213 9.63 239 9.67 524 9.67 556 9.67 589 9.67 622 9. 67 654 0.32 476 0.32 444 0.32 411 0.32 378 0.32 346 9.95 609 9.95 603 9.95 597 9.95 591 9.95 585
25 26 27 28 29 9.63 266 9.63 292 9.63 319 9.63 345 9.63 372 9.67 687 9. 67 719 9.67 752 9.67 785 9.67 817 0.32 313 0.32 281 0.32 248 0. 32 215 0.32 183 9.95 579 9.95 573 9.95 567 9.95 561 9.95 555 35 34 33 32 31 30 29 28 27 26
30 31 32 33 34 9.63 398 9. 63 425 9. 63 451 9. 63 478 9.63 504 9. 67 850 9.67 882 9.67 915 9.67 947 9. 67 980 0.32 150 0. 32 118 0. 32 085 0.32 053 0.32 020 9.95 549 9.95 543 9.95 537 9. 95 531 9.95 525
35 36 37 38 39 9.63 531 9.63 557 9.63 583 9.63 610 9. 63 636 9. 68 012 9.68 044 9.68 077 9.68 109 9. 68 142 0. 31 988 0. 31 956 0. 31 923 0. 31 891 0. 31 858 9.95 519 9.95 513 9. 95 507 9.95 500 9.95 494 25 24 23 22 21
40 41 42 43 44 9.63 662 9.63 689 9.63 715 9.63 741 9.63 767 9.68 174 9.68 206 9. 68 239 9. 68 271 9. 68 303 0.31 826 0.31 794 0.31 761 0.31 729 0.31 697 9.95 488 9.95 482 9.95 476 9.95 470 9.95 464 20 19 18 17 16
45 46 47 48 49 9.63 794 9.63 820 9.63 846 9.63 872 9. 63 898 9.68 336 9.68 368 9.68 400 9.68 432 9.68 465 0. 31 664 0. 31 632 0.31 600 0.31 568 0.31 535 9.95 458 9. 95 452 9.95 446 9.95 440 9.95 434 15 14 13 12 11
50 51 52 53 54 9.63 924 9.63 950 9. 63 976 9.64 002 9.64 028 9.68 497 9.68 529 9.68 561 9.68 593 9.68 626 0. 31 503 0.31 471 0.31 439 0. 31 407 0.31 374 9.95 427 9.95 421 9.95 415 9.95 409 9.95 403 10 9 8 7 6
55 56 57 58 59 9.64 054 9.64 080 9.64 106 9.64 132 9.64 158 9.68 658 9.68 690 9. 68 722 9.68 754 9.68 786 0.31 342 0.31 310 0.31 278 0.31 246 0.31 214 9.95 397 9.95 391 9.95 384 9.95 378 9.95 372 5 4 3 2 1
60 9.64 184 9.68 818 0.31 182 9.95 366 0
L Sin d L Tan cd L Cot L Cos d / 334°-, 154°-
L Cos L Cot L Tan L Sin 244°-, 64°-
66
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
26°-, 206°- / L Sin d L Tan cd L Cot L Cos d Prop. pts.
116°-, 296°- L Cos L Cot L Tan L Sin
0 1 2 3 4 9. 64 184 9. 64 210 9.64 236 9. 64 262 9. 64 288 26 26 26 26 25 26 26 26 26 25 26 26 25 26 26 25 26 25 26 25 26 25 26 25 26 25 26 25 25 26 25 25 26 25 25 25 26 25 25 25 25 25 26 25 25 25 25 25 25 25 25 25 25 25 24 25 25 25 25 25 9. 68 818 9.68 850 9. 68 882 9. 68 914 9. 68 946 32 32 32 32 32 32 32 32 32 32 32 32 32 32 32 31 32 32 32 32 31 32 32 32 31 32 32 31 32 32 31 32 31 32 32 31 32 31 32 31 32 31 32 31 32 31 31 32 31 32 31 31 32 31 31 32 31 31 31 32 0.31 182 0.31 150 0.31 118 0.31 086 0. 31 054 9.95 366 9.95 360 9. 95 354 9.95 348 9.95 341 6 6 6 7 6 6 6 6 7 6 6 6 6 7 6 6 6 7 6 6 6 7 6 6 6 7 6 6 7 6 6 6 7 6 6 7 6 6 7 6 6 7 6 7 6 6 7 6 6 7 6 7 6 6 7 6 7 6 6 7 60 59 58 57 56 32 31 1 3.2 3.1 2 6.4 6.2 3 9.6 9.3 4 12.8 12.4 5 16.0 15.5 6 19.2 18.6 7 22.4 21.7 8 25.6 24.8 9 28.8 27.9 26 1 2.6 2 5.2 3 7.8 4 10.4 5 13.0 6 15.6 7 18.2 8 20.8 9 23.4 25 1 2.5 2 5.0 3 7.5 4 10.0 5 12.5 6 15.0 7 17.5 8 20.0 9 22.5 24 1 2.4 2 4.8 3 7.2 4 9.6 5 12.0 6 14.4 7 16.8 8 19.2 9 21.6 7 6 1 0.7 0.6 2 1.4 1.2 3 2.1 1.8 4 2.8 2.4 5 3.5 3.0 6 4.2 3.6 7 4.9 4.2 8 5.6 4.8 9 6.3 5.4
5 6 7 8 9 9.64 313 9. 64 339 9. 64 365 9. 64 391 9. 64 417 9. 68 978 9. 69 010 9.69 042 9.69 074 9.69 106 0. 31 022 0. 30 990 0.30 958 0.30 926 0.30 894 9.95 335 9.95 329 9. 95 323 9. 95 317 9. 95 310 55 54 53 52 51
10 11 12 13 14 9. 64 442 9.64 468 9. 64 494 9. 64 519 9.64 545 9.69 138 9.69 170 9. 69 202 9. 69 234 9. 69 266 0.30 862 0. 30 830 0. 30 798 0.30 766 0. 30 734 9.95 304 9.95 298 9. 95 292 9.95 286 9.95 279 50 49 48 47 46
15 16 17 18 19 9.64 571 9.64 596 9. 64 622 9.64 647 9. 64 673 9. 69 298 9. 69 329 9.69 361 9. 69 393 9.69 425 0. 30 702 0. 30 671 0. 30 639 0.30 607 0.30 575 9.95 273 9. 95 267 9.95 261 9.95 254 9.95 248 45 44 43 42 41
20 21 22 23 24 9.64 698 9.64 724 9. 64 749 9.64 775 9.64 800 9.69 457 9. 69 488 9.69 520 9. 69 552 9.69 584 0.30 543 0.30 512 0.30 480 0.30 448 0.30 416 9.95 242 9.95 236 9.95 229 9.95 223 9. 95 217 40 39 38 37 36
25 26 27 28 29 9.64 826 9. 64 851 9. 64 877 9.64 902 9. 64 927 9. 69 615 9. 69 647 9. 69 679 9. 69 710 9.69 742 0.30 385 0. 30 353 0.30 321 0. 30 290 0.30 258 9.95 211 9.95 204 9.95 198 9.95 192 9.95 185 35 34 33 32 31
30 31 32 33 34 9.64 953 9. 64 978 9.65 003 9. 65 029 9.65 054 9. 69 774 9. 69 805 9.69 837 9. 69 868 9. 69 900 0. 30 226 0.30 195 0.30 163 0.30 132 0.30 100 9.95 179 9.95 173 9.95 167 9.95 160 9.95 154 30 29 28 27 26
35 36 37 38 39 9.65 079 9. 65 104 9. 65 130 9.65 155 9.65 180 9. 69 932 9. 69 963 9. 69 995 9.70 026 9.70 058 0. 30 068 0.30 037 0.30 005 0.29 974 0. 29 942 9.95 148 9.95 141 9.95 135 9.95 129 9.95 122 25 24 23 22 21
40 41 42 43 44 9.65 205 9. 65 230 9.65 255 9. 65 281 9.65 306 9.70 089 9.70 121 9. 70 152 9.70 184 9.70 215 0. 29 911 0.29 879 0.29 848 0.29 816 0.29 785 9.95 116 9.95 110 9.95 103 9.95 097 9.95 090 20 19 18 17 16
45 46 47 48 49 9.65 331 9. 65 356 9.65 381 9. 65 406 9.65 431 9. 70 247 9.70 278 9. 70 309 9. 70 341 9.70 372 0.29 753 0.29 722 0. 29 691 0.29 659 0.29 628 9.95 084 9.95 078 9. 95 071 9.95 065 9.95 059 15 14 13 12 11
50 51 52 53 54 9.65 456 9.65 481 9. 65 506 9.65 531 9. 65 556 9.70 404 9. 70 435 9.70 466 9. 70 498 9.70 529 0.29 596 0. 29 565 0. 29 534 0. 29 502 0.29 471 9.95 052 9.95 046 9.95 039 9.95 033 9.95 027 10 9 8 7 6
55 56 57 58 59 9.65 580 9.65 605 9. 65 630 9.65 655 9.65 680 9. 70 560 9. 70 592 9. 70 623 9.70 654 9. 70 685 0. 29 440 0. 29 408 0. 29 377 0.29 346 0.29 315 9.95 020 9.95 014 9.95 007 9.95 001 9.94 995 5 4 3 2 1
60 9.65 705 9.70 717 0. 29 283 9.94 988 0
L Sin d L Tan cd L Cot L Cos d / 333°-, 153°-
L Cos L Cot L Tan L Sin 243°-, 63°-
67
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
27°-, 207°- 117-°, 297°- / L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9.65 705 9.65 729 9. 65 754 9.65 779 9.65 804 9.65 828 9.65 853 9.65 878 9. 65 902 9.65 927 9.65 952 9.65 976 9.66 001 9.66 025 9.66 050 9.66 075 9.66 099 9.66 124 9.66 148 9.66 173 9.66 197 9.66 221 9.66 246 9.66 270 9.66 295 9.66 319 9. 66 343 9.66 368 9.66 392 9.66 416 9.66 441 9.66 465 9.66 489 9.66 513 9.66 537 9.66 562 9. 66 586 9.66 610 9.66 634 9.66 658 9.66 682 9.66 706 9. 66 731 9.66 755 9.66 779 9.66 803 9.66 827 9. 66 851 9.66 875 9.66 899 9.66 922 9.66 946 9.66 970 9.66 994 9. 67 018 9.67 042 9.67 066 9.67 090 9.67 113 9.67 137 9.67 161 24 25 25 25 24 25 25 24 25 25 24 25 24 25 25 24 25 24 25 24 24 25 24 25 24 24 25 24 24 25 24 24 24 24 25 24 24 24 24 24 24 25 24 24 24 24 24 24 24 23 24 24 24 24 24 24 24 23 24 24 9. 70 717 9. 70 748 9.70 779 9. 70 810 9. 70 841 9. 70 873 9. 70 904 9. 70 935 9. 70 966 9. 70 997 9.71 028 9.71 059 9. 71 090 9.71 121 9.71 153 9.71 184 9. 71 215 9. 71 246 9. 71 277 9. 71 308 9. 71 339 9. 71 370 9.71 401 9.71 431 9. 71 462 9. 71 493 9. 71 524 9.71 555 9. 71 586 9.71 617 9. 71 648 9.71 679 9.71 709 9.71 740 9. 71 771 9. 71 802 9. 71 833 9. 71 863 9. 71 894 9. 71 925 9. 71 955 9. 71 986 9.72 017 9. 72 048 9. 72 078 9. 72 109 9. 72 140 9. 72 170 9. 72 201 9. 72 231 9.72 262 9. 72 293 9.72 323 9. 72 354 9. 72 384 9.72 415 9. 72 445 9. 72 476 9. 72 506 9. 72 537 9.72 567 31 31 31 31 32 31 31 31 31 31 31 31 31 32 31 31 31 31 31 31 31 31 30 31 31 31 31 31 31 31 31 30 31 31 31 31 30 31 31 30 31 31 31 30 31 31 30 31 30 31 31 30 31 30 31 30 31 30 31 30 0. 29 283 0.29 252 0.29 221 0. 29 190 0.29 159 0.29 127 0.29 096 0.29 065 0. 29 034 0. 29 003 0. 28 .972 0.28 941 0.28 910 0.28 879 0.28 847 0. 28 816 0.28 785 0. 28 754 0.28 723 0.28 692 0. 28 661 0. 28 630 0.28 599 0.28 569 0.28 538 0.28 507 0.28 476 0.28 445 0. 28 414 0. 28 383 0.28 352 0. 28 321 0.28 291 0.28 260 0.28 229 0.28 198 0.28 167 0. 28 137 0.28 106 0.28 075 0.28 045 0. 28 014 0.27 983 0. 27 952 0.27 922 0.27 891 0.27 860 0.27 830 0.27 799 0. 27 769 0.27 738 0. 27 707 0.27 677 0.27 646 0. 27 616 0.27 585 0.27 555 0. 27 524 0. 27 494 0.27 463 0.27 433 9. 94 988 9.94 982 9.94 975 9.94 969 9.94 962 9.94 956 9.94 949 9.94 943 9. 94 936 9. 94 930 9.94 923 9. 94 917 9. 94 911 9.94 904 9.94 898 9.94 891 9.94 885 9.94 878 9. 94 871 9. 94 865 9. 94 858 9.94 852 9.94 845 9. 94 839 9.94 832 9. 94 826 9.94 819 9.94 813 9.94 806 9.94 799 9.94 793 9. 94 786 9. 94 780 9.94 773 9.94 767 9. 94 760 9. 94 753 9.94 747 9.94 740 9.94 734 9.94 727 9.94 720 9.94 714 9.94 707 9.94 700 9.94 694 9.94 687 9.94 680 9.94 674 9.94 667 9.94 660 9. 94 654 9.94 647 9.94 640 9.94 634 9. 94 627 9.94 620 9. 94 614 9.94 607 9. 94 600 9.94 593 6 7 6 7 6 7 6 7 6 7 6 6 7 6 7 6 7 7 6 7 6 7 6 7 6 7 6 7 7 6 7 6 7 6 7 7 6 7 6 7 7 6 7 7 6 7 7 6 7 7 6 7 7 6 7 7 6 7 7 7 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 32 31 1 3.2 3.1 2 6.4 6.2 3 9.6 9.3 4 12.8 12.4 5 16.0 15.5 6 19.2 18.6 7 22.4 21.7 8 25.6 24.8 9 28.8 27.9 30 1 3.0 2 6.0 3 9.0 4 12.0 ' 5 15.0 6 18.0 7 21.0 8 24.0 9 27.0 25 24 1 2.5 2.4 2 5.0 4.8 3 7.5 7.2 4 10.0 9.6 5 12.5 12.0 6 15.0 14.4 7 17.5 16.8 8 20.0 19.2 9 22.5 21.6 23 1 2.3 2 4.6 3 6.9 4 9.2 5 11.5 6 13.8 7 16.1 8 18.4 9 20.7 7 6 1 0.7 0.6 2 1.4 1.2 3 2.1 1.8 4 2.8 2.4 5 3.5 3.0 6 4.2 3.6 7 4.9 4.2 8 5.6 4.8 9 6.3 5.4
L Sin d L Tan L Cot L Cos d / 332°-, 152°-
L Cos L Cot J L Tan L Sin 242°-, 62°-
68
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
28°-, 208°- 118°-, 298°- / L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9. 67 161 9. 67 185 9. 67 208 9.67 232 9. 67 256 9. 67 280 9. 67 303 9. 67 327 9. 67 350 9.67 374 9. 67 398 9.67 421 9. 67 445 9. 67 468 9.67 492 9. 67 515 9. 67 539 9. 67 562 9. 67 586 9. 67 609 9. 67 633 9. 67 656 9. 67 680 9. 67 703 9. 67 726 9. 67 750 9. 67 773 9. 67 796 9. 67 820 9. 67 843 9. 67 866 9. 67 890 9. 67 913 9. 67 936 9. 67 959 9. 67 982 9. 68 006 9. 68 029 9. 68 052 9. 68 075 9. 68 098 9. 68 121 9. 68 144 9. 68 167 9.68 190 9. 68 213 9. 68 237 9. 68 260 9. 68 283 9. 68 305 9. 68 328 9. 68 351 9. 68 374 9. 68 397 9. 68 420 9. 68 443 9. 68 466 9. 68 489 9. 68 512 9. 68 534 9. 68 557 24 23 24 24 24 23 24 23 24 24 23 24 23 24 23 24 23 24 23 24 23 24 23 23 24 23 23 24 23 23 24 23 23 23 23 24 23 23 23 23 23 23 23 23 23 24 23 23 22 23 23 23 23 23 23 23 23 23 22 23 9. 72 567 9. 72 598 9. 72 628 9. 72 659 9. 72 689 9. 72 720 9. 72 750 9. 72 780 9. 72 811 9. 72 841 9. 72 872 9. 72 902 9. 72 932 9. 72 963 9. 72 993 9. 73 023 9. 73 054 9. 73 084 9. 73 114 9. 73 144 9. 73 175 9.73 205 9. 73 235 9. 73 265 9. 73 295 9. 73 326 9. 73 356 9. 73 386 9. 73 416 9. 73 446 9. 73 476 9. 73 507 9. 73 537 9. 73 567 9. 73 597 9.73 627 9. 73 657 9. 73 687 9. 73 717 9. 73 747 9. 73 777 9. 73 807 9. 73 837 9. 73 867 9. 73 897 9. 73 927 9. 73 957 9. 73 987 9. 74 017 9. 74 047 9. 74 077 9. 74 107 9. 74 137 9. 74 166 9. 74 196 9. 74 226 9. 74 256 9. 74 286 9. 74 316 9. 74 345 9. 74 375 31 30 31 30 31 30 30 31 30 31 30 30 31 30 30 31 30 30 30 31 30 30 30 30 31 30 30 30 30 30 31 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 29 30 30 30 30 30 29 30 0. 27 433 0. 27 402 0.27 372 0. 27 341 0. 27 311 0. 27 280 0.27 250 0.27 220 0.27 189 0.27 159 0.27 128 0. 27 098 0. 27 068 0.27 037 0. 27 007 0. 26 977 0. 26 946 0. 26 916 0.26 886 0. 26 856 0. 26 825 0.26 795 0. 26 765 0. 26 735 0.26 705 0.26 674 0. 26 644 0. 26 614 0. 26 584 0. 26 354 0. 26 524 0. 26 493 0.26 463 0. 26 433 0. 26 403 0. 26 373 0. 26 343 0. 26 313 0.26 283 0.26 253 0. 26 223 0. 26 193 0. 26 163 0. 26 133 0. 26 103 0. 26 073 0. 26 043 0. 26 013 0. 25 983 0. 25 953 0. 25 923 0. 25 893 0. 25 863 0. 25 834 0. 25 804 0. 25 774 0.25 744 0. 25 714 0. 25 684 0.25 655 0. 25 625 9.94 593 9.94 587 9. 94 580 9.94 573 9.94 567 9.94 560 9.94 553 9.94 546 9. 94 540 9.94 533 9. 94 526 9. 94 519 9.94 513 9. 94 506 9. 94 499 9.94 492 9.94 485 9.94 479 9. 94 472 9.94 465 9.94 458 9.94 451 9. 94 445 9.94 438 9. 94 431 9.94 424 9. 94 417 9. 94 410 9. 94 404 9. 94 397 9.94 390 9.94 383 9.94 376 9. 94 369 9. 94 362 9.94 355 9. 94 349 9.94 342 9. 94 335 9.94 328 9.94 321 9. 94 314 9.94 307 9. 94 300 9.94 293 9.94 286 9.94 279 9.94 273 9.94 266 9. 94 259 9. 94 252 9.94 245 9.94 238 9. 94 231 9. 94 224 9.94 217 9. 94 210 9. 94 203 9. 94 196 9. 94 189 9.94 182 6 7 7 6 7 7 7 6 7 7 7 6 7 7 7 7 6 7 7 7 7 6 7 7 7 7 7 6 7 7 7 7 7 7 7 6 7 7 7 7 7 7 7 7 7 7 6 7 7 7 7 7 7 7 7 7 7 7 7 7 GO 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 31 30 1 3.1 3.0 2 6.2 6.0 3 9.3 9.0 4 12.4 12.0 5 15.5 15.0 6 18.6 18.0 7 21.7 21.0 8 24.8 24.0 9 27.9 27.0 29 1 2.9 2 5.8 3 8.7 4 11.6 5 14.5 6 17.4 7 20.3 8 23.2 9 26.1 24 23 1 2.4 2.3 ,2 4.8 4.6 3 7.2 6.9 4 9.6 9.2 5 12.0 11.5 6 14.4 13.8 7 16.8 16.1 8 19.2 18.4 9 21.6 20.7 22 1 2.2 2 4.4 3 6.6 4 8.8 5 11.0 6 13.2 7 15.4 8 17.6 9 19.8 7 6 1 0.7 0.6 2 1.4 1.2 3 2.1 1.8 4 2.8 2.4 5 3.5 3.0 6 4.2 3.6 7 4.9 4.2 8 5.6 4.8 9 6.3 5.4
L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d / 331°-, 151°- 241°-, 61°-
69
Table III. Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
29°-, 209°- / L Sin L Tan L Cot L Cos
119-°, 299°- a " cd d Prop. pts.
L Cos L Cot L Tan L Sin
0 9. 68 557 23 9.74 375 30 on 0.25 625 9.94 182 60
1 9. 68 580 23 9.74 405 0. 25 595 9. 94 175 59
2 9.68 603 22 9. 74 435 ou oa 0.25 565 9.94 168 / 58
3 9. 68 625 23 9.74 465 OU on 0. 25 535 9.94 161 7 57 30
4 9. 68 648 23 9. 74 494 30 0.25 506 9.94 154 7 7 56 1 3.0
5 9.68 671 oo 9. 74 524 0.25 476 9. 94 147 55 2 6.0
6 9. 68 694 9.74 554 30 0.25 446 9. 94 140 7 54 3 9.0
7 9. 68 716 9. 74 583 29 0. 25 417 9.94 133 7 53 4 12.0
8 9. 68 739 9. 74 613 30 0.25 387 9.94 126 7 52 5 15.0
9 9.68 762 22 9. 74 643 30 30 0.25 357 9. 94 119 7 7 51 6 7 18. 0 21.0
10 9.68 784 oo 9. 74 673 0. 25 327 9.94 112 50 8 24.0
11 9.68 807 22 9. 74 702 zy 0. 25 298 9. 94 105 7 49 9 27.0
12 13 9. 68 829 9.68 852 23 9. 74 732 9. 74 762 ou 30 0.25 268 0. 25 238 9.94 098 9. 94 090 7 8 48 47
14 9.68 875 22 9. 74 791 zy 30 0. 25 209 9. 94 083 7 7 46
15 9. 68 897 oo 9. 74 821 0. 25 179 9.94 076 45 2.9
16 9. 68 920 9. 74 851 30 0. 25 149 9. 94 069 7 44 1
17 9. 68 942 Oq 9. 74 880 29 0.25 120 9.94 062 7 43 2 5. 8
18 9.68 965 9. 74 910 30 0.25 090 9.94 055 7 7 7 42 3 8. 7
19 9.68 987 23 9. 74 939 29 30 0.25 061 9.94 048 41 4 5 11.6 14. 5
20 9.69 010 22 23 9. 74 969 on 0. 25 031 9.94 041 40 6 17.4
21 9.69 032 9. 74 998 zy OA 0. 25 002 9. 94 034 7 39 7 20.3
22 9.69 055 22 9.75 028 ou 0. 24 972 9. 94 027 7 38 8 23. 2
23 9.69 077 23 22 9.75 058 OU 90 0.24 942 9. 94 020 7 37 9 26.1
24 9.69 100 9. 75 087 zy 30 0. 24 913 9.94 012 8 7 36
25 9. 69 122 22 9. 75 117 on 0. 24 883 9. 94 005 35
26 9.69 144 23 9. 75 146 OA 0. 24 854 9. 93 998 7 34 23
27 28 9.69 167 9. 69 189 22 9. 75 176 9. 75 205 OU 29 0. 24 824 0.24 795 9. 93 991 9. 93 984 7 7 33 32 1 2.3
29 9. 69 212 22 9. 75 235 ou 29 0.24 765 9.93 977 7 7 31 2 3 4. 6 6.9
30 31 32 9. 69 234 9. 69 256 9. 69 279 22 23 99 9. 75 264 9. 75 294 9. 75 323 30 29 30 0.24 736 0. 24 706 0. 24 677 9. 93 970 9. 93 963 9. 93 955 7 8 30 29 28 4 5 6 9.2 11.5 13.8
33 9. 69 301 22 9. 75 353 0. 24 647 9. 93 948 7 27 7 16.1
34 9. 69 323 22 9. 75 382 zy 29 0. 24 618 9.93 941 7 7 26 8 9 18. 4 20.7
35 9. 69 345 oo 9.75 411 30 0. 24 589 9.93 934 25
36 9.69 368 22 9. 75 441 0. 24 559 9. 93 927 7 24
37 9. 69 390 22 9. 75 470 29 0.24 530 9. 93 920 7 23
38 9.69 412 22 9. 75 500 30 on 0. 24 500 9.93 912 8 22 22
39 9. 69 434 22 9. 75 529 29 0. 24 471 9. 93 905 7 7 21 1 2.2
40 9. 69 456 oo 9. 75 558 0. 24 442 9.93 898 20 2 1.4
41 9.69 479 Zo 99 9. 75 588 30 0. 24 412 9.93 891 7 19 3 6. 6
42 9. 69 501 22 22 9. 75 617 29 0.24 383 9.93 884 7 18 4 8.8
43 9. 69 523 9. 75 647 30 0. 24 353 9.93 876 8 17 5 11. 0
44 9.69 545 22 9. 75 676 zy 29 0.24 324 9.93 869 7 7 16 6 7 13. 2 15.4
45 9.69 567 22 22 9. 75 705 QA 0.24 295 9.93 862 15 8 17.6
46 9.69 589 9. 75 735 OU 0. 24 265 9.93 855 7 14 9 19.8
47 9. 69 611 22 9.75 764 on 0. 24 236 9.93 847 8 13
48 9. 69 633 22 22 9.75 793 zy 29 0.24 207’ 9.93 840 7 12
49 9. 69 655 9.75 822 30 0. 24 178 9.93 833 7 7 11
50 9.69 677 22 9.75 852 29 0. 24 148 9. 93 826 10 8 7
51 9.69 699 22 9. 75 881 9Q 0.24 119 9.93 819 7 9 1 0.8 0.7
52 9.69 721 22 9.75 910 29 0.24 090 9.93 811 8 8 2 1.6 1.4
53 9. 69 743 22 9. 75 939 30 29 0. 24 061 9.93 804 7 7 3 2.4 2.1
54 9. 69 765 22 9.75 969 0.24 031 9.93 797 7 8 6 4 5 6 3.2 4.0 4.8 2.8 3.5 4.2
55 9.69 787 22 9.75 998 29 0.24 002 9.93 789 5
56 9. 69 809 22 9. 76 027 9Q 0.23 973 9.93 782 7 4 7 Fi 6 4.9
57 9.69 831 22 9. 76 056 zy QA 0. 23 944 9.93 775 7 3 8 6.4 5.6
58 9.69 853 22 9.76 086 OU on 0.23 914 9. 93 768 7 2 9 7.2 6.3
59 9.69 875 22 9.76 115 29 0. 23 885 9.93 760 8 7 1
60 9. 69 897 9. 76 144 0. 23 856 9.93 753 0
L Sin d L Tan L Cot L Cos / 330°- 150°-
L Cos | L Cot cu L Tan L Sin d 240° -, 60°-
70
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
30°-, 210°- 120°-, 300°- / L Sin L Cos a L Tan L Cot cd L Cot L Tan L Cos L Sin d Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9. 69 897 9. 69 919 9.69 941 9.69 963 9. 69 984 9. 70 006 9. 70 028 9. 70 050 9. 70 072 9. 70 093 9.70 115 9. 70 137 9. 70 159 9. 70 180 9. 70 202 9. 70 224 9. 70 245 9. 70 267 9. 70 288 9. 70 310 9. 70 332 9. 70 353 9. 70 375 9. 70 396 9.70 418 9. 70 439 9. 70 461 9. 70 482 9. 70 504 9. 70 525 9. 70 547 9. 70 568 9. 70 590 9. 70 611 9. 70 633 9. 70 654 9.70 675 9. 70 697 9. 70 718 9. 70 739 9. 70 761 9.70 782 9.70 803 9. 70 824 9.70 846 9. 70 867 9. 70 888 9. 70 909 9. 70 931 9. 70 952 9.70 973 9. 70 994 9.71 015 9.71 036 9.71 058 9. 71 079 9.71 100 9.71 121 9.71 142 9.71 163 9. 71 184 22 22 22 21 22 22 22 22 21 22 22 22 21 22 22 21 22 21 22 22 21 22 21 22 21 22 21 22 21 22 21 22 21 22 21 21 22 21 21 22 21 21 21 22 21 21 21 22 21 21 21 21 21 22 21 21 21 21 21 21 9. 76 144 9. 76 173 9. 76 202 9. 76 231 9.76 261 9. 76 290 9. 76 319 9. 76 348 9. 76 377 9.76 406 9. 76 435 9. 76 464 9. 76 493 9. 76 522 9. 76 551 9. 76 580 9. 76 609 9. 76 639 9. 76 668 9.76 697 9. 76 725 9.76 754 9. 76 783 9. 76 812 9. 76 841 9.76 870 9.76 899 9. 76 928 9. 76 957 9.76 986 9. 77 015 9. 77 044 9.77 073 9. 77 101 9.77 130 9.77 159 9. 77 188 9. 77 217 9. 77 246 9.77 274 9. 77 303 9. 77 332 9. 77 361 9. 77 390 9. 77 418 9. 77 447 9. 77 476 9. 77 505 9.77 533 9.77 562 9. 77 591 9. 77 619 9.77 648 9.77 677 9.77 706 9. 77 734 9.77 763 9. 77 791 9.77 820 9. 77 849 9.77 877 29 29 29 30 29 29 29 29 29 29 29 29 29 29 29 29 30 29 29 28 29 29 29 29 29 29 29 29 29 29 29 29 28 29 29 29 29 29 28 29 29 29 29 28 29 29 29 28 29 29 28 29 29 29 28 29 28 29 29 28 0.23 856 0. 23 827 0. 23 798 0. 23 769 0. 23 739 0. 23 710 0. 23 681 0. 23 652 0. 23 623 0. 23 594 0. 23 565 0. 23 536 0. 23 507 0. 23 478 0.23 449 0. 23 420 0.23 391 0.23 361 0.23 332 0.23 303 0. 23 275 0.23 246 0. 23 217 0.23 188 0.23 159 0.23 130 0.23 101 0.23 072 0.23 043 0 23.014 0.22 985 0. 22 956 0.22 927 0.22 899 0.22 870 0.22 841 0. 22 812 0.22 783 0.22 754 0. 22 726 0.22 697 0. 22 668 0. 22 639 0. 22 610 0. 22 582 0. 22 553 0. 22 524 0.22 495 0. 22 467 0. 22 438 0.22 409 0. 22 381 0.22 352 0.22 323 0. 22 294 0.22 266 0. 22 237 0. 22 209 0. 22 180 0. 22 151 0.22 123 9.93 753 9. 93 746 9. 93 738 9.93 731 9.93 724 9.93 717 9 93 709 9.93 702 9.93 695 9.93 687 9. 93 680 9.93 673 9. 93 665 9. 93 658 9.93 650 9.93 643 9. 93 636 9 93 628 9. 93 621 9.93 614 9.93 606 9.93 599 9.93 591 9.93 584 9.93 577 9.93 569 9. 93 562 9.93 554 9.93 547 9. 93 539 9.93 532 9.93 525 9.93 517 9.93 510 9.93 502 9.93 495 9.93 487 9.93 480 9. 93 472 9.93 465 9. 93 457 9. 93 450 9.93 442 9. 93 435 9.93 427 9.93 420 9. 93 412 9.93 405 9. 93 397 9.93 390 9. 93 382 9. 93 375 9. 93 367 9.93 360 9.93 352 9. 93 344 9.93 337 9. 93 329 9.93 322 9.93 314 9.93 307 7 8 7 7 7 8 7 7 8 7 7 8 7 8 7 7 8 7 7 8 7 8 7 7 8 7 8 7 8 7 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 8 7 8 7 8 7 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 30 29 1 3.0 2.9 2 6.0 5.8 3 9.0 8.7 4 12.0 11.6 5 15.0 14.5 6 18.0 17.4 7 21.0 20.3 8 24.0 23.2 9 27.0 26.1 28 1 2.8 2 5.6 3 8.4 4 11.2 5 14.0 6 16.8 7 19.6 8 22.4 9 25.2 22 1 2.2 2 4.4 3 6,6 4 8.8 5 11.0 6 13.2 7 15.4 8 17.6 9 19.8 21 1 2.1 2 4.2 3 6.3 4 8.4 5 10.5 6 12.6 7 14.7 8 16.8 9 18.9 8 7 1 0.8 0.7 2 1.6 1.4 3 2.4 2.1 4 3.2 2.8 5 4.0 3.5 6 4.8 4.2 7 5.6 4.9 8 6.4 5.6 9 7.2 6.3
L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d / 329°-, 149°- 239°-, 59°-
71
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—-
Continued
31°-, 211°- / L Sin - d L Tan cd L Cot L Cos - d Prop. pts.
