FIGURE OF EQUILIBRIUM OF A ROTATING MASS OF LIQUID. 
21 
In addition to the integrals which were given in the previous paper,* I have 
calculated the following values of additional integrals needed for the computation of 
third-order terms. 
J B 5 — 
: 0-9637364, 
J B * C = U392786, 
J b sq2 — 2 024097, 
J B-C 3 = 
= 2-948174, 
J BC * = 4-316064, 
J c , = 6-336915, 
•I A f. — 
: 0-0001716853, 
J a6b = 0-0006851396, 
J A , C = 0-000942028, 
Ja“B j — 
5 0-002877084, 
J a*bc = 0-004027127, 
J A 4 C , = 0-005675881, 
Ja»B 8 = 
: 0-01256355, 
J a 3 B 2 C = 0-01783828, 
J A , BC , = 0-02547622, 
J A 3 C s = 
= 0-0365761, 
J A2fi4 = 0-0565289, 
Jaw = 0-0811833, 
J A‘ 2 B-C ! = 
: 0-1172029, 
Jaw = 0-1698776, 
J a2C 4 = 0-2473229, 
Jab 5 — 
0-260331, 
Jab 4 c = 0'377266, 
J AB 3 C2 = 0-549771, 
JaB s C 3 = 
0-802462, 
Jabc 4 = 1-177387, 
J AC s = 1731910, 
J B 6 = 
1-221051, 
J B5C = 1-781565, 
J B+C 2 = 2-621427, 
J B 3 C S = 
3-837093, 
J b-c 4 = 5-679960, 
J c6 = 12-448855, 
J BC5 = 8-391280, 
II 
0-0000434660, 
J A 6 b = 0-000177533, 
J A e c = 0-000245881, 
J A 5 B- 
0-000757892, 
J A5BC = 0-00106671, 
J A 5 C , = 0-00151097, 
Ja 4 b 3 = 
0-00334922, 
Ja 4 b s c = 0"00477536, 
Jaw = 0-00684621, 
Ja 4 c 3 " 
0-00986287, 
J A s B 4 = 0-0152016, 
J A . BSC = 0-0219023, 
J A 3 B 2 C 2 — 
0-0317157, 
Ja 3 bc 3 = 0"0460906, 
J A 3 C4 = 0-0672671, 
J a 2 b 5 = 
0-0704673, 
Ja-’b 4 c = d 102374, 
Jaw- = 0*149566, 
Ja 2 B 2 C s = 
0-218724, 
J A 2 BC 4 = 0-321581, 
J A 2c 5 ~ 0 473857, 
Jab 6 — 
0-332181, 
Jab 5 c = 0*485553, 
J ab 4 c 2 = 0-716300, 
Jab 3 c 3 = 
1 "04926, 
Jab 2 c 4 = 1 "55682, 
Jabc 5 = 2*30256, 
J AC s = 3-42068. 
The first task is the evaluation of f u , c 12 , , C 33 . These quantities are connected by 
the three relations (68)-(70), so that only three of the six quantities need have been 
calculated. I have, however, calculated four coefficients, namely, C 12 , C 13 , C 22 and C 33 
quite independently, the object being to obtain a check on the accuracy of the 
computations. In this way a check is obtained at every step of the computations. 
* The following are true values of integrals which were incorrectly given in the previous paper:— 
J BCC = U3419631, J AABCC = 0-09510324, I cccc = 0-4781180. 
In each ease the error was one of printing only, and did not enter into the computations. The whole 
table given in the previous paper was recomputed before extending it for purposes of the present paper. 
