238 GEOGRAPHIC TABLES AND FORMULAS. [bull.214. 
Table of corrections to longitude for difference in arc and sine. 
logs (-) 
S.'^(+) 
log s ( - 
S !<*■"< + ) 
log s ( -) 
flfenie. **"<+> 
3.876 
0. 000 0001 
2.385 
4.871 
0. 000 0098 
3.380 
5. 172 
0. 000 0392 
3.681 
4.026 
02 
2.535 
4.882 
103 
3.391 
5.178 
402 
3.687 
4.114 
03 
2.623 
4.892 
108 
3.401 
5. 183 
412 
3.692 
4.177 
04 
2.686 
4.903 
114 
3.412 
5. 188 
422 
3.697 
4.225 
05 
2.734 
4.913 
119 
3.422 
5. 193 
433 
3.702 
4.265 
06 
2.774 
4.922 
124 
3.431 
5.199 
443 
3.708 
4. 298 
07 
2.807 
4.932 
130 
3.441 
5.204 
453 
3.713 
4.327 
08 
2.836 
4.941 
136 
3.450 
5. 209 
464 
3.718 
4.353 
09 
2. 862 
4. 950 
142 
3.459 
5.214 
474 
3.723 
4.376 
10 
2.885 
4.959 
147 
3.468 
5.219 
486 
3.728 
4.396 
11 
2.905 
4.968 
153 
3. 477 
5.223 
497 
3.732 
4.415 
12 
2. 924 • 
4.976 
160 
3.485 
5.228 
508 
3.737 
4.433 
13 
2.942 
4.985 
166 
3.494 
5.233 
519 
3.742 
4.449 
14 
2.958 
4.993 
172 
3. 502 
5.238 
530 
3.747 
4.464 
15 
2. 973 
5.002 
179 
3.511 
5. 242 
541 
3.751 
4.478 
16 
2.987 
5.010 
186 
3.519 
5.247 
553 
3.756 
4.491 
17 
3.000 
5. 017 
192 
3.526 
5.251 
565 
3.760 
4.503 
18 
3.012 
5. 025 
199 
3.534 
5. 256 
577 
3.765 
4.526 
20 
3. 035 
5. 033 
206 
3.542 
5.260 
588 
3.769 
4.548 
23 
3.057 
5.040 
213 
3.549 
5. 265 
600 
3.774 
4.570 
25 
3. 079 
5.047 
221 
3. 556 
5. 269 
613 
3.778 
4.591 
27 
3.100 
5.054 
228 
3.563 
5. 273 
625 
3. 782 
4. 612 
30 
3.121 
5.062 
236 
3.571 
5. 278 
637 
3.787 
4.631 
33 
3.140 
5. OtiS 
243 
3. 577 
5.282 
650 
3.791 
4.649 
36 
3. 158 
5. 075 
251 
3.584 
5.286 
663 
3.795 
4.667 
39 
3. 176 
5.082 
259 
3.591 
5.290 
671 
3. 79'.) 
4.684 
42 
3.193 
5. 088 
267 
3.597 
5. 294 
687 
3. 803 
4.701 
45 
3.210 
5. 095 
275 
3. 604 
5. 299 
702 
3.808 
4.716 
48 
3.225 
5. 102 
284 
3.611 
5.303 
716 
3. 812 
1. 732 
52 
3.241 
5. 108 
292 
3. 617 
5. 307 
729 
3.816 
i.Tir. 
56 
3. 255 
5.114 
300 
3. 623 
5.311 
713 
3. 820 
4.761 
59 
3. 270 
5.120 
309 
3. 629 
5. 315 
757 
3. 824 
1.771 
63 
3. 283 
5. 126 
318 
3. 635 
5.319 
771 
3.828 
1.788 
67 
3. 297 
5. 132 
327 
3.641 
5. 323 
785 
3.832 
4.801 
71 
3. 310 
5. 138 
336 
3.647 
5. 327 
800 
3.836 
1.813 
75 
3. 322 
:>. 1 11 
345 
3. 653 
5. 331 
814 
3. S40 
4.825 
80 
3.334 
5. 150 
354 
3. 659 
5. 335 
829 
3.844 
4.834 
M 
3.343 
5. 156 
364 
3.665 
5. 339 
845 
3.848 
1.849 
89 
3. 358 
5.161 
373 
3.670 
5. 343 
861 
3. 852 
4.860 
94 
3.369 
5.167 
383 
3.676 
5.347 
877 
3.856 
INVERSE SOLUTION. 
Having Latitudes and Longitudes of Two Points to Compute Azimuths and 
i >istances. 
The following example shows the method of performing* the opera- 
tion. The northernmost point should be used as the initial position, 
then all signs for (I), (II), and (III) are +, and for (IV) -. The 
value of z/A may be either + or — , but this sign need only be used 
in determining in which quadrant the azimuth angle a falls, i. e., the 
sign of tan a (12). An inspection of a rough plat of the positions 
will also determine this. The correction to A\ is found from a 
distance scaled off from the plat, and need not be very close. In 
(8) the term (I-f-11) 2 is the square of the difference of latitude Acp in 
seconds. Since (IV) is always small, log (I) in (8) may be taken as 
log of Acp from (1). If cos a is smaller than sin «, find S" from 
log s - cos a in (11). As a check on the work compute the second 