121-°, 301°- L Cos L Cot L Tan L Sin
0 9.71 184 21 9. 77 877 90 0. 22 123 9. 93 307 GO
1 9. 71 205 21 9. 77 906 zy 90 0. 22 094 9. 93 299 8 59
2 9.71 226 21 9. 77 935 zy 0. 22 065 9. 93 291 8 58 29
3 9.71 247 21 9. 77 963 Zo 90 0. 22 037 9. 93 284 7 57 1 2 9
4 9. 71 268 21 9. 77 992 zy 28 0. 22 008 9.93 276 8 7 56 2 5.8
5 9. 71 289 21 9. 78 020 90 0. 21 980 9. 93 269 55 3 4 8.7 11. 6
6 9. 71 310 21 9. 78 049 zy 9ft 0. 21 951 9. 93 261 8 54 5 14 5
7 9.71 331 21 9. 78 077 Z<5 90 0. 21 923 9. 93 253 8 53 6 17. 4
8 9. 71 352 21 9. 78 106 zy 90 0. 21 894 9. 93 246 7 52 7 20 3
9 9. 71 373 20 9. 78 135 zy 28 0. 21 865 9.93 238 8 8 51 8 23.2
10 11 9. 71 393 9. 71 414 21 21 9. 78 163 9. 78 192 29 9ft 0. 21 837 0. 21 808 9.93 230 9. 93 223 7 50 49 9 26.1
12 9. 71 435 21 9. 78 220 zo 90 0.21 780 9. 93 215 8 48
13 9. 71 456 21 9. 78 249 zy 0. 21 751 9. 93 207 8 47
14 9. 71 477 21 9. 78 277 Zo 29 0.21 723 9.93 200 7 8 46 28
15 9. 71 498 21 9. 78 306 9R 0. 21 694 9.93 192 45 1 2 2.8 5. 6
16 9. 71 519 20 9. 78 334 ZO 90 0. 21 666 9. 93 184 8 44 3 8 4
17 9. 71 539 21 9. 78 363 zy 9ft 0.21 637 9.93 177 7 43 4 11. 2
18 9.71 560 21 9. 78 391 zo 9ft 0.21 609 9. 93 169 8 42 5 14.0
19 9. 71 581 21 9. 78 419 Zo 29 0. 21 581 9.93 161 8 7 41 6 16.8
20 9. 71 602 20 9. 78 448 or 0. 21 552 9.93 154 40 7 8 19. 6 22.4
21 9. 71 622 21 9. 78 476 zo 9Q 0.21 524 9. 93 146 8 39 9 2.v 2
22 9. 71 643 21 9. 78 505 zy 9ft 0. 21 495 9. 93 138 8 38
23 9. 71 664 21 9. 78 533 Zo 90 0. 21 467 9. 93 131 7 37
24 9. 71 685 20 9. 78 562 zy 28 0. 21 438 9.93 123 8 8 36
25 9. 71 705 21 9. 78 590 9Q 0. 21 410 9. 93 115 35 21
26 9.71 726 21 9. 78 618 zo 90 0. 21 382 9. 93 108 7 34 1 2.1
27 9. 71 747 20 9. 78 647 zy 9ft 0. 21 353 9. 93 100 8 33 2 4 2
28 9. 71 767 21 9. 78 675 zo 90 0. 21 325 9.93 092 8 32 3 6. 3
29 9. 71 788 21 9. 78 704 zy 28 0.21 296 9. 93 084 8 7 31 4 8.4
30 9. 71 809 20 9. 78 732 28 0. 21 268 9.93 077 30 5 6 10. 5 12. 6
31 9. 71 829 21 9. 78 760 29 0. 21 240 9. 93 069 8 29 7 14. 7
32 9. 71 850 20 9. 78 789 9ft 0.21 211 9. 93 061 8 28 8 16 8
33 9. 71 870 21 9. 78 817 zo 9ft 0. 21 183 9. 93 053 8 27 9 1R Q
34 9. 71 891 20 9. 78 845 zo 29 0.21 155 9. 93 046 7 8 26
35 9. 71 911 21 9. 78 874 28 9Q 0. 21 126 9. 93 038 25
36 9. 71 932 20 9. 78 902 0. 21 098 9. 93 030 8 24
37 9. 71 952 21 9. 78 930 zo 90 0. 21 070 9. 93 022 8 23 20
38 9. 71 973 21 9. 78 959 zy 9ft 0. 21 041 9. 93 014 8 22 1 2 0
39 9. 71 994 20 9. 78 987 zo 28 0. 21 013 9. 93 007 7 8 21 2 4.0
40 9. 72 014 20 9. 79 015 9ft 0. 20 985 9. 92 999 20 3 4 6.0 8. 0
41 9. 72 034 21 9. 79 043 zo 90 0. 20 957 9. 92 991 8 19 5 10 0
42 9. 72 055 20 9. 79 072 zy 28 0. 20 928 9. 92 983 8 18 6 12.0
43 9. 72 075 21 9. 79 100 28 0. 20 900 9. 92 976 z 17 7 14.0
44 9. 72 096 20 9. 79 128 28 0.20 872 9.92 968 8 16 8 16.0
45 9.72 116 21 9. 79 156 90 0. 20 844 9. 92 960 15 9 18.0
46 9. 72 137 20 9. 79 185 zy 9ft 0. 20 815 9. 92 952 8 14
47 9. 72 157 20 9. 79 213 zo 9ft 0. 20 787 9. 92 944 8 13
48 9. 72 177 21 9. 79 241 ZO 9ft 0. 20 759 9. 92 936 8 12
49 9. 72 198 20 9. 79 269 ZO 28 0.20 731 9. 92 929 7 8 11 8 7
50 9. 72 218
20 9. 79 297 29 0. 20 703 9. 92 921 10 1 0. 8 0. 7
51 9. 72 238 21 9. 79 326 28 0. 20 674 9. 92 913 8 9 2 1 6 1. 4
52 9. 72 259 20 9. 79 354 28 0. 20 646 9. 92 905 8 8 3 2. 4 2.1
53 9. 72 279 20 9. 79 382 28 0. 20 618 9. 92 897 8 7 4 3. 2 2.8
54 9. 72 299 21 9. 79 410 28 0. 20 590 9. 92 889 8 8 6 5 4.0 3.5
55 9. 72 320 20 9. 79 438 28 0. 20 562 9. 92 881 5 6 7 4. 8 5.6 4. 2 4. 9
56 9. 72 340 20 9. 79 466 29 0. 20 534 9. 92 874 7 4 8 6.4 5. 6
57 9. 72 360 21 9. 79 495 28 0. 20 505 9. 92 866 8 3 9 7.2 6.3
58 9. 72 381 20 9. 79 523 28 0. 20 477 9. 92 858 8 2
59 9. 72 401 20 9. 79 551 28 0. 20 449 9.92 850 8 8 1
60 9.72 421 9.79 579 0.20 421 9.92 842 0
L Sin L Tan L Cot L Cos 328°- 148°-
d
L Cos L Cot L Tan L Sin d 238° 58°-
72
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutei
Continued
32°-, 212°- / L Sin d L Tan cd L Cot L Cos d Prop. pts.
122°-, 302°- L Cos L Cot L Tan L Sin
0 1 2 3 4 9.72 421 9.72 441 9.72 461 9. 72 482 9.72 502 20 20 21 20 20 20 20 20 20 20 21 20 20 20 20 20 20 20 20 20 20 20 20 19 20 20 20 20 20 20 19 20 20 20 20 19 20 20 20 19 20 20 19 20 20 19 20 20 19 20 19 20 19 20 19 20 19 20 19 20 9.79 579 9.79 607 9.79 635 9.79 663 9.79 691 28 28 28 28 28 28 29 28 28 28 28 28 28 28 28 28 28 28 28 28 28 27 28 28 28 28 28 28 28 28 28 27 28 28 28 28 28 28 27 28 28 28 28 27 28 28 28 27 28 28 28 27 28 28 27 28 28 27 28 28 0.20 421 0.20 393 0. 20 365 0.20 337 0.20 309 9.92 842 9. 92 834 9. 92 826 9. 92 818 9. 92 810 8 8 8 8 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 8 8 8 8 8 8 8 8 9 8 8 8 8 8 8 9 8 8 8 8 8 9 8 60 59 58 57 56 29 28 1 2.9 2.8 2 5.8 5.6 3 8.7 8.4 4 11.6 11.2 5 14.5 14.0 6 17.4 16.8 7 20.3 19.6 8 23.2 22.4 9 26.1 25.2 27 1 2.7 2 5.4 3 8.1 4 10.8 5 13.5 6 16.2 7 18.9 8 21.6 9 24.3 21 20 1 2.1 2.0 2 4.2 4.0 3 6.3 6.0 4 8.4 8.0 5 10.5 10.0 6 12.6 12.0 7 14.7 14.0 8 16.8 16.0 9 18 9 18.0 19 9 1 1.9 0.9 2 3.8 1.8 3 5.7 2.7 4 7.6 3.6 5 9.5 4.5 6 11.4 5.4 7 13.3 6.3 8 15.2 7.2 9 17.1 8.1 8 7 1 0.8 0.7 2 1.6 1.4 3 2.4 2.1 4 3.2 2.8 5 4.0 3.5 6 4.8 4.2 7 5.6 4.9 8 6.4 5.6 9 7.2 6.3
5 6 7 8 9 9,72 522 9. 72 542 9. 72 562 9.72 582 9. 72 602 9.79 719 9. 79 747 9. 79 776 9.79 804 9.79 832 0. 20 281 0.20 253 0.20 224 0.20 196 0.20 168 9. 92 803 9.92 795 9.92 787 9. 92 779 9. 92 771 55 54 53 52 51
10 11 12 13 14 9.72 622 9. 72 643 9. 72 663 9. 72 683 9..72 703 9.79 860 9. 79 888 9. 79 916 9.79 944 9.79 972 0.20 140 0.20 112 0.20 084 0.20 056 0.20 028 9.92 763 9.92 755 9.92 747 9.92 739 9.92 731 50 49 48 47 46
15 16 17 18 19 9.72 723 9. 72 743 9.72 763 9.72 783 9.72 803 9. 80 000 9.80 028 9.80 056 9. 80 084 9. 80 112 0.20 000 0.19 972 0.19 944 0.19 916 0.19 888 9.92 723 9.92 715 9.92 707 9. 92 699 9. 92 691 45 44 43 42 41
20 21 22 23 24 9.72 823 9.72 843 9.72 863 9. 72 883 9. 72 902 9.80 140 9.80 168 9.80 195 9.80 223 9.80 251 0.19 860 0.19 832 0.19 805 0.19 777 0.19 749 9.92 683 9.92 675 9. 92 667 9. 92 659 9. 92 651 40 39 38 37 36
25 26 27 28 29 9. 72 922 9.72 942 9. 72 962 9.72 982 9. 73 002 9.80 279 9.80 307 9.80 335 9. 80 363 9.80 391 0.19 721 0.19 693 0.19 665 0.19 637 0.19 609 9. 92 643 9. 92 635 9.92 627 9. 92 619 9.92 611 35 34 33 32 31
30 31 32 33 34 9. 73 022 9.73 041 9. 73 061 9. 73 081 9.73 101 9.80 419 9.80 447 9.80 474 9.80 502 9.80 530 0.19 581 0.19 553 0.19 526 0.19 498 0.19 470 9.92 603 9.92 595 9. 92 587 9.92 579 9.92 571 30 29 28 27 26
35 36 37 38 39 9.73 121 9.73 140 9.73 160 9.73 180 9. 73 200 9.80 558 9.80 586 9.80 614 9.80 642 9.80 669 0.19 442 0.19 414 0.19 386 0.19 358 0.19 331 9. 92 563 9.92 555 9.92 546 9. 92 538 9.92 530 25 24 23 22 21
40 41 42 43 44 9.73 219 9.73 239 9. 73 259 9.73 278 9. 73 298 9.80 697 9.80 725 9.80 753 9.80 781 9.80 808 0.19 303 0.19 275 0.19 247 0.19 219 0.19 192 9.92 522 9.92 514 9. 92 506 9. 92 498 9. 92 490 20 19 18 17 16
45 46 47 48 49 9.73 318 9.73 337 9. 73 357 9.73 377 9. 73 396 9.80 836 9.80 864 9.80 892 9.80 919 9. 80 947 0.19 164 0.19 136 0.19 108 0.19 081 0.19 053 9. 92 482 9.92 473 9.92 465 9.92 457 9.92 449 15 14 13 12 11
50 51 52 53 54 9.73 416 9. 73 435 9. 73 455 9. 73 474 9.73 494 9.80 975 9.81 003 9. 81 030 9. 81 058 9.81 086 0.19 025 0.18 997 0.18 970 0.18 942 0.18 914 9.92 441 9. 92 433 9.92 425 9.92 416 9. 92 408 10 9 8 7 6
55 56 57 58 59 9.73 513 9. 73 533 9.73 552 9. 73 572 9. 73 591 9.81 113 9.81 141 9.81 169 9.81 196 9.81 224 0.18 887 0.18 859 0.18 831 9.18 804 0.18 776 9. 92 400 9. 92 392 9.92 384 9. 92 376 9.92 367 5 4 3 2 1
60 9.73 611 9.81 252 0.18 748 9.92 359 0
L Sin d L Tan cd L Cot L Cos d f 327°-, 147°-
L Cos L Cot L Tan L Sin 237°-, 57°-
73
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
33°-, 213°- / L Sin d L Tan cd L Cot L Cos - d Prop. pts.
123°-, 303°- L Cos L Cot L Tan L Sin
0 1 2 3 4 9.73 611 9. 73 630 9. 73 650 9. 73 669 9. 73 689 19 20 19 20 19 19 20 19 19 20 19 19 20 19 19 20 19 19 19 19 20 19 19 19 19 20 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 18 19 9.81 252 9.81 279 9.81 307 9.81 335 9.81 362 ■ 27 28 28 27 28 28 27 28 27 28 28 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 28 27 27 28 27 28 27 27 28 27 28 27 27 28 27 27 28 27 27 28 27 27 27 0.18 748 0.18 721 0.18 693 0.18 665 0.18 638 9. 92 359 9.92 351 9.92 343 9. 92 335 9.92 326 8 8 8 9 8 8 8 9 8 8 8 9 8 8 9 8 8 8 9 8 8 9 8 8 9 8 8 9 8 8 9 8 8 9 8 9 8 8 9 8 9 8 8 9 8 9 8 9 8 9 8 9 8 9 8 9 8 9 8 9 60 59 58 57 56 28 27 1 2.8 2.7 2 5.6 5.4 3 8.4 8.1 4 11.2 10.8 5 14.0 13.5 6 16.8 16.2 7 19.6 18.9 8 22.4 21.6 9 25.2 24.3 20 1 2.0 2 4.0 3 6.0 4 8.0 5 10.0 6 12.0 7 14.0 8 16.0 9 18.0 19 1 1.9 2 3.8 3 5.7 4 7.6 5 9.5 6 11.4 7 13.3 8 15.2 9 17.1 18 1 1.8 2 3.6 3 5.4 4 7.2 5 9.0 6 10.8 7 12.6 8 14.4 9 16.2 9 8 1 0.9 0.8 2 1.8 1.6 3 2.7 2.4 4 3.6 3.2 5 4.5 4.0 6 5.4 4.8 7 6.3 5.6 8 7.2 6.4 9 8.1 7.2
5 6 7 8 9 9. 73 708 9. 73 727 9. 73 747 9. 73 766 9. 73 785 9.81 390 9. 81 418 9. 81 445 9.81 473 9. 81 500 0.18 610 0.18 582 0.18 555 0.18 527 0.18 500 9.92 318 9.92 310 9. 92 302 9.92 293 9. 92 285 55 54 53 52 51
10 11 12 13 14 9. 73 805 9. 73 824 9. 73 843 9. 73 863 9. 73 882 9. 81 528 9.81 556 9.81 583 9.81 611 9. 81 638 0.18 472 0.18 444 0.18 417 0.18 389 0.18 362 9. 92 277 9. 92 269 9. 92 260 9. 92 252 9.92 244 50 49 48 47 46
15 16 17 18 19 9. 73 901 9. 73 921 9. 73 940 9. 73 959 9. 73 978 9.81 666 9.81 693 9.81 721 9.81 748 9.81 776 0.18 334 0.18 307 0.18 279 0.18 252 0.18 224 9. 92 235 9. 92 227 9. 92 219 9. 92 211 9.92 202 45 44 43 42 41
20 21 22 23 24 9. 73 997 9. 74 017 9. 74 036 9. 74 055 9. 74 074 9.81 803 9.81 831 9.81 858 9. 81 886 9. 81 913 0.18 197 0.18 169 0.18 142 0.18 114 0.18 087 9. 92 194 9. 92 186 9. 92 177 9. 92 169 9. 92 161 40 39 38 37 36
25 26 27 28 29 9. 74 093 9. 74 113 9. 74 132 9.74 151 9. 74 170 9. 81 941 9.81 968 9. 81 996 9. 82 023 9. 82 051 0.18 059 0.18 032 0.18 004 0.17 977 0.17 949 9.92 152 9. 92 144 9.92 136 9.92 127 9. 92 119 35 34 33 32 31
30 31 32 33 34 9.74 189 9. 74 208 9. 74 227 9. 74 246 9. 74 265 9. 82 078 9. 82 106 9.82 133 9.82 161 9.82 188 0.17 922 0.17 894 0.17 867 0.17 839 0.17 812 9. 92 111 9. 92 102 9. 92 094 9. 92 086 9.92 077 30 29 28 27 26
35 36 37 38 39 9. 74 284 9. 74 303 9. 74 322 9. 74 341 9. 74 360 9. 82 215 9.82 243 9. 82 270 9.82 298 9. 82 325 0.17 785 0.17 757 0.17 730 0.17 702 0.17 675 9. 92 069 9.92 060 9. 92 052 9. 92 044 9.92 035 25 24 23 22 21
40 41 42 43 44 9. 74 379 9. 74 398 9. 74 417 9. 74 436 9. 74 455 9. 82 352 9. 82 380 9.82 407 9. 82 435 9. 82 462 0.17 648 0.17 620 0.17 593 0.17 565 0.17 538 9. 92 027 9. 92 018 9. 92 010 9. 92 002 9.91 993 20 19 18 17 16
45 46 47 48 49 9. 74 474 9. 74 493 9. 74 512 9. 74 531 9. 74 549 9.82 489 9. 82 517 9. 82 544 9. 82 571 9. 82 599 0.17 511 0.17 483 0.17 456 0.17 429 0.17 401 9.91 985 9. 91 976 9. 91 968 9.91 959 9. 91 951 15 14 13 12 11
50 51 52 53 54 9. 74 568 9. 74 587 9. 74 606 9. 74 625 9. 74 644 19 19 19 19 18 19 19 19 18 19 9. 82 626 9.82 653 9. 82 681 9.82 708 9.82 735 0.17 374 0.17 347 0.17 319 0.17 292 0.17 265 9. 91 942 9.91 934 9.91 925 9.91 917 9. 91 908 10 9 8 7 6
55 56 57 58 59 9. 74 662 9. 74 681 9. 74 700 9. 74 719 9. 74 737 9. 82 762 9. 82 790 9.82 817 9. 82 844 9. 82 871 28 27 27 27 28 0.17 238 0.17 210 0.17 183 0.17 156 0.17 129 9. 91 900 9. 91 891 9. 91 883 9. 91 874 9. 91 866 5 4 3 2 1
60 9. 74 756 9.82 899 0.17 101 9. 91 857 0
L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d / 326°-, 146°- 236°-, 56°-
74
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—-
Continued
34°-, 214°- 124°-, 304°- / L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9. 74 756 9. 74 775 9. 74 794 9. 74 812 9. 74 831 9. 74 850 9. 74 868 9. 74 887 9. 74 906 9. 74 924 9. 74 943 9. 74 961 9. 74 980 9. 74 999 9. 75 017 9. 75 036 9. 75 054 9.75 073 9. 75 091 9.75 110 9.75 128 9.75 147 9.75 165 9.75 184 9. 75 202 9. 75 221 9. 75 239 9. 75 258 9. 75 276 9. 75 294 9. 75 313 9. 75 331 9. 75 350 9. 75 368 9. 75 386 9. 75 405 9. 75 423 9. 75 441 9. 75 459 9. 75 478 9. 75 496 9. 75 514 9. 75 533 9. 75 551 9. 75 569 9. 75 587 9. 75 605 9. 75 624 9. 75 642 9. 75 660 9. 75 678 9. 75 696 9. 75 714 9. 75 733 9. 75 751 9. 75 769 9. 75 787 9. 75 805 9. 75 823 9. 75 841 9. 75 859 19 19 18 19 19 18 19 19 18 19 18 19 19 18 19 18 19 18 19 18 19 18 19 18 19 18 19 18 18 19 18 19 18 18 19 18 18 18 19 18 18 19 18 18 18 18 19 18 18 18 18 18 19 18 18 18 18 18 18 18 9.82 899 9.82 926 9.82 953 9.82 980 9.83 008 9.83 035 9.83 062 9.83 089 9.83 117 9.83 144 9.83 171 9.83 198 9.83 225 9.83 252 9.83 280 9.83 307 9.83 334 9.83 361 9.83 388 9.83 415 9.83 442 9. 83 470 9.83 497 9.83 524 9.83 551 9. 83 578 9.83 605 9.83 632 9.83 659 9.83 686 9.83 713 9.83 740 9.83 768 9.83 795 9.83 822 9.83 849 9.83 876 9. 83 903 9.83 930 9.83 957 9.83 984 9.84 011 9.84 038 9. 84 065 9.84 092 9.84 119 9. 74 146 9.84 173 9.84 200 9. 84 227 9.84 284 9.84 280 9.84 307 9.84 334 9.84 361 9.84 388 9.84 415 9.84 442 9.84 469 9.84 496 9.84 523 27 27 27 28 27 27 27 28 27 27 27 27 27 28 27 27 27 27 27 27 28 27 27 27 27 27 27 27 27 27 27 28 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 26 27 27 27 27 27 27 27 27 27 0.17 101 0.17 074 0.17 047 0.17 020 0.16 992 0.16 956 0.16 938 0.16 911 0.16 883 0.16 856 0.16 829 0.16 802 0.16 775 0.16 748 0.16 720 0.16 693 0.16 666 0.16 639 0.16 612 0.16 585 0.16 558 0.16 530 0.16 503 0.16 476 0.16 449 0.16 422 0.16 395 0.16 368 0.16 341 0.16 314 0.16 287 0.16 260 0.16 232 0.16 205 0.16 178 0.16 151 0.16 124 0.16 097 0.16 070 0.16 043 0.16 016 0.15 989 0.15 962 0.15 935 0.15 908 0.15 881 0.15 854 0.15 827 0.15 800 0.15 773 0.15 746 0.15 720 0.15 693 0.15 666 0.15 639 0.15 612 0.15 585 0.15 558 0.15 531 0.15 504 0.15 477 9.91 857 9. 91 849 9.91 840 9.91 832 9.91 823 9.91 815 9. 91 806 9.91 798 9.91 789 9.91 781 9.91 772 9.91 763 9.91 755 9.91 746 9.91 738 9.91 729 9.91 720 9.91 712 9. 91 703 9.91 695 9. 91 686 9.91 677 9.91 669 9.91 660 9.91 651 9.91 643 9. 91 634 9.91 625 9.91 617 9.91 608 9.91 599 9.91 591 9.91 582 9.91 573 9.91 565 9.91 556 9.91 547 9.91 538 9.91 530 9. 91 521 9.91 512 9.91 504 9. 91 495 9.91 486 9.91.477 9. 91 469 9.91 460 9.91 451 9. 91 442 9.91 433 9.91 425 9.91 416 9. 91 407 9.91 398 9. 91 389 9.91 381 9.91 372 9.91 363 9.91 354 9.91 345 9.91 336 8 9 8 9 8 9 8 9 8 9 9 8 9 8 9 9 8 9 8 9 9 8 9 9 8 9 9 8 9 9 8 9 9 8 9 9 9 8 9 9 8 9 9 9 8 9 9 9 9 8 9 9 9 9 8 9 9 9 9 9 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 28 27 1 2.8 2.7 2 5.6 5.4 3 8.4 8.1 4 11.2 10.8 5 14.0 13.5 6 16.8 16.2 7 19.6 18.9 8 22.4 21.6 9 25.3 24.3 26 1 2.6 2 5.2 3 7.8 4 10.4 5 13.0 6 15.6 7 18.2 8 20.8 9 23.4 19 1 1.9 2 3.8 3 5.7 4 7.6 5 9.5 6 11.4 7 13.3 8 15.2 9 17.1 18 1 1.8 2 3.6 3 5.4 4 7.2 5 9.0 6 10.8 7 12.6 8 14.4 9 16.2 9 8 1 0.9 0.8 2 1.8 1.6 3 2.7 2.4 4 3.6 3.2 5 4.5 4.0 6 5.4 4.8 7 6.3 5.6 8 7.2 6.4 9 8.1 7.2
L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d / 325°-, 145°- 235°-, 55°-
75
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
35°-, 215°- / L Sin d L Tan cd L Cot L Cos - d Prop. pts.
125-°, 305°- L Cos L Cot L Tan L Sin
0 1 2 3 4 9. 75 859 9.75 877 9. 75 895 9. 75 913 9.75 931 18 18 18 18 18 9.84 523 9.84 550 9.84 576 9.84 603 9.84 630 27 26 27 27 27 0.15 477 0.15 450 0.15 424 0.15 397 0.15 370 9.91 336 9.91 328 9.91 319 9. 91 310 9.91 301 8 9 9 9 9 60 59 58 57 56 1 27 2.7 5.4 8.1 0.8 3.5 6.2 R Q 26 2.6 5.2 7.8 10.4 13.0 15.6 18.2 20.8 23.4
5 6 7 8 9 9.75 949 9. 75 967 9.75 985 9.76 003 9. 76 021 18 18 18 18 18 9.84 657 9.84 684 9.84 711 9.84 738 9.84 764 27 27 27 26 27 0.15 343 0.15 316 0.15 289 0.15 262 0.15 236 9.91 292 9.91 283 9. 91 274 9. 91 266 9.91 257 9 9 8 9 9 55 54 53 52 51 2 3 4 5 6 7 1 1 1
10 11 12 13 14 9.76 039 9.76 057 9. 76 075 9.76 093 9. 76 111 18 18 18 18 18 9.84 791 9.84 818 9.84 845 9.84 872 9.84 899 27 27 27 27 26 0.15 209 0.15 182 0.15 155 0.15 128 0.15 101 9. 91 248 9.91 239 9. 91 230 9.91 221 9.91 212 9 9 9 9 9 50 49 48 47 46 8 9 21.6 24.3
15 16 17 18 19 9.76 129 9.76 146 9.76 164 9.76 182 9. 76 200 17 18 18 18 18 9. 84 925 9.84 952 9. 84 979 9.85 006 9.85 033 27 27 27 27 26 0.15 075 0.15 048 0.15 021 0.14 994 0.14 967 9.91 203 9.91 194 9.91 185 9.91 176 9.91 167 9 9 9 9 9 45 44 43 42 41 1 2 3 4 5 6 7 8 9 18 1.8 3.6 5.4 7.2
20 21 22 23 24 9. 76 218 9.76 236 9. 76 253 9. 76 271 9.76 289 18 17 18 18 18 9.85 059 9.85 086 9.85 113 9.85 140 9.85 166 27 27 27 26 27 0.14 941 0.14 914 0.14 887 0.14 860 0.14 834 9.91 158 9.91 149 9.91 141 9.91 132 9. 91 123 9 8 9 9 9 43 39 38 37 36 10.8 12.6 14.4 16.2
25 26 27 28 29 9.76 307 9. 76 324 9. 76 342 9. 76 360 9. 76 378 17 18 18 18 17 9.85 193 9.85 220 9.85 247 9.85 273 9.85 300 27 27 26 27 27 0.14 807 0.14 780 0.14 753 0.14 727 0.14 700 9.91 114 9.91 105 9. 91 096 9.91 087 9.91 078 9 9 9 9 9 35 34 33 32 31 1 2 3 4 5 7 3 17 1.7 3.4
30 31 32 33 34 9. 76 395 9. 76 413 9. 76 431 9. 76 448 9. 76 466 18 18 17 18 18 9.85 327 9.85 354 9.85 380 9.85 407 9.85 434 27 26 27 27 26 0.14 673 0.14 646 0.14 620 0.14 593 0.14 566 9. 91 069 9. 91 060 9.91 051 9. 91 042 9.91 033 9 9 9 9 10 30 29 28 27 26 6.8 8.5 10.2 11.9 13.6 15.3 10
35 36 37 38 39 9. 76 484 9. 76 501 9. 76 519 9.76 537 9. 76 554 17 18 18 17 18 9.85 460 9.85 487 9.85 514 9.85 540 9.85 567 27 27 26 27 27 0.14 540 0.14 513 0.14 486 0.14 460 0.14 433 9. 91 023 9.91 014 9.91 005 9.90 996 9.90 987 9 9 9 9 9 25 24 23 22 21
40 41 42 43 44 9.76 572 9.76 590 9. 76 607 9. 76 625 9. 76 642 18 17 18 17 18 9.85 594 9.85 620 9.85 647 9.85 674 9.85 700 26 27 27 26 27 0.14 406 0.14 380 0.14 353 0.14 326 0.14 300 9. 90 978 9. 90 969 9. 90 960 9. 90 951 9.90 942 9 9 9 9 9 20 19 18 17 16 4 2 3 4 5 6 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0
45 46 47 48 49 9. 76 660 9. 76 677 9. 76 695 9.76 712 9.76 730 17 18 17 18 17 9.85 727 9.85 754 9.85 780 9.85 807 9.85 834 27 26 27 27 26 0.14 273 0.14 246 0.14 220 0.14 193 0.14 166 9.90 933 9.90 924 9.90 915 9.90 906 9. 90 896 9 9 9 10 9 15 14 13 12 11 7 8 9
50 51 52 53 54 9. 76 747 9. 76 765 9. 76 782 9.76 800 9.76 817 18 17 18 17 18 9.85 860 9.85 887 9.85 913 9. 85 940 9.85 967 27 26 27 27 26 0.14 140 0.14 113 0.14 087 0.14 060 0.14 033 9.90 887 9.90 878 9.90 869 9. 90 860 9.90 851 9 9 9 9 9 10 9 8 7 6 1 2 3 4 9 0.9 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 8 0.8 1.6 2.4 3.2
55 56 57 58 59 9.76 835 9. 76 852 9. 76 870 9. 76 887 9. 76 904 17 18 17 17 18 9.85 993 9.86 020 9.86 046 9. 86 073 9.86 100 27 26 27 27 26 0.14 007 0.13 980 0.13 954 0.13 927 0.13 900 9. 90 842 9. 90 832 9.90 823 9. 90 814 9.90 805 10 9 9 9 9 5 4 3 2 1 5 6 7 8 9 4.0 4.8 5.6 6.4 7.2
60 9. 76 922 9.86 126 0.13 874 9.90 796 0
L Sin d L Tan L Cot L Cos / 324° 144°-
L Cos L Cot L Tan L Sin d 34° 54°-
76
Table III.—Common Logarithms of Functions of Angles in Degrees andMinutes—
Continued
36°-, 216°- 126°-, 306°- / L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9. 76 922 9.76 939 9. 76 957 9. 76 974 9.76 991 9.77 009 9. 77 026 9. 77 043 9.77 061 9. 77 078 9. 77 095 9.77 112 9.77 130 9. 77 147 9.77 164 9. 77 181 9.77 199 9.77 216 9.77 233 9. 77 250 9. 77 268 9.77 285 9. 77 302 9. 77 319 9. 77 336 9. 77 353 9.77 370 9. 77 387 9. 77 405 9. 77 422 9.77 439 9. 77 456 9.77 473 9.77 490 9.77 507 9.77 524 9. 77 541 9. 77 558 9. 77 575 9. 77 592 9. 77 609 9.77 626 9. 77 643 9. 77 660 9. 77 677 9. 77 694 9.77 711 9.77 728 9. 77 744 9.77 761 9.77 778 9. 77 795 9. 77 812 9.77 829 9.77 846 9. 77 862 9. 77 879 9.77 896 9. 77 913 9. 77 930 9.77 946 17 18 17 17 18 17 17 18 17 17 17 18 17 17 17 18 17 17 17 18 17 17 17 17 17 17 17 18 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 17 16 17 17 17 17 17 17 16 17 17 17 17 16 9. 86 126 9.86 153 9.86 179 9.86 206 9.86 232 9.86 259 9. 86 285 9.86 312 9.86 338 9.86 365 9.86 392 9.86 418 9. 86 445 9.86 471 9.86 498 9.86 524 9.86 551 9.86 577 9.86 603 9.86 630 9.86 656 9.86 683 9.86 709 9.86 736 9.86 762 9. 86 789 9.86 815 9.86 842 9.86 868 9.86 894 9. 86 921 9. 86 947 9.86 974 9.87 000 9.87 027 9. 87 053 9.87 079 9. 87 106 9. 87 132 9.87 158 9.87 185 9. 87 211 9.87 238 9. 87 264 9.87 290 9.87 317 9.87 343 9. 87 369 9. 87 396 9.87 422 9.87 448 9.87 475 9. 87 501 9.87 527 9. 87 554 9.87 580 9.87 606 9.87 633 9.87 659 9.87 685 9.87 711 27 26 27 26 27 26 27 26 27 27 26 27 26 27 26 27 26 26 27 26 27 26 27 26 27 26 27 26 26 27 26 27 26 27 26 26 27 26 26 27 26 27 26 26 27 26 26 27 26 26 27 26 26 27 26 26 27 26 26 26 0.13 874 0.13 847 0.13 821 0.13 794 0.13 768 0.13 741 0.13 715 0.13 688 0.13 662 0.13 635 0.13 608 0.13 582 0.13 555 0.13 529 0.13 502 0.13 476 0.13 449 0.13 423 0.13 397 0.13 370 0.13 344 0.13 317 0.13 291 0.13 264 0.13 238 0.13 211 0.13 185 0.13 158 0.13 132 0.13 106 0.13 079 0.13 053 0.13 026 0.13 000 0.12 973 0.12 947 0.12 921 0.12 894 0.12 868 0.12 842 0.12 815 0.12 789 0.12 762 0.12 736 0.12 710 0.12 683 0.12 657 0.12 631 0.12 604 0.12 578 0.12 552 0.12 525 0.12 499 0.12 473 0.12 446 0.12 420 0.12 394 0.12 367 0.12 341 0.12 315 0.12 289 9.90 796 9.90 787 9.90 777 9.90 768 9.90 759 9.90 750 9.90 741 9.90 731 9.90 722 9.90 713 9. 90 704 9.90 694 9.90 685 9. 90 676 9.90 667 9.90 657 9.90 648 9.90 639 9.90 630 9.90 620 9.90 611 9.90 602 9.90 592 9.90 583 9.90 574 9.90 565 9.90 555 9.90 546 9.90 537 9.90 527 9.90 518 9.90 509 9.90 499 9.90 490 9.90 480 9. 90 471 9.90 462 9.90 452 9.90 443 9.90 434 9. 90 424 9.90 415 9. 90 405 9.90 396 9. 90 386 9. 90 377 9.90 368 9.90 358 9.90 349 9.90 339 9.90 330 9.90 320 9.90 311 9.90 301 9.90 292 9.90 282 9. 90 273 9.90 263 9.90 254 9.90 244 9.90 235 9 10 9 9 9 9 10 9 9 9 10 9 9 9 10 9 9 9 10 9 9 10 9 9 9 10 9 9 10 9 9 10 9 10 9 9 10 9 9 10 9 10 9 10 9 9 10 9 10 9 10 9 10 9 10 9 10 9 10 9 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 27 26 1 2.7 2.6 2 5.4 5.2 3 8.1 7.8 4 10.8 10.4 5 13.5 13.0 6 16.2 15.6 7 18.9 18.2 8 21.6 20.8 9 24.3 23.4 18 1 1.8 2 3.6 3 5.4 4 7.2 5 9.0 6 10.8 7 12.6 8 14.4 9 16.2 17 1 1.7 2 3.4 3 5.1 4 6.8 5 8.5 6 10.2 7 11.9 8 13.6 9 15.3 16 1 1.6 2 3.2 3 4.8 4 6.4 5 8.0 6 9.6 7 11.2 8 12.8 9 14.4 10 9 1 1.0 0.9 2 2.0 1.8 3 3.0 2.7 4 4.0 3.6 5 5.0 4.5 6 6.0 5.4 7 7.0 6.3 8 8.0 7.2 9 9.0 8.1
L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d / 323°-, 143°- 233°-, 53°-
609023°—44----6
77
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
37°-, 217°- 127°-, 307°- / L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d Prop. pts.
