EQUILIBRIUM OF ROTATING MASSES OF FLUID. 
401 
Table of (k, y). 
0 = + 
P = i 
A = 2 
•839 
1167 
CO 
II 
1-433 
2-012 
k = 4 
2-204 
3-123 
k = 5 
3-163 
4-536 
Table of \k, i, y\ 
P = i 
7c = 2, 
7 = 2 
5-460 
7-847 
lc = 2, 
i — 3 
9-494 
13-895 
k-2, 
7 = 4 
14-875 
22-201 
A= 2, 
i = 5 
21-780 
33-190 
k = 3, 
i = 2 
9-494 
13-895 
A = 3, 
t = 3 
16-667 
24-969 
k = 3, 
i — 4 
26-384 
40-517 
k - 3, 
i = 5 
39-047 
61-574 
k = 4, 
i = 2 
14-875 
22-201 
k = 4, 
t= 3 
26-384 
40-517 
k = 4, 
i = 4 
42-214 
66-840 
7c = 4, 
7 — 5 
63183 
103-372 
7c = 5, 
7= 2 
21-780 
33-190 
k= 5, 
t = 3 
39-047 
61-574 
k — 5, 
7 = 4 
63-183 
103-372 
k = 5, 
7 = 5 
95-690 
162-831 
Table of [k, y). 
f 
0 = 4 
k 
= 2 
•177 
•268 
k 
= 3 
•190 
•298 
k 
= 4 
•205 
•331 
k 
= 5 
•221 
•369 
Table of 
i, y • 
k = 2, 
7 = 2 
•177 
•268 
k = 2, 
7 = 3 
■475 
•744 
7c = 2, 
i = 4 
1024 
1-655 
7c =2, 
7 = 5 
1-933 
3-229 
A- = 3, 
7 = 2 
•190 
•298 
7c. = 3, 
7 = 3 
•519 
"844 
7c = 3, 
7 = 4 
1-137 
1-921 
7c = 3, 
7=5 
2-183 
3-837 
A = 4, 
7 = 2 
•205 
•331 
7c = 4, 
i — 3 
•569 
•961 
7c = 4, 
7 = 4 
1-266 
2-238 
7c = 4, 
7=5 
2-471 
4-578 
7c = 5, 
7 = 2 
•221 
•369 
7c = 5, 
i = 3 
•624 
1096 
A = 5, 
7=4 
1412 
2-616 
k = 5, 
7 = 5 
2-803 
5-479 
With these values for the series, we have to compute the coefficients of the systems 
of simultaneous equations (73). The equations lend themselves more readily to 
solution if we consider hi — 1,^—1,/^- — 1, as the unknowns instead of h 2 , X,-. 
The results are given in the following equations. 
MDCCCLXXXVJI.—A. 3 F 
