12 MR. J. H. JEANS ON THE INSTABILITY OF THE PEAR-SHAPED 
- ff [26±A V + P *CV + 6 A A 2 Ba 2 /3 + 6 A A 2 Ca 2 y 
+ If AB 2 «/3 2 + if AC 2 ay 2 P liABCa/?y + AB 2 C/3 2 y + A-BC 2 /3y 2 ] 
-^ 2 /[6AAV/3+5|A 2 B aj 8 2 +l|A 2 Ca/3y + 21fAB 2 /3 3 + AAC 2 /3y 2 p lfABC/3 2 y] 
- £f/[6 A-AVy + l|A 2 Ba/3y+5|A 2 C a y 2 + A AB 2 /3 2 y P 2yf AC 2 y 3 +liABC/3y 2 ] 
-£/ [6AAV/C plfA 2 Ba/3*PlfA 2 CayK + A A B 2 /3 2 k P A A C 2 y 2 /c P fABC/V] 
+ f : y [6AA 2 La + AB 2 (Ma+2w/3)+AC 2 (Na + 2wy)+|AB (L/3p2na) 
pfAO (Ly p 2 ma) p fBC (/a + m/3 P ny)] 
+ ^/[A-A 2 (L/3 p 2na) + 2{-fB 2 M/3 + AC 2 (N/3 p 2A) + lfAB (Ma + 2n/3) 
+ |AC (/a + m /3 p ny) + fBC (My+2 1/3)] 
+ ^ 2 /[ffA 2 (Ly + 2ma) + A® 2 (My + 2 1/3) + 2AC 2 Ny + fAB (/a + m/3+ny) 
p if AC (Na + 2ny) p fBC (N /3 p 2 ly)] 
+ if [ffA 2 (L/c + 2ap) P AB 2 (M/c + 2/3q) P AC 2 (N« + 2yr) + f AB (n* + uq + /3p) 
P fAC (?n/c A y/J P a/') PfBC (A P y(J_ P fiv )] 
~ff [lflLAp fltB P ptltC] 
-Uf [fnApfJtfBp |IC] 
-ff [fmAp ilBpfNC] 
-if [fpAp pH Bp |rC] p if 2 G, ..(53) 
where f stands for A^ 2 p B>/ 2 P C£ 2 — 1, and G is given by 
G = A {^Wp WA 2 B«^+WWy PM-AB^ 
P ffAC 2 ay 2 p f|ABCa/3y P fp 3 /3 3 + 
+ AB 2 C/3 2 yPABC 2 /3y 2 } 
—VAA 3 La-ifA 2 B (L/3p2na)-f|A 2 C (L y p2ma) 
—AtAB 2 (Map2n/3) —AAC 2 (NaP2ny)-AABC (la + m/3+ny) 
-ifB 3 M/3-MC 3 Ny-AB 2 C (My + 2//3)-ABC 2 (N/3p2Zy) 
p ffA 2 H p AB 2 fE p &C 2 & p A^Cl p A ACm p A ABn. . . (54) 
12. The potential of the distorted ellipsoid 
/p eP P e 2 Q P e 3 R =0,.(55) 
can now be written down as far as terms in d\ The terms in e and e 2 , which of 
course involve only P and Q, have been calculated in the previous paper. The terms 
in e 3 in Y b , the potential at the boundary A = 0, are (cf. equation (3)), 
e 3 y (a) [u 3 +fv 3 ) d\ = — 7 rpabce 3 \ " 3 ' ' 3 d\, .... (56) 
Jo Jo A 
in which u 3 +fv 3 has the value just given in equation (53). 