■ 0 1 2 3 4 9. 77 946 9. 77 963 9. 77 980 9. 77 997 9. 78 013 17 17 17 16 17 17 16 17 17 16 17 17 16 17 17 16 17 16 17 17 16 17 16 17 16 17 16 17 16 17 16 17 16 16 17 16 17 16 16 17 16 17 16 16 17 16 16 16 17 16 16 17 16 16 16 16 17 16 16 16 9.87 711 9.87 738 9.87 764 9. 87 790 9. 87 817 27 26 26 27 26 26 26 27 26 26 26 27 26 26 26 26 27 26 26 26 26 27 26 26 26 26 27 26 26 26 26 26 27 26 26 26 26 26 26 26 27 26 26 26 26 26 26 26 26 26 26 27 26 26 26 26 26 26 26 26 0.12 289 0.12 262 0.12 236 0.12 210 0.12 183 9. 90 235 9.90 225 9.90 216 9.90 206 9.90 197 10 9 10 9 10 9 10 9 io 10 . 9 10 9 10 10 9 10 9 10 10 9 10 10 9 10 10 9 10 10 9 10 10 9 10 10 10 9 10 10 10 9 10 10 10 9 10 10 10 10 9 10 10 10 10 10 9 10 10 10 10 60 59 58 57 56 27 1 2.7 2 5.4 3 8.1 4 10.8 5 13.5 6 16.2 7 18.9 8 21.6 9 24.3 26 1 2.6 2 5.2 3 7.8 4 10.4 5 13.0 6 15.6 7 18.2 8 20.8 9 23.4 17 1 1.7 2 3.4 3 5.1 4 6.8 5 8.5 6 10.2 7 11.9 8 13.6 9 15.3 16 1 1.6 2 3.2 3 4.8 4 6.4 5 8.0 6 9.6 7 11.2 8 12.8 9 14.4 10 9 1 1.0 0.9 2 2.0 1.8 3 3.0 2.7 4 4.0 3.6 5 5.0 4.5 6 6.0 5.4 7 7.0 6.3 8 8.0 7.2 9 9.0 8.1
5 6 7 8 9 9. 78 030 9. 78 047 9. 78 063 9. 78 080 9. 78 097 9. 87 843 9. 87 869 9. 87 895 9. 87 922 9. 87 948 0.12 157 0.12 131 0.12 105 0.12 078 0.12 052 9. 90 187 9. 90 178 9.90 168 9.90 159 9.90 149 55 54 53 52 51
10 11 12 13 14 9. 78 113 9. 78 130 9. 78 147 9. 78 163 9. 78 180 9.87 974 9. 88 000 9.88 027 9.88 053 9.88 079 0.12 026 0.12 000 0.11 973 0.11 947 0.11 921 9.90 139 9.90 130 9.90 120 9. 90 111 9.90 101 50 49 48 47 46
15 16 17 18 19 9. 78 197 9. 78 213 9. 78 230 9. 78 246 9.78 263 9.88 105 9.88 131 9. 88 158 9.88 184 9.88 210 0.11 895 0.11 869 0.11 842 0.11 816 0.11 790 9.90 091 9.90 082 9.90 072 9. 90 063 9.90 053 45 44 43 42 41
20 21 22 23 24 9. 78 280 9. 78 296 9. 78 313 9. 78 329 9. 78 346 9.88 236 9. 88 262 9.88 289 9.88 315 9.88 341 0.11 764 0.11 738 0.11 711 0.11 685 0.11 659 9. 90 043 9. 90 034 9.90 024 9. 90 014 9.90 005 40 39 38 37 36
25 26 27 28 29 9. 78 362 9. 78 379 9. 78 395 9. 78 412 9. 78 428 9. 88 367 9. 88 393 9.88 420 9.88 446 9. 88 472 0.11 633 0.11 607 0.11 580 0.11 554 0.11 528 9. 89 995 9. 89 985 9.89 976 9. 89 966 9.89 956 35 34 33 32 31
30 31 32 33 34 9. 78 445 9. 78 461 9. 78 478 9. 78 494 9. 78 510 9.88 498 9.88 524 9.88 550 9.88 577 9.88 603 0.11 502 0.11 476 0.11 450 0.11 423 0.11 397 9.89 947 9.89 937 9. 89 927 9.89 918 9.89 908 30 29 28 27 26
35 36 37 38 39 9. 78 527 9. 78 543 9. 78 560 9. 78 576 9. 78 592 9. 88 629 9.88 655 9.88 681 9.88 707 9.88 733 0.11 371 0.11 345 0.11 319 0.11 293 0.11 267 9.89 898 9.89 888 9.89 879 9.89 869 9.89 859 25 24 23 22 21
40 41 42 43 44 9. 78 609 9. 78 625 9. 78 642 9. 78 658 9. 78 674 9.88 759 9. 88 786 9. 88 812 9. 88 838 9. 88 864 0.11 241 0.11 214 0.11 188 0.11 162 0.11 136 9.89 849 9.89 840 9.89 830 9. 89 820 9. 89 810 20 19 18 17 16 15 14 13 12 11
45 46 47 48 49 9. 78 691 9. 78 707 9. 78 723 9. 78 739 9. 78 756 9. 88 890 9. 88 916 9.88 942 9.88 968 9. 88 994 0.11 110 0.11 084 0.11 058 0.11 032 0.11 006 9.89 801 9.89 791 9.89 781 9. 89 771 9.89 761
50 51 52 53 54 9. 78 772 9. 78 788 9. 78 805 9. 78 821 9. 78 837 9. 89 020 9. 89 046 9. 89 073 9. 89 099 9. 89 125 0.10 980 0.10 954 0.10 927 0.10 901 0.10 875 9.89 752 9.89 742 9.89 732 9. 89 722 9.89 712 10 9 8 7 6
55 56 57 58 59 9. 78 853 9. 78 869 9. 78 886 9. 78 902 9. 78 918 9. 89 151 9. 89 177 9.89 203 9.89 229 9. 89 255 0.10 849 0.10 823 0.10 797 0.10 771 0.10 745 9. 89 702 9. 89 693 9. 89 683 9.89 673 9. 89 663 5 4 3 2 1
60 9. 78 934 9. 89 281 0.10 719 9. 89 653 0
L Sin d L Tan cd L Cot L Cos d / 322°-, 142°-
L Cos L> Cot L Tan L Sin 232°-, 52°-
78
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
38°-, 218°- / L Sin d L Tan cd L Cot L Cos d Prop. pts.
128°-, 308°- L Cos L Cot L Tan L Sin
X 0 1 2 3 4 9.78 934 9.78 950 9.78 967 9.78 983 9.78 999 16 17 16 16 16 16 16 16 16 16 16 17 16 16 16 16 16 16 16 16 16 16 16 15 16 16 16 16 16 16 16 16 16 15 16 16 16 16 16 15 16 16 16 15 16 16 16 15 16 16 15 16 16 15 16 16 15 16 16 15 9 89 281 8.. 89 307 9.89 333 9.89 359 9.89 385 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 25 26 26 26 26 26 26 26 26 26 26 25 26 26 26 26 26 26 26 25 26 26 26 26 26 26 25 26 26 26 0.10 719 0.10 693 0.10 667 0.10 641 0.10 615 9.89 653 9.89 643 9.89 633 9.89 624 9.89 614 10 10 10 10 10 10 10 10 10 10 10 10 ' 10 10 10 9 10 10 10 10 10 10 10 10 10 10 10 10 11 10 10 10 10 10 10 10 10 10 10 10 10 11 10 10 10 10 10 10 11 10 10 10 10 10 11 10 10 10 11 10 60 59 58 57 56 26 25 1 2.6 2.5 2 5.2 5.0 3 7.8 7.5 4 10.4 10.0 5 13.0 12.5 6 15.6 15.0 7 18.2 17.5 8 20.8 20.0 9 23.4 22.5 17 1 1.7 2 3.4 3 5.1 4 6.8 5 8.5 6 10.2 7 11.9 8 13.6 9 15.3 16 15 1 1.6 1.5 2 3.2 3.0 3 1.8 4.5 4 6.4 6.0 5 8.0 7.5 6 9.6 9.0 7 11.2 10.5 8 12.8 12.0 9 14.4 13.5 11 1 1.1 2 2.2 3 3.3 4 4.4 5 5.5 6 6.6 7 7.7 8 8.8 9 9.9 10 9 1 1.0 0.9 2 2.0 1.8 3 3.0 2.7 4 4.0 3.6 5 5.0 4.5 6 6.0 5.4 7 7.0 6.3 8 8.0 7.2 9 9.0 8.1
5 6 7 8 9 9.79 015 9.79 031 9.79 047 9.79 063 9.79 079 9. 89 411 9.89 437 9.89 463 9. 89 489 9.89 515 0.10 589 0.10 563 0.10 537 0.10 511 0.10 485 9. 89 604 9.89 594 9. 89 584 9. 89 574 9. 89 564 55 54 53 52 51
10 11 12 13 14 9. 79 095 9. 79 111 9.79 128 9. 79 144 9.79 160 9.89 541 9.89 567 9.89 593 9. 89 619 9.89 645 0.10 459 0.10 433 0.10 407 0.10 381 0.10 355 9. 89 554 9.89 544 9.89 534 9.89 524 9. 89 514 50 49 48 47 46
15 16 17 18 19 9. 79 176 9.79 192 9. 79 208 9. 79 224 9. 79 240 9.89 671 9. 89 697 9.89 723 9. 89 749 9.89 775 0.10 329 0.10 303 0.10 277 0.10 251 0.10 225 9.89 504 9.89 495 9.80 485 9.89 475 9.89 465 45 44 43 42 41
20 21 22 23 24 9. 79 256 9. 79 272 9.79 288 9. 79 304 9. 79 319 9.89 801 9.89 827 9. 89 853 9. 89 879 9.89 905 0.10 199 0.10 173 0.10 147 0.10 121 0.10 095 9. 89 455 9.89 445 9. 89 435 9.89 425 9. 89 415 40 39 38 37 36
25 26 27 28 29 9. 79 335 9. 79 351 9.79 367 9. 79 383 9. 79 399 9.89 931 9.89 957 9. 89 983 9. 90 009 9. 90 035 0.10 069 0.10 043 0.10 017 0. 09 991 0.09 965 9. 89 405 9. 89 395 9.89 385 9.89 375 9.89 364 35 34 33 32 31
30 31 32 33 34 9. 79 415 9. 79 431 9. 79 447 9. 79 463 9. 79 478 9.90 061. 9.90 086 9.90 112 9. 90 138 9. 90 164 0.09 939 0.09 914 0. 09 888 0.09 862 0.09 836 9.89 354 9.89 344 9.89 334 9.89 324 9.89 314 30 29 28 27 26
35 36 37 38 39 9. 79 494 9. 79 510 9.79 526 9.79 542 9. 79 558 9.90 190 9.90 216 9. 90 242 9. 90 268 9.90 294 0.09 810 0. 09 784 0. 09 758 0. 09 732 0.09 706 9.89 304 9. 89 294 9.89 284 9. 89 274 9. 89 264 25 24 23 22 21
40 41 42 43 44 9. 79 573 9.79 589 9. 79 605 9. 79 621 9.79 636 9.90 320 9. 90 346 9.90 371 9. 90 397 9. 90 423 0. 09 680 0.09 654 0. 09 629 0. 09 603 0.09 577 9.89 254 9. 89 244 9. 89 233 9. 89 223 9.89 213 20 19 18 17 16
45 46 47 48 49 9.79 652 9. 79 668 9. 79 684 9.79 699 9. 79 715 9.90 449 9.90 475 9.90 501 9.90 527 9.90 553 0.09 551 0.09 525 0.09 499 0.09 473 0.09 447 9. 89 203 9. 89 193 9.89 183 9.89 173 9.89 162 15 14 13 12 11
50 51 52 53 54 9. 79 731 9. 79 746 9.79 762 9.79 778 9. 79 793 9.90 578 9.90 604 9.90 630 9.90 656 9.90 682 0.09 422 0. 09 396 0.09 370 0.09 344 0. 09 318 9.89 152 9.89 142 9. 89 132 9.89 122 9.89 112 10 9 8 7 6
55 56 57 58 59 60 9. 79 809 9. 79 825 9. 79 840 9. 79 856 9. 79 872 9.79 887 9. 90 708 9.90 734 9. 90 759 9. 90 785 9.90 811 9.90 837 0.09. 292 0.09 266 0.09 241 0.09 215 0.09 189 0.09 163 9. 89 101 9.89 091 9.89 081 9. 89 071 9.89 060 9.89 050 5 4 3 2 1 0
L Sin d L Tan cd L Cot L Cos d / 321°-, 141°-
L Cos L Cot L Tan L Sin 231°-, 51°-
79
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—-
Continued
39°-, 219°- / L Sin d L Tan cd L Cot L Cos d Prop. pts.
129°-, 309°- L Cos L Cot L Tan L Sin
0 9.79 887 16 9.90 837 26 0.09 163 9. 89 050 60
1 9. 79 903 15 9. 90 863 9A 0.09 137 9.89 040 10 59
2 9. 79 918 16 9. 90 889 0.09 111 9. 89 030 10 58 26
3 9. 79 934 16 9. 90 914 zo 9A 0.09 086 9.89 020 10 57
4 9. 79 950 15 9.90 940 26 0.09 060 9.89 009 11 10 56 1 2 2.6 5.2
5 9. 79 965 16 9. 90 966 26 0. 09 034 9.88 999 55 3 7.8
6 9. 79 981 15 9. 90 992 26 0.09 008 9.88 989 10 11 54 4 10.4
7 9. 79 996 16 9. 91 018 25 0.08 982 9. 88 978 11 53 5 13.0
8 9.80 012 15 9.91 043 26 0.08 957 9. 88 968 10 in 52 6 15.6
9 9. 80 027 16 9. 91 069 26 0.08 931 9.88 958 1U 10 51 7 18.2
9. 80 043 — — 8 20.8
10 15 9. 91 095 26 0.08 905 9.88 948 11 50 9 23.4
11 9. 80 058 16 9.91 121 9A 0.08 879 9. 88 937 11 49
12 9.80 074 15 9.91 147 9£ 0. 08 853 9.88 927 10 48
13 9.80 089 16 9.91 172 26 26 0.08 828 9. 88 917 10 11 47
14 9.80 105 15 9.91 198 0.08 802 9.88 906 11 10 46 25
15 9.80 120 16 9.91 224 26 0. 08 776 9.88 896 45 1 2.5
16 9. 80 136 15 9.91 250 90 0.08 750 9. 88 886 10 44 2 5.0
17 9.80 151 15 9.91 276 25 0.08 724 9. 88 875 11 in 43 3 7.5
18 9.80 166 16 9. 91 301 26 0. 08 699 9.88 865 1U 42 4 10.8
19 9.80 182 15 9. 91 327 26 0.08 673 9.88 855 10 11 41 5 12.5
9. 80 197 ■ ■ - , 6 15.0
20 16 9.91 353 26 0. 08 647 9.88 844 in 40 7 17.5
21 9.80 213 15 9. 91 379 25 0.08 621 9.88 834 in 39 8 20.0
22 9.80 228 16 9.91 404 26 0.08 596 9.88 824 1U 11 38 9 22.5
23 9. 80 244 15 9. 91 430 26 0. 08 570 9.88 813 11 in 37
24 9.80 259 15 9.91 456 26 0.08 544 9.88 803 1U 10 36
9.80 274
25 16 9. 91 482 25 0.08 518 9.88 793 35
26 9. 80 290 15 9. 91 507 26 0.08 493 9.88 782 11 i n 34 16
27 9.80 305 15 9.91 533 26 0.08 467 9. 88 772 1U 11 33 1 1.6
28 9.80 320 16 9.91 559 26 0.08 441 9.88 761 11 in 32 2 3.2
29 9.80 336 15 9.91 585 25 0.08 415 9. 88 751 1U 10 31 3 4.8
■ ■ ■■ 4 6.4
30 9.80 351 15 9.91 610 26 0.08 390 9. 88 741 11 30 5 8.0
31 9. 80 366 16 9. 91 636 2fi 0.08 364 9.88 730 ii in 29 6 9.6
32 9.80 382 15 9.91 662 26 0.08 338 9. 88 720 1U 11 28 7 11.2
33 9. 80 397 15 9. 91 688 25 0.08 312 9.88 709 ii in 27 8 12.8
34 9.80 412 16 9. 91 713 26 0.08 287 9.88 699 1U 11 26 9 14.4
9.80 428 ' ■ ■
35 15 9.91 739 26 0.08 261 9. 88 688 in 25
36 9.80 443 15 9.91 765 26 0.08 235 9.88 678 1U 24
37 9.80 458 15 9.91 791 25 0.08 209 9. 88 668 10 23
38 9. 80 473 16 9. 91 816 26 0.08 184 9. 88 657 11 in 22 10
39 9.80 489 15 9.91 842 26 0.08 158 9.88 647 1U 11 21 1 1.5
9.80 504 ■ 2 3.0
40 15 9. 91 868 25 0.08 132 9. 88 636 in 20 3 4.5
41 9. 80 519 15 9.91 893 26 0.08 107 9. 88 626 1U 21 19 4 6.0
42 9. 80 534 16 9. 91 919 26 0.08 081 9.88 615 in 18 5 7.5
43 9.80 550 15 9. 91 945 26 0.08 055 9. 88 605 1U 11 17 6 9.0
44 45 9. 80 565 9. 80 580 15 15 9. 91 971 9. 91 996 25 26 0.08 029 0.08 004 9. 88 594 9.88 584 11 10 11 16 15 7 8 9 10.5 12.0 13.5
46 9. 80 595 15 9. 92 022 9A 0.07 978 9. 88 573 11 14
47 9.80 610 15 9.92 048 9K 0.07 952 9.88 563 10 13
48 9. 80 625 16 9. 92 073 9A 0.07 927 9.88 552 11 12
49 9. 80 641 15 9.92 099 26 0.07 901 9.88 542 10 11 11 11 10
50 9.80 656 15 9. 92 125 25 0.07 875 9.88 531 in 10 1 .1 1.0
51 9. 80 671 15 9.92 150 26 0.07 850 9.88 521 1U 11 9 2 2.2 2.0
52 9.80 686 15 | 9.92 176 26 0.07 824 9.88 510 11 11 8 3 3.3 3.0
53 9. 80 701 15 9.92 202 25 0. 07 798 9.88 499 11 in 7 4 4.4 4.0
54 9. 80 716 15 9. 92 227 26 0.07 773 9.88 489 1U 11 6 5 5.5 5.0
9.80 731 — —■ ■ 6 6.6 6.0
55 15 9. 92 253 9A 0.07 747 9. 88 478 5 7 7.7 7.0
56 9. 80 746 16 9.92 279 25 0.07 721 9. 88 468 10 4 8 8.8 8.0
57 9. 80 762 15 9.92 304 9A 0.07 696 9.88 457 11 1 A 3 9 9.9 9.0
58 9. 80 777 15 9. 92 330 9A 0.07 670 9.88 447 1U 2
59 9.80 792 15 9. 92 356 25 0.07 644 9. 88 436 11 11 1
9.80 807 — ■
60 9.92 381 0.07 619 9.88 425 0
L Sin L Tan L Cot L Cos 320° 140°-
— d — cd — d / —
L Cos L Cot L Tan L Sin 230°-, 50°-
— — —
80
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
40°-, 220°- / L Sin L Tan cd L Cot L Cos d Prop. pts.
130°-, 310°- L Cos L Cot L Tan L Sin
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9. 80 807 9. 80 822 9.80 837 9.80 852 9.80 867 9. 80 882 9.80 897 9.80 912 9. 80 927 9.80 942 9. 80 957 9. 80 972 9. 80 987 9. 81 002 9.81 017 9.81 032 9.81 047 9.81 061 9.81 076 9.81 091 9.81 106 9.81 121 9.81 136 9.81 151 9.81 166 9.81 180 9.81 195 9.81 210 9.81 225 9. 81 240 9.81 254 9.81 269 9.81 284 9.81 299 9.81 314 9. 81 328 9.81 343 9. 81 358 9. 81 372 9. 81 387 9.81 402 9.81 417 9.81 431 9.81 446 9.81 461 9.81 475 9.81 490 9.81 505 9.81 519 9.81 534 9. 81 549 9.81 563 9.81 578 9.81 592 9.81 607 9.81 622 9.81 636 9.81 651 9.81 665 9.81 680 9. 81 694 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 14 15 15 15 15 15 15 15 14 15 15 15 15 14 15 15 15 15 14 15 15 14 15 15 15 14 15 15 14 15 15 14 15 15 14 15 14 15 15 14 15 14 15 14 9. 92 381 9.92 407 9.92 433 9.92 458 9.92 484 9.92 510 9.92 535 9.92 561 9. 92 587 9.92 612 9.92 638 9. 92 663 9.92 689 9. 92 715 9.92 740 9.92 766 9.92 792 9. 92 817 9. 92 843 9. 92 868 9.92 894 9. 92 920 9.92 945 9. 92 971 9.92 996 9.93 022 9. 93 048 9. 93 073 9.93 099 9. 93 124 9.93 150 9.93 175 9.93 201 9.93 227 9.93 252 9.93 278 9.93 303 9.93 329 9.93 354 9.93 380 9.93 406 9. 93 431 9.93 457 9.93 482 9.93 508 9. 93 533 9.93 559 9. 93 584 9. 93 610 9. 93 636 9. 93 661 9.93 687 9.93 712 9.93 738 9.93 763 9. 93 789 9. 93 814 9. 93 840 9. 93 865 9.93 891 9.93 916 26 26 25 26 26 25 26 26 25 26 25 26 26 25 26 26 25 26 25 26 26 25 26 25 26 26 25 26 25 26 25 26 26 25 26 25 26 25 26 26 25 26 25 26 25 26 25 26 26 25 26 25 26 25 26 25 26 25 26 25 0.07 619 0.07 593 0.07 567 0.07 542 0. 07 516 0. 07 490 0.07 465 0.07 439 0.07 413 0. 07 388 0.07 362 0.07 337 0.07 311 0.07 285 0.07 260 0.07 234 0.07 208 0.07 183 0.07 157 0.07 132 0.07 106 0. 07 080 0.07 055 0. 07 029 0.07 004 0. 06 978 0. 06 952 0. 06 927 0.06 901 0.06 876 0.06 850 0.06 825 0.06 799 0.06 773 0.06 748 0. 06 722 0.06 697 0. 06 671 0. 06 646 0.06 620 0.06 594 0.06 569 0.06 543 0. 06 518 0. 06 492 0.06 467 0. 06 441 0. 06 416 0. 06 390 0.06 364 0.06 339 0. 06 313 0.06 288 0. 06 262 0.06 237 0. 06 211 0. 06 186 0. 06 160 0.06 135 0.06 109 0.06 084 9. 88 425 9. 88 415 9.88 404 9.88 394 9.88 383 9.88 372 9. 88 362 9.88 351 9.88 340 9.88 330 9.88 319 9.88 308 9.88 298 9.88 287 9.88 276 9.88 266 9. 88 255 9.88 244 9.88 234 9.88 223 9.88 212 9.88 201 9. 88 191 9. 88 180 9.88 169 9. 88 158 9.88 148 9. 88 137 9.88 126 9.88 115 9. 88 105 9.88 094 9. 88 083 9. 88 072 9.88 061 9.88 051 9. 88 040 9.88 029 9. 88 018 9.88 007 9. 87 996 9.87 985 9. 87 975 9. 87 964 9.87 953 9. 87 942 9. 87 931 9.87 920 9. 87 909 9. 87 898 9.87 887 9. 87 877 9.87 866 9. 87 855 9.87 844 9.87 833 9.87 822 9. 87 811 9.87 800 9.87 789 9.87 778 10 11 10 11 11 10 11 11 10 11 11 10 11 11 10 11 11 10 11 11 11 10 11 11 11 10 11 11 11 10 11 11 11 11 10 11 11 11 11 11 11 10 11 11 11 11 11 11 11 11 10 11 11 11 11 11 11 11 11 11 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 27 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 26 1 2.6 2 5.2 3 7.8 4 10.4 5 13.0 6 15.6 7 18.2 8 20.8 9 23.4 25 1 2.5 2 5.0 3 7.5 4 10.0 5 12.5 6 15.0 7 17.5 8 20.0 9 22.5 15 1 1.5 2 3.0 3 4.5 4 6.0 5 7.5 6 9.0 7 10.5 8 12.0 9 13.5 14 1 1.4 2 2.8 3 4.2 4 5.6 5 7.0 6 8.4 7 9.8 8 11.2 9 12.6 11 10 1 1.1 1.0 2 2.2 2.0 3 3.3 3.0 4 4.4 4.0 5 5.5 5.0 6 6.6 6.0 7 7.7 7.0 8 8.8 8.0 9 9.9 9.0
LSin L Tan cd L Cot L Cos d / 319°- 139°-
L Cos L Cot L Tan L Sin 229°-, 49°-
81
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
41°-, 221°- 131°-, 311°- / L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos LSin d Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9.81 694 9.81 709 9.81 723 9.81 738 9.81 752 9.81 767 9.81 781 9.81 796 9. 81 810 9.81 825 9. 81 839 9.81 854 9.81 868 9.81 882 9.81 897 9.81 911 9.81 926 9.81 940 9.81 955 9.81 969 9.81 983 9.81 998 9.82 012 9.82 026 9.82 041 9.82 055 9.82 069 9. 82 084 9. 82 098 9.82 112 9. 82 126 9. 82 141 9.82 155 9.82 169 9.82 184 9.82 198 9.82 212 9.82 226 9.82 240 9.82 255 9.82 269 9.82 283 9.82 297 9.82 311 9. 82 326 9.82 340 9.82 354 9.82 368 9. 82 382 9.82 396 9.82 410 9.82 424 9. 82 439 9.82 453 9.82 467 9.82 481 9.82 495 9.82 509 9.82 523 9.82 537 9. 82 551 15 14 15 14 15 14 15 14 15 14 15 14 14 15 14 15 14 15 14 14 15 14 14 15 14 14 15 14 14 14 15 14 14 15 14 14 14 14 15 14 14 14 14 15 14 14 14 14 14 14 14 15 14 14 14 14 14 14 14 14 9. 93 916 9. 93 942 9. 93 967 9. 93 993 9.94 018 9.94 044 9. 94 069 9. 94 095 9. 94 120 9. 94 146 9.94 171 9.94 197 9. 94 222 9.94 248 9.94 273 9. 94 299 9.94 324 9. 94 350 9. 94 375 9.94 401 9. 94 426 9.94 452 9.94 477 9.94 503 9.94 528 9.94 554 9.94 579 9.94 604 9. 94 630 9.94 655 9.94 681 9.94 706 9.94 732 9.94 757 9. 94 783 9. 94 808 9. 94 834 9.94 859 9.94 884 9. 94 910 9.94 935 9.94 961 9.94 986 9.95 012 9.95 037 9.95 062 9.95 088 9.95 113 9. 95 139 9.95 164 9.95 190 9. 95 215 9. 95 240 9.95 266 9.95 291 9.95 317 9.95 342 9. 95 368 9.95 393 9. 95 418 9.95 444 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 26 25 25 26 25 26 25 26 25 26 25 26 25 25 26 25 26 25 26 25 25 26 25 26 25 26 25 25 26 25 26 25 26 25 25 26 0.06 084 0.06 058 0.06 033 0.06 007 0.05 982 0.05 956 0.05 931 0.05 905 0.05 880 0.05 854 0.05 829 0.05 803 0.05 778 0.05 752 0.05 727 0.05 701 0.05 676 0.05 650 0.05 625 0.05 599 0.05 574 0.05 548 0.05 523 0.05 497 0.05 472 0.05 446 0.05 421 0.05 396 0.05 370 0.05 345 0.05 319 0.05 294 0.05 268 0.05 243 0.05 217 0.05 192 0.05 166 0.05 141 0.05 116 0.05 090 0.05 065 0.05 039 0.05 014 0.04 988 0.04 963 0.04 938 0.04 912 0.04 887 0.04 861 0.04 836 0.04 810 0.04 785 0.04 760 0.04 734 0.04 709 0.04 683 0.04 658 0.04 632 0.04 607 0.04 582 0.04 556 9. 87 778 9.87 767 9. 87 756 9. 87 745 9.87 734 9.87 723 9. 87 712 9. 87 701 9.87 690 9. 87 679 9.87 668 9.87 657 9. 87 646 9. 87 635 9.87 624 9.87 613 9.87 601 9.87 590 9. 87 579 9.87 568 9.87 557 9. 87 546 9.87 535 9.87 524 9. 87 513 9.87 501 9.87 490 9.87 479 9.87 468 9.87 457 9.87 446 9.87 434 9.87 423 9. 87 412 9.87 401 9.87 390 9.87 378 9.87 367 9.87 356 9.87 345 9. 87 334 9.87 322 9.87 311 9.87 300 9.87 288 9.87 277 9.87 266 9.87 255 9.87 243 9.87 232 9.87 221 9.87 209 9.87 198 9.87 187 9.87 175 9.87 164 9.87 153 9. 87 141 9.87 130 9.87 119 9.87 107 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 11 11 11 11 11 11 11 11 12 11 11 11 11 11 12 11 11 11 11 12 11 11 11 11 12 11 11 12 11 11 11 12 11 11 12 11 11 12 11 11 12 11 11 12 GO 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 26 1 2.6 2 5.2 3 7.8 4 10.4 5 13.0 6 15.6 7 18.2 8 20.8 9 23.4 25 1 2.5 2 5.0 3 7.5 4 10.0 5 12.5 6 15.0 7 17.5 8 20.0 9 22.5 15 1 1.5 2 3.0 3 4.5 4 6.0 5 7.5 6 9.0 7 10.5 8 12.0 9 13.5 14 1 1.4 2 2.8 3 4.2 4 5.6 5 7.0 6 8.4 7 9.8 8 11.2 9 12.6 12 11 1 1.2 1.1 2 2.4 2.2 3 3.6 3.3 4 4.8 4.4 5 6.0 5.5 6 7.2 6.6 7 8.4 7.7 8 9.6 8.8 9 10.8 9.9
LSin L Cos d L Tan L Cot cd L Cot L Tan L Cos LSin d / 318°-, 138°- 228°-, 48°-
82
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
42°-, 222°- / L Sin d L Tan cd L Cot L Cos d Prop. pts.
132°-, 312°- L Cos L Cot L Tan L Sin
0 1 2 3 4 9. 82 551 9. 82 565 9. 82 579 9. 82 593 9. 82 607 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 13 14 14 14 14 14 14 13 14 14 14 14 14 13 14 14 14 13 14 14 14 13 14 14 14 13 14 14 13 14 14 13 14 13 14 14 13 14 13 14 14 13 14 13 9.95 444 9.95 469 9.95 495 9. 95 520 9. 95 545 25 26 25 25 26 25 26 25 25 26 25 25 26 25 26 25 25 26 25 26 25 25 26 25 25 26 25 26 25 25 26 25 25 26 25 25 26 25 25 26 25 26 25 25 26 25 25 26 25 25 26 25 25 26 25 25 26 25 25 26 0.04 556 0.04 531 0.04 505 0.04 480 0. 04 455 9.87 107 9. 87 096 9. 87 085 9. 87 073 9. 87 062 11 11 12 11 12 11 11 12 11 12 11 12 11 12 11 12 11 11 12 11 12 12 11 12 11 12 11 12 11 12 11 12 12 11 12 11 12 12 11 12 12 11 12 12 11 12 12 11 12 12 12 11 12 12 11 12 12 12 11 12 60 59 58 57 56 26 1 2.6 2 5.2 3 7.8 4 10.4 5 13.0 6 15.6 7 18.2 8 20.8 9 23.4 25 1 2.5 2 5.0 3 7.5 4 10.0 5 12.5 6 15.0 7 17.5 8 20.0 9 22.5 14 1 1.4 2 2.8 3 4.2 4 5.6 5 7.0 6 8.4 7 9.8 8 11.2 9 12.6 13 1 1.3 2 2.6 3 3.9 4 5.2 5 6.5 6 7.8 7 9.1 8 10.4 9 11.7 12 11 1 1. 2 1. 1 2 2.4 2.2 3 3.6 3.3 4 4.8 4.4 5 6.0 ' 5.5 6 7.2 6.6 7 8.4 7.7 8 9.6 8.8 9 10.8 9.9
5 6 7 8 9 9. 82 621 9. 82 635 9.82 649 9. 82 663 9. 82 677 9. 95 571 9. 95 596 9.95 622 9. 95 647 9. 95 672 0. 04 429 0.04 404 0. 04 378 0. 04 353 0.04 328 9.87 050 9. 87 039 9. 87 028 9.87 016 9.87 005 55 54 53 52 51
10 11 12 13 14 9. 82 691 9. 82 705- 9.82 719 9. 82 733 9. 82 747 9. 95 698 9.95 723 9. 95 748 9. 95 774 9.95 799 0. 04 302 0. 04 277 0. 04 252 0. 04 226 0. 04 201 9. 86 993 9. 86 982 9.86 970 9. 86 959 9. 86 947 50 49 48 47 46
15 16 17 18 19 9. 82 761 9. 82 775 9. 82 788 9. 82 802 9. 82 816 9. 95 825 9. 95 850 9.95 875 9. 95 901 9.95 926 0. 04 175 0. 04 150 0. 04 125 0. 04 099 0.04 074 9.86 936 9. 86 924 9. 86 913 9.86 902 9. 86 890 45 44 43 42 41
20 21 22 23 24 9. 82 830 9.82 844 9. 82 858 9. 82 872 9. 82 885 9. 95 952 9. 95 977 9. 96 002 9. 96 028 9. 96 053 0.04 048 0.04 023 0.03 998 0. 03 972 0.03 947 9. 86 879 9. 86 867 9. 86 855 9. 86 844 9. 86 832 40 39 38 37 36
25 26 27 28 29 9. 82 899 9. 82 913 9. 82 927 9. 82 941 9. 82 955 9.96 078 9. 96 104 9. 96 129 9. 96 155 9. 96 180 0. 03 922 0.03 896 0. 03 871 0. 03 845 0. 03 820 9. 86 821 9. 86 809 9.86 798 9. 86 786 9. 86 775 35 34 33 32 31
30 31 32 33 34 9. 82 968 9. 82 982 9. 82 996 9. 83 010 9. 83 023 9. 96 205 9.96 231 9. 96 256 9. 96 281 9. 96 307 0. 03 795 0. 03 769 0. 03 744 0. 03 719 0. 03 693 9. 86 763 9. 86 752 9. 86 740 9. 86 728 9. 86 717 30 29 28 27 26
35 36 37 38 39 9. 83 037 9. 83 051 9. 83 065 9.83 078 9. 83 092 9. 96 332 9. 96 357 9.96 383 9. 96 408 9. 96 433 0.03 668 0. 03 643 0. 03 617 0. 03 592 0. 03 567 9. 86 705 9. 86 694 9. 86 682 9. 86 670 9.86 659 25 24 23 22 21
40 41 42 43 44 9. 83 106 9.83 120 9.83 133 9.83 147 9.83 161 9. 96 459 9. 96 484 9. 96 510 9.96 535 9. 96 560 0.03 541 0.03 516 0.03 490 0. 03 465 0. 03 440 9. 86 647 9. 86 635 9.86 624 9.86 612 9.86 600 20 19 18 17 16
45 46 47 48 49 9. 83 174 9.83 188 9.83 202 9. 83 215 9.83 229 9. 96 586 9.96 611 9. 96 636 9. 96 662 9. 96 687 0. 03 414 0. 03 389 0.03 364 0.03 338 0. 03 313 9. 86 589 9. 86 577 9.86 565 9. 86 554 9. 86 542 15 14 13 12 11
50 51 52 53 54 9. 83 242 9.83 256 9. 83 270 9. 83 283 9. 83 297 9. 96 712 9. 96 738 9. 96 763 9.96 788 9.96 814 0. 03 288 0. 03 262 0. 03 237 0. 03 212 0.03 186 9. 86 530 9.86 518 9.86 507 9. 86 495 9. 86 483 10 9 8 7 6
55 56 57 58 59 9. 83 310 9. 83 324 9.83 338 9. 83 351 9. 83 365 9. 96 839 9. 96 864 9. 96 890 9. 96 915 9. 96 940 0. 03 161 0. 03 136 0.03 110 0. 03 085 0. 03 060 9. 86 472 9. 86 460 9. 86 448 9. 86 436 9. 86 425 5 4 3 2 1
60 9.83 378 9. 96 966 0. 03 034 9. 86 413 0
L Sin d L Tan cd L Cot L Cos d / 317°-, 137°-
L Cos LCot L Tan L Sin 227°-, 47°-
83
Table HL—Common Logarithms of Functions of Angles in Degrees and Minutes—
Continued
43°-, 223°- / L Sin L Tan cd L Cot L Cos d Prop. pts.
