298 PROFESSOR G. H. DARWIN ON THE STABILITY OF THE PEAPt-SHAPED 
The next step is to find 
L = 
sin j3 
4 cos /9 cos 7 
1 — 
cos^/S ' 
D + /c- 
M. 
sin 13 
4 Dq^ cos (3 cos 7 
COS^yd \ 
D-^-r 
where D~ = 1 — k^k '^. 
The numerical values are logZ> = 9’9840165, log Z = '6454565, log J/ = '9591960. 
From'these we obtain r = Lcf)^, "D = whence 
Ik 
Co 
- -0.55837 
" GF H - 
•000804 
1) = 
•031701 
Denominator = 
- -023332 
In accordance Avith (32) the Numerator divided by the Denominator is — - 
So)- 
4:77 pc^ 
and I thus find 
log , 
” 4:7rpc 
- = (-) 7-94578. 
It was foimd in § 7 of the “ Pear-shaped Figure ” that the angular velocity of the 
critical Jacobian was given by ~—= '14200. Accordingly, the scpiare of the angular 
velocity of the pear being w® + Ave haAm 
OJ 
+ Sw" = co3[l — -1243146^]. 
From the formulse (31) I then find 
= -150686^ /y = '50839eb 
Jj 
The other /■* are equal to " and are giAmn in the preceding table. From (28) 
and the definitions of a, li, t, ti it appears that the moment of inertia of the pear is 
Aj A,. — 
With log a = 9'8559758, I find 
3il/2n 
Trpkg 
1 + - e" + - A — - /y 
q 1/2"! 
A; - A. = [1 + '131011c2]. 
27Tpk^ 
The angular velocity of the pear is 
y/ (c>^ -f- Scu") — ^ K1 — '06215/ 
