FIGURE AND STABILITY OF A LIQUID SATELLITE. 
207 
Therefore 
Whence 
k / /2 , \ k sin y o? / r> \ o \ 
— (To-TjAf “+...) = —■ . . - '-X - 3 (3 + X + cos" y + v). 
sm y 3 (1 + X) cos f3 cos y r 3 in 
— — o /1 + y. cos (3 cos y r„— t x k 2 + t 2 k' 1 — t 3 k ,<] ... 
r* ' sin 2 y 3 + X + cos 2 y +17 
• (<«>). 
Thus a table of values of t 0 , t 15 r a , r 3 enables,us to compute r for a given value of y, 
when k' has been found. 
In the following tables the v’s and r’s were computed for the even degrees of y and 
interpolated for the odd degrees. These functions are found as the differences 
between large numbers, and therefore great care would be required to determine them 
Table of Auxiliary Functions. 
7- 
Log v 0 . 
v i- 
Log vi. 
Log v 2 . 
Log v 3 . 
T 0- 
Log n. 
Log To. 
Log t 3 . 
0 
30 
9-94493 
0-14279 
9-15470 
7-9576 
7-15 
0-010592 
6-85440 
5-9805 
5-222 
31 
9-94085 
0-15461 
9-18925 
8-0264 
7-25 
0-012124 
6•94587 
6-1063 
5 • 378 
32 
9-93661 
0-16722 
9-22329 
8-0941 
7-36 
0-013824 
7-03507 
6-2288 
5-533 
33 
9-93222 
0-18065 
9-25684 
8-1607 
7-47 
0-015702 
7-12194 
6-3478 
5-685 
34 
9-92764 
0-19493 
9-28988 
8-2263 
7-58 
0-017774 
7-20666 
6-4639 
5-834 
35 
9-92285 
0-21006 
9-32234 
8-2906 
7-67 
0-020052 
7-28937 
6-5780 
5-979 j 
36 
9-91786 
0-22613 
9-35436 
8-3541 
7-76 
0-022554 
7-37022 
6-6899 
6-122 
37 
9-91269 
0-24327 
9-38608 
8-4173 
7-87 
0-025294 
7-44939 
6-7994 
6-262 
38 
9-90731 
0-26150 
9-41747 
8-4800 
7-97 
0-028290 
7-52697 
6-9069 
6-400 
39 
9-90167 
0-28091 
9-44857 
8-5418 
8-06 
0-031559 
7•60306 
7-0127 
6-536 
40 
9-89578 
0-30160 
9-47943 
8-6031 
8-14 
0-035121 
7-67777 
7-1167 
6-669 
41 
9-88965 
0-32368 
9-51011 
8-6646 
8-23 
0-038994 
7-75120 
7-2192 
6-802 
42 
9-88327 
0-34724 
9-54063 
8-7259 
8-32 
0-043203 
7-82342 
7-3202 
6-932 
43 
9-87665 
0-37244 
9-57105 
8-7869 
8-42 
0-047768 
7-89452 
7-4200 
7-061 
44 
9-86974 
0-39937 
9-60138 
8-8476 
8-51 
0-052713 
7-96459 
7-5186 
7-189 
45 
9-86257 
0-42823 
9-63168 
8-9081 
8-60 
0-058064 
8-03371 
7-6162 
7-316 
46 
9-85509 
0-45917 
9-66197 
8-9685 
8-69 
0-063847 
8-10195 
7-7128 
7-442 
47 
9-84729 
0-49239 
9-69231 
9-0290 
8-79 
0-070093 
8-16939 
7-8087 
7-567 
48 
9-83915 
0-52812 
9-72274 
9-0896 
8-87 
0-076830 
8-23608 
7-9036 
7-691 
49 
9-83069 
0-56656 
9-75325 
9-1505 
8-96 
0-084093 
8-30210 
7-9981 
7-814 
50 
9-82187 
0-60804 
9-78393 
9-2117 
9-05 
0-091916 
8-36752 
8-0920 
7-938 
51 
9-81263 
0-65278 
9-81477 
9-2733 
9-15 
0-100336 
8-43241 
8-1855 
8-061 
52 
9-80300 
0-70121 
9-84585 
9•3353 
9-24 
0-109394 
8-49682 
8-2786 
8-183 
53 
9-79298 
0-75372 
9-87721 
9-3976 
9-33 
0-119134 
8-56082 
8-3716 
8-306 
54 
9-78252 
0-81075 
9-90889 
9-4606 
9-43 
0-129601 
8-62447 
8-4643 
8-429 
55 
9-77159 
0-87288 
9-94095 
9-5245 
9-52 
0-140845 
8•68785 
8-5570 
8-552 
56 
9-76016 
0-94064 
9-97342 
9-5893 
9-62 
0-152919 
8-75103 
8•6500 
8-676 
57 
9-74819 
1-01471 
•00634 
9-6550 
9-72 
0-165883 
8-81407 
8-7431 
8-801 
58 
9-73565 
1-09590 
•03977 
9-7216 
9-82 
0-179801 
8-87703 
8-8367 
8-926 
59 
9-72252 
1-18517 
•07378 
9-7893 
9-92 
0-194740 
8-93999 ; 
8-9306 
9-052 
60 
9-70874 
1-28362 
•10844 
9-8582 
•02 
0-210779 
9-00303 
9-0252 
9-179 
61 
9-69426 
1-39268 
•14385 
9-9287 
•13 
0-227997 
9-06626 
9-1206 
9-308 
62 
9-67910 
1-51349 
•17998 
•0006 
•24 
0-246485 
9-12966 
9-2168 
9-439 ! 
63 
9-66319 
1-6480 
•21696 
•0743 
•36 
0-266343 
9-19331 
9-3140 
9-572 l 