133°-, 313°- L Cos L Cot L Tan L Sin
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9.83 378 9. 83 392 9.83 405 9.83 419 9.83 432 9.83 446 9.83 459 9.83 473 9.83 486 9.83 500 9.83 513 9. 83 527 9.83 540 9.83 554 9.83 567 9.83 581 9.83 594 9.83 608 9.83 621 9.83 634 9.83 648 9. 83 661 9.83 674 9.83 688 9.83 701 9.83 715 9.83 728 9.83 741 9.83 755 9.83 768 9.83 781 9.83 795 9.83 808 9.83 821 9.83 834 9.83 848 9. S3 861 9.83 874 9.83 887 9.83 901 9.83 914 9.83 927 9.83 940 9.83 954 9.83 967 9. S3 980 9.83 993 9.84 006 9. 84 020 9.84 033 9. 84 046 9.84 059 9.84 072 9.84 085 9.84 098 9.84 112 9.84 125 9.84 138 9.84 151 9.84 164 9.84 177 14 13 14 13 14 13 14 13 14 13 14 13 14 13 14 13 14 13 13 14 13 13 14 13 14 13 13 14 13 13 14 13 13 13 14 13 13 13 14 13 13 13 14 13 13 13 13 14 13 13 13 13 13 13 14 13 13 13 13 13 9. 96 966 9.96 991 9. 97 016 9.97 042 9.97 067 9.97 092 9.97 118 9.97 143 9.97 168 9.97 193 9.97 219 9. 97 244 9.97 269 9.97 295 9.97 320 9.97 345 9.97 371 9. 97 396 9.97 421 9. 97 447 9.97 472 9. 97 497 9.97 523 9.97 548 9.97 573 9.97 598 9.97 624 9. 97 649 9.97 674 V- 97 700 9.97 725 9.97 750 9.97 776 9.97 801 9.97 826 9.97 851 9.97 877 9.97 902 9. 97 927 9.97 953 9.97 978 9.98 003 9.98 029 9. 98 054 9.98 079 9.98 104 9.98 130 9.98 155 9.98 180 9.98 206 9. 98 231 9.98 256 9.98 281 9.98 307 9.98 332 9.98 357 9.98 383 9.98 408 9.98 433 9. 98 458 9.98 484 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 26 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 25 26 0.03 034 0.03 009 0.02 984 0.02 958 0.02 933 0.02 908 0.02 882 0.02 857 0.02 832 0.02 807 0.02 781 0.02 756 0.02 731 0.02 705 0.02 680 0.02 655 0.02 629 0.02 604 0. 02 579 0.02 553 0. 02 528 0.02 503 0.02 477 0. 02 452 0.02 427 0.02 402 0. 02 376 0.02 351 0.02 326 0.02 300 0.02 275 0.02 250 0. 02 224 0.02 199 0.02 174 0.02 149 0.02 123 0.02 098 0.02 073 0.02 047 0.02 022 0.01 997 0.01 971 0.01 946 0. 01 921 0.01 896 0.01 870 0.01 845 0.01 820 0.01 794 0.01 769 0.01 744 0.01 719 0.01 693 0.01 668 0.01 643 0.01 617 0.01 592 0.01 567 0.01 542 0.01 516 9.86 413 9.86 401 9.86 389 9.86 377 9.86 366 9.86 354 9. 86 342 9.86 330 9.86 318 9.86 306 9.86 295 9.86 283 9. 86 271 9. 86 259 9.86 247 9.86 235 9.86 223 9.86 211 9.86 200 9.86 188 9.86 176 9.86 164 9.86 152 9.86 140 9. 86 128 9.86 116 9.86 104 9. 86 092 9. 86 080 9.86 068 9.86 056 9. 86 044 9.86 032 9. 86 020 9.86 008 9.85 996 9. 85 984 9.85 972 9.85 960 9.85 948 9.85 936 9.85 924 9.85 912 9.85 900 9.85 888 9. 85 876 9. 85 864 9.85 851 9.85 839 9.85 827 9.85 815 9.85 803 9.85 791 9.85 779 9.85 766 9. 85 754 9.85 742 9. 85 730 9.85 718 9.85 706 9.85 693 12 12 12 11 12 12 12 12 12 11 12 12 12 12 12 12 12 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 12 12 12 12 12 12 13 12 12 12 12 12 13 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 26 1 2.6 2 5.2 3 7.8 4 10.4 5 13.0 6 15.6 7 18.2 8 20.8 9 23.4 25 1 2.5 2 5.0 3 7.5 4 10.0 5 12.5 6 15.0 7 17.5 8 20.0 9 22.5 14 1 1.4 2 2.8 3 4.2 4 5.6 5 7.0 6 8.4 7 9.8 8 11.2 9 12.6 13 1 1.3 2 2.6 3 3.9 4 5.2 5 6.5 6 7.8 7 9.1 8 10.4 9 11.7 12 11 1 1.2 1.1 2 2.4 2.2 3 3.6 3.3 4 4.8 4.4 5 6.0 -5.5 6 7.2 6.6 7 8.4 7.7 8 9.6 8.8 9 10.8 9.9
L Sin d L Tan cd L Cot L Cos d / 316°-, 136°-
L Cos L Cot L Tan L Sin 226°-, 46°-
84
Table III.—Common Logarithms of Functions of Angles in Degrees and Minutes Continued
44°-, 224°- 134°-, 314°- f L Sin L Cos d L Tan L Cot cd L Cot L Tan L Cos L Sin d Prop. pts.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 9.84 177 9. 84 190 9.84 203 9. 84 216 9.84 229 9.84 242 9.84 255 9.84 269 9.84 282 9.84 295 9.84 308 9.84 321 9. 84 334 9.84 347 9.84 360 9.84 373 9.84 385 9.84 398 9.84 411 9.84 424 9.84 437 9.84 450 9.84 463 9.84 476 9.84 489 9.84 502 9.84 515 9.84 528 9.84 540 9.84 553 9.84 566 9.84 579 9.84 592 9. 84 605 9.84 618 9 84 630 9.84 643 9.84 656 9.84 669 9.84 682 9.84 694 9.84 707 9.84 720 9.84 733 9.84 745 9.84 758 9.84 771 9.84 784 9.84 796 9.84 809 9.84 822 9.84 835 9.84 847 9.84 860 9.84 873 9.84 885 9.84 898 9.84 911 9.84 923 9.84 936 9.84 949 13 13 13 13 13 13 14 13 13 13 13 13 13 13 13 12 13 13 13 13 13 13 13 13 13 13 13 12 13 13 13 13 13 13 12 13 13 13 13 12 13 13 13 .12 13 13 13 12 13 13 13 12 13 13 12 13 13 12 13 13 9.98 484 9.98 509 9.98 534 9.98 560 9.98 585 9.98.610 9.98.635 9.98 661 9.98 686 9.98 711 9.98 737 9.98 762 9.98 787 9.98.812 9.98 838 9.98 863 9.98 888 9.98 913 9.98 939 9.98 964 9.98 989 9 99 015 9.99 040 9.99 065 9. 99 090 9.99 116 9.99 141 9.99 166 9.99 191 9.99 217 9.99 242 9. 99 267 9.99 293 9.99 318 9. 99 343 9.99 368 9.99 394 9.99 419 9.99 444 9. 99 469 9.99 495 9.99 520 9.99 545 9.99 570 9. 99 596 9.99 621 9.99 646 9. 99 672 9.99 697 9.99 722 9.99 747 9.99 773 9.99 798 9. 99 823 9.99 848 9.99 874 9.99 899 9.99 924 9.99 949 9.99 975 0.00 000 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 25 26 25 0.01 516 0.01 491 0.01 466 0.01 440 0.01 415 0.01 390 0. 01 365 0.01 339 0.01 314 0.01 289 0.01 263 0.01 238 0.01 213 0.01 188 0.01 162 0.01 137 0.01 112 0.01 087 0.01 061 0.01 036 0.01 011 0.00 985 0.00 960 0.00 935 0.00 910 0.00 884 0.00 859 0. 00 834 0.00 809 0.00 783 0.00 758 0.00 733 0. 00 707 0.00 682 0.00 657 0.00 632 0.00 606 0.00 581 0.00 556 0.00 531 0.00 505 0.00 480 0.00 455 0.00 430 0.00 404 0.00 379 0.00 354 0.00 328 0.00 303 0.00 278 0.00 253 0.00 227 0.00 202 0. 00 177 0.00 152 0.00 126 0.00 101 0.00 076 0.00 051 0.00 025 0.00 000 9.85 693 9.85 681 9.85 669 9.85 657 9.85 645 9.85 632 9.85 620 9.85 608 9.85 596 9.85 583 9.85 571 9.85 559 9.85 547 9.85 534 9.85 522 9.85 510 9.85 497 9.85 485 9.85 473 9.85 460 9.85 448 9.85 436 9.85 423 9.85 411 9.85 399 9.85 386 8.85 374 9.85 361 9.85 349 9.85 337 9.85 324 9.85 312 9.85 299 9.85 287 9.85 274 9.85 262 9.85 250 9.85 237 9.85 225 9.85 212 9.85 200 9.85 187 9.85 175 9.85 162 9.85 150 9.85 137 9.85 125 9.85 112 9.85 100 9.85 087 9.85 074 9.85 062 9.85 049 9.85 037 9.85 024 9.85 012 9.84 999 9.84 986 9.84 974 9.84 961 9.84 949 12 12 12 12 13 12 12 12 13 12 12 12 13 12 12 13 12 12 13 12 12 13 12 12 13 12 13 12 12 13 12 13 12 13 12 12 13 12 13 12 13 12 13 12 13 12 13 12 13 13 12 13 12 13 12 13 13 12 13 12 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 26 1 2.6 2 5.2 3 7.8 4 10.4 5 13.0 6 15.6 7 18.2 8 20.8 9 23.4 25 1 2.5 2 5.0 3 7.5 4 10.0 5 12.5 6 15.0 7 17.5 8 20.0 9 22.5 14 1 1.4 2 2.8 3 4.2 4 5.6 5 7.0 6 8.4 7 '9.8 8 11.2 9 12.6 13 1 1.3 2 2.6 3 3.9 4 5.2 5 6.5 6 7.8 7 9.1 8 10.4 9 11.7 12 r i.2 2 2.4 3 3.6 4 4.8 5 6.0 6 7.2 7 8.4 8 9.6 9 10.8
L Sin L Cos d L Tan L Cot Cd L Cot L Tan L Cos L Sin d / 315°-, 135°- 225°-, 45°-
85
Table IV.—Stadia Reductions
1. Stadia reductions. Stadia work involves observing_____
a. The angle by which the line of sight departs from a horizontal line. This reading is the argument for entering the table.
b. The rod interval intercepted by the stadia wires, which are usually adjusted so that the distance to the rod is exactly 100 times the reading on the rod when the telescope is level. This distance, however, is measured from the principal focus of the object glass, which is an appreciable distance to the front. Hence the reading must be increased by two small increments; first, the distance from the principal focus to the object glass, and, second, the distance from the object glass to the transit plumb line.
c. The table gives horizontal distances and differences of elevation for unit readings on rod and for angles of elevation from 0° to 30°. The three lines at foot of tables give three values for C; the value selected depends upon the instrument used; the quantity C includes the two increments described in the last sentence of b above.
d. Example: Rod reading is 3.25 feet and angle of inclination is 5°35'- focal distance C=1.00. ’
Horizontal distance = 99.05X3.25 + 0.99 = 322.90 feet.
Difference of elevation = 9.68X3.25 + 0.09 = 31.55.
2. Stadia reduction formulae. The following formulae are used in computing stadia reductions:
Horizontal distance = 7? cos2 a + C cos a.
Vertical distance = R % sin 2 « + C sin a.
R=Stadia readingxdistan2e from object glass t0 outer f°cus_ distance between cross hairs ° i'
C-Distance (/) from object glass to outer focus + distance (c) from object glass to center of instrument =/+c.
a=angle of elevation for mid reading.
The distance (/) from object glass to outer focus is equal to the distance from object glass to cross wires.
3
- cross
I a \ \ i k
| h\
1 n\
a A
A
lit \ \
9 A \ \ o \ \
s 4 \ \
A ' \
A ' \
A \ \
A \ \
j____f_I - \ \
<—Reading
Verbco^| •
Distance .
86
Table IV.—Stadia Reductions
(Horizontal distances and elevations from stadia readings)
Minutes 0° 1° 2° 3°
Hor. dist. Diff. elev. Hor. dist. Diff. elev. Hor. dist. Diff. elev. Hor. dist. Diff. elev.
0 100. 00 0.00 99.97 1.74 99. 88 3. 49 99 73 5 23
2 100. 00 0.06 99.97 1.80 99.87 3 55 99 72 5 28
4. 100. 00 0.12 99. 97 1.86 99 87 3 60 99 71 5 34
6 100. 00 0.17 99. 96 1. 92 99. 87 3 66 99 71 5 40
8 100.00 0. 23 99. 96 1. 98 99 86 3 72 99 70 5 46
10 100.00 0. 29 99.96 2.04 99 86 3 78 99 69 5 52
12 100. 00 0. 35 99. 96 2.09 99 85 3 84 99 69 5 57
14 100. 00 0. 41 99. 95 2.15 99. 85 3 90 99 68 5 63
16 100.00 0. 47 99. 95 2. 21 99 84 3 95 99 68 5 69
18 100. 00 0. 52 99. 95 2. 27 99 84 4 01 99 67 5 75
20 100.00 0. 58 99. 95 2. 33 99. 83 4 07 99 66 5 80
22 100. 00 0.64 99. 94 2. 38 99 83 4 13 99 66 5 86
24 100. 00 0.70 99.94 2. 44 99 82 4 18 99 65 5. 92
26 99. 99 0. 76 99 94 2 50 99 82 4 24 99 64 5 98
28 99. 99 0. 81 99 93 2 56 99 81 4 30 99 63 6 04
30 99. 99 0.87 99 93 2 62 99 81 4 36 99 63 6 09
32 99.99 0.93 99. 93 2. 67 99 80 4 42 99 62 6 15
34 99. 99 0.99 99. 93 2.73 99. 80 4 48 99 62 6 21
36 . 99. 99 1. 05 99. 92 2.79 99 79 4 53 99 61 6 27
38 99.99 1.11 99. 92 2.85 99. 79 4.59 99 60 6 33
40 99. 99 1.16 99.92 2. 91 99.78 4 65 99 59 6 38
42 99. 99 1. 22 99. 91 2.97 99.78 4 71 99 59 6 44
44 99. 98 1. 28 99. 91 3. 02 99. 77 4 76 99 58 6 50
46 99. 98 1. 34 99. 90 3.08 99.77 4. 82 99 57 6 56
48 99. 98 1.40 99. 90 3.14 99. 76 4 88 99 56 6 61
50 99. 98 1.45 99. 90 3. 20 99.76 4. 94 99 56 6 67
52 99. 98 1.51 99.89 3. 26 99 75 4 99 99 55 6 73
54 99. 98 1.57 99. 89 3. 31 99.74 5.05 99 54 6 78
56 99. 97 1. 63 99. 89 3. 37 99. 74 5.11 99 53 6 84
58 99. 97 1.69 99. 88 3.43 99 73 5.17 99 52 6 90
60 99. 97 1. 74 99.88 3. 49 99.73 5.23 99.51 6.96
C=0.75 0.75 0. 01 0.75 0.02 0.75 0.03 0. 75 0.05
C = 1.00 1.00 0.01 1.00 0.03 1.00 0. 04 1. 00 0.06
C = 1.25 1.25 0.02 1.25 0.03 1. 25 0.05 1. 25 0.08
87
Table IV.—Stadia Reductions—Continued
Minutes 4° 5° 6° T
Hor. dist. Diff. elev. Her. dist. Diff. elev. Hor. dist. Diff. elev. Hor. dist. Diff. elev.
0. 2 4 6 8. 10. 12. 14.. 16... 18... 20... 22 24 26.. 28... 30 32.. 34 36 38 40 42 44 46 48 50 52. 54 56... 58 60 99.51 99.51 99.50 99.49 99.48 99.47 99.46 99.46 99.45 99.44 99.43 99.42 99.41 99.40 99.39 99.38 99.38 99.37 99.36 99.35 99.34 99.33 99.32 99.31 99.30 99.29 I 99.28 99.27 99.26 99.25 99.24 6.96 7.02 7.07 7.13 7.19 7.25 7.30 7.36 7.42 7.48 7.53 7.59 7.65 7.71 7.76 7.82 7.88 7.94 7.99 8.05 8.11 8.17 8.22 8.28 8.34 8.40 8.45 8. 51 8.57 8.63 8.68 99.24 99.23 99.22 99.21 99.20 99.19 99.18 99.17 99.16 99.15 99.14 99.13 99.11 99.10 99.09 99.08 99.07 99.06 99.05 99.04 99.03 99.01 99.00 98.99 98.98 98.97 98.96 98.94 98.93 98.92 98.91 8.68 8.74 8.80 8.85 8.91 8.97 9.03 9.08 9.14 9.20 9.25 9.31 9.37 9.43 9.48 9.54 9.60 9.65 9.71 9.77 9.83 9.88 9.94 10.00 10.05 10.11 10.17 10.22 10.28 10.34 10.40 98.91 98.90 98.88 98.87 98.86 98.85 98.83 98.82 98.81 98.80 98.78 98.77 98.76 98.74 98.73 98.72 98.71 98.69 98.68 98.67 98.65 98.64 98.63 98.61 98.60 98.58 98.57 98.56 98.54 98.53 98.51 10.40 10.45 10.51 10.57 10.62 10.68 10.74 10.79 10.85 10.91 ! 10.96 * 11.02 11.08 11.13 11.19 11.25 11.30 11.36 11.42 11.47 11.53 11.59 11.64 11.70 11.76 11.81 11.87 11.93 11.98 12.04 12.10 98.51 98.50 98.48 98.47 98.46 98.44 98.43 98.41 98.40 98.39 98.37 98.36 98.34 98.33 98.31 98.29 98.28 98.27 98.25 98.24 98.22 98.20 ‘98.19 98.17 98.16 98.14 98.13 98.11 98.10 98.08 98.06 12.10 12.15 12.21 12.26 12.32 12.38 12.43 12.49 12.55 12.60 12.66 12.72 12.77 12.83 12.88 12.94 13.00 13.05 13.11 13.17 13.22 13.28 13.33 13.39 13.45 13.50 13.56 13.61 13.67 13.73 13.78
C=0.75... 0.75? 0.06 0.75 0.07 0.75 0.08 0.74 0.10
C=1.00... 1.00 0.08 0.99 0.09 0.99 0.11 0.99 0.13
C=1.25... 1.25 0.10 1.24 0.11 1.24 0.14 1.24 0.16
88
Table IV.—Stadia Reductions—Continued
Minutes 8° 9° 10° 11°
Hot. dist. Diff. elev. Hor. dist. Diff. elev. Hor. dist. Diff. elev. Hor. dist. Diff. elev.
0 98.06 13.78 97.55 15.45 96.98 17.10 96 36 18 73
2„ 98.05 13.84 97.53 15.51 96.96 17.16 96 34 18 78
4. 98.03 13.89 97.52 15.56 96.94 17 21 96 32 18 84
6 98.01 13.95 97.50 15.62 96.92 17 26 96 29 18* 89
8 98.00 14.01 97.48 15.67 96.90 17.32 96 27 18 95
10 97.98 14.06 97.46 15.73 96.88 17.37 96.25 19 00
12 97.97 14.12 97.44 15.78 96.86 17 43 96 23 19 05
14 97.95 14.17 97.43 15.84 96.84 17.48 96.21 19 11
16 97.93 14.23 97.41 15.89 96.82 17 54 96 18 19 16
18 97.92 14.28 97.39 15.95 96.80 17 59 96 16 19 21
20 97.90 14.34 97.37 16.00 96.78 17.65 96 14 19,27
22 97.88 14.40 97.35 16.06 96.76 17.70 96.12 19 32
24 97.87 14.45 97.33 16.11 96.74 17.76 96.09 19.38
26-_ 97.85 14.51 97.31 16.17 96.72 17.81 96 07 19 43
28 97.83 14.56 97.29 16.22 96.70 17 86 96 05 19 48
30 97.82 14.62 97.28 16.28 96.68 17.92 96.03 19.54
32 97.80 14.67 97.26 16.33 96. 66 17.97 96 00 19 59
34 97.78 14.73 97.24 16.39 96.64 18.03 95 98 19 64
36 97.76 14.79 97.22 16.44 96.62 18.08 95.96 19.70
38 97.75 14.84 97.20 16. 50 96.60 18.14 95.93 19 75
40 97.73 14.90 97.18 16.55 96.57 18.19 95.91 19 80
42„ 97.71 14.95 97.16 16.61 96.55 18.24 95.89 19.86
44 97.69 15.01 97.14 16.66 96.53 18.30 95.86 19.91
46 97.68 15.06 97.12 16.72 96.51 18.35 95.84 19 96
48 97.66 15.12 97.10 16. 77 96.49 18.41 95.82 20.02
50 97.64 15.17 97.08 16.83 96.47 18.46 95.79 20.07
52.. 97.62 15.23 97.06 16.88 96.45 18.51 95.77 20.12
54 97.61 15.28 97.04 16.94 96.42 18.57 95.75 20.18 '
56 97.59 15.34 97.02 16.99 96.40 18.62 95.72 20.23
58 97.57 15.40 97.00 17.05 96.38 18.68 95. 70 20.28
60 97.55 15.45 96.98 17.10 96.36 18.73 95.68 20.34
C=0.75— . 0.74 0.11 0.74 0.12 0.74 0.14 0.73 0.15
0=1.00— 0.99 0.15 0.99 0.16 0.98 0.18 0.98 0.20
C=1.25— 1.23 0.18 1.23 0.21 1.23 0.23 1.22 0.25
89
Table IV.—Stadia Reductions—Continued
Minutes 1 2° 13° 4° 15°
Hor. dist. Diff. elev. Hor. dist. Diff. elev. Hor. dist. Diff. elev. Hor. dist. Diff. elev.
SSSSK 85S5KG Sooo^o । • । • i । । । । । । । । । । । । । । । i i ■!!!!! 11,11 । । । । । । । t । । iii ' ' । • • ■ ■ । । । । । । । । । । iii ! ! “tan ^U+B)
or
A a sin C tan cos c
and the group
a2=ft2+c2—26c cos A b2=a2+c2~2ac cos B c2=a2+b2—2ab cos C
101
The relations for angles greater than 90° are shown in the following tabulation positive represents an anSle in first quadrant where all the functions are
angle sine cosine tangent cotangent
X 90°+x 180°+x 270°+x + sin x + cos X — sin x — cos X • + COS X — sin x — cosx + sin x + tan x — cot X + tan x — cot X + cot X — tan x + cot X — tan x
2. Conversion factors.
Yards X 0.9144—meters
Meters X 1.094 —yards
Kilometers X 0.62 —miles
Miles X 1.61 —kilometers
Degrees X 1.111 — grades
Minutes X 0.0185—grades
Grades X 0.90 —degrees
Mils X 0.0625 —grades
Grades X16.0 —mils
102
Table X.—Greek Alphabet
Caps Lower ease Greek name English sound Caps Lower case Greek name English sound
A a Alpha A N p Nu N
B P s Beta B t Xi X
r y Gamma G 0 o 0 micron 0 short
A d Delta D n 7T & Pi P
E € Epsilon E short p p Rho R
Z r Zeta Z s Sigma S
H V Eta E long T Tau T
e eo Theta Th T V Upsilon, U
i Iota I $ Phi F
K K Kappa K X X Chi Ch
A X Lambda L * 4 8 Psi Ps
M M Mu M a> Omega 0 long
10
103
Table XI.—Standard Time Signals
1. Schedule. The following schedule gives the hours of ending of Naval Observatory time signal transmissions in Greenwich time. Under the call letters of each radio station are listed the frequencies in kilocycles used in transmitting via those stations. 1,000 kilocycles — 1 megacycle. For example: 4,390 kilocycles == 4.39 megacycles. '
Hour NSS NSS NSS NSS NPG NPM NBA
0 115
3 Note 1
4 122 4390 9425 12630 Note 2
5 Note 3
8 Note 1
10 122 4390 9425 12630
15 Note 1
16 122 4390 9425 12630 Note 5
17 115 115 Note 4
20 Note 6
22 122 4390 9425 12630
NSS=U. S. Naval Radio Station, Annapolis, Md.
NPG=U. S. Naval Radio Station, Mare Island, Calif.
NPM=U. S. Naval Radio Station, Pearl Harbor, T. H.
NBA = U. S. Naval Radio Station, Balboa, C. Z.
Note 1: 115, 9255, and 12540 kc.
Note 2: 16.68 (or 56 kc. standby), 9090, 14390,17370 kc.
Note 3: 148, 5515, and 11080 kc.
Note 4: 148, 2170, 5515, and 11080 kc.
Note 5: 16.68 (or 56 kc. standby), 4525, 6380, 9090, 14390 kc.
Note 6: 16.68 (or 56 kc. standby), 4525, 6380, 9090,14390, 17370 kc.
2. Standard time. a. Since the sun does not rise and set in different parts of the world at the same time, it is evident that Mean Solar Time varies from place to place. In order to reduce confusion, standard time zones have been adopted. All the places in each zone use one uniform time which generally differs from the times of the adjoining zones by 1 hour, and from Greenwich Mean Solar Time by some whole number of hours. The continental United States, excepting Alaska, is divided into four time zones, namely, Eastern, Central, Mountain, and Pacific. Eastern Standard Time is the same as the Local Mean Solar Time of the 75th meridian west of Greenwich; it is 5 hours less advanced than Greenwich Time. Eastern War Time is 4 hours less advanced than Greenwich Time. Pacific Standard Time is the Local Time of the 120th meridian; it is 8 hours less advanced, and Pacific War Time is 7 hours less advanced than Greenwich Time. The Naval Observatory Time Signal sent out at 4 hours, Greenwich Time, serves as a midnight signal according to Eastern War Time, as an 11:00 PM signal according to Central War Time, etc.
b. The transmission of signals begins at 55 minutes 0 seconds of some hour, and continues for 5 minutes. Signals are transmitted on every second during that
104
time, except that there is no signal on the 29th second, nor on certain seconds at
the end of the minutes, as shown in the following diagram:
Minute Second 50 51 52 53 54 55 56 57 58 59 60
55 . 56 57 1 1 1 — 1 1 — 1 1 1 1 1 1 1 1 1 |
59 — —
The dashes shown above indicate the seconds on which signals are transmitted. The seconds marked “60” are the zero seconds of the following minutes. All seconds from 0 to 50, inclusive, are transmitted, except the 29th second, as explained previously. The signal on the beginning of the hour (shown as 59 minutes 60 seconds above) is much longer than the others. In all cases the beginnings of the signals indicate the beginnings of the seconds; the ends of the signals are without significance. Note that the number of signals sent in the group at the end of any minute indicates the number of minutes yet to be broadcast.
c. A complete list of foreign time signal broadcasts is given in H. O. No. 204, “Radio Navigation Aids,” published by the Hydrographic Office, U. S. Navy.
105
Table XII.—Azimuths of Polaris at Elongation, for the years 1944-54 (Computed by the U. S. Naval Observatory)
Lat. 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954
2? 1 1 1 1 h3 1 f:? 1 1 3.9 I 3.5 ; 3.1 I0 2.8 Corr^/or^o/
27 7.5 7.2 6.8 6.5 6.1 5 7 5.3 ' 46 42 38
8’2 7.8 7.4 7.1 6.7 6.3 5.9 A6 52 48 II -----------------—----
30 9.5 L H Io 7.1 7.2 6.8 II 61 57 For middle of-
1 H II 1:5 It k II II It-----------------------------------------—
33 11-8 11.4 11.0 10.6 10.2 9.8 9.4 9 0 8 6 8 2 7 8 Tan n k
34 12.6 12.2 11.8 11.4 11.0 10.6 10.2 18 14 9.0 8 6 Feb'------- Zo’a
35 J3-5 13.1 12.7 12.3 11.9 11.5 11.1 10.6 10.2 9 8 9 4 Mar o'3
36 14.4 14.0 13.6 13.2 12.8 12.4 11.9 11.5 111 10’7 10 3 Anr-------- _o 1
37 15.4 15.0 14.6 14.1 13.7 13.3 12.9 12.5 12.0 11.6 112 Mav 4-0 1
33 16.4 16.0 15.6 15.1 14.7 14.3 13.9 13.4 13 0 12 6 12 2 Tune ±n o
39 17-4 17.0 16.6 16.2 15.8 15.3 14.9 14.5 14 0 13 6 13 2 Mv--------- ±no
■40 18-6 18.2 17.7 17.3 16.9 16.4 16.0 lie 15 1 7 it 2 AuL"T""“ +0?
41 1?" I 19.3 18.9 18.5 18.0 17.6 17.1 16.7 16.2 15.8 15 4 Sent —n 1
21’2 20-6 ^’l I9-7 19-2 18.8 18.3 17.9 17.4 17:0 16:5 Oct. Z —0 3
43 22.3 21.9 21.4 21.0 20.5 20.0 19.6 19.1 18.7 18.2 17:8 Nov." ' —0 6
44 23.7 23.2 22.8 22.3 21.9 21.4 20.9 20.5 20.0 19.5 19.1 Dec —0 8
45 25.1 24.7 24.2 23.7 23.3 22.8 22.3 21.8 21 4 20 9 20 4 °
46 26.6 26.2 25.7 25.2 24.8 24.3 23.8 23.3 22.9 22.4 21.9
47 28.3 27. 8 27.3 26.8 26.3 25.8 25.3 24.9 24 4 23 9 23 4
48 30.0 29.5 29.0 28.5 28.0 27.5 27.0 26 5 26 0 25 5 25 0
49 31.7 31.3 30.8 30.3 29.8 29.2 28.7 28^ 27.7 27.2 26 7
50 1 33.6 1 33.2 jl 32.6 1 32.1 1 31.6 1 31.1 1 30.6 1 30.0 1 29.5 1 29.0 1 28+
These data may be secured annually from the current Nautical Ephemeris or other similar source.
106
Table XIII.—Mean Astronomic Refraction, With Corrections
(Correction is always subtracted from apparent altitude. Table is computed for barometric pressure of 29.9 inches (759 mm), and temperature of 50° F. (+10° C.)
Appar- Mean Differ- Appar- Mean Differ- Appar- Mean Differ- Appar- Mean
ent alti- refrae- ence ent alti- refrac- ence ent alti- refrac- ence ent alti- refrac-
tude tion for 1' tude tion for 1' tude . tion for 1' tude tion for 1'
o / r rr o z z o / z zz o z z zz
0 00 34 09 11.7 5 20 9 22 1.5 10 40 5 00 0.5 18 00 2 57 0.2
10 32 16 10.9 30 9 08 1.4 50 4 56 0.4 20 2 54 0.2
20 30 31 10.1 40 8 54 1.3 11 00 4 51 0.4 40 2 51 0.2
30 28 54 9.6 50 8 41 1.3 10 4 47 0.4 19 00 2 48 0. 2
40 27 18 9.2 6 00 8 29 1.2 20 4 43 0.4 20 2 45 0.2
50 25 50 8.5 10 8 17 1.2 30 4 39 0.4 40 2 42 0.2
1 00 24 28 7.8 20 8 05 1.1 40 4 35 0.4 20 00 2 39 0.1
10 23 13 7.2 30 7 54 1.1 50 4 31 0.4 20 2 36 0.1
20 22 05 6.6 40 7 44 1.0 12 00 4 27 0.4 40 2 33 0.1
30 21 02 6.1 50 7 34 1.0 10 4 24 0.4 21 00 2 31 0.1
40 20 04 5.6 7 00 7 24 0.9 20 4 20 0.3 20 2 28 0.1
50 19 10 5.2 10 7 15 0.9 30 4 17 0.3 40 2 26 0.1
2 00 18 20 4.8 20 7 06 0.9 40 4 13 0.3 22 00 2 23 0.1
10 17 33 4.5 30 6 57 0.8 50 4 10 0.3 20 2 21 0.1
20 16 50 4.2 40 6 49 0.8 13 00 4 07 0.3 40 2 19 0.1
30 16 09 3.9 50 6 41 0.8 10 4 04 0.3 23 00 2 16 0.1
40 15 32 3.6 8 00 6 33 0.8 20 4 01 0.3 20 2 14 0.1
50 14 57 3.4 10 6 26 0.7 30 3 58 0.3 40 2 12 0.1
3 00 14 24 3-. 2 20 6 19 0.7 40 3 55 0.3 24 00 2 10 0.1
10 13 54 3.0 30 6 12 0.7 50 3 52 0.3 20 2 08 0.1
20 13 25 2.8 40 6 05 0.7 14 00 3 49 0.3 40 2 06 0.1
30 12 58 2.6 50 5 59 0.6 20 3 44 0.3 25 00 2 04 0.1
40 12 32 2.5 9 00 5 53 0.6 40 3 39 0.2 20 2 02 0.1
50 12 09 2.3 10 5 47 0.6 15 00 3 34 0.2 40 2 01 0.1
4 00 11 46 2.2 20 5 41 0.6 29 3 29 0.2 26 00 1 59 0.1
10 11 25 2.1 30 5 35 0.6 40 3 25 0.2 20 1 57 0.1
20 11 04 2.0 40 5 30 0.5 16 00 3 20 0.2 40 1 55 0.1
30 10 45 1.9 50 5 24 0.5 20 3 16 0.2 27 00 1 54 0.1
40 10 26 1.8 10 00 5 19 0.5 40 3 12 0.2 20 1 52 0.1
50 10 09 1.7 10 5 14 0.5 17 00 3 08 0.2 40 1 51 0.1
5 00 9 53 1.6 20 5 09 0.5 20 3 04 0.2
10 9 37 1.5 30 5 05 0.5 40 3 01 0.2
Appar- Mean Appar- Mean Appar- Mean Appar- Mean Appar- Mean Appar- Mean
ent al- refrac- ent al- refrac- ent al- refrac- ent al- refrac- ent al- refrac- ent al-
titude tion titude tion titude tion titude tion titude tion titude tion
o Z , n o z z zz o r z zz o t z zz o z z zz o z z zz
28 00 1 49 35 00 1 23 42 00 1 05 49 00 0 51 63 00 0 30 77 00 0 13
30 1 47 30 1 21 30 1 03 50 00 49 64 00 28 78 00 12
29 00 1 45 36 00 1 20 43 00 1 02 51 00 47 65 00 27 79 00 11
30 1 42 30 1 18 30 1 01 52 00 45 66 00 26 80 00 10
30 00 1 40 37 00 1 17 44 00 1 00 53 00 44 67 00 25 81 00 09
30 1 38 30 1 16 30 0 59 54 00 42 68 00 24 82 00 08
31 00 1 37 38 00 1 14 45 00 58 55 00 41 69 60 22 83 00 07
30 1 35 30 1 13 30 57 56 00 39 70 00 21 84 00 06
32 00 1 33 39 00 1 12 46 00 56 57 00 38 71 00 20 85 00 05
30 1 31 30 1 10 30 55 58 00 36 72 00 19 86 00 04
33 00 1 29 40 00 1 09 47 00 54 59 00 35 73 00 18 87 00 03
30 1 28 30 1 08 30 53 60 00 34 74 00 17 88 00 02
34 00 1 26 41 00 1 07 48 00 52 61 00 32 75 00 16 89 00 01
30 1 24 30 1 06 30 52 62 00 31 76 00 15 90 00 00
12
13
107
Table XIII.
(Corrections to be applied to mean refraction for temperatures other than 50° F.)
Temperature Correction for mean refraction of—
F. 0. 1' 2' 3' V 5’ 6' T 8' 9' 10'
o o
0 5 -17.8 -15.0 +06 06 +13 11 +19 17 +26 23 +32 28 +39 35 +45 40 +52 46 +58 52 +65 58
10 —12.2 05 10 15 20 25 31 36 41 46 51
15 —9.4 04 09 13 17 22 26 31 35 39 44
20 —6.7 04 07 11 15 19 22 26 30 33 37
25 30 -3.9 -1.1 +03 02 +06 05 +09 07 +12 10 +15 12 +18 15 +21 17 +24 20 +28 22 +31 25
35 +1-7 02 04 05 07 09 11 13 14 16 18
40 +4.4 01 02 04 05 06 07 08 10 H
45 +7.2 +01 +01 +02 +02 +03 +04 +04 +05 +05 +06
50 +10.0 00 00 00 00 00 00 00 00 00 00
55 +12.8 -01 -01 -02 -02 -03 -04 —04 —05 —05 06
60 +15. 6 01 02 04 05 06 07 08 10 11 12
65 +18.3 02 03 05 07 08 10 12 13 15
70 +21.1 02 05 07 09 11 14 16 18 20
75 +23.9 03 06 08 11 14 17 20 23 25 28
80 +26.7 -03 -07 -10 -13 -16 -20 -23 —26 30
85 +29.4 04 08 11 15 19 23 27 31 34 38 43
90 +32. 4 04 09 13 17 22 26 30 35 39
95 —f~3£j. 0 | 05 10 15 19 24 29 34 39 44
100 +37.8 -05 -11 -16 -21 -27 -32 -37 -43 -48 -53
(Corrections to be applied to mean refraction for barometric pressures other than
29.9 inches)
To be subtracted Correction for mean refraction of— To be added
Barometer 1' •a 3' 4' 5' 6' T 8' O' 10' Barometer
Ins. mm. » >' » mm. Ins.
28.4 721 03 06 09 12 15 18 21 24 28 31
.5 .6 .7 .8 724 726 729 732 03 06 08 11 14 17 20 23 25 28
05 05 08 11 13 16 18 21 24 26
07 10 09 12 15 17 20 22 25
04 07 11 13 16 18 20 22 787 31.0 30.9
.9 734 02 04 06 08 10 12 14 16 18 20 785
29.0 737 02 04 05 07 09 11 13 14 16 18 782 _ ft
. 1 739 02 03 05 06 08 10 11 13 15 16 780 7
.2 742 01 03 04 06 07 09 10 11 13 14 777 t 0
.3 744 01 02 04 05 06 08 09 10 11 12 775 K
.4 747 01 03 04 05 06 07 08 09 10 772 30.4
29.5 749 01 02 03 03 04 05 06 07 08 08 770 13
.6 752 01 01 02 03 03 04 05 05 06 07 767 2
.7 754 00 01 01 02 02 03 03 04 04 05 765 I
.8 757 00 00 01 01 01 01 02 02 02 02 762 30.0 29.9
.9 759 00 00 00 00 00 00 00 00 00 00 759
108
Table XIV.—Parallax and Altitude of the Sun
Altitude Parallax Altitude Parallax
o o //
0 5 10 15 20 25 30 35 40 45 9 9 9 8 8 8 8 7 7 6 50 55 60 65 70 75 80 85 90 6 5 4 4 3 2 2 1 0
Correction is always added to apparent altitude.
