FIGURE AND STABILITY OF A LIQUID SATELLITE. 
231 
The computed values are so very close to the conjectural ones, in so far as they 
have been as yet computed, that we might be content, but in order to illustrate the 
process when the conjectures are less satisfactory, I proceed to the next stage. 
By far the greater part of the discrepancy between assumed and computed values 
(which in some cases was considerable) arises from error in the assumed values of r. 
Now assuming « and K to be correct, it is very easy to correct the results for a 
changed value of r. 
O 
In this case I find 
corrected £ 0-056274 0-064873 0-074271 
„ e 0-04545 0-04811 0-05030 
„ 77 0-32012 0-36431 0-40867 
corrected £ 0'047890 0*062253 0-082137 
„ E 0-14020 0-17423 0-21889 
„ H 0-40546 0-52583 0-69385 
Recomputing 
sin -1 k unchanged sin -1 K unchanged 
corrected log r 0-40240 0-39591 0-39047 corrected log r 0"41069 0-39768 0-38695. 
By means of these we find two formulae of interpolation, namely :— 
^ = 2-4884 — 0-0342 + 0"0032 ( ?'~* 8 j, 
- = 2-4985-0-0685 ( l —— Wo’0075 
a \ 2 / 
These two expressions may be equated to one another, and therefore we have the 
means of finding simultaneous values of y and T, and thence by another formula of 
interpolation of k and K. Hence I obtain 
y . 46°. 48°. 50°. U 32°. 34°. 36°. 
r 33° 13'-4 34° 17'-9 35° 17'-4 y 43° 47'*4 47° 25'*4 51° 34'-4 
sin' 1 K 50° 52'-2 51° 29'-5 52° 6'*3 sin" 1 k 67° 12'T 69° 12'*3 71° 35'*6. 
Comparison with the initial values shows that the conjectures were very good. 
It now remains to compute the moment of momentum, and as we are dealing with 
Roche’s problem the rotational momentum of the larger ellipsoid is not required. It 
follows that the values of T and K are not used, and since they are only required 
for finding the shape of the larger ellipsoid, there was no necessity for a high degree 
of accuracy in them. The moment of momentum is represented by the quantity jx l 
of § 18. I find then 
y. 46°. 48°. 50°. 
Pi 0-348640 0-348300 0-348519. 
By formulse of interpolation the minimum value occurs when y = 48° 12'"9 and 
k = sin 69° 39'T. The corresponding values are — = 2"4848, V = 34° 25 /- 6, 
