FIGURE AND STABILITY OF A LIQUID SATELLITE. 
235 
Away from larger ellipsoid 
A. 
0-4. 
0-7. 
1-0. 
8c 3 
-0-0193 
-0-0283 
-0-0194 
8c 3 2 
-0-00039 
-0-00068 
2 
8c a 
+ 0-00472 
+ 0-00886 
+ 0-00911 
8c 5 
-o-ooiio 
-0-00384 
-0-00629 
Total 8c 
-0-0161 
-0-0240 
-0-0166 
c 
0-8433 
0-9006 
0-9270 
c + 8c 
0-8272 
0-8766 
0-9104 
8c 
c 
1/52 
1/37 
1/56 
The last line in each division of this table has been given in order to show the 
relative importance of the total correction. It is clear that the ellipsoid remains a 
substantially correct solution. 
These corrections to the semi-major axes are indicated by dotted lines at the 
extremities of the longest axis of the smaller mass in figs. 2 and 3, and of both masses 
in fig. 4. 
We have in the last section tabulated r— (c+(7), the distance between the two 
vertices. Now, although I have not calculated the deformations of the larger 
ellipsoid, it is pretty clear that they must bear to those of the smaller one approxi¬ 
mately the ratio of A to unity. Accepting this conjecture, we have for the 8 C of the 
larger ellipsoid towards the smaller one the following values:— 
A. 0-4. 0-7. 1-0. 
8C 0-010 0-029 0-035 
The distance between the two surfaces of liquid is clearly r— (c + Sc + C+8C). 
Thus we have 
A. 
0-4. 
0-7. 
1-0. 
r—(c+ C) 
0-653 
0-638 
0-660 
8c + 8C 
0-036 
0-071 
0-070 
"—(c + 8c+C+8C) 
0-617 
0-567 
0-590 
23. Certain Tests and Verifications. 
In order to test how nearly the solution for a 3 /r 3 by series in (40) of §11 would 
agree with the solution (36) of § 10 in terms of the F elliptic integral, I computed for 
A = 0"7 the value of rj a in the two ways for three values of y, and found the 
following results :— 
A = 0-7. 
y. 42°. 
r/a by series 2-5355 
r/a by elliptic integrals 2-5359 
2 H 2 
46°. 
2-4500 
2-4495 
44°. 
2*4888 
2-4881 