14
109
609023°—44---8
Table XV.—Curvature and Refraction
The corrections in the table are always to be added to the altitude of the point as determined from the vertical angle from a station of known altitude.
R Range (yards) H Correction (feet) R Range (yards) H Correction (feet)
1,000 0.2 16,000 47.3
2,000 .7 17, 000 53.4
3,000 1.7 18,000 59.8
4,000 3.0 19, 000 66.7
5,000 4.6 20,000 73.9
6,000 6.6 21, 000 81.4
7,000 9.0 22,000 89.4
8,000 11.8 23,000 97.7
9,000 15.0 24, 000 106.4
10,000 18.5 25. 000 115.4
11,000 22.3 26,000 124.8
12,000 26.6 27,000 134.6
13,000 31.2 28, 000 144.8
14,000 36.2 29, 000 155.3
15,000 41.6 ' 30,000 166.2
Formula: H^R* x .1847
H = Correction in feet
7? = Range in thousands of yards; that is, for 10,000 yards, _R=10 Note.—The correction may be neglected when the range is less than 5,000 yards.
110
Table XVI.—Natural Sines and Cosines of Angles in Mils
Values of the sines and cosines of angles are given for each mil from 0 to 1,600 mils.
With hundreds of mils indicated at the top of the page, use the column designations at the top. With hundreds of mils indicated at the bottom of the page, use the column designations at the bottom.
With hundreds of mils indicated at the top of the page, use the unit mil column at the left. With hundreds of mils indicated at the bottom of the page, use the unit mil column at the right.
15
16
ill
Table XVI.—Natural Sines and Cosines of Angles in Mils
Mils Sin 000 Cos Sin 100 Cos Sin 200 Cos Sin 300 Cos Mils
0 .00000 1. .09802 .99519 .19509 .98079 .29028 .95694 100
1 00098 1. 09899 99509 19605 98059 29122 95665 99
2 00196 1. 09997 99499 19702 98040 29216 95637 98
3 00295 1. 10095 99489 19798 98021 29310 95608 97
1 00393 .99999 10192 99479 19894 98001 29404 95579 96
5 00491 99999 10290 99469 19990 97982 29498 95550 95
' 6 00589 99998 10388 99459 20086 97962 29592 95521 94
7 00687 99998 10485 99449 20183 97942 29685 95492 93
8 00785 99997 10583 99438 20279 97922 29779 95463 92
9 00884 99996 10681 99428 20375 97902 29873 95434 91
10 00982 99995 10778 99417 20471 97882 29967 95404 90
11 01080 99994 10876 99407 20567 97862 30060 95375 89
12 01178 99993 10973 99396 20663 97842 30154 95345 88
13 01276 99992 11071 99385 20759 97822 30247 95316 87
14 01374 99991 11169 99374 20855 97801 30341 95286 86
15 01473 99989 11266 99363 20951 97781 30434 95256 85
16 01571 99988 11364 99352 21047 97760 30528 95226 84
17 01669 99986 11461 99341 21143 97739 30621 95196 83
18 01767 99984 11559 99330 21239 97718 30715 95166 82
19 01865 99983 11656 99318 21335 97698 30808 95136 81
20 01963 99981 11754 99307 21431 97677 30902 95106 80
21 02062 99979 11851 99295 21527 97656 30995 95075 79
22 02160 99977 11949 99284 21623 97634 31088 95045 78
23 02258 99975 12046 99272 21719 97613 31182 95014 77
24 02356 99972 12144 99260 21814 97592 31275 94984 76
25 02454 99970 12241 99248 21910 97570 31368 94953 75
26 02552 99967 12338 99236 22006 97549 31461 94922 74
27 02650 99965 12435 99224 22102 97527 31555 94891 73
28 02749 99962 12533 99211 22197 97505 31648 94860 72
29 02847 99959 12631 99199 22293 97483 31741 94829 71
30 02945 99957 12728 99187 22389 97461 31834 94798 70
31 03043 99954 12825 99174 22484 97439 31927 94766 69
32 03141 99951 12923 99161 22580 97417 32020 94735 68
33 03239 99948 13020 99149 22676 97395 32113 94704 67
34 03337 99944 13118 99136 22771 97373 32206 94672 66
35 03435 99941 13215 99123 22867 97350 32299 94640 65
36 03534 99938 13312 99110 22963 97328 32392 94609 64
37 03632 99934 13409 99097 23058 97305 32485 94577 63
38 03730 99930 13507 99084 23154 97283 32577 94545 62
39 03828 99927 13604 99070 23259 97260 32670 94513 61
40 03926 99923 13701 99057 23345 97237 32763 94481 60
41 04024 99919 13798 99043 23440 97214 32856 94448 59
42 04122 99915 13896 99030 23535 97191 32948 94416 58
43 04220 99911 13993 99016 23631 97168 33041 94384 57
44 04318 99907 14090 99002 23726 97145 33134 94351 56
45 04416 99902 14187 98988 23822 97121 33226 94319 55
46 04515 99898 14284 98975 23917 97098 33319 94286 54
47 04613 99894 14382 98960 24012 97074 33412 94253 53
48 04711 99889 14479 98946 24108 97051 33504 94220 52
49 04809 99884 14576 98932 24203 97027 33597 94187 51
50 04907 99880 14673 98918 24298 97003 33689 94154 50
Mils Cos 1500 Sin Cos 1400 Sin Cos 1300 Sin Cos 1200 Sin Mils
112
Table XVI.—Natural Sines and Cosines of Angles in Mils—Continued
Mils Sin 000 Cos Sin 100 Cos Sin 200 Cos Sin 300 Cos Mils
50 . 04907 . 99880 . 14673 .98918 . 24298 . 97003 .33689 .94154 50
51 05005 99875 14770 98903 24393 96979 33781 94121 49
52 05103 99870 14867 98889 24488 96955 33874 94088 48
53 05201 99865 14964 98874 24584 96931 33966 94055 47
54 05299 99860 15061 98859 24679 96907 34058 94021 46
55 05397 99854 15158 98844 24774 96883 34151 93988 45
56 05495 99849 15255 98830 24869 96858 34243 93954 44
57 05593 99843 15352 98814 24964 96834 34335 93921 43
58 05691 99838 15449 98799 25059 96809 34427 93887 42
59 05789 99832 15546 98784 25154 96785 34520 93853 41
60 05887 99827 15643 98769 25249 96760 34612 93819 40
61 05985 99821 15740 98753 25344 96735 34704 93785 39
62 06083 99815 15837 98738 25439 96710 34796 93751 38
63 06181 99809 15934 98722 25534 96685 34888 93717 37
64 06279 99803 16031 98707 25629 96660 34980 93682 36
65 06377 99796 16128 98691 25724 96635 35072 93648 35
66 06475 99790 16225 98675 25819 96610 35164 93613 34
67 06573 99784 16322 98659 25914 96584 35256 93579 33
68 06671 99777 16419 98643 26008 96559 35347 93544 32
69 06769 99771 16516 98627 26103 96533 35439 93510 31
70 06867 ' 99764 16612 98610 26198 96507 35531 93475 30
71 06965 99757 16709 98594 26293 96482 35623 93440 29
72 07063 99750 16806 98578 26387 96456 35715 93405 28
73 07161 99743 16903 98561 26482 96430 35806 93370 27
74 07259 99736 16999 98545 26577 96404 35898 93335 26
75 07356 99729 17096 98528 26671 96378 35990 93299 25
76 07454 99722 17193 98511 26766 96351 36081 93264 24
77 07552 99714 17290 98494 26860 96325 36173 93228 23
78 07650 99707 17386 98477 26955 96299 36264 93193 22
79 07748 99699 17483 98460 27050 96272 36356 93157 21
80 07846 99692 17580 98443 27144 96246 36447 93121 20
81 07944 99684 17676 98425 27239 96219 36538 93086 19
82 08042 99676 17773 98408 27333 96192 36630 93050 18
83 08139 99668 17869 98390 27427 96165 36721 93014 17
84 08237 99660 17966 98373 27522 96138 36812 92978 16
85 08335 99652 18063 98355 27616 96111 36904 92941 15
86 08433 99644 18159 98337 27711 96084 36995 92905 14
87 08531 99635 18256 98320 27805 96057 37086 92869 13
88 08629 99627 18352 98302 27899 96029 37177 92832 12
89 08726 99619 18449 98283 27993 96002 37268 92796 11
90 08824 99610 18545 98265 28088 95974 37359 92759 10
91 08922 99601 18642 98247 28182 95947 37451 92722 9
92 09020 99592 18738 98229 28276 95919 37542 92686 8
93 09118 99583 18835 98210 28370 95891 37633 92649 7
94 09215 99574 18931 98192 28464 95863 37723 92612 6
95 09313 99565 19027 98173 28558 95835 37814 92575 5
96 09411 99556 19124 98154 28652 95807 37905 92538 4
97 09509 99547 19220 98136 28746 95779 37996 92500 3
98 09606 99538 19316 98117 28840 95751 38087 92463 2
99 09704 99528 19413 98098 28934 95722 38178 92425 1
100 09802 99519 19509 98079 29028 95694 38268 92388 0
Mils Cos 1500 Sin Cos 1400 Sin Cos 1300 Sin Cos 1200 Sin Mils
113
Table XVI.—Natural Sines and Cosines of Angles in Mils—Continued
Mils Sin 400 Cos Sin 500 Cos Sin 600 Cos Sin 700 Cos Mils
0 .38268 . 92388 . 47140 .88192 . 55557 . 83147 .63439 .77301 100
1 38359 92350 47226 88146 55639 83092 63515 77239 99
2 38450 92313 47313 88099 55720 83038 63591 77176 98
3 38540 92275 47399 88053 55802 82983 63667 77114 97
4 38631 92237 47486 88006 55883 82928 63742 77051 96
5 38721 92199 47572 87960 55964 82873 63818 76989 95
6 38812 92161 47658 87913 56046 82818 63893 76926 94
7 38902 92123 47745 87866 56127 82763 63969 76863 93
8 38993 92085 47831 87819 56208 82708 64044 76800 92
9 39083 92046 47917 87772 56290 82653 64120 76737 91
10 39174 92008 48003 87725 56371 82598 64195 76674 90
11 39264 91969 48089 87678 56452 82542 64270 76611 89
12 39354 91931 48175 87631 56533 82487 64346 76548 88
13 39444 91892 48261 87583 56614 82431 64421 76485 87
14 39535 91853 48347 87536 56695 82376 64496 76422 86
15 39625 91814 48433 87488 56775 82320 64571 76358 85
16 39715 91775 48519 87441 56856 82264 64646 76295 84
17 39805 91736 48605 87393 56937 82208 64721 76232 83
18 39895 91697 48691 87345 57018 82152 64795 76168 82
19 39985 91658 48776 87298 57098 82096 64870 76104 81
20 40075 91619 48862 87250 57179 82040 64945 76041 80
21 40165 91579 48948 87202 57259 81984 65019 75977 79
22 40255 91540 49033 87153 57340 81928 65094 75913 78
23 40345 91500 49119 87105 57420 81871 65168 75849 77
24 40434 91461 49204 87057 57501 81815 65243 75785 76
25 40524 91421 49290 87009 57581 81759 65317 75721 75
26 40614 91381 49375 86960 57661 81702 65392 75657 74
27 40704 91341 49461 86912 57741 81645 65466 75592 73
28 40793 91301 49546 86863 57821 81589 65540 75528 72
29 40883 91261 49631 86814 57901 81532 65614 75464 71
30 40972 91221 49716 86766 57981 81475 65688 75399 70
31 41062 91181 49802 86717 58061 81418 65762 75335 69
32 41151 91140 49887 86668 58141 81361 65836 75270 68
33 41241 91100 49972 86619 58221 81304 65910 75206 67
34 41330 91059 50057 86570 58301 81247 65984 75141 66
35 41420 91019 50142 86521 58381 81189 66058 75076 65
36 41509 90978 50227 86471 58460 81132 66131 75011 64
37 41598 90937 50311 86422 58540 81074 66205 74946 63
38 41688 90896 50396 86372 58620 81017 66278 74881 62
39 41777 90855 50481 86323 58699 80959 66352 74816 61
40 41866 90814 50566 86273 58779 80902 66425 74751 60
41 41955 90773 50650 86224 58858 80844 66499 74686 59
42 42044 90732 50735 86174 58937 80786 66572 74620 58
43 42133 90691 50820 86124 59017 80728 66645 74555 57
44 42222 90649 50904 86074 59096 80670 66718 74489 56
45 42311 90608 50989 86024 59175 80612 66791 74424 55
46 42400 90566 51073 85974 59254 80554 ■ 66864 74358 54
47 42489 90524 51157 85924 59343 80496 66937 74293 53
48 42578 90483 51242 85874 59412 80438 67010 74227 52
49 42667 90441 51326 85823 59491 80379 67083 74161 51
50 42756 90399 51410 85773 59570 80321 67156 74095 50
Mils Cos 1100 Sin Cos 1000 Sin Cos 900 Sin Cos 800 Sin Mils
114
Table XVI.—Natural Sines and Cosines of Angles in Mils—Continued
Mils Sin 400 Cos Sin 500 Cos Sin 600 Cos Sin 700 Cos Mils
50 .42756 .90399 .51410 .85773 .59570 .80321 .67156 .74095 50
51 42844 90357 51494 85722 59649 80262 67229 74029 49
52 42933 90315 51579 85672 59728 80204 67301 73963 48
53 43022 90273 51663 85621 59806 80145 67374 73897 47
54 43110 90230 51747 85570 59885 80086 67446 73831 46
55 43199 90188 51831 85519 59963 80027 67519 73765 45
56 43287 90146 51915 85469 60042 79968 67591 73698 44
57 43376 90103 51999 85418 60121 79909 67664 73632 43
58 43464 90060 52082 85366 60199 79850 67736 73565 42
59 43553 90018 52166 85315 60277 79791 67808 73499 41
60 43641 89975 52250 85264 60356 79732 67880 73432 40
61 43729 89932 52334 85213 60434 79673 67952 73366 39
62 43818 89889 52417 85161 60512 79613 68024 73299 38
63 43906 89846 52501 85110 60590 79554 68096 73232 37
64 43994 89803 52584 85058 60668 79494 68168 73165 36
65 44082 89760 52668 85007 60746 79435 68240 73098 35
66 44170 89716 52751 84955 60824 79375 68311 73031 34
67 44258 89673 52835 84903 60902 79315 68383 72964 33
68 44346 89629 52918 84851 60980 79256 68455 72897 32
69 44434 89586 53001 84799 61058 79196 68526 72829 31
70 44522 89542 53084 84747 61135 79136 68598 72762 30
71 44610 89498 53168 84695 61213 79076 68669 72695 29
72 44698 89454 53251 84643 61291 79016 68740 72627 28
73 44786 89410 53334 84590 61368 78955 68812 72560 27
74 44873 89366 53417 84538 61446 78895 68883 72492 26
75 44961 89322 53500 84485 61523 78835 68954 72425 25
76 45049 89278 53583 84433 61601 78774 69025 72357 24
77 45136 89234 53666 84380 61678 78714 69096 72289 23
78 45224 89190 53748 84327 61755 78653 69167 72221 22
79 45312 89145 53831 84275 61832 78592 69238 72153 21
80 45399 89101 53914 84222 61909 78532 69309 72085 20
81 45487 89056 53996 84169 61986 78471 69379 72017 19
82 45574 89011 54079 84116 62063 78410 69450 71949 18
83 45661 88967 54162 84063 62140 78349 69521 71881 17
84 45749 88922 54244 84009 62217 78288 69591 71813 16
85 45836 88877 54327 83956 62294 78227 69662 71744 15
86 45923 88832 54409 83903 62371 78166 69732 71676 14
87 46010 88787 54491 83849 62448 78104 69802 71607 13
88 46097 88741 54574 83796 62524 78043 69873 71539 12
89 46184 88696 54656 83742 62601 77982 69943 71470 11
90 46271 88651 54738 83688 62677 77920 70013 71401 10
91 46358 88605 54820 83635 62754 77859 70083 71333 9
92 46445 88560 54902 83581 62830 77797 70153 71264 8
93 46532 88514 54984 83527 62907 77735 70223 71195 7
94 46619 88468 55066 83473 62983 77673 70293 71126 6
95 46706 88422 55148 83419 63059 77612 70363 71057 5
96 46793 88377 55230 83364 63135 77550 70432 70988 4
97 46880 88331 55312 83310 63211 77488 70502 70919 3
98 46966 88285 55394 83256 63287 77425 70572 70849 2
99 47053 88238 55475 83201 63363 77363 70641 70780 1
100 47140 88192 55557 83147 63439 77301 70711 70711 0
Mils Cos 1100 Sin Cos 1000 Sin Cos 900 Sin Cos 800 Sin Mils
115
Table XVII.—Natural Tangents and Cotangents of Angles in Mils
Values of the tangents and cotangents of angles are given for each mil from 0 to 1,600 mils.
Values of the tangents in hundreds of mils appear at the top of the page. For values of tangents, use the unit mil column at the left.
Values of the cotangents in hundreds of mils appear at the bottom of the page. For values of cotangents, use the unit mil column at the right.
116
Table XVII.—Natural Tangents and Cotangents of Angles in Mils—Continued
Tan 000 100 200 300 400 500 600 700 Mils
0 . 00000 .09849 .19891 . 30335 . 41421 . 53451 .66818 . 82068 100
1 00098 09948 19993 30442 41536 53577 66960 82232 99
2 00196 10047 20095 30549 41652 53704 67102 82397 98
3 00295 10147 20198 30657 41767 53830 67245 82562 97
4 00393 10246 20300 30764 41882 53957 67387 82727 96
5 00491 10345 20402 30872 41998 54084 67530 82893 95
6 00589 10444 20504 30979 42113 54211 67673 83058 94
7 00687 10544 20607 31087 42229 54338 67817 83225 93
8 00785 10643 20709 31194 42345 54465 67960 83391 92
9 00884 10742 20811 31302 42460 54593 68104 83557 91
10 00982 10841 20914 31410 42576 54720 68247 83724 . 90
11 01080 10941 21016 31518 42692 54848 68391 83891 89
12 01178 11040 21119 31626 42808 54975 68536 84059 88
13 01276 11139 21221 31734 42925 55103 68680 84226 87
14 01375 11239 21324 31842 43041 55231 68825 84394 86
15 01473 11338 21427 31950 43157 55360 68969 84563 85
16 01571 11438 21529 32058 43274 55488 69114 84731 84
17 01669 11537 21632 32167 43390 55616 69259 84900 83
18 01767 11637 21735 32275 43507 55745 69405 85069 82
19 01866 11736 21838 32383 43624 55874 69550 85238 81
20 01964 11836 21941 32492 43741 56003 69696 85408 80
21 02062 11935 22044 32601 43858 56132 69842 85578 79
22 02160 12035 22147 32709 43975 56261 69988 85748 78
23 02258 12135 22250 32818 44092 5639,0 70135 85919 77
24 02357 12234 22353 32927 44210 56520 70281 86090 76
25 02455 12334 22456 33036 44327 56649 70428 86261 75
26 02553 12434 22559 33144 44444 56779 70575 86432 74
27 02651 12533 22662 33253 44562 56909 70722 86604 73
28 02750 12633 22765 33363 44680 57039 70869 86776 72
29 02848 12733 22869 33472 44798 57169 71017 86948 71
30 02946 12832 22972 33581 44916 57300 71165 87120 70
31 03044 12932 23075 33690 45034 57430 71313 87293 69
32 03143 13032 23179 33800 45152 57561 71461 87466 68
33 03241 13132 23282 33909 45270 57691 71609 87640 67
34 03339 13232 23386 34018 45388 57822 71758 87814 66
35 03437 13332 23489 34128 45507 57953 71907 87988 65
36 03536 13432 23593 34238 45625 58085 72056 88162 64
37 03634 13532 23697 34347 45744 58216 72205 88336 63
38 03732 13632 23800 34457 45863 58348 72355 88511 62
39 03831 13732 23904 34567 45982 58479 72504 88687 61
40 03929 13832 24008 34677 46101 58611 72654 88862 60
41 04027 13932 24112 34787 46220 58743 72804 89038 59
42 04126 14032 24216 34897 46339 58875 72955 89214 58
43 04224 14132 24320 35007 46458 59007 73105 89391 57
44 04322 14232 24424 35118 46578 59140 73256 89567 56
45 04421 14332 24528 35228 46697 59272 73407 89745 55
46 04519 14432 24632 35338 46817 59405 73558 89922 54
47 04617 14533 24736 35449 46937 59538 73710 90100 53
48 04716 14633 24840 35559 47056 59671 73861 90278 52
49 04814 14733 24944 35670 47176 59804 74013 90456 51
50 04913 14834 25049 35781 47296 59938 74165 90635 50
Mils 1500 1400 1300 1200 1100 1000 900 800 Cot
117
Table XVII.-—Natural Tangents and Cotangents of Angles in Mils—Continued
Tan 000 100 200 300 400 500 600 700 Mils
50 .04913 . 14834 .25049 . 35781 .47296 . 59938 .74165 . 90635 50
51 05011 14934 25153 35891 47417 60071 74317 90814 49
52 05110 15034 25257 36002 47537 60205 74470 90993 48
53 05208 15135 25362 36113 47657 60339 74623 91173 47
54 05306 15235 25466 36224 47778 60473 74776 91353 46
55 05405 15336 25571 36335 47899 60607 74929 91533 45
56 05503 15436 25676 36446 48019 60741 75082 91713 44
57 05602 15537 25780 36558 48140 60876 75236 91894 43
58 05700 15637 25885 36669 48261 61010 75390 92076 42
59 05799 15738 25990 36780 48382 61145 75544 92257 41
60 05897 15838 26095 36892 48503 61280 75698 92439 40
61 05996 15939 26200 37004 48625 61415 75853 92621 39
62 06094 16040 26304 37115 48746 61550 76007 92804 38
63 06193 16140 26409 37227 48868 61686 76162 92987 37
64 06291 16241 26515 37339 48989 61822 76318 93170 36
65 06390 16342 26620 37451 49111 61957 76473 93354 35
66 06489 16443 26725 37563 49233 62093 76629 93537 34
67 06587 16544 26830 37675 49355 62229 76785 93722 33
68 06686 16645 26935 37787 49477 62366 76941 93906 32
69 06784 16745 27041 37899 49600 62502 77097 94091 31
70 06883 16846 27146 38011 49722 62639 77254 94276 30
71 06982 16947 27251 38124 49845 62775 77411 94462 29
72 07080 17048 27357 38236 49967 62912 77568 94648 28
73 07179 17149 27462 38349 50090 63050 77725 94834 27
74 07278 17251 27568 38462 50213 63187 77883 95021 26
75 07376 17352 27674 38574 50336 63324 78041 95208 25
76 07475 17453 27779 38687 50459 63462 78199 95395 24
77 07574 17554 27885 38800 50582 63600 78357 95583 23
78 07673 17655 27991 38913 50705 63738 78516 95771 22
79 07771 17756 28097 39026 50829 63876 78675 95959 21
80 07870 17858 28203 39139 50953 64014 78834 96148 20
81 07969 17959 28309 39253 51076 64153 78993 96337 19
82 08068 18060 28415 39366 51200 64291 79153 96527 18
83 08167 18162 28521 39479 51324 64430 79312 96717 17
84 08265 18263 28627 39593 51448 64569 79472 96907 16
85 08364 18365 28734 39706 51572 64708 79633 97097 15
86 08463 18466 28840 39821 51697 64848 79793 97288 14
87 08562 18568 28946 39934 51821 64987 79954 97479 13
88 08661 18669 29053 40048 51946 65127 80115 97671 12
89 08760 18771 29159 40162 52071 65267 80276 97863 11
90 08859 18873 29266 40276 52195 65407 80438 98056 10
91 08958 18974 29372 40390 52320 65547 80600 98248 9
92 09057 19076 29479 40504 52446 65688 80762 98441 8
93 09156 19178 29586 40618 52571 65828 80924 98635 7
94 09255 19280 29693 40733 52696 65969 81087 98829 6
.95 ■ 09354 19381 29799 40847 52822 66110 81250 99023 5
96 09453 19483 29906 40962 52947 66251 81413 99218 4
97 09552 19585 30013 41077 53073 66393 81576 99413 3
98 09651 19687 30120 41192 53199 66534 81740 99608 2
99 09750 19789 30227 41306 53325 66676 81904 99804 1
100 09849 19891 30335 41421 53451 66818 82068 1. 0
Mils 1500 1400 1300 1200 1100 1000 900 800 Cot
118
Table XVII.—Natural Tangents and Cotangents of Angles in Mils—Continued
Tan | . 800 900 1000 1100 1200 1300 1400 1500 Mils
0 1.00000 1.21850 1.49661 1.87087 2.41421 3.29656 5.02734 10.15317 106
1 1.00197 1.22095 1.49979 1.87529 2.42093 3.30825 5.05326 10.25639 99
2 1.00393 1.22339 1.50299 1.87974 2.42769 3.32001 5.07944 10.36170 98
3 1.00591 1.22585 1.50619 1.88420 2.43447 3.33185 5.10589 10.46918 97
4 1.00788 1.22831 1.50940 1.88867 2.44129 3.34377 5.13260 10.57890 96
5 1.00987 1.23077 1.51263 1.89316 2.44813 3.35577 5.15958 10.69091 95
6 1.01185 1.23325 1.51586 1.89767 2.45502 3.36785 5.18683 10.80530 94
7 1.01384 1.23572 1.51910 1.90220 2.46193 3.38000 5.21437 10.92215 93
8 1.01583 1.23821 1.52235 1.90674 2.46888 3.39224 5.24218 11.04152 92
9 1.01783 1.24070 1.52562 1.91130 2.47586 3.40456 5.27029 11.16352 91
10 1.01983 1.24319 1.52889 1.91588 2.48288 3.41697 5.29869 11.28822 90
11 1.02184 1.24570 1.53217 1.92047 2.48993 3.42945 5.32738 11.41571 89
12 1.02384 1.24820 1.53546 1.92508 2.49702 3.44202 5.35638 11.54609 88
13 1.02586 1.25072 1.53876 1.92971 2.50414 3.45468 5.38568 11.67947 87
14 1.02787 1.25324 1.54207 1.93436 2.51129 3.46742 5.41530 11.81593 86
15 1.02989 1.25577 1.54540 1.93902 2.51849 3.48025 5.44523 11.95560 85
16 1.03192 1.25830 1.54873 1.94370 2.52571 3.49317 5.47548 12.09859 84
17 1.03395 1.26084 1.55207 1.94840 2.53297 3.50617 5.50606 12.24501 83
18 1.03598 1.26338 1.55542 1.95312 2.54027 3.51927 5.53697 12.39500 82
19 1.03802 1.26594 1.55878 1.95786 2.54761 3.53245 5.56822 12.54869 81
20 1.04006 1.26849 1.56215 1.96261 2.55498 3.54573 5.59981 12.70620 80
21 1.04211 1.27106 1.56554 1.96738 2.56239 3.55910 5.63176 12.86770 79
22 1.04416 1.27363 1.56893 1.97217 2.56984 3.57257 5.66406 13.03333 78
23 1.04621 1.27621 1.57233 1.97698 2.57732 3.58613 5.69671 13.20325 77
24 1.04827 1.27879 1.57575 1.98181 2.58484 3.59978 5.72974 13.37764 76
25 1.05033 1.28138 1.57917 1.98666 2.59240 3.61354 5.76314 13.55667 75
26 1.05240 1.28398 1.58261 1.99152 2'. 60000 3.62739 5.79692 13.74053 74
27 1.05447 1.28658 1.58605 1.99641 2.60764 3.64134 5.83109 13.92941 73
28 1.05655 1.28919 1.58951 2.00131 2.61532 3.65538 5.86565 14.12354 72
29 1.05863 1.29181 1.59298 2.00624 2.62303 3.66953 5.90061 14.32312 71
30 1.06071 1.29443 1.59646 2.01118 2.63079 3.68379 5.93598 14.52839 70
31 1.06280 1.29706 1.59995 2.01614 2.63859 3.69814 5.97176 14.73961 69
32 1.06489 1.29970 1.60345 2.02113 2.64642 3.71260 6.00797 14.95703 68
33 1.06699 1.30234 1.60696 2.02613 2.65430 3.72717 6.04460 15.18093 67
34 1.06909 1.30499 1.61048 2.03115 2.66222 3.74185 6.08167 15.41160 66
35 1.07120 1.30765 1.61401 2.03619 2.67018 3.75663 6.11919 15.64936 65
36 1.07331 1.31031 1.61756 2.04125 2.67818 3.77152 6.15716 15.89454 64
37 1.07542 1.31298 1.62112 2.04634 2.68623 3.78652 6.19560 16.14750 63
38 1.07754 1.31566 1.62468 2.05144 2.69432 3.80163 6.23450 16.40860 62
39 1.07967 1.31835 1.62826 2.05656 2.70245 3.81686 6.27388 16.67826 61
40 1.08179 1.32104 1.63185 2.06171 2.71062 3.83220 6.31375 16.95689 60
41 1.08393 1.32374 1.63545 2.06687 2.71884 3.84766 6.35412 17.24495 59
42 1.08606 1.32644 1.63907 2.07206 2.72710 3.86324 6.39499 17.54294 58
43 1.08821 1.32916 1.64269 2.07727 2.73540 3.87893 6.43638 17.85137 57
44 1.09035 1.33187 1.64633 2.08250 2.74375 3.89474 6.47830 18.17081 56
45 1.09250 1.33460 1.64998 2.08775 2.75215 3.91068 6.52076 18.50185 55
46 1.09466 1.33734 1.65364 2.09302 2.76059 3.92674 6.56376 18.84513 54
47 1.09682 1.34008 1.65731 2.09831 2.76907 3.94292 6.60732 19.20136 53
48 1.09899 1.34283 1.66099 2.10363 2.77761 3.95923 6.65144 19.57128 52
49 1.10116 1.34558 1.66469 2.10896 2.78619 3.97566 6.69615 19.95569 51
50 1.10333 1.34834 1.66840 2.11432 2.79481 3.99222 6.74145 20.35547 50
Mils 700 600 500 400 300 200 100 000 Cot
119
Table XVII.—Natural Tangents and Cotangents of Angles in Mils—Continued
Tan 800
50 1.10333
51 1.10551
52 1.10769
53 1.10988
54 1.11208
55 1.11427
5G 1.11648
57 1.11868
58 1.12090
59 1.12312
eo 1.12534
61 1.12757
62 1.12980
63 1.13203
64 1.13428
65 1.13652
66 1.13878
67 1.14103
68 1.14330
69 1.14556
70 1.14784
71 1.15011
72 1.15240
73 1.15469
74 1.15698
75 1.15928
76 1.16158
77 1.16389
78 1.16620
79 1.16852
80 1.17085
81 1.17318
82 1.17552
83 1.17786
84 1.18020
85 1.18256
86 1.18491
87 1.18728
88 1.18964
89 1.19203
90 1.19440
91 1.19678
92 1.19917
93 1.20157
94 1.20397
95 1.20638
96 1.20879
97 1.21121
98 1.21364
99 1.21607
100 1.21850
Mils 700
900 1000
1.34834 1.66840
1.35111 1.67212
1.35389 1.67585
1.35668 1.67960
1.35947 1.68336
1.36227 1.68713
1.36508 1.69091
1.36789 1.69470
1.37071 1.69851
1.37354 1.70233
1.37638 1.70616
1.37923 1.71001
1.38208 1.71387
1.38494 1.71774
1.38781 1.72163
1.39069 1.72552
1.39357 1.72944
1.39646 1.73336
1.39936 1.73730
1.40227 1.74125
1.40519 1.74522
1.40811 1.74919
1.41104 1.75319
1.41399 1.75719
1.41693 1.76121
1.41989 1.76525
1.42286 1.76929
1.42583 1.77336
1.42881 1.77743
1.43180 1.78152
1.43480 1.78563
1.43781 1.78975
1.44082 1.79388
1.44385 1.79803
1.44688 1.80219
1.44992 1.80637
1.45297 1.81056
1.45603 1.81477
1.45910 1.81899
1.46217 1.82323
1.46526 1.82748
1.46835 1.83175
1.47146 1.83604
1.47457 1.84033
1.47769 1.84465
1.48082 1.84898
1.48396 1.85333
1.48711 1.85769
1.49026 1.86206
1.49343 1.86646
1.49661 1.87087
600 500
1100 1200
2.11432 2.79481
2.11970 2.80349
2.12511 2.81221
2.13053 2.82098
2.13598 2.82980
2.14146 2.83867
2.14695 2.84758
2.15247 2.85655
2.15801 2.86557
2.16358 2.87464
2.16917 2.88376
2.17478 2.89293
2.18042 2.90215
2.18608 2.91143
2.19176 2.92076
2.19748 2.93014
2.20321 2.93958
2.20897 2.94908
2.21475 2.95862
2.22056 2.96823
2.22640 2.97789
2.23226 2.98760
2.23815 2.99738
2.24406 3.00721
2.25000 3.01710
2.25596 3.02704
2.26196 3.03705
2.26797 3.04712
2.27402 3.05725
2.28009 3.06743
2.28619 3.07768
2.29232 3.08800
2.29847 3.09837
2.30465 3.10881
2.31086 3.11931
2.31710 3.12988
2.32337 3.14051
2.32966 3.15121
2.33599 3.16197
2.34234 3.17280
2.34873 3.18370
2.35514 3.19467
2.36158 3.20570
2.36805 3.21681
2.37455 3.22798
2.38109 3.23923
2.38765 3.25055
2.39424 3.26194
2.40087 3.27341
2.40753 3.28495
2.41421 3.29656
400 300
1300 1400
3.99222 6.74145
4.00892 6.78736
4.02574 6.83387
4.04270 6.88102
4.05980 6.92881
4.07703 6.97725
4.09440 7.02637
4.11191 7.07616
4.12956 7.12665
4.14736 7.17785
4.16530 7.22978
4.18339 7.28245
4.20163 7.33588
4.22002 7.39009
4.23856 7.44509
4.25725 7.50089
4.27611 7.55753
4.29512 7.61501
4.31430 7.67336
4.33363 7.73259
4.35313 7.79273
4.37280 7.85380
4.39264 7.91581
4.41266 7.97880
4.43284 8.04278
4.45320 8.10779
4.47374 8.17383
4.49446 8.24094
4.51537 8.30915
4.53646 8.37848
4.55774 8.44896
4.57921 8.52062
4.60088 8.59348
4.62274 8.66759
4.64480 8.74297
4.66707 8.81965
4.68954 8.89768
4.71221 8.97708
4.73510 9. 05789
4.75820 9.14015
4.78152 9.22390
4.80506 9.30918
4.82882 9.39603
4.85280 9.48451
4.87702 9.57464
4.90147 9.66649
4.92616 9.76009
4.95108 9.85551
4.97625 9.95279
5.00167 10.0520
5.02734 10.1532
200 100
1500 Mils
20.35547 50
20.77155 49
21.20495 48
21.65678 47
22.12824 46
22.62064 45
23.13541 44
23.67410 43
24.23844 42
24.83028 41
25.45170 40
26.10497 39
26.79261 38
27.51739 37
28.28243 36
29.09116 35
29.94745 34
30.85561 33
31.82052 32
32.84765 31
33.94324 30
35.11436 29
36.36911 28
37.71678 27
39.16809 26
40.73548 25
42.43346 24
44.27907 23
46.29242 22
48.49749 21
50.92304 20
53.60387 19
56.58253 18
59.91159 17
63.65674 16
67.90120 15
72.75196 14
78.34895 13
84.87871 12
92.59564 11
101.8559 10
113.1739 9
127.3213 8
145.5108 7
169.7633 6
203.7167 5
254.6466 4
339.5296 3
509.2952 2
1018.591 1
cc 0
000 Cot
120
Table XVIII.—Natural Sines and Cosines of Angles in Degrees and Minutes
Values of the sines and cosines of angles are given for each minute from 0° to 90°.
For degrees indicated at the top of the page, use the column designations at the top. For degrees indicated at the bottom of the page, use the column designations at the bottom.
For degrees indicated at the top of the page, use the minute column at the left. For degrees indicated at the bottom of the page, use the minute column at the right.
18
121
Iable XVIII. Natural Sines and Cosines of Angles in Degrees and Minutes (For every minute of the quadrant)
M. 0° 1° 2° 3° 4°
Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin Cos.
0 O.OOOOC 1. oooc 0.01745 0.99985 0.0349C 0.99931 0.05234 0.99863 0.06976 0. 99751 60
1 029 ooc 774 984 51£ 933 263 861 . 07005 754 59
2 058 ooc 803 984 543 937 292 86C 034 752 58
3 087 ooc 832 983 577 936 321 858 062 75C 57
4 116 ooo 862 983 606 935 35C 857 092 748 56
5 .00145 1.0000 . 01891 .99982 . 03635 .099934 . 05379 .99855 .07121 . 9974C 55
6 175 000 920 982 6ft 933 408 854 15C 744 54
7 204 ooo 949 981 693 932 437 852 179 742 53
8 233 000 978 980 723 931 466 851 208 74(1 52
9 262 ooo .02007 980 752 930 495 849 237 738 51
10 .00291 1.0000 . 02036 .99979 .03781 .99929 .05524 . 99847 . 07266 99736 50
11 320 . 99999 065 979 81( 927 553 846 295 734 49
12 349 999 094 978 839 926 582 844 324 731 48
13 378 999 123 977 868 925 611 842 353 729 47
14 407 999 152 977 897 924 640 841 382 727 46
15 .00436 . 99999 .02181 .99976 . 03926 .99923 . 05669 .99839 .07411 9972.5 45
16 465 999 211 976 955 922 698 838 440 723 44
17 495 999 240 975 984 921 727 836 469 721 43
18 524 999 269 974 . 04013 919 756 834 498 719 42
19 553 998 298 974 042 918 785 833 527 716 41
20 .00582 . 99998 .02327 .99973 .04071 .99917 . 05814 .99831 .07556 99714 40
21 611 998 356 972 10C 916 844 829 585 712 39
22 640 998 385 972 129 915 873 827 614 710 38
23 669 998 414 971 159 913 902 826 643 708 37
24 698 998 443 970 188 912 931 824 672 705 36
25 .00727 .99997 .02472 .99969 . 04217 .99911 . 05960 .99822 .07701 99703 35
26 756 997 501 969 246 910 989 821 730 701 34
27 785 997 530 968 275 909 . 06018 819 759 699 33
28 814 997 560 967 304 907 047 817 788 696 32
29 844 996 589 966 333 906 076 815 817 694 31
30 .00873 . 99996 .02618 .99966 .04362 . 99905 .06105 . 99813 . 07846 99692 30
31 902 996 647 965 391 904 134 812 875 689 29
32 931 996 676 964 420 902 163 810 904 687 28
33 960 995 705 963 449 901 192 808 933 68.5 27
34 989 995 734 963 478 900 221 806 962 683 26
35 . 01018 .99995 .02763 .99962 .04507 . 99898 .06250 .99804 .07991 99680 25
36 047 995 792 961 536 897 279 803 . 08020 678 24
37 076 994 821 960 565 896 308 801 049 676 23
38 105 994 850 959 594 894 337 799 078 673 22
39 134 994 879 959 623 893 366 797 107 671 21
40 .01164 . 99993 .02908 .99958 .04653 . 99892 . 06395 .99795 . 08136 99668 20
41 193 993 938 957 682 890 424 793 165 660 19
42 222 993 967 956 711 889 453 792 194 664 18
43 251 992 996 955 740 888 482 790 223 661 17
44 280 992 . 03025 954 769 886 511 788 252 659 16
45 .01309 . 99991 .03054 .99953 .04798 .99885 . 06540 . 99786 .08281 / 996.57 15
46 338 991 083 952 827 883 569 784 310 6.54 14
47 367 991 112 952 856 882 598 782 339 6.52 13
48 396 990 141 951 885 881 627 780 368 649 12
49 425 990 170 950 914 879 656 778 397 647 11
50 .01454 . 99989 .03199 .99949 . 04943 .99878 . 06685 .99776 .08426 .99644 10
51 483 989 228 948 972 876 714 774 455 642 9
52 513 989 257 947 .05001 875 743 772 484 639 8
53 542 988 286 946 030 873 773 770 513 637 7
54 571 988 316 945 059 872 802 768 542 635 6
55 .01600 .99987 .03345 .99944 .05088 .99870 .06831 .99766 .08571 .99632 5
56 629 987 374 943 117 869 860 764 600 630 4
57 658 986 403 942 146 867 889 762 629 627 3
58 687 986 432 941 175 866 918 760 658 62.5 2
59 716 985 461 940 205 864 947 758 687 622 1
60 .01745 .99985 . 03490 . 99939 .05234 .99863 . 06976 . 99756 .08716 .99619 0
Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin.
89° 88° 87 0 86 85 1 M.
122
1 able XVIII.—Natural Sines and Cosines of Angles in Degrees and Minutes—
Continued
M. 5° 6° 7° 8° 9°
Sin. Cos. Sin. Cos. Sin. Cos. Sin. Oos. Sin. Oos.
0 0.08716 0.99619 0.10453 0.99452 0.12187 0.99255 0.13917 0.99027 0.15643 0.98769 60
1 745 617 482 44£ 216 251 946 023 672 764 59
2 774 614 511 440 245 248 975 01S 701 760 58
3 803 612 540 443 27' 24' .1400' 015 730 755 57
4 831 609 569 440 302 240 033 on 758 751 56
5 .08860 .99607 .10597 .99437 .12331 .99237 . 14061 . 99006 . 15787 .98746 55
6 889 604 626 43' 36C 233 090 002 816 741 54
7 918 602 655 431 38£ 23C lli . 98998 845 737 53
8 947 599 684 428 418 226 148 994 873 732 52
9 976 596 713 424 447 222 177 990 902 728 51
10 . 09005 .99594 .10742 .99421 .12476 .99219 .14205 .98986 .15931 .98723 50
11 034 591 771 4U 504 215 234 982 959 718 49
12 063 588 800 415 533 211 263 978 988 714 48
13 092 586 829 412 562 208 292 973 .16017 709 47
14 121 583 858 409 591 204 320 969 046 704 46
15 .09150 . 99580 .10887 .99406 .12620 .99200 .14349 .98965 .16074 .98700 45
16 179 578 916 402 649 197 378 961 103 695 44
17 208 575 945 399 678 193 407 957 132 690 43
18 237 572 973 396 706 189 436 953 160 686 42
19 266 570 .11002 393 735 186 464 948 189 681 41
20 .09295 . 99567 .11031 .99390 .12764 . 99182 . 14493 .98944 .16218 98676 40
21 324 564 060 380 793 178 522 940 246 671 39
22 353 562 089 383 822 175 551 936 275 667 38
23 382 559 118 380 851 171 580 931 304 662 37
24 411 556 147 377 880 167 608 927 333 657 36
25 .09440 .99553 .11176 .99374 .12908 .99163 . 14637 .98923 .16361 .98652 35
26 469 551 205 370 937 160 666 919 390 648 34
27 498 548 234 367 966 156 695 914 419 643 33
28 527 545 263 364 995 152 723 910 447 638 32
29 556 542 291 360 .13024 148 752 906 476 633 31
30 .09585 .99540 . 11320 .99357 .13053 .99144 .14781 .98902 .16505 .98629 30
31 614 537 349 354 081 141 810 897 533 624 29
32 642 534 378 351 110 137 838 893 562 619 28
33 671 531 407 347 139 133 867 889 591 614 27
34 700 528 436 344 168 129 896 884 620 609 26
35 .09729 .99526 . 11465 .99341 . 13197 .99125 .14925 .98880 .16648 . 98604 25
36 758 523 494 337 226 122 954 876 677 600 24
37 787 520 523 334 254 118 982 871 706 595 23
38 816 517 552 331 283 '.14 . 15011 867 734 590 22
39 845 514 580 327 312 110 040 863 763 585 21
40 .09874 . 99511 .11609 .99324 .13341 .99106 .15069 .98858 . 16792 . 98580 20
41 903 508 638 320 370 102 097 854 820 575 19
42 932 506 667 317 399 098 126 849 849 570 18
43 961 503 696 314 427 094 155 845 878 565 17
44 990 500 725 310 456 091 184 841 906 561 16
45 .10019 . 99497 .11754 .99307 . 13485 . 99087 .15212 .98836 .16935 .98556 15
46 048 494 783 303 514 083 241 832 964 551 14
47 077 491 812 300 543 079 270 827 992 546 13
48 106 488 840 297 572 075 299 823 .17021 541 12
49 135 485 869 293 600 071 327 818 050 536 11
50 .10164 .99482 ,11898 .99290 .13629 .99067 .15356 .98814 .17078 .98531 10
51 192 479 927 286 658 063 385 809 107 526 9
52 221 476 956 283 687 059 414 805 136 521 8
53 250 473 985 279 716 055 442 800 164 516 7
54 279 470 .12014 276 744 051 471 796 193 511 6
55 . 10308 .99467 . 12043 .99272 .13773 .99047 .15500 .98791 .17222 .98506 5
56 337 464 071 269 802 043 529 787 250 501 4
57 366 461 100 265 831 039 557 782 279 496 3
58 395 458 129 262 860 035 586 778 308 491 2
59 424 455 158 258 889 031 615 773 336 486 1
60 .10453 .99452 .12187 99255 .13917 .99027 .15643 .98769 .17365 .98481 0
Oos. Sin. Oos. Sin. Oos. Sin. Oos. Sin. Cos. Sin.
84° 83 82 0 81 80 M.
123
Table XVIII. Natural Sines and Cosines of Angles in Degrees and Minutes—
Continued
M 10° 11° 12° 13° 14°
Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos.
0 0.1736E 0.98481 0.19081 0.98163 0. 20791 0.97815 0. 2249' 0.9743’' 0. 24191 0.97030 60
1 392 47C 10S 157 82C 80S 52C 43C 22C 020 59
2 422 471 138 152 843 801 552 424 24S 015 58
3 451 465 167 146 877 797 58C 417 277 008 57
4 47S 461 195 140 905 791 608 411 305 001 56
5 -17508 . 98455 . 19224 .98135 .20933 .97784 .22637 .97404 .24333 . 96994 55
6 537 450 252 129 962 778 665 398 362 987 54
7 565 445 281 124 99C 772 693 391 39C 980 53
8 594 440 309 118 . 21011 766 722 384 418 973 52
9 623 435 338 112 047 760 75C 378 446 966 51
10 -17651 .98430 .19366 . 98107 . 21076 .97754 .22778 .97371 . 24474 .96959 50
11 680 425 395 101 10' 748 807 365 503 952 49
12 708 420 423 096 132 742 835 358 531 945 48
13 737 414 452 090 161 735 863 351 559 937 47
14 766 409 481 084 189 729 892 345 587 930 46
15 .17794 .98404 .19509 . 98079 . 21218 .97723 . 22920 . 97338 .24615 .96923 45
16 823 399 538 073 246 717 948 331 644 916 44
17 852 394 566 067 275 711 977 325 672 909 43
18 880 389 595 061 303 705 .23005 318 700 902 42
19 909 383 623 056 331 698 033 311 728 894 41
20 .17937 . 98378 .19652 .98050 . 21360 .97692 .23062 .97304 .24756 .96887 40
21 966 373 680 044 388 686 090 298 784 880 39
22 995 368 709 039 417 680 118 291 813 873 38
23 .18023 362 737 033 445 673 146 284 841 866 37
24 . 052 357 766 027 474 667 175 278 869 858 36
25 .18081 .98352 . 19794 .98021 . 21502 .97661 .23203 .97271 .24897 . 96851 35
26 109 347 823 016 530 655 231 264 925 844 34
27 138 341 851 010 559 648 260 257 954 837 33
28 166 336 880 004 587 642 288 251 982 829 32
29 195 331 908 .97998 616 636 316 244 . 25010 822 31
30 .18224 .98325 . 19937 .97992 . 21644 . 97630 .23345 .97237 .25038 .96815 30
31 252 320 965 987 672 623 373 230 066 807 29
32 281 315 994 981 701 617 401 223 094 800 28
33 309 310 . 20022 975 729 611 429 217 122 793 27
34 338 304 051 969 758 604 458 210 151 786 26
35 .18367 . 98299 .20079 .97963 . 21786 . 97598 .23486 . 97203 . 25179 .96778 25
36 395 294 108 958 814 592 514 196 207 771 24
37 424 288 136 952 843 585 542 189 235 764 23
38 452 283 165 946 871 579 571 182 263 756 22
39 481 277 193 940 899 573 599 176 291 749 21
40 •. 18509 .98272 . 20222 . 97934 .21928 .97566 .23627 .97169 .25320 . 96742 20
41 538 267 250 928 956 560 656 162 348 734 19
42 567 261 279 922 985 553 684 155 376 727 18
43 595 256 307 916 .22013 547 712 148 404 719 17
44 624 250 836 910 041 541 740 141 432 712 16
45 .18652 .98245 . 20364 .97905 .22070 . 97534 .23769 .97134 . 25460 .96705 15
46 681 240 393 899 098 528 797 127 488 697 14
47 710 234 421 893 126 521 825 120 516 690 13
48 738 229 450 887 155 515 853 113 545 682 12
49 767 223 478 881 183 508 882 106 573 675 11
50 .18795 . 98218 . 20507 .97875 . 22212 .97502 .23910 .97100 .25601 . 96667 10
51 824 212 535 869 240 496 938 093 629 660 9
52 852 207 563 863 268 489 966 086 657 653 8
53 881 201 592 857 297 483 995 079 685 645 7
54 910 196 620 851 325 476 . 24023 072 713 638 6
55 .18938 . 98190 . 20649 .97845 . 22353 .97470 . 24051 .97065 .25741 .96630 5
56 967 185 677 839 382 463 079 058 769 623 4
57 995 179 706 833 410 457 108 051 798 615 3
58 .19024 174 734 827 438 450 136 044 826 608 2
59 052 168 763 821 467 444 164 037 854 600 1
60 . 19081 .98163 .20791 .97815 .22495 .97437 .24192 .97030 .25882 .96593 0
Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin.
79 0 78 0 77 0 76 0 7 5° M.
124
Table XVIII. Natural Sines and Cosines of Angles in Degrees and Minutes—
Continued
M. 15° 16° 17° 18° 19°
Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos.
0 0. 25882 0.96593 0. 27564 0.96120 0. 29237 0.95630 0.30902 0.95106 0.32557 0.94552 60
1 910 585 592 118 265 622 929 097 584 542 59
2 938 578 620 no 291 611 957 088 612 533 58
3 966 570 648 102 321 605 985 079 639 523 57
4 994 562 676 094 348 596 .31012 070 667 514 56
5 .26022 . 96555 . 27704 . 96086 .29376 . 95588 .31040 . 95061 . 32694 .94504 55
6 050 547 731 078 401 57£ 086 052 722 495 54
7 079 540 759 07( 432 571 095 043 749 485 53
8 107 532 787 062 460 562 123 033 777 476 52
9 135 524 815 054 487 554 151 024 804 466 51
10 . 26163 . 96517 .27843 . 96046 .29515 . 95545 .31178 . 95015 .32832 . 94457 50
11 191 509 871 037 541 536 206 006 859 447 49
12 219 502 891 02' 571 528 233 . 94997 887 438 48
13 247 494 927 02] 599 519 261 988 914 428 47
14 275 486 955 013 626 511 289 979 942 418 46
15 . 26309 .96479 .27983 . 96005 .29654 . 95502 . 31316 .94970 . 32969 .94409 45
16 331 471 . 28011 . 95997 682 493 344 961 997 399 44
17 35£ 463 039 989 710 485 372 952 .33024 390 43
18 387 456 067 981 737 476 39S 943 051 380 42
19 415 448 095 972 765 467 427 933 079 370 41
20 .26443 .96440 .28123 .95964 .29793 . 95459 .31454 . 94924 . 33106 . 94361 40
21 471 433 150 956 821 450 482 915 134 351 39
22 500 425 178 948 840 441 510 906 161 342 38
23 528 417 206 940 876 433 537 807 189 332 37
24 556 410 234 931 904 424 565 888 216 322 36
25 . 26584 .96402 .28262 .95923 .29932 .95415 . 31593 .94878 .33244 .94313 35
26 612 394 290 915 960 407 620 869 271 303 34
27 640 386 318 907 987 398 648 860 298 293 33
28 668 379 346 898 .30015 389 675 851 326 284 32
29 696 371 374 890 043 380 703 842 353 274 31
30 .26724 . 96363 .28402 .95882 .30071 .95372 . 31730 .94832 .33381 .94264 30
31 752 355 429 874 098 363 758 823 408 254 29
32 780 347 457 865 126 354 786 814 436 245 28
33 808 340 485 857 154 345 813 805 463 235 27
34 836 332 513 849 182 337 841 795 490 225 26
35 . 26864 .96324 .28541 . 95841 . 30209 .95328 .31868 . 94786 .33518 . 94215 25
36 892 316 569 832 237 319 896 777 545 206 24
37 920 308 597 824 265 310 923 768 573 196 23
38 948 301 625 816 292 301 951 758 600 186 22
39 976 293 652 807 320 293 979 749 627 176 21
40 .27004 .96285 .28680 . 95799 . 30348 .95284 .32006 .94740 .33655 . 94167 20
41 032 277 708 791 376 275 034 730 682 157 19
42 060 269 736 782 403 266 061 721 710 147 18
43 088 261 764 774 431 257 089 712 737 137 17
44 116 253 792 766 459 248 116 702 764 127 16
45 . 27144 .96246 . 28820 .95757 .30486 .95240 .32144 .94693 .33792 .94118 15
46 172 238 847 749 514 231 171 684 819 108 14
47 200 230 875 740 542 222 199 674 846 098 13
48 228 222 903 732 570 213 227 665 874 088 12
49 256 214 931 724 597 204 254 656 901 078 11
50 .27284 .96206 . 28959 .95715 .30625 . 95195 .32282 .94646 .33929 . 94068 10
51 312 198 987 707 653 186 309 637 956 058 9
52 340 190 . 29015 698 680 177 337 627 983 049 8
53 368 182 042 690 708 168 364 618 .34011 039 7
54 396 174 070 681 736 159 392 609 038 029 6
55 .27424 .96166 .29098 .95673 .30763 . 95150 .32419 .94599 .34065 . 94019 5
56 452 158 126 664 791 142 447 590 093 009 4
57 480 150 154 656 819 133 474 580 120 .93999 3
58 508 142 182 647 846 124 502 571 147 989 2
59 536 134 209 639 874 115 529 561 175 979 1
60 .27564 .96126 .29237 .95630 .30902 .95106 . 32557 .94552 . 34202 .93969 0
Oos. Sin. Cos. Sin. Oos. Sin. Cos. Sin. Cos. Sin. M.
74° 73° 72 0 71 0 70
609023°—44----9 125
1 able XVIII. Natural Sines and Cosines of Angles in Degrees and Minutes—
Continued
M. 20° 21° 22° 23° 24°
Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos.
0 0.34201 0. 93969 0.3583' 0.93358 0.37461 0.92718 0.39073 0.9205C 0.40674 0.9135. 60
1 229 959 864 348 488 70' 10C 03£ 70C 343 59
2 25 949 891 33' 51. 697 127 028 72' 331 58
3 281 939 91? 32" 542 680 153 016 75: 31< 57
4 311 929 941 310 561 675 180 006 786 30' 56
5 .34339 . 93919 . 35973 . 93300 .37595 .92661 . 39207 . 91994 . 40806 . 91291 55
6 36C 90S .3600C 295 622 6K 23' 982 833 283 54
7 393 899 027 285 640 642 260 97: 86C 272 53
8 421 889 054 274 670 63: 287 95S 886 26C 52
9 448 879 081 264 703 620 314 948 913 24? 51
10 .34475 .93869 .36108 .93253 . 37730 . 92609 .39341 . 91936 . 40939 .91236 50
11 503 859 135 241 757 598 367 925 966 224 49
12 530 849 162 232 78' 587 394 914 992 212 48
13 557 839 190 222 8L 576 421 902 .41019 20C 47
14 584 829 217 211 838 565 448 891 045 188 46
15 .34612 . 93819 .36244 . 93201 37865 .92554 .39474 . 91879 .41072 .91176 45
16 639 809 271 190 892 548 501 868 098 164 44
17 666 799 298 180 919 532 528 856 125 152 43
18 694 789 325 169 946 521 555 845 151 140 42
19 721 779 352 159 973 510 581 833 178 128 41
20 .34748 .93769 .36379 .93148 .37999 .92499 . 39608 .91822 .41204 .91116 40
21 775 759 406 137 .38026 488 635 810 231 104 39
22 803 748 434 127 053 477 661 799 257 092 38
23 830 738 461 116 080 466 688 787 284 080 37
24 857 728 488 106 107 455 715 775 310 068 36
25 .34884 .93718 .36515 . 93095 .38134 .92444 .39741 .91764 . 41337 .91056 35
26 912 708 542 084 161 432 768 752 363 044 34
27 939 698 569 074 188 421 795 741 390 032 33
28 966 688 596 063 215 410 822 729 416 020 32
29 993 677 623 052 241 399 848 718 443 008 31
30 .35021 .93667 . 36650 . 93042 .38268 .92388 .39875 .91706 .41469 .90996 30
31 048 657 677 031 295 377 902 694 496 984 29
32 075 647 704 020 322 366 928 683 522 972 28
33 102 637 731 010 349 355 955 671 549 960 27
34 130 626 758 . 92999 376 343 982 660 575 948 26
35 .35157 .93616 . 36785 . 92988 . 38403 .92332 .40008 .91648 .41602 .90936 25
36 184 606 812 978 430 321 035 636 628 924 24
37 211 596 839 967 456 310 062 625 655 911 23
38 239 585 867 956 483 299 088 613 681 899 22
39 266 575 894 945 510 287 115 601 707 887 21
40 .35293 .93565 . 36921 .92935 .38537 .92276 .40141 . 91590 .41734 .90875 20
41 320 555 948 924 564 265 168 578 760 863 19
42 347 544 975 913 591 254 195 566 787 851 18
43 375 534 .37002 902 617 243 221 555 813 839 17
44 402 524 029 892 644 231 248 543 840 826 16
45 .35429 .93514 .37056 .92881 .38671 .92220 .40275 .91531 .41866 . 90814 15
46 456 503 083 870 698 209 301 519 892 802 14
47 484 493 110 859 725 198 328 508 919 790 13
48 511 483 137 849 752 186 355 496 945 778 12
49 538 472 164 838 778 175 381 484 972 766 11
50 .35565 . 93462 .37191 .92827 .38805 .92164 . 40408 . 91472 . 41998 .90753 10
51 592 452 218 816 832 152 434 461 .42024 741 9
52 619 441 245 805 859 141 461 449 051 729 8
53 647 431 272 794 886 130 488 437 077 717 7
54 674 420 299 784 912 119 514 425 104 704 6
55 .35701 .93410 .37326 .92773 .38939 .92107 .40541 .91414 .42130 .90692 5
56 728 400 353 762 966 096 567 402 156 680 4
57 755 389 380 751 993 085 594 390 183 668 3
58 782 379 407 740 .39020 073 621 378 209 655 2
59 810 368 434 729 046 062 647 366 235 643 1
60 .35837 .93358 .37461 .92718 .39073 .92050 .40674 .91355 .42262 . 90631 0
Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin.
69 68 67 66 65 M.
126
Table XVIII. Natural Sines and Cosines of Angles in Degrees and Minutes—-
Continued
M. 25° 26° 27° 28° 29°
Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos.
0 0.42262 0.90631 0.43837 0.89879 0.45399 0.89101 0.46947 0.88295 0.48481 0.87462 60
1 288 618 863 867 425 087 973 281 506 448 59
2 315 606 889 854 451 07z 999 267 532 434 58
3 341 594 916 841 477 061 .47024 254 557 420 57
4 367 582 942 828 503 048 050 240 583 406 56
5 .42394 .90569 .43968 . 89816 . 45529 . 89035 . 47076 . 88226 .48608 .87391 55
6 420 557 994 803 554 021 101 213 634 377 54
7 446 545 .44020 79C 58C 008 127 199 659 363 53
8 473 532 046 777 606 . 88995 153 185 684 349 52
9 499 520 072 764 632 981 178 172 710 335 51
10 .42525 .90507 . 44098 .89752 .45658 .88968 . 47204 .88158 .48735 . 87321 50
11 552 495 124 739 684 955 229 144 761 306 49
12 578 483 151 726 710 942 255 130 786 292 48
13 604 470 177 713 736 928 281 117 811 278 47
14 631 458 203 700 762 915 306 103 837 264 46
15 . 42657 .90446 .44229 . 89687 . 45787 .88902 . 47332 .88089 .48862 .87250 45
16 683 433 255 674 813 888 358 075 888 235 44
17 709 421 281 662 839 875 382 062 913 221 43
18 736 408 307 649 865 862 409 048 938 207 42
19 762 396 333 636 891 848 434 034 964 193 41
20 .42788 . 90383 .44359 .89623 .45917 .88835 .47460 . 88020 .48989 .87178 40
21 815 371 385 610 942 822 486 006 .49014 164 39
22 841 358 411 597 968 808 511 .87993 040 150 38
23 867 346 437 584 994 795 537 979 065 136 37
24 894 334 464 571 .46020 782 562 905 090 121 36
25 .42920 .90321 . 44490 .89558 . 46046 .88768 .47588 .87951 .49116 .87107 35
26 946 309 516 545 072 755 614 937 141 093 34
27 972 296 542 532 097 741 639 923 166 079 33
28 999 284 568 519 123 728 665 909 192 064 32
29 . 43025 271 594 506 149 715 690 896 217 050 31
30 . 43051 . 90259 .44620 .89493 .46175 .88701 . 47716 .87882 .49242 .87036 30
31 077 246 646 480 201 688 741 868 268 021 29
32 104 233 672 467 226 674 767 854 293 007 28
33 130 221 698 454 252 661 793 840 318 .86993 27
34 156 208 724 441 278 647 818 826 344 978 26
35 .43182 . 90196 .44750 .89428 .46304 .88634 . 47844 .87812 .49369 .86964 25
36 209 183 776 415 330 620 869 798 394 949 24
37 235 171 802 402 355 607 895 784 419 935 23
38 261 158 828 389 381 593 920 770 445 921 22
39 287 146 854 376 407 580 946 756 470 906 21
40 .43313 .90133 .44880 . 89363 .46433 .88566 . 47971 .87743 .49495 .86892 20
41 340 120 906 350 458 553 997 729 521 878 19
42 366 108 932 337 484 539 .48022 715 546 863 18
43 392 095 958 324 510 526 048 701 571 849 17
44 418 082 984 311 536 512 073 687 596 834 16
45 .43445 .90070 .45010 .89298 .46561 .88499 .48099 .87673 .49622 .86820 15
46 471 057 036 285 587 485 124 659 647 805 14
47 497 045 062 272 613 472 150 645 672 791 13
48 523 032 088 259 639 458 175 631 697 777 12
49 549 019 114 245 664 445 201 617 723 762 11
50 . 43575 .90007 .45140 .89232 .46690 .88431 . 48226 .87603 . 49748 .86748 10
51 602 . 89994 166 219 716 417 252 589 773 733 9
52 628 981 192 206 742 404 277 575 798 719 8
53 654 968 218 193 767 390 303 561 824 704 7
54 680 956 243 180 793 377 328 546 849 690 6
55 .43706 .89943 .45269 .89167 .46819 .88363 .48354 .87532 . 49874 .86675 5
56 733 930 295 153 844 349 379 518 899 661 4
57 759 918 321 140 870 336 405 504 924 646 3
58 785 905 347 127 896 322 430 490 950 632 2
59 811 892 373 114 921 308 456 476 975 617 1
60 . 43837 .89879 .45399 .89101 .46947 .88295 .48481 .87462 .50000 .86603 0
Cos. 64 Sin. 0 Cos. J 63 Sin. Cos. | 62 Sin. Cos. 61 Sin. D Cos. | 60 Sin. M.
127
Table XVIII. Natural Sines and Cosines of Angles in Degrees and Minutes—
Continued
M. 30° 31° 32° 33° 34°
Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos.
0 0.5000( 0.8660.' 0.5150 0.8571 0. 5299. 0. 8480. 0.5440' 0.8386' 0.55911 0.8290' 60
1 02 585 52 70. . 5301 781 481 851 941 88' 59
2 051 571 55' 68 04 774 5K 83. 968 871 58
3 076 55£ 57< 671 06i 751 53' 81t 992 85. 57
4 101 544 60' 65' 091 743 561 804 .56011 831 56
5 . 50126 . 8653C .51625 .85641 . 5311. .84728 .54581 .83788 .56040 . 82822 55
6 7 151 515 655 62' 14C 712 61C 772 064 806 54
17t 501 675 611 16- 697 635 756 088 790 53
8 201 48b 70.: 59/ 181 681 659 740 112 773 52
9 227 471 725 581 214 666 683 724 136 757 51
10 .50252 .86457 . 51753 . 85567 .53236 . 84650 . 54708 . 83708 .56160 .82741 50
11 277 442 775 551 26: 635 732 692 184 724 49
12 302 427 803 536 288 612 756 676 208 708 48
13 327 413 828 521 312 604 781 660 232 692 47
14 352 398 852 506 337 588 805 645 256 675 46
15 . 50377 . 86384 . 51877 .85491 .53361 .84573 . 54829 .83629 . 56280 .82659 45
16 403 369 902 476 386 557 854 613 305 643 44
17 428 354 927 461 411 542 878 597 329 626 43
18 453 340 952 446 435 526 902 581 353 610 42
19 478 325 977 431 460 511 927 565 377 593 41
20 .50503 .86310 .52002 .85416 . 53484 .84495 . 54951 .83549 . 56401 . 82577 40
21 528 295 026 401 509 480 975 533 425 561 39
22 553 281 051 385 534 464 999 517 449 544 38
23 578 266 076 370 558 448 . 55024 501 473 528 37
24 603 251 101 355 583 433 048 485 497 511 36
25 .50628 . 86237 .52126 .85340 .53607 .84417 . 55072 .83469 .56521 .82495 35
26 654 222 151 325 632 402 097 453 545 478 34
27 679 207 175 310 656 386 121 437 569 462 33
28 704 192 200 294 681 370 145 421 593 446 32
29 729 178 225 279 705 355 169 405 617 429 31
30 .50754 .86163 .52250 . 85264 .53730 .84339 . 55194 . 83389 .56641 .82413 30
31 779 148 275 249 754 324 218 373 665 396 29
32 804 133 299 234 779 308 242 356 689 380 28
33 829 119 324 218 804 292 266 340 713 363 27
34 854 104 349 203 828 277 291 324 736 347 26
35 .50879 . 86089 .52374 .85188 .53853 .84261 . 55315 .83308 .56760 .82330 25
36 904 074 399 173 877 245 339 292 784 314 24
37 929 059 423 157 902 230 363 276 808 297 23
38 954 045 448 142 926 214 388 260 832 281 22
39 979 030 473 127 951 198 412 244 856 264 21
40 .51004 . 86015 .52498 .85112 . 53975 . 84182 . 55436 .83228 . 56880 . 82248 20
41 029 000 522 096 . 54000 167 460 212 904 231 19
42 054 .85985 547 081 024 151 484 195 928 214 18
43 079 970 572 066 049 135 509 179 952 198 17
44 104 956 597 051 073 120 533 163 976 181 16
45 . 51129 . 85941 .52621 . 85035 .54097 .84104 . 55557 . 83147 . 57000 .82165 15
46 154 926 646 020 122 088 581 131 024 148 14
47 179 911 671 005 146 072 605 115 047 132 13
48 204 896 696 . 84989 171 057 630 098 071 115 12
49 229 881 720 974 195 041 654 082 095 098 11
50 .51254 . 85866 .52745 . 84959 .54220 . 84025 . 55678 . 83066 .57119 .82082 10
51 279 851 770 943 244 009 702 050 143 065 9
52 304 836 794 928 269 .83994 726 034 167 048 8
53 329 821 819 913 293 978 750 017 191 032 7
54 354 806 844 897 317 962 775 001 215 015 6
55 .51379 .85792 . 52869 . 84882 .54342 .83946 . 55799 .82985 .57238 .81999 5
56 404 777 893 866 366 930 823 969 262 982 4
57 429 762 918 851 391 915 847 953 286 965 3
। 58 454 747 943 836 415 899 871 936 310 949 2
' 59 479 732 967 820 440 883 895 920 334 932 1
60 . 51504 .85717 .52992 . 84805 .54464 . 83867 . 55919 .82904 .57358 .81915 0
Cos. J Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin. M.
59c 58c 57c 56c 55c
128
Table XVIII.—Natural Sines and Cosines of Angles in Degrees and Minutes—
Continued
M. 35° 36° 37° 38° 39°
Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos.
0 0. 57358 0.81915 0.58779 0.80902 0.60182 0.79864 0.61566 0.78801 0.62932 0. 77715 60
1 381 899 802 885 205 846 589 783 955 696 59
2 405 882 826 867 228 829 612 765 977 678 58
2 429 865 849 85C 251 811 635 747 . 6300C 660 57
4 453 848 873 833 274 793 658 729 022 641 56
5 .57477 . 81832 .58896 .80816 .60298 . 79776 . 61681 . 78711 .63045 .77623 55
6 501 815 920 799 321 758 70- 694 068 605 54
7 524 798 943 782 344 743 726 676 090 586 53
8 548 782 967 765 367 723 749 658 113 568 52
9 572 765 990 748 390 706 772 640 135 550 51
10 . 57596 . 81748 .59014 .80730 .60414 .79688 . 61795 .78622 .63158 .77531 50
11 619 731 037 711 437 671 818 604 180 513 49
12 643 714 061 696 46C 653 841 586 203 494 48
13 667 698 084 679 483 635 861 568 225 476 47
14 691 681 108 662 506 618 887 550 248 458 46
15 . 57715 . 81664 . 59131 .80644 .60529 . 79600 .61909 .78532 . 63271 . 77439 45
16 738 647 154 627 553 583 932 514 293 421 44
17 762 631 178 61( 576 565 955 496 316 402 43
18 786 614 201 593 599 547 978 478 338 384 42
19 810 597 225 576 622 530 . 62001 460 361 366 41
20 . 57833 .81580 .59248 .80558 .60645 . 79512 . 62024 .78442 . 63383 . 77347 40
21 857 563 272 541 668 494 046 424 406 329 39
22 881 546 295 524 691 477 069 405 428 310 38
23 904 530 318 507 714 459 092 387 451 292 37
24 928 513 342 489 738 441 115 369 473 273 36
25 . 57952 . 81496 . 59365 .80472 .60761 . 79424 .62138 . 78351 . 63496 . 77255 35
26 976 479 389 455 784 406 160 333 518 236 34
27 999 462 412 438 807 388 183 315 540 218 33
28 .58023 445 436 420 830 371 206 297 563 199 32
29 047 428 459 403 853 353 229 279 585 181 31
30 . 58070 .81412 .59482 .80386 .60876 . 79335 .62251 .78261 .63608 .77162 30
31 094 395 506 368 899 318 274 243 630 144 29
32 118 378 529 351 922 300 297 225 653 125 28
33 141 361 552 334 945 282 320 206 675 107 27
34 165 344 576 316 968 264 342 188 698 088 26
35 . 58189 .81327 . 59599 .80299 .60991 .79247 .62365 .78170 .63720 . 77070 25
36 212 310 622 282 .61015 229 388 152 742 051 24
37 236 293 646 264 038 211 411 134 765 033 23
38 260 276 669 247 061 193 433 116 787 014 22
39 283 259 693 230 084 176 456 098 810 . 76996 21
40 . 58307 .81242 .59716 .80212 .61107 .79158 .62479 . 78079 . 63832 . 76977 20
41 330 225 739 195 130 140 502 061 854 959 19
42 354 208 763 178 153 122 524 043 877 940 18
43 378 191 786 160 176 105 547 025 899 921 17
44 401 174 809 143 199 087 570 007 922 903 16
45 .58425 .81157 . 59832 \ 80125 . 61222 . 79069 .62592 .77988 . 63944 . 76884 15
46 449 140 856 108 245 051 615 970 966 866 14
47 472 123 879 091 268 033 638 952 989 847 13
48 496 106 902 073 291 016 660 934 .64011 828 12
49 519 089 926 056 314 . 78998 683 916 033 810 11
50 .58543 . 81072 . 59949 .80038 .61337 . 78980 . 62706 . 77897 .64056 .76791 10
51 567 055 972 021 360 962 728 879 078 772 9
52 590 038 995 003 383 944 751 861 100 754 8
53 614 021 .60019 . 79986 406 926 774 843 123 735 7
54 637 004 042 968 429 908 796 824 145 717 6
55 .58661 .80987 .60065 . 79951 .61451 . 78891 .62819 .77806 . 64167 .76698 5
56 684 970 089 934 474 873 842 788 190 679 4
57 708 953 112 916 497 855 864 769 212 661 3
58 731 936 135 899 520 837 887 751 234 642 2
59 755 919 158 881 543 819 909 733 256 623 1
60 .58779 .80902 .60182 . 79864 .61566 .78801 .62932 . 77715 .64279 .76604 0
Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin. Cos. Sin.
54 • 1 53 o 52 0 51 o 50 o
129
I able XVIII. N atural Sines and Cosines of Angles in Degrees and Minutes—
Continued
M. 40° 41° 42° 43° 44°
Sin. Cos. Sin. Cos. Sin. Cos. Sin. Oos. Sin. Cos.
0 0.64271 0.7660- 0.65606 0.7547] 0. 66918 0.74314 0.68206 0.7313 0.69461 0.71931 60
1 30 58f 628 451 93. 295 22 11 48' 914 59
2 32C 56' 65( 432 955 276 241 09 50! 894 58
3 341 548 671 414 978 256 26' 07 521 873 57
4 368 531 694 39. 991 237 28. 05( 54f 853 56
5 .64396 .76511 .65718 . 75375 . 67021 . 74217 . 68306 . 7303( . 6957C . 71833 55
6 412 492 738 351 048 198 32/ Olf 591 813 54
7 435 472 751 33' 06< 178 346 . 7299f 612 792 53
8 457 455 781 318 081 151 376 97f 633 772 52
9 479 436 803 299 107 139 391 95’ 654 752 51
10 .64501 .76417 . 65825 .75286 .67129 .74120 .68412 . 72931 . 69675 .71732 50
n 524 398 847 261 151 106 434 911 696 711 49
12 546 380 869 241 172 086 455 891 717 691 48
13 568 361 891 222 19' 061 476 871 737 671 47
14 590 342 913 203 215 041 497 857 758 650 46
15 .64612 .76323 . 65935 . 75184 .67237 . 74022 .68518 .72837 . 69779 . 71630 45
16 635 304 956 165 258 002 539 817 800 610 44
17 657 286 978 146 28C .73983 561 797 821 590 43
18 679 267 .66000 126 301 963 582 777 842 569 42
19 701 248 022 107 323 944 603 757 862 549 41
20 .64723 .76229 .66044 .75088 .67344 . 73924 .68624 .72737 .69883 .71529 40
21 746 210 066 069 366 904 645 717 904 508 39
22 /()& 192 088 050 387 885 666 697 925 488 38
23 790 173 109 030 409 865 688 677 946 468 37
24 812 154 131 011 430 846 709 657 966 447 36
25 .64834 . 76135 .66153 .74992 .67452 . 73826 .68730 . 72637 .69987 .71427 35
26 856 116 175 973 473 806 751 617 .70008 407 34
27 878 097 197 953 495 787 772 597 029 386 33
28 901 078 218 934 516 767 793 577 049 366 32
29 923 059 240 915 538 747 814 557 070 345 31
30 .64945 . 76041 . 66262 .74896 .67559 .73728 .68835 . 72537 . 70091 . 71325 30
31 967 022 284 876 580 708 857 517 112 305 29
32 989 003 306 857 602 688 878 497 132 284 28
33 .65011 .75984 327 838 623 669 899 477 153 264 27
34 033 965 349 818 645 649 920 457 174 243 26
35 .65055 .75946 . 66371 .74799 . 67666 .73629 . 68941 .72437 . 70195 .71223 25
36 077 927 393 780 688 610 962 417 215 203 24
37 100 908 414 760 709 590 983 397 236 182 23
38 122 889 436 741 730 570 . 69004 377 257 162 22
39 144 870 458 722 752 551 025 357 277 141 21
40 41 .65166 188 . 75851 832 .66480 501 .74703 683 .67773 795 . 73531 511 .69046 067 .72337 317 .70298 319 . 71121 100 20 19
42 210 813 523 664 816 491 088 297 339 080 18
43 232 794 545 644 837 472 109 277 360 059 17
44 254 775 566 625 859 452 130 257 381 039 16
45 .65276 .75756 .66588 .74606 . 67880 .73432 . 69151 .72236 .70401 .71019 15
46 298 738 610 586 901 413 172 216 422 . 70998 14
47 320 719 632 567 923 393 193 196 443 978 13
48 342 700 653 548 944 373 214 176 463 957 12
49 364 680 675 528 965 353 235 156 484 937 11
50 .65386 .75661 .66697 .74509 . 67987 .73333 .69256 .72136 . 70505 .70916 10
51 408 642 718 489 . 68008 314 277 116 525 896 9
52 430 623 740 470 029 294 298 095 546 875 8
53 452 604 762 451 051 274 319 075 567 855 7
54 474 585 783 431 072 254 340 055 587 834 6
55 56 .65496 518 .75566 547 . 66805 827 .74412 392 .68093 115 .73234 215 . 69361 382 .72035 015 . 70608 628 . 70813 793 5 4
57 540 528 848 373 136 195 403 . 71995 649 772 3
58 562 509 870 353 157 175 424 974 670 752 2
59 584 490 891 334 179 155 445 954 690 731 1
60 .65606 .75471 .66913 . 74314 .68200 . 73135 . 69466 .71934 . 70711 .70711 0
Oos. Sin. Oos. Sin. Oos. Sin. Cos. Sin. Oos. Sin. M.
49° 48° 47° 46 45
130
Table XIX. Natural Tangents and Cotangents of Angles in Degrees and Minutes
Values of the tangents and cotangents of angles are given for each minute from 0° to 90°.
For degrees indicated at the top of the page, use the column designations at the top. For degrees indicated at the bottom of the page, use the column designations at the bottom.
For degrees indicated at the top of the page, use the minute column at the left, lor degrees indicated at the bottom of the page, use the minute column at the right.
19
131
Table XIX. Natural Tangents and Cotangents of Angles in Degrees and Minutes
(For every minute of the quadrant.)
M 0° 1° 2° 3°
Tan. Cot. Tan. Got. Tan. Got. Tan. Got.
0 0. 00000 0 0.01746 57. 2900 0.03492 28. 6363 0.05241 19. 0811 60
1 029 3437. 75 775 56. 3506 521 .3994 270 18.9755 59
2 058 1718.87 804 55.4415 550 . 1664 299 .8711 58
3 087 1145.92 833 54. 5613 579 27. 9372 328 .7678 57
4 116 859.436 862 53. 7086 609 .7117 357 .6656 56
5 .00145 687. 549 . 01891 52. 8821 .03638 27.4899 .05387 18. 5645 55
6 175 572. 957 920 52. 0807 667 .2715 416 .4645 54
7 204 491.106 949 51. 3032 696 .0566 445 .3655 53
8 233 429. 718 978 50. 5485 725 26. 8450 474 .2677 52
9 262 381. 971 .02007 49.8157 754 .6367 503 . 1708 51
10 .00291 343. 774 . 02036 49.1039 .03783 26. 4316 . 05533 18. 0750 50
11 320 312. 521 066 48. 4121 812 .2296 562 17.9802 49
12 349 286. 478 095 47. 7395 842 .0307 591 .8863 48
13 378 264.441 124 47. 0853 871 25. 8348 620 .7934 47
14 407 245. 552 153 46.4489 900 .6418 649 .7015 46
15 . 00436 229.182 .02182 45. 8294 .03929 25.4517 . 05678 17.6106 45
16 465 214. 858 211 45. 2261 958 .2644 708 .5205 44
17 495 202. 219 240 44. 6386 987 .0798 737 .4314 43
18 524 190. 984 269 44. 0661 . 04016 24.8978 766 .3432 42
19 553 180.932 298 43. 5081 046 .7185 795 .2558 41
20 .00582 171.885 .02328 42. 9641 .04075 24. 5418 .05824 17.1693 40
21 611 163. 700 357 42.4335 104 .3675 854 .0837 39
22 640 156. 259 386 41. 9158 133 .1957 883 16. 9990 38
23 669 149.465 415 41.4106 162 .0263 912 .9150 37
24 698 143.237 444 40.9174 191 23. 8593 941 .8319 36
25 .00727 137. 507 .02473 40.4358 . 04220 23. 6945 . 05970 16. 7496 35
26 756 132.219 502 39. 9655 250 .5321 999 .6681 34
27 785 127. 321 531 39. 5059 279 .3718 .06029 .5874 33
28 815 122. 774 560 39. 0568 308 .2137 058 .5075 32
29 844 118. 540 589 38.6177 337 .0577 087 .4283 31
30 .00873 114. 589 .02619 38.1885 . 04366 22.9038 .06116 16. 3499 30
31 902 110.892 648 37. 7686 395 .7519 145 .2722 29
32 931 107. 426 677 37. 3579 424 .6020 175 . 1952 28
33 960 104.171 706 36. 9560 454 .4541 204 . 1190 27
34 989 101.107 735 36. 5627 483 .3081 233 .0435 26
35 . 01018 98. 2179 .02764 36.1776 . 04512 22.1640 .06262 15. 9687 25
36 047 95. 4895 793 35.8006 541 .0217 291 .8945 24
37 076 92. 9085 822 35.4313 570 21.8813 321 .8211 23
38 105 90. 4633 851 35. 0695 599 .7426 350 .7483 22
39 135 88.1436 881 34. 7151 628 .6056 379 .6762 21
40 .01164 85.9398 . 02910 34. 3678 . 04658 21. 4704 . 06408 15.6048 20
41 193 83. 8435 939 34. 0273 687 .3369 438 .5340 19
42 222 81. 8470 968 33.6935 716 .2049 467 .4638 18
43 251 79. 9434 997 33. 3662 745 .0747 496 .3943 17
44 280 78.1263 . 03026 33. 0452 774 20.9460 525 .3254 16
45 .01309 76. 3900 . 03055 32. 7303 .04803 20. 8188 . 06554 15. 2571 15
46 338 74. 7292 084 32. 4213 833 .6932 584 . 1893 14
47 367 73.1390 114 32.1181 862 .5691 613 .1222 13
48 396 71. 6151 143 31. 8205 891 .4465 642 .0557 12
49 425 70.1533 172 31. 5284 920 .3253 671 14. 9898 11
50 .01455 68. 7501 .03201 31.2416 . 04949 20.2056 . 06700 14. 9244 10
51 484 67. 4019 230 30. 9599 978 .0872 730 .8596 9
52 513 66.1055 259 30. 6833 . 05007 19. 9702 759 .7954 8
53 542 64. 8580 288 30. 4116 037 .8546 788 .7317 7
54 571 63. 6567 317 30.1446 066 .7403 817 .6685 6
55 .01600 62. 4992 . 03346 29. 8823 .05095 19. 6273 . 06847 14. 6059 5
56 629 61. 3829 376 29. 6245 124 .5156 876 .5438 4
57 658 60.3058 405 29. 3711 153 .4051 905 .4823 3
58 687 59. 2659 434 29.1220 182 .2959 934 .4212 2
59 716 58. 2612 463 28.8771 212 .1879 963 .3607 1
60 . 01746 57. 2900 .03492 28. 6363 .05241 19. 0811 . 06993 14. 3007 0
Got. 89 Tan. 0 Got. 88 Tan. o Got. S. Tan. 0 Got. 86 Tan. o M.
132
Table XIX.—Natural Tangents and Cotangents of Angles in Degrees and Minutes—
Continued
M. 4° 5° 6° 7°
Tan. Cot. Tan. Cot. Tan. Cot. Tan. Cot.
0 0.06993 14. 3007 0.08749 11. 4301 0.10510 9. 51436 0.12278 8.14435 60
1 .07022 .2411 778 .3919 540 .48781 308 . 12481 59
2 051 .1821 807 .3540 569 . 46141 338 . 10536 58
3 080 .1235 837 .3163 599 . 43515 367 .08600 57
4 no .0655 866 .2789 628 . 40904 397 . 06674 56
5 .07139 14.0079 .08895 11.2417 .10657 9.38307 .12426 8.04756 55
6 168 13.9507 925 .2048 687 . 35724 456 .02848 54
7 197 .8940 954 .1681 716 . 33155 485 .00948 53
8 227 .8378 983 .1316 746 . 30599 515 7.99058 52
9 256 .7821 .09013 .0954 775 .28058 544 . 97176 51
10 .07285 13.7267 .09042 11.0594 . 10805 9.25530 .12574 7.95302 50
11 314 .6719 071 .0237 834 .23016 603 . 93438 49
12 344 .6174 101 10.9882 863 . 20516 633 . 91582 48
13 373 .5634 130 .9529 893 . 18028 662 . 89734 47
14 402 .5098 159 .9178 922 .15554 692 . 87895 46
15 .07431 13.4566 .09189 10.8829 . 10952 9.13093 . 12722 7. 86064 45
16 461 .4039 218 .8483 981 .10646 751 .84242 44
17 490 .3515 247 .8139 .11011 .08211 781 .82428 43
18 519 .2996 277 .7797 040 .05789 810 . 80622 42
19 548 .2480 306 .7457 070 .03379 840 . 78825 41
20 .07578 13.1969 .09335 10.7119 .11099 9. 00983 .12869 7. 77035 40
21 607 .1461 365 .6783 128 8.98598 899 . 75254 39
22 636 .0958 394 .6450 158 . 96227 929 . 73480 38
23 665 .0458 423 .6118 187 . 93867 ' 958 . 71715 37
24 695 12.9962 453 .5789 217 . 91520 988 . 69957 36
25 .07724 12.9469 .09482 10. 5462 .11246 8.89185 . 13017 7.68208 35
26 753 .8981 511 .5136 276 . 86862 047 . 66466 34
27 782 .8496 541 .4813 305 . 84551 076 . 64732 33
28 812 .8014 570 .4491 335 . 82252 106 . 63005 32
29 841 .7536 600 .4172 364 . 79964 136 .61287 31
30 .07870 12.7062 .09629 10.3854 .11394 8.77689 . 13165 7. 59575 30
31 899 .6591 658 .3538 423 .75425 195 .57872 29
32 929 .6124 688 .3224 452 . 73172 224 . 56176 28
33 958 .5660 717 .2913 482 . 70931 254 .54487 27
34 987 .5199 746 .2602 511 . 68701 284 .52806 26
35 .08017 12. 4742 .09776 10.2294 .11541 8.66482 .13313 7. 51132 25
36 046 .4288 805 .1988 570 . 64275 343 . 49465 24
37 075 .3838 834 .1683 600 . 62078 372 . 47806 23
38 104 .3390 864 .1381 629 . 59893 402 . 46154 22
39 134 .2946 893 .1080 659 . 57718 432 . 44509 21
40 .08163 12. 2505 .09923 10.0780 . 11688 8. 55555 .13461 7. 42871 20
41 192 .2067 952 .0483 718 .53402 491 .41240 19
42 221 .1632 981 .0187 747 .51259 521 . 39616 18
43 251 .1201 .10011 9.98931 777 .49128 550 . 37999 17
44 280 .0772 040 .96007 806 .47007 580 . 36389 16
45 .08309 12.0346 .10069 9.93101 . 11836 8. 44896 .13609 7.34786 15
46 339 11.9923 099 . 90211 865 .42795 639 .33190 14
47 368 .9504 128 . 87338 895 .40705 669 .31600 13
48 397 .9087 158 . 84482 924 . 38625 698 . 30018 12
49 427 .8673 187 . 81641 954 . 36555 728 .28442 11
50 .08456 11.8262 .10216 9.78817 .11983 8.34496 . 13758 7.26873 10
51 485 .7853 246 . 76009 .12013 . 32446 787 .25310 9
52 514 .7448 275 .73217 042 . 30406 817 . 23754 8
53 544 .7045 305 . 70441 072 . 28376 846 . 22204 7
54 573 .6645 334 .67680 101 . 26355 876 . 20661 6
55 .08602 11. 6248 . 10363 9.64935 . 12131 8.24345 .13906 7.19125 5
56 632 .5853 393 . 62205 160 . 22344 935 .17594 4
57 661 .5461 422 . 59490 190 . 20352 965 .16071 3
58 690 .5072 452 . 56791 219 . 18370 995 . 14553 2
59 720 .4685 481 . 54106 249 . 16398 .14024 . 13042 1
60 .08749 11.-4301 .10510 9. 51436 . 12278 8.14435 .14054 7.11537 0
Cot. Tan. Cot. Tan. Cot. Tan. Cot. Tan. M.
85 0 84 0 83 0 1 82 o
133
Table XIX. Natural Tangents and Cotangents of Angles in Degrees and Minutes—
Continued
M. 8° 9° 10° 11°
Tan. Cot. Tan. Cot. Tan. Cot. Tan. Cot.
0 0.14054 7.11537 0.15838 6. 31375 0.17633 5.67128 0.19438 5.14455 60
1 084 . 10038 868 .30189 663 . 66165 468 . 13658 59
2 113 .08546 898 . 29007 693 . 65205 498 . 12862 58
3 143 . 07059 928 . 27829 723 .64248 529 . 12069 57
4 173 . 05579 958 . 26655 753 .63295 559 . 11279 56
5 .14202 7.04105 . 15988 6.25486 .17783 5.62344 .19589 5.10490 55
6 232 . 02637 . 16017 .24321 813 .61397 619 . 09704 54
7 262 . 01174 047 . 23160 843 . 60452 649 .08921 53
8 291 6. 99718 077 .22003 873 . 59511 680 .08139 52
9 321 .98268 107 .20851 903 . 58573 710 .07360 51
10 .14351 6. 96823 . 16137 6.19703 . 17933 5. 57638 . 19740 5.06584 50
11 381 .95385 167 .18559 963 . 56706 770 .05809 49
12 410 . 93952 196 . 17419 993 . 55777 801 .05037 48
13 440 . 92525 226 .16283 .18023 . 54851 831 .04267 47
14 470 . 91104 256 . 15151 053 . 53927 861 .03499 46
15 .14499 6.89688 .16286 6.14023 .18083 5. 53007 . 19891 5.02734 45
16 529 . 88278 316 . 12899 113 . 52090 921 . 01971 44
17 559 . 86874 346 . 11779 143 . 51176 952 . 01210 43
18 588 . 85475 376 . 10664 173 . 50264 982 . 00451 42
19 618 . 84082 405 . 09552 203 . 49356 .20012 4.99695 41
20 .14648 6.82694 .16435 6.08444 .18233 5.48451 .20042 4.98940 40
21 678 .81312 465 .07340 263 .47548 073 . 98188 39
22 707 .79936 495 . 06240 293 . 46648 103 . 97438 38
23 737 . 78564 525 . 05143 323 . 45751 133 .96690 37
24 767 . 77199 555 . 04051 353 . 44857 164 .95945 36
25 . 14796 6. 75838 .16585 6.02962 .18384 5.43966 .20194 4.95201 35
26 826 .74483 615 . 01878 414 . 43077 224 .94460 34
27 856 .73133 645 . 00797 444 . 42192 254 . 93721 33
28 886 .71789 674 5. 99720 474 . 41309 285 .92984 32
29 915 . 70450 704 .98646 504 . 40429 315 .92249 31
30 .14945 6.69116 . 16734 5.97576 .18534 5.39552 .20345 4.91516 30
31 975 .67787 764 . 96510 564 .38677 376 .90785 29
32 .15005 . 66463 794 .95448 594 . 37805 406 .90056 28
33 034 . 65144 824 . 94390 624 . 36936 436 . 89330 27
34 064 . 63831 854 . 93335 654 . 36070 466 .88605 26
35 . 15094 6. 62523 . 16884 5.92283 .18684 5.35206 .20497 4.87882 25
36 124 . 61219 914 . 91236 714 .34345 527 .87162 24
37 153 . 59921 944 . 90191 745 .33487 557 .86444 23
38 183 . 58627 974 . 89151 775 . 32631 588 . 85727 22
39 213 . 57339 .17004 .88114 805 .31778 618 . 85013 21
40 .15243 6. 56055 . 17033 5.87080 .18835 5.30928 . 20648 4.84300 20
41 272 . 54777 063 . 86051 865 . 30080 679 .83590 19
42 302 . 53503 093 . 85024 895 . 29235 709 .82882 18
43 332 . 52234 123 . 84001 925 . 28393 739 .82175 17
44 362 . 50970 153 . 82982 955 . 27553 770 .81471 16
45 . 15391 6.49710 . 17183 5. 81966 .18986 5. 26715 .20800 4.80769 15
46 421 .48456 213 . 80953 . 19016 .25880 830 .80068 14
47 451 . 47206 243 . 79944 046 . 25048 861 . 79370 13
48 481 . 45961 273 . 78938 076 . 24218 891 . 78673 12
49 511 . 44720 303 .77936 106 .23391 921 . 77978 11
50 .15540 6. 43484 .17333 5. 76937 .19136 5.22566 .20952 4. 77286 10
51 570 .42253 363 . 75941 166 . 21744 982 .76595 9
52 600 . 41026 393 . 74949 197 . 20925 . 21013 .75906 8
53 630 . 39804 423 . 73960 227 .20107 043 . 75219 7
54 660 . 38587 453 . 72974 257 .19293 073 . 74534 6
55 . 15689 6. 37374 . 17483 5. 71992 .19287 5.18480 .21104 4. 73851 5
56 719 . 36165 513 . 71013 317 . 17671 134 .73170 4
57 749 . 34961 543 .70037 347 .16863 164 .72490 3
58 779 . 33761 573 . 69064 378 . 16058 195 . 71813 2
59 809 . 32566 603 .68094 408 . 15256 225 .71137 1
60 .15838 6.31375 .17633 5. 67128 . 19438 5.14455 . 21256 4.70463 0
Cot. Tan. Cot. Tan. Cot. Tan, Cot. Tan.
81 0 80° 79° 78° M.
134
Table XIX.—Natural Tangents and Cotangents of Angles in Degrees and Minutes—-
Continued
M. 12° 13° 14° 15°
Tan. Oot. Tan. Cot. Tan. Cot. Tan. Oot.
0 0.21256 4. 70463 0.23087 4.33158 0. 24933 4.01078 0. 26795 3. 73205 60
1 286 . 69791 117 . 32573 964 . 00582 826 . 72771 59
2 316 . 69121 148 .32001 995 . 00086 857 . 72338 58
3 347 . 68452 179 .31430 . 25026 3.99592 888 . 71907 57
4 377 . 67786 209 .30860 056 .99099 920 . 71476 56
5 .21408 4.67121 .23240 4.30291 . 25087 3.98607 . 26951 3. 71046 55
6 438 . 66458 271 . 29724 118 .98117 982 . 70616 54
7 469 . 65797 301 . 29159 149 .97627 . 27013 . 70188 53
8 499 . 65138 332 . 28595 180 .97139 044 . 69761 52
9 529 . 64480 363 .28032 211 .96651 076 . 69335 51
10 . 21560 4.63825 . 23393 4. 27471 .25242 3.96165 . 27107 3. 68909 50
11 590 .63171 424 .26911 273 . 95680 138 .68485 49
12 621 . 62518 455 . 26352 304 . 95196 169 68061 48
13 651 . 61868 485 25795 335 .94713 201 . 67638 47
14 682 . 61219 516 .25239 366 .94232 232 . 67217 46
15 . 21712 4.60572 .23547 4. 24685 .25397 3.93751 . 27263 3. 66796 45
16 743 .59927 578 . 24132 428 . 93721 294 . 66376 44
17 773 .59283 608 . 23580 459 .92793 326 .65957 43
18 804 . 58641 639 . 23030 490 .92316 357 . 65538 42
19 834 .58001 670 .22841 521 . 91839 388 . 65121 41
20 .21864 4. 57363 .23700 4. 21933 .25552 3. 91364 . 27419 3.64705 40
21 895 . 56726 731 . 21387 583 . 90890 451 .64289 39
22 925 . 56091 762 . 20842 614 . 90417 482 .63874 38
23 956 . 55458 793 . 20298 645 . 89945 513 .63461 37
24 986 . 54826 823 . 19756 676 . 89474 545 .63048 36
25 . 22017 4. 54196 . 23854 4.19215 .25707 3.89004 . 27576 3.62636 35
26 047 . 53568 885 .18675 738 .88536 607 .62224 34
27 078 . 52941 916 .18137 769 . 88068 638 . 61814 33
28 108 . 52316 946 .17600 800 . 87601 670 . 61405 32
29 139 . 51693 977 .17064 831 . 87136 701 . 60996 31
30 . 22169 4. 51071 . 24008 4.16530 .25862 3.86671 .27732 3.60588 30
31 200 . 50451 039 .15997 893 .86208 764 . 60181 29
32 231 .49832 69 . 15465 924 .85745 795 . 59775 28
33 261 . 49215 100 . 14934 955 .85284 826 . 59370 27
34 292 . 48600 131 . 14405 986 .84824 858 . 58966 26
35 .22322 4. 47986 .24162 4.13877 . 26017 3. 84364 .27889 3.58562 25
36 353 . 47374 193 . 13350 048 . 83906 921 .58160 24
37 383 . 46764 223 . 12825 079 . 83449 952 . 57758 23
38 414 . 46155 254 . 12301 110 . 82992 983 . 57357 22
39 444 . 45548 285 . 11778 141 . 82537 .28015 . 56957 21
40 .22475 4. 44942 .24316 4.11256 .26172 3. 82083 .28046 3. 56557 20
41 505 . 44338 347 .10736 203 . 81630 077 . 56159 19
42 536 .43735 377 .10216 235 .81177 109 . 55761 18
43 567 .43134 408 . 09699 266 . 80726 140 . 55364 17
44 597 . 42534 439 .09182 297 .80276 172 . 54968 16
45 . 22628 4. 41936 . 24470 4.08666 .26328 3. 79827 .28203 3. 54573 15
46 658 .41340 501 . 08152 359 . 79378 234 . 54179 14
47 689 . 40745 532 . 07639 390 . 78931 266 .53785 13
48 719 . 40152 562 . 07127 421 . 78485 297 . 53393 12
49 750 . 39560 593 . 06616 452 . 78040 329 . 53001 11
50 .22781 4. 38969 . 24624 4. 06107 .26483 3. 77595 .28360 3. 52609 10
51 811 .38381 655 . 05599 515 . 77152 391 . 52219 9
52 842 . 37793 686 . 05092 546 . 76709 423 . 51829 8
53 872 . 37207 717 . 04586 577 . 76268 454 . 51441 7
54 903 . 36623 747 . 04081 608 .75828 486 . 51053 6
55 .22934 4. 36040 . 24778 4. 03578 .26639 3. 75388 .28517 3. 50666 5
56 964 .35459 809 .03076 670 . 74950 549 .50279 4
57 995 . 34879 840 .02574 701 . 74512 580 .49894 3
58 .23026 . 34300 871 . 02074 733 . 74075 612 . 49509 2
59 056 .33723 902 .01576 764 . 73640 643 . 49125 1
60 .23087 4.33148 .24933 4.01078 .26795 3. 73205 .28675 3. 48741 0
Oot. Tan. Oot. Tan. Oot. Tan. Cot. Tan.
77 76c 75 74 M.
135
Table XIX.—Natural Tangents and Cotangents of Angles in Degrees and Minutes—
Continued
M. 16° 17° 18° 19°
Tan. Cot. Tan. Got. Tan. Got. Tan. Cot.
0 0.28675 3.48741 0.30573 3. 27085 0.32492 3.07768 0.34433 2.90421 60
1 706 . 48359 605 .26745 524 . 07464 465 .90147 59
2 738 . 47927 637 . 26406 556 . 07160 498 .89873 58
3 769 . 47596 669 . 26067 588 . 06857 530 . 89600 57
4 801 . 47216 700 .25729 621 . 06554 563 . 89327 56
5 .28832 3. 46837 . 30732 3. 25392 .32653 3.06252 .34596 2.89055 55
6 864 .46458 764 .25055 685 . 05950 628 . 88783 54
7 895 .46080 796 .24719 717 . 05649 661 . 88511 53
8 927 . 45705 828 .24383 749 . 05349 693 . 88240 52
9 958 . 45327 860 . 24049 782 . 05049 726 . 87970 51
10 .28990 3. 44951 .30891 3. 23714 .32814 3.04749 . 34758 2. 87700 50
11 .29021 . 44576 923 . 23381 846 .04450 791 .87430 49
12 053 . 44202 955 .23048 878 .04152 824 . 87161 48
13 084 . 43829 987 . 22715 911 . 03854 856 . 86892 47
14 116 . 43456 .31019 .22384 943 . 03556 889 .86624 46
15 .29147 3. 43084 . 31051 3. 22053 .32975 3.03260 .34922 2. 86356 45
16 179 . 42713 083 . 21722 . 33007 .02963 954 . 86089 44
17 210 . 42343 115 . 21392 040 . 02607 987 . 85822 43
18 242 . 41973 147 . 21063 072 .02372 . 35020 . 85555 42
19 274 . 41604 178 . 20734 104 . 02077 052 .85289 41
20 .29305 3.41236 . 31210 3.20406 .33136 3.01783 .35085 2. 85023 40
21 337 . 40869 242 .20079 169 . 01489 118 .84758 39
22 368 . 40502 274 . 19752 201 .01196 150 .84494 38
23 400 . 40136 300 . 19426 233 .00903 183 .84229 37
24 432 . 39771 338 . 19100 266 . 00611 216 .83965 36
25 .29463 3.39406 .31370 3.18775 .33298 3.00319 .35248 2.83702 35
26 495 .39042 402 .18451 330 .00028 281 . 83439 34
27 526 . 38679 434 . 18127 363 2.99738 314 .83176 33
28 558 . 38317 466 . 17804 395 .99447 346 . 82914 32
29 590 . 37955 498 . 17481 427 .99158 379 .82653 31
30 .29621 3.37594 .31530 3.17159 .33460 2.98868 .35412 2.82391 30
31 653 . 37234 562 .16838 492 .98560 445 .82130 29
32 685 . 36875 594 . 16517 524 .98292 477 .81870 28
33 716 . 36516 626 . 16197 557 .98004 510 . 81610 27
34 748 .36158 658 . 15877 589 . 97717 543 .81350 26
35 .29780 3. 35800 .31690 3.15558 .33621 2.97430 . 35576 2.81091 25
36 811 . 35443 722 . 15140 654 .97144 608 .80633 24
37 843 . 35087 754 . 14922 686 .96858 641 .80574 23
38 875 . 34732 786 . 14605 718 . 96573 674 .80316 22
39 906 . 34377 818 .14288 751 .96288 707 . 80059 21
40 .29938 3.34023 .31850 3.13972 .33783 2.96004 . 35740 2.79802 20
41 970 . 33670 882 . 13656 816 .95721 772 .79545 19
42 . 30001 . 33317 914 . 13341 848 . 95437 805 .79289 18
43 033 .32965 946 . 13027 881 . 95155 838 .79033 17
44 065 .32614 978 . 12713 913 . 94872 871 .78778 16
45 . 30097 3. 32264 .32010 3.12400 .33945 2.94591 .35904 2.78523 15
46 128 .31914 042 . 12087 978 . 94309 937 .78269 14
47 160 .31565 074 . 11775 .34010 . 94028 969 . 78014 13
48 192 .31216 106 . 11464 043 . 93748 . 36002 . 77761 12
49 224 .30868 139 . 11153 075 . 93468 035 . 77507 11
50 .30255 3. 30521 .32171 3.10842 .34108 2.93189 .36068 2.77254 10
51 287 . 30174 203 .10532 140 . 92910 101 .77002 9
52 319 .29829 235 .10223 173 . 92632 134 . 76750 8
53 351 . 29483 267 .09914 205 . 92354 167 . 76498 7
54 382 . 29139 299 .09606 238 . 92076 199 . 76247 6
55 . 30414 3. 28795 .32331 3.09298 .34270 2.91799 .36232 2.75996 5
56 446 . 28452 363 .08991 303 .91523 265 . 75746 4
57 478 . 28109 396 .08685 335 .91246 298 . 75496 3
58 509 . 27767 428 .08379 368 .90971 331 .75246 2
59 541 .27426 460 .08073 400 . 90696 364 .74997 1
60 .30573 3.27085 .32492 3.07768 .34433 2.90421 .36397 2. 74748 0
Got. Tan. Cot. Tan. Got. Tan. Got. Tan. M.
73 72° 71° 76 °
136
Table XIX.—Natural Tangents and Cotangents of Angles in Degrees and Minutes—
Continued
M. 20° 21° 22° 23°
Tan. Cot. Tan. Cot. Tan. Cot. Tan. Oot.
0 0.36397 2. 74748 0.38386 2. 60509 0.40403 2.47509 0.42447 2.35585 60
1 430 . 74499 420 .60283 436 .47302 482 .35395 59
2 364 .74251 453 .60057 470 .47095 516 . 35205 58
3 496 . 74004 487 . 59831 504 . 46888 551 . 35015 57
4 529 . 73756 520 .59606 538 . 46682 585 . 34825 56
5 .36562 2.73509 .38553 2. 59381 .40572 2.46476 .42619 2.34636 55
6 595 . 73263 587 .59156 606 . 46270 654 .34447 54
7 628 . 73017 620 .58932 640 . 46065 688 . 34258 53
8 661 . 72771 654 .58708 674 . 45860 722 . 34069 52
9 694 . 72526 687 . 58484 707 .45655 757 . 33881 51
10 .36727 2.72281 .38721 2. 58261 .40741 2.45451 .42791 2. 33693 50
11 760 .72036 754 . 58038 775 .45246 826 . 33505 49
12 793 .71792 787 . 57815 809 .45043 860 . 33317 48
13 826 . 71548 821 . 57593 843 . 44839 894 . 33130 47
14 859 . 71305 854 .57371 877 . 44636 929 .32943 46
15 .36892 2. 71062 .38888 2.57150 .40911 2.44433 .42963 2. 32756 45
16 925 . 70819 921 . 56928 945 .44230 998 .32570 44
17 958 . 70577 955 . 56707 979 .44027 .43032 . 32383 43
18 991 . 70335 988 .56487 .41013 . 43825 067 . 32197 42
19 .37024 . 70094 . 39022 . 56266 047 . 43623 101 . 32012 41
20 .37057 2. 69853 .39055 2. 56046 .41081 2.43422 . 43136 2.31826 40
21 090 .69612 089 .55827 115 . 43220 170 .31641 39
22 123 . 69371 122 . 55608 149 . 43019 205 .31456 38
23 157 . 69131 156 . 55389 183 .42819 239 .31271 37
24 190 .68892 190 . 55170 217 .42618 274 .31086 36
25 .37223 2. 68653 .39223 2.54952 .41251 2.42418 .43308 2.30902 35
26 256 . 68414 257 .54734 285 .42218 343 .30718 34
27 289 . 68175 290 . 54516 319 .42019 378 . 30534 33
28 322 .67937 324 .54299 353 . 41819 412 .30351 32
29 355 . 67700 357 .54082 387 . 41620 447 .30167 31
30 .37388 2.67462 .39391 2.53865 .41421 2.41421 .43481 2.29984 30
31 422 .67225 425 .53648 455 . 41223 516 . 29801 29
32 455 . 66989 458 .53432 490 . 41025 550 . 29619 28
33 488 . 66752 492 . 53217 524 .40827 585 . 29437 27
34 521 . 66516 526 .53001 558 . 40629 620 .29254 26
35 .37554 2.66281 . 39559 2. 52786 .41592 2.40432 .43654 2. 29073 25
36 588 .66046 593 . 52571 626 .40235 689 .28891 24
37 621 . 65811 626 .52357 660 .40038 724 .28710 23
38 654 . 65576 660 .52142 694 .39841 758 .28528 22
39 687 . 65342 694 .51929 728 .39645 793 .28348 21
40 .37720 2.65109 . 39727 2. 51715 .41763 2.39449 .43828 2. 28167 20
41 754 .64875 761 . 51502 797 .39253 862 . 27987 19
42 787 .64642 795 . 51289 831 . 39058 897 . 27806 18
43 820 .64410 829 . 51076 865 . 38863 932 . 27626 17
44 853 .64177 862 .50864 899 . 38668 966 . 27447 16
45 .37887 2.63945 . 39896 2. 50652 .41933 2. 38473 .44001 2.27267 15
46 920 . 63714 930 . 50440 968 . 38279 036 .27088 14
47 953 .63483 963 . 50229 .42002 . 38084 071 . 26909 13
48 986 . 63252 997 . 50018 036 . 37891 105 . 26730 12
49 .38020 . 63021 .40031 . 49807 070 . 37697 140 . 26552 11
50 .38053 2.62791 .40065 2. 49597 .42105 2.37594 .44175 2. 26374 10
51 086 . 62561 098 .49386 139 .37311 210 .26196 9
52 120 .62332 132 . 49177 173 .37118 244 . 26018 8
53 153 . 62103 166 .48967 207 .36925 279 .25840 7
54 186 . 61874 200 .48758 242 .36733 314 .25663 6
55 .38220 2.61646 .40234 2.48549 .42276 2.36541 .44349 2. 25486 5
56 253 . 61418 267 .48340 310 . 36349 384 . 25309 4
57 286 . 61190 301 .48132 345 . 36158 418 . 25132 3
58 320 . 60963 335 .47924 379 . 35967 453 . 24956 2
59 353 .60736 369 .47716 413 . 35776 488 .24780 1
60 .38386 2.60509 .40403 2.47509 .42447 2. 35585 .44523 2.24604 0
Got. | Tan. Oot. Tan. Oot. | Tan. Oot. Tan. M.
69 0 68 □ 67 66
137
Table XIX. Natural Tangents and Cotangents of Angles in Degrees and Minutes—
Continued
M. 24° 25° 26° 27°
Tan. Cot. Tan. Cot. Tan. Cot. Tan. Cot.
0 0.44523 2.24604 0.46631 2.14451 0.48773 2.05030 0.50953 1.96261 60
1 558 .24428 666 14288 809 .04879 989 .96120 59
2 593 .24252 702 .14125 845 .04728 . 51026 . 95979 58
3 627 .24077 737 .13963 881 .04577 063 . 95838 57
4 662 .23902 772 .13801 917 .04426 099 . 95698 56
5 .44697 2.23727 .46808 2.13639 .48953 2.04276 .51136 1.95557 55
6 732 . 23553 843 .13477 989 . 04125 173 .95417 54
7 767 . 23378 879 . 13316 .49026 . 03975 209 .95277 53
8 802 .23204 914 . 13154 062 . 03825 246 .95137 52
9 837 . 23030 950 . 12993 098 . 03675 283 .94997 51
10 .44872 2. 22857 .46985 2.12832 .49134 2.03526 .51319 1.94858 50
11 12 907 942 . 22683 . 22510 .47021 056 .12671 .12511 170 206 .03376 .03227 356 393 .94718 .94579 49 48
13 977 . 22337 092 .12350 242 .03078 430 .94440 47
14 .45012 .22164 128 .12190 278 .02929 467 . 94301 46
15 .45047 2. 21992 .47163 2.12030 . 49315 2.02780 .51503 1. 94162 45
16 082 .21819 199 . 11871 351 .02631 540 . 94023 44
17 117 .21647 234 .11711 387 .02483 577 . 93885 43
18 152 . 21475 270 .11552 423 . 02335 614 .93746 42
19 187 . 21304 305 . 11392 459 .02187 651 .93608 41
20 .45222 2. 21132 . 47341 2.11233 .49495 2.02039 .51688 1.93470 40
21 257 . 20961 377 .11075 532 .01891 724 .93332 39
22 292 . 20790 412 .10916 568 .01743 761 .93195 38
23 327 . 20619 448 . 10758 604 .01596 798 . 93057 37
24 362 . 20449 483 . 10600 640 .01499 835 .92920 36
25 .45397 2.20278 .47519 2.10442 .49677 2.01302 .51872 1.92782 35
26 432 .20108 555 . 10284 713 .01155 909 . 92645 34
27 467 .19938 590 .10126 749 .01008 946 . 92508 33
28 502 .19769 626 .09969 786 .00862 983 . 92371 32
29 538 .19599 662 .09811 822 .00715 .52020 .92235 31
30 .45573 2.19430 .47698 2.09654 . 49858 2.00569 .52057 1.92098 30
31 608 .19261 733 .09498 894 .00423 094 . 91962 29
32 643 .19092 769 .09341 931 .00277 131 . 91826 28
33 678 .18923 805 .09184 967 .00131 168 . 91690 27
34 713 .18755 840 .09028 .50004 1.99986 205 .91554 26
35 . 45748 2.18587 .47876 2.08872 .50040 1.99841 .52242 1.91418 25
36 784 .18419 912 .08716 076 . 99695 279 .91282 24
37 819 .18251 948 . 08560 113 . 99550 316 .91147 23
38 854 . 18084 984 . 08405 149 .99406 353 .91012 22
39 889 . 17916 .48019 08250 185 . 99261 390 .90876 21
40 .45924 2.17749 . 48055 2.08094 .50222 1.99116 .52427 1.90741 20
41 960 .17582 091 .07939 258 .98972 464 . 90607 19
42 995 . 17416 127 .07785 295 .98828 501 .90472 18
43 .46030 .17249 163 .07630 331 . 98684 538 . 90337 17
44 065 .17083 198 .07476 368 .98540 575 .90203 16
45 .46101 2.16917 .48234 2.07321 .50404 1.98396 . 52613 1. 90069 15
46 136 . 16751 270 .07167 441 .98253 650 . 89935 14
47 171 .16585 306 .07014 477 . 98110 687 . 89801 13
48 206 .16420 342 .06860 514 . 97966 724 . 89667 12
49 242 .16255 378 .06706 550 . 97823 761 .89533 11
50 .46277 2.16090 .48414 2.06553 .50587 1.97681 . 52798 1.89400 10
51 312 . 15925 450 .06400 623 .97538 836 .89266 9
52 348 . 15760 486 . 06247 660 .97395 873 .89133 8
53 383 . 15596 521 . 06094 696 . 97253 910 .89000 7
54 418 . 15432 557 .05942 733 . 97111 947 .88867 6
55 .46454 2.15268 .48593 2. 05790 .50769 1.96969 .52985 1. 88734 5
56 489 .15104 629 .05637 806 . 96827 .53022 .88602 4
57 525 . 14940 665 . 05485 843 . 96685 059 .88469 3
58 560 . 14777 701 .05333 879 . 96544 096 . 88337 2
59 595 . 14614 737 . 05182 916 . 96402 134 . 88205 1
60 .46631 2.14451 .48773 2.05030 .50953 1.96261 .53171 1.88073 0
Cot. Tan. Cot. Tan. Oot. Tan. Oot. Tan.
6 5° 64 63° 62 ° 1 M.
138
Table XIX.—Natural Tangents and Cotangents of Angles in Degrees and Minutes —
Continued
M. 28° 29° 30° 31°
Tan. Cot. Tan. Cot. Tan. Cot. Tan. Cot.
0 0.53171 1. 88073 0.55431 1.80405 0.57735 1.73205 0.60086 1.66428 60
1 208 . 87941 469 . 80281 774 .73089 126 .66318 59
2 246 .87809 507 .80158 813 . 72973 165 .66209 58
3 283 .87677 545 .80034 851 . 72857 205 .66099 57
4 320 .87546 583 .79911 890 . 72741 245 .65990 56
5 .53358 1. 87415 .55621 1.79788 . 57929 1.72625 .60284 1.65881 55
6 395 . 87283 659 .79665 968 . 72509 324 . 65772 54
7 432 . 87152 697 .79542 .58007 . 72393 364 . 65663 53
8 470 . 87021 736 .79419 046 .72278 403 .65554 52
9 507 . 86891 774 .79296 085 . 72163 443 . 65445 51
10 .53545 1.86760 .55812 1.79174 .58124 1.72047 .60483 1. 65337 50
11 582 .86630 850 . 79051 162 . 71932 522 .65228 49
12 620 . 86499 888 . 78929 201 . 71817 562 .65120 48
13 657 . 86369 926 . 78807 240 . 71702 602 .65011 47
14 694 . 86239 964 . 78685 279 . 71588 642 .64903 46
15 .53732 1.86109 .56003 1.78563 .58318 1.71473 .60681 1.64795 45
16 769 . 85979 041 . 78441 357 . 71358 721 .64687 44
17 807 . 85850 079 . 78319 396 . 71244 761 . 64579 43
18 844 . 85720 117 . 78198 435 .71129 801 . 64471 42
19 882 . 85591 156 . 78077 474 . 71015 841 .64363 41
20 .53920 1. 85462 . 56194 1.77955 .58513 1.70901 . 60881 1.64256 40
21 957 . 85333 232 . 77834 552 . 70787 921 .64148 39
22 995 . 85204 270 . 77713 591 . 70673 960 . 64041 38
23 .54032 . 85075 309 . 77592 631 . 70560 . 61000 . 63934 37
24 070 . 84946 347 . 77471 670 .70446 040 . 63826 36
25 .54107 1. 84818 .56385 1.77351 .58709 1.70332 .61080 1.63719 35
26 145 . 84689 424 . 77230 748 .70219 120 .63612 34
27 183 . 84561 462 . 77110 787 . 70106 160 .63505 33
28 220 . 84433 501 . 76990 826 . 69992 200 . 63398 32
29 258 . 84305 539 . 76869 865 .69879 240 . 63292 31
30 .54296 1. 84177 .56577 1. 76749 .58905 1.69766 .61280 1. 63185 30
31 333 . 84049 616 . 76629 944 .69653 320 . 63079 29
32 371 . 83922 654 . 76510 983 . 69541 360 . 62972 28
33 409 . 83794 693 . 76390 .59022 . 69428 400 . 62866 27
34 446 .83667 731 . 76271 061 . 69316 440 .62760 26
35 .54484 1. 83540 .56769 1.76151 .59101 1.69203 . 61480 1.62654 25
36 522 . 83413 808 . 76032 140 . 69091 520 . 62548 24
37 560 .83286 846 . 75913 179 . 68979 561 . 62442 23
38 597 . 83159 885 . 75794 218 .68866 601 . 62336 22
39 635 . 83033 923 .75675 258 .68754 641 . 62230 21
40 .54673 1.82906 . 56962 1. 75556 .59297 1.68643 .61681 1.62125 20
41 711 .82780 . 57000 .75437 336 . 68531 721 . 62019 19
42 748 .82654 039 .75319 376 . 68419 761 . 61914 18
43 786 . 82528 078 . 75200 415 .68308 801 . 61808 17
44 824 . 82402 116 .75082 454 .68196 842 . 61703 16
45 .54862 1.82276 .57155 1.74964 . 59494 1.68085 .61882 1. 61598 15
46 900 .82150 193 .74846 533 . 67974 922 .61493 14
47 938 . 82025 232 . 74728 573 . 67863 962 .61388 13
48 975 . 81899 271 . 74610 612 . 67752 .62003 . 61283 12
49 . 55013 . 81774 309 . 74492 651 .67641 043 . 61179 11
50 . 55051 1. 81649 .57348 1.74375 .59691 1.67530 .62083 1.61074 10
51 089 .81524 386 . 74257 730 .67419 124 .60970 9
52 127 .81399 425 . 74140 770 .67309 164 .60865 8
53 165 .81274 464 . 74022 809 .67198 204 .60761 7
54 203 .81150 503 . 73905 849 .67088 245 . 60657 6
55 .55241 1.81025 . 57541 1.73788 .59888 1.66978 . 62285 1.60553 5
56 279 . 80901 580 .73671 928 .66867 325 . 60449 4
57 317 . 80777 619 .73555 967 .66757 366 . 60345 3
58 355 .80653 657 .73438 .60007 . 66647 406 . 60241 2
59 393 .80529 696 . 73321 046 . 66538 446 .60137 1
60 .55431 1.80405 .57735 1.73205 .60086 1.66428 .62487 1.60033 0
Got. Tan. Cot. Tan. Cot. Tan. Cot. Tan.
61 0 60° 59° 58 °
139
TM 20-230
ERRATA SHEET
Table XIX.—Natural Tangents and Cotangents of Angles in Degrees and Minutes— Continued
M. 32° 33° 34° 35°
Tan. Cot. Tan. Cot. Tan. Cot. Tan. Cot.
0 0.62487 1.60033 0.64941 1. 53986 0. 67451 1.48256 0. 70021 1.42815 60
1 527 . 59930 982 . 53888 493 .48163 064 .42726 59
2 568 . 59826 . 65024 . 53791 536 . 48070 107 .42638 58
3 608 . 59723 065 . 53693 578 . 47977 151 .42550 57
4 649 . 59620 106 . 53595 620 .47885 194 .42462 56
5 . 62689 1. 59517 .65148 1. 53497 . 67663 1.47792 . 70238 1. 42374 55
6 730 . 59414 189 .53400 705 .47699 281 .42286 54
7 770 .59311 231 .53302 748 .47607 325 . 42198 53
8 811 . 59208 272 . 53205 790 .47514 368 .42110 52
9 852 . 59105 314 . 53107 832 .47422 412 .42022 51
10 .62892 1.59002 . 65355 1. 53010 .67875 1. 47330 . 70455 1. 41934 50
11 933 . 58900 397 .52913 917 .47238 499 . 41847 49
12 973 .58797 438 .52816 960 .47146 542 .41759 48
13 .63014 . 58695 480 .52719 .68C02 . 47053 586 .41672 47
14 055 . 58593 521 .52622 045 . 46962 629 .41584 46
15 . 63095 1. 58490 . 65563 1. 52525 . 68088 1.46870 . 70673 1. 41497 45
16 136 .58388 604 . 52429 130 .46778 717 . 41409 44
17 177 . 58286 646 .52332 173 . 46686 760 . 41322 43
18 217 . 58184 688 . 52235 215 . 46595 804 . 41235 42
19 258 . 58083 729 . 52139 258 . 46503 848 . 41148 41
20 . 63299 1. 5798i . 65771 1.52043 . 68301 1.46411 . 70891 1. 41061 40
21 340 .57879 813 .51946 343 .46320 935 .40974 39
22 380 . 57778 854 .51850 386 . 46229 979 .40887 38
23 421 . 57676 896 .51754 429 .46137 . 71023 . 40800 37
24 462 .57575 938 . 51658 471 .46046 066 . 40714 36
25 . 63503 1.57474 . 65980 1. 51562 .68514 1.45955 .71110 1. 40627 35
26 544 . 57372 . 66021 .51466 557 .45864 154 .40540 34
27 584 . 57271 063 .51370 600 .45773 198 . 40454 33
28 625 .57170 105 .51275 642 .45682 242 . 40367 32
29 666 .57069 147 . 51179 685 .45592 285 . 40281 31
30 .63707 1.56969 .66189 1. 51084 .68728 1.45501 . 71329 1.40195 30
31 748 .56868 230 .50988 771 .45410 373 . 40109 29
32 789 . 56767 272 .50893 814 .45320 417 . 40022 28
33 830 . 56667 314 . 50797 857 .45229 461 .39936 27
34 871 . 56566 356 .50702 900 .45139 505 .39850 26
35 .63912 1. 56466 .66398 1. 50607 . 68942 1.45049 .71549 1.39764 25
36 953 . 56366 440 .50512 985 .44958 593 . 39679 24
37 994 . 56265 482 . 50417 .69028 .44868 637 . 39593 23
38 .64035 . 56165 524 . 50322 071 . 44778 681 . 39507 22
39 076 .56065 566 . 50228 114 .44688 725 . 39421 21
40 .64117 1. 55966 .66608 1. 50133 . 69157 1.44598 . 71769 1.39336 20
41 158 . 55866 650 .50038 200 .44508 813 . 39250 19
42 199 . 55766 692 .49944 243 .44418 857 . 39165 18
43 240 . 55666 734 . 49849 286 .44329 901 .39079 17
44 281 . 55567 776 . 49755 329 . 44239 946 .38994 16
45 .64322 1.55467 . 66818 1.49661 . 69372 1.44149 .71990 1.38909 15
46 363 . 55368 860 .49566 416 . 44060 .72034 .38824 14
47 404 . 55269 902 .49472 459 . 43970 078 .38738 13
48 446 . 55170 944 .49378 502 . 43881 122 .38653 12
49 487 . 55071 986 .49284 545 . 43792 167 . 38568 11
50 .64528 1. 54972 .67028 1.49190 . 69588 1.43703 . 72211 1.38484 10
51 569 . 54873 071 .49097 631 . 43614 255 .38399 9
52 610 . 54774 113 .49003 675 . 43525 299 .38314 8
53 652 . 54675 155 .48909 718 . 43436 344 . 38229 7
54 693 .54576 197 .48816 761 . 43347 388 . 38145 6
55 .64734 1.54478 .67239 1.48722 . 69804 1. 43258 .72432 1.38060 5
56 775 . 54379 282 . 48629 847 . 43169 477 .37976 4
57 817 . 54281 324 . 48536 891 . 43080 521 . 37891 3
58 858 . 54183 366 . 48442 934 . 42992 565 . 37807 2
59 899 . 54085 409 .48349 977 .42903 610 . 37722 1
60 .64941 1. 53986 .67451 1.48256 .70021 1.42815 .72654 1.37638 0
Cot. 57 Tan. • 1 Cot. 56 Tan. Cot. 55 Tan. • 1 Cot. 54 Tan. 0 M.
U. S. GOVERNMENT PRINTING OFFICE: 1945
140
AGO 200B 622602°—45
Table XIX.—Natural Tangents and Cotangents of Angles in Degrees and Minutes—
Continued
M. 36° 37° 38° 39°
Tan. Cot. Tan. Cot. Tan. Cot. Tan. Cot.
0 0.72654 1.37638 0. 75355 1.32704 0.78129 1.2794 0.80978 1. 23490 60
1 699 . 37554 401 .32624 175 .27917 .81027 . 23416 59
2 743 . 37470 447 . 32544 222 . 27841 075 . 23343 58
3 788 . 37386 492 .32464 269 . 27764 123 . 23270 57
4 832 . 37302 538 . 32384 316 . 27688 171 . 23196 56
5 .72877 1.37218 .75584 1. 32304 .78363 1.27611 .81220 1.23123 55
6 921 .37134 629 .32224 410 . 27535 268 . 23050 54
7 966 . 37050 675 .32144 457 . 27458 316 . 22977 53
8 . 73010 . 36967 721 . 32064 504 . 27382 364 . 22904 52
9 055 . 36883 767 . 31984 551 . 27306 413 . 22831 51
10 .73100 1. 36800 . 75812 1.31904 . 78598 1.27230 .81461 1.22758 50
11 144 . 36716 858 .31825 645 . 27153 510 .22685 49
12 189 . 36633 904 . 31745 692 . 27077 558 .22612 48
13 234 .36549 950 . 31666 739 . 27001 606 . 22539 47
14 278 .36466 996 . 31586 786 . 26925 655 . 22467 46
15 .73323 1.36383 .76042 1.31507 .78834 1.26849 .81703 1. 22394 45
16 368 . 36300 088 .31427 881 . 26774 752 . 22321 44
17 413 .36217 134 . 31348 928 . 26698 800 . 22249 43
18 457 . 36134 180 .31269 975 . 26622 849 . 22176 42
19 502 .36051 226 .31190 .79022 . 26546 898 .22104 41
20 .73547 1. 35968 .76272 1. 31110 .79070 1.26471 . 81946 1. 22031 40
21 592 .35885 318 . 31031 117 . 26395 995 .21959 39
22 637 .35802 364 . 30952 164 . 26319 .82044 . 21886 38
23 681 .35719 410 . 30873 212 . 26244 092 . 21814 37
24 726 . 35637 456 . 30795 259 . 26169 141 . 21742 36
25 .73771 1.3554 .76502 1.30716 .79306 1.26093 .82190 1.21670 35
26 816 . 35472 548 . 30637 354 . 26018 238 . 21598 34
27 861 . 35389 594 . 30558 401 . 25943 287 . 21526 33
28 906 . 35307 640 . 30480 449 . 25867 336 . 21454 32
29 951 . 35244 686 . 30401 496 . 25792 385 . 21382 31
30 .73996 1.35142 .76733 1. 30323 .79544 1.25717 . 82434 1. 21310 30
31 . 74041 . 35060 779 . 30244 591 . 25642 483 . 21238 29
32 086 . 34978 825 . 30166 639 . 25567 531 . 21166 28
,33 131 . 34896 871 . 30087 686 . 25492 580 . 21094 27
34 176 . 34814 918 .30009 734 . 25417 629 . 21023 26
35 . 74221 1.34732 . 76964 1.29931 . 79781 1.25343 . 82678 1. 20951 25
36 267 . 34650 . 77010 . 29853 829 . 25268 727 . 20879 24
37 312 . 34568 057 .29775 877 . 25193 776 . 20808 23
38 357 . 34487 103 .29696 924 . 25118 825 . 20736 22
39 402 .34405 149 . 29618 972 . 25044 874 . 20665 21
40 . 74447 1.34323 . 77196 1.29541 . 80020 1.24969 .82923 1. 20593 20
41 492 .34242 242 . 29463 067 .24895 972 .20522 19
42 538 . 34160 289 . 29385 115 .24820 .83022 . 20451 18
43 583 . 34079 335 . 29307 163 .24746 071 . 20379 17
44 628 . 33998 382 . 29229 211 . 24672 120 . 20308 16
45 .74674 1.33916 .77428 1. 29152 .80258 1. 24597 .83169 1. 20237 15
46 719 . 33835 475 . 29074 306 . 24523 218 . 20166 14
47 764 . 33754 521 . 28997 354 . 24449 268 . 20095 13
48 810 . 33673 568 .28919 402 . 24375 317 . 20024 12
49 855 . 33592 615 .28842 450 . 24301 366 . 19953 11
50 .74900 1.33511 . 77661 1. 28764 . 80498 1.24227 . 83415 1.19882 10
51 946 . 33430 708 .28687 546 . 24153 465 . 19811 9
52 991 . 33349 754 .28610 594 . 24079 514 .19740 8
53 .75037 . 33268 801 .28533 642 . 24405 564 .19669 7
54 082 . 33187 848 .28456 690 . 23931 613 .19599 6
55 .75128 1. 33107 .77895 1.28379 . 80738 1.23858 . 83662 1.19528 5
56 173 . 33026 941 .28302 786 . 23784 712 .19457 4
57 219 . 32946 988 .28225 834 . 23710 761 . 19387 3
58 264 . 32865 .78035 . 28148 882 . 23637 811 . 19316 2
59 310 .32785 082 . 28071 930 . 23563 860 . 19246 1
60 .75355 1. 32704 .78129 1. 27994 .80978 1.23490 .83910 1.19175 0
Cot. Tan. Cot. Tan. Cot. Tan. Cot. Tan.
K J° 52° 51° 50°
609023°—44---10
141
Table XIX.—Natural Tangents and Cotangents of Angles in Degrees and Minutes—
Continued
M. 40° 41° 42° 43°
Tan. Cot. Tan. Cot. Tan. Cot. Tan. Cot.
0 0. 83910 1.19175 0.86929 1. 15037 0.90040 1.11061 0.93252 1. 07237 60
1 960 .19105 980 . 14969 093 . 10996 306 .07174 59
2 .84009 . 19035 .87031 . 14902 146 . 10931 360 .07112 58
3 059 . 18964 082 . 14834 199 . 10867 415 . 07049 57
4 108 . 18894 133 . 14767 251 . 10802 469 . 06987 56
5 .84158 1.18824 .87184 1.14699 .90304 1.10737 .93524 1.06925 55
6 208 .18754 236 .14632 357 .10672 578 . 06862 54
7 258 .18684 287 . 14565 410 .10607 633 . 06800 53
8 307 . 18614 338 .14498 463 .10543 688 . 06738 52
9 357 . 18544 389 . 14430 516 . 10478 742 . 06676 51
10 .84407 1.18474 .87441 1.14363 .90569 1.10414 .93797 1.06613 50
11 457 . 18404 492 . 14296 621 . 10349 852 . 06551 49
12 507 . 18334 543 . 14229 674 . 10285 906 .06489 48
13 556 . 18264 595 . 14162 727 . 10220 961 .06427 47
14 606 . 18194 646 . 14095 781 . 10156 . 94016 .06365 46
15 .84656 1.18125 .87698 1.14028 .90834 1.10091 . 94071 1. 06303 45
16 706 .18055 749 .13961 887 . 10027 125 . 06241 44
17 756 .17986 801 . 13894 940 . 09963 180 . 06179 43
18 806 . 17916 852 . 13828 993 . 09899 235 .06117 42
19 856 . 17846 904 . 13761 .91046 . 09834 290 .06056 41
20 .84906 1.17777 . 87955 1.13694 .91099 1.09770 . 94345 1. 05994 40
21 956 .17708 . 88007 .13627 153 . 09706 400 . 05932 39
22 . 85006 . 17638 059 .13561 206 . 09642 455 . 05870 38
23 057 . 17569 110 . 13494 259 . 09578 510 . 05809 37
24 107 . 17500 162 .13428 313 . 09514 565 . 05747 36
25 .85157 1.17430 .88214 1.13361 .91366 1. 09450 .94620 1.05685 25
26 207 .17361 265 .13295 419 .09386 676 .05624 34
27 257 . 17292 317 . 13228 473 .09322 731 . 05562 33
28 308 . 17223 369 . 13162 526 .09258 786 . 05501 32
29 358 . 17154 421 . 13096 580 .09195 841 . 05439 31
30 . 85408 1.17085 .88473 1.13029 .91633 1. 09131 . 94896 1. 05378 30
«31 458 . 17016 524 . 12963 687 .09067 952 . 05317 29
32 509 . 16947 576 . 12897 710 . 09003 . 95007 . 05255 28
33 559 . 16878 628 . 12831 794 . 08940 062 . 05194 27
34 609 . 16809 680 . 12765 847 .08876 118 . 05133 26
35 . 85660 1.16741 . 88732 1.12699 .91901 1. 08813 .95173 1. 05072 25
36 710 . 16672 784 .12633 955 . 08749 229 . 05010 24
37 761 . 16603 836 .12567 .92008 . 08686 284 . 04949 23
38 811 . 16535 888 . 12501 062 . 08622 340 . 04888 22
39 862 .16466 940 .12435 116 . 08559 395 . 04827 21
40 . 85912 1.16398 . 88992 1.12369 . 92170 1. 08496 . 95451 1.04766 20
41 9b3 . 16329 . 89045 . 12303 224 . 08432 506 . 04705 19
42 . 86014 . 16261 097 . 12238 277 . 08369 562 . 04644 18
43 064 . 16192 149 . 12172 331 . 08306 618 . 04583 17
44 115 . 16124 201 . 12106 385 .08243 673 . 04522 16
45 . 86166 1.16056 .89253 1.12041 .92439 1. 08179 . 95729 1. 04461 15
46 216 . 15987 306 . 11975 493 .08116 785 . 04401 14
47 267 . 15919 358 . 11909 547 .08053 841 . 04340 13
48 318 . 15851 410 . 11844 601 . 07990 897 . 04279 12
49 368 . 15783 463 . 11778 655 . 07927 952 . 04218 11
50 .86419 1.15715 .89515 1.11713 .92709 1. 07864 . 96008 1.04158 10
51 470 . 15647 567 . 11648 763 .07801 064 .04097 9
52 521 . 15579 620 . 11582 817 .07738 120 04036 8
53 572 . 15511 672 . 11517 872 .07676 176 03976 7
54 623 .15443 725 . 11452 926 . 07613 232 . 03915 6
55 . 86674 1. 15375 .89777 1.11387 .92980 1. 07550 . 96288 1 03855 5
56 725 . 15308 830 . 11321 .93034 .07487 344 03794 4
57 776 . 15240 883 . 11256 088 .07425 400 .03734 3
58 827 . 15172 935 .11191 143 . 07362 457 . 03674 2
59 878 . 15104 988 .11126 197 . 07299 513 .03613 1
60 .86929 1.15037 . 90040 1.11061 .93252 1.07237 .96569 1.03553 0
Oot. Tan. Oot. Tan. Oot. Tan. Cot. Tan.
49c 48c 47c 1 46 M.
142
Table XIX.—Natural Tangents and Cotangents of Angles in Degrees and Minutes—Continued
44°
M.
Tan. Cot.
0 0.96569 1. 03553 60
1 625 . 03493 59
2 681 . 03433 58
3 738 . 03372 57
4 794 . 03312 56
5 .96850 1.03252 55
6 907 .03192 54
7 963 .03132 53
8 .97020 .03072 52
9 076 .03012 51
10 .97133 1.02952 50
11 189 .02892 49
12 246 .02832 48
13 302 . 02772 47
14 359 . 02713 46
15 . 97416 1.02653 45
16 472 .02593 44
17 529 .02533 43
18 586 .02474 42
19 643 . 02414 41
20 .97700 1.02355 40
21 756 .02295 39
22 813 .02236 38
23 870 .02176 37
24 927 .02117 36
25 . 97984 1.02057 35
26 . 98041 . 01998 34
27 098 . 01939 33
28 155 . 01879 32
29 213 . 01820 31
30 .98270 1. 01761 30
31 327 .01702 29
32 384 .01642 28
33 441 . 01583 27
34 499 . 01524 26
35 .98556 1.01465 25
36 613 .01406 24
37 671 .01347 23
38 728 . 01288 22
39 786 .01229 21
40 . 98843 1.01170 20
41 901 .01112 19
42 958 . 01053 18
43 .99016 . 00994 17
44 073 .00935 16
45 .99131 1.00876 15
46 189 .00818 14
47 247 . 00759 13
48 304 . 00701 12
49 362 .00642 11
50 . 99420 1.00583 10
51 478 .00525 9
52 536 .00467 8
53 594 .00408 7
54 652 . 00350 6
55 .99710 1.00291 5
56 768 .00233 4
57 826 .00175 3
58 884 .00116 2
59 942 .00058 1
60 1.00000 1.00000 0
Cot. I Tan. M.
45°
143
Table XX.—Corrections to Ay for Magnification of Scale
(Correction is in yards per thousand yards. It is subtracted when determining actual distance and direction from map coordinates; it is added when converting data from observations or ground measurements into map coordinates.)
Zone and longitude
o r o o / o O f o o / Q o / o
A, 68 30 69 69 30 70 70 30 71 71 30 72 72 30 73
B, 76 30 77 77 30 78 78 30 79 79 30 80 80 30 81
C, 84 30 85 85 30 86 86 30 87 87 30 88 88 30 89
D, 92 30 93 93 30 94 94 30 95 95 30 96 96 30 97
E,100 30 101 101 30 102 102 30 103 103 30 104 104 30 105
F, 108 30 109 109 30 110 110 30 111 111 30 112 112 30 113
G, 116 30 117 117 30 118 118 30 119 119 30 120 120 30 121
o 24 2.574 2.034 1.557 1.144 0.794 0.508 0.286 0.127 0.032 0. ooo
25 2.533 2.002 1.533 1.126 .782 .500 .281 .125 .031 ooo
26 2.492 1.969 1.507 1.107 .769 .492 .277 .123 .031 ooo
27 2. 449 1.935 1.481 1.088 .756 .484 .272 .121 .030 ooo
28 2.404 1.900 1.455 1.069 .742 .475 .267 .119 .030 ooo
29 2.359 1.864 1.427 1.049 .728 .466 .262 .117 .029 .000
30 2. 313 1.828 1.399 1.028 .714 .457 .257 .114 .029 ooo
31 2.266 1.790 1.371 1.007 .699 .448 .252 .112 . 028 ooo
32 2.218 1.753 1.342 .986 .685 .438 .246 .110 .027 ooo
33 2.169 1.714 1.312 .964 .670 .429 .241 .107 .027 ooo
34 2.120 1.675 1.282 .942 .654 .419 .236 .105 .026 .000
35 2.070 1.635 1.252 .920 .639 .409 .230 .102 .026 ooo
36 2.018 1.595 1.221 .897 .623 .399 .224 .100 .025 ooo
37 1.967 1.554 1.190 .874 .607 .389 .219 .097 .024 ooo
38 1.915 1.513 1.159 .851 .591 .378 .213 .095 .024 ooo
39 1.863 1.472 1.127 .828 .575 .368 .207 .092 .023 .000
40 1.810 1.430 1.095 .804 .559 .358 .201 .089 .022 ooo
41 1.757 1.388 1.063 .781 .542 .347 .195 .087 .022 ooo
42 1.703 1. 346 1.030 .757 .526 .336 .189 .084 .021 ooo
43 1.650 1.303 .997 .733 .509 .326 .183 .081 .020 ooo
44 1.596 1.261 .965 .709 .493 .315 .177 .079 .020 .000
45 1.542 1.218 .933 .685 .476 .305 .171 .076 .019 ooo
46 1.488 1.176 .900 .661 .459 .294 .165 .073 .018 ooo
47 1.435 1.133 .868 .638 .443 .283 .159 .071 .018 ooo
48 1.381 1.091 .835 .614 .426 .273 .153 .068 .017 ooo
49 1.328 1.049 .803 .590 .410 .262 .148 .066 .016 ooo
50 1.274 1.007 .771 .566 .393 .252 .142 .063 .016 .000
144
Table XX.—Corrections to Sy for Magnification of Scale—Continued
Zone and longitude
o O f 0 0 t 0 o f o o t o o /
Latitude A, 73 73 30 74 74 30 75 75 30 76 76 30 77 77 30
B, 81 81 30 82 82 30 83 83 30 84 84 30 85 85 30
C, 89 89 30 90 90 30 91 91 30 92 92 30 93 93 30
D, 97 97 30 98 98 30 99 99 30 100 100 30 101 101 30
E, 105 105 30 106 106 30 107 107 30 108 108 30 109 109 30
F, 113 113 30 114 114 30 115 115 30 116 116 30 117 117 30
G, 121 121 30 122 122 30 123 123 30 124 124 30 125 125 30
o 24 0.000 0.032 0.127 0. 286 0.508 0.794 1.144 1.557 2.034 2.574
25 .000 .031 .125 .281 .500 .782 1.126 1. 533 2.002 2.533
26 .000 .031 .123 .277 .492 .769 1.107 1.507 1.969 2.492
27 .000 .030 .121 .272 .484 .756 1,088 1.481 1.935 2.449
28 .000 .030 .119 .267 .475 .742 1.069 1.455 1.900 2,404
29 .000 .029 .117 .262 .466 .728 1.049 1.427 1.864 2.359
30 .000 .029 .114 .257 .457 .714 1.028 1.399 1. 828 2.313
31 .000 .028 .112 .252 .448 .699 1. 007 1.371 1.790 2.266
32 .000 .027 .110 .246 .438 .685 .986 1.342 1.753 2.218
33 .000 .027 .107 .241 .429 .670 .964 1.312 1. 714 2.169
34 .000 .026 .105 .236 .419 .654 .942 1.282 1.675 2.120
35 .000 .026 .102 .230 .409 .639 .920 1.252 1.635 2.070
36 .000 .025 .100 .224 .399 .623 .897 1.221 1. 595 2.018
37 .000 .024 .097 .219 .389 .607 .874 1.190 1. 554 1.967
38 .000 .024 .095 .213 .378 .591 .851 1.159 1. 513 1. 915
39 .000 .023 .092 .207 .368 .575 .828 1.127 1.472 1.863
40 .000 .022 .089 .201 .358 .559 .804 1.095 1.430 1. 810
41 .000 .022 .087 .195 .347 .542 .781 1.063 1.388 1.757
42 .000 .021 .084 .189 .336 .526 .757 1.030 1.346 1.703
43 .000 .020 .081 .183 .326 .509 .733 .997 1.303 1.650
44 .000 .020 .079 .177 .315 .493 .709 .965 1.261 1.596
45 .000 .019 .076 .171 .305 .476 .685 .933 1.218 1.542
46 .000 .018 .073 .165 .294 .459 .661 .900 1.176 1.488
47 .000 .018 .071 .159 .283 .443 .638 .868 1.133 1.435
48 .000 .017 .068 .153 .273 .426 .614 .835 1.091 1.381
49 .000 .016 .066 .148 .262 .410 .590 .803 1.049 1.328
50 .000 .016 .063 .142 .252 .393 .566 .771 1.007 1.274
20
145
NTSU LIBRARY
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