14 
MR. J. H. JEANS ON THE INSTABILITY OF THE PEAR-SHAPED 
The value of C 13 can be written down from symmetry. 
t 22 = 
AAB 
[If A 2 a /3 2 + If AB/3 3 + |AC/3 2 y -f A (M« + 2 n/3) 
- lfBM/3 - f C (My + 2 1/3) + |iH ] dX 
A \ B ;i f-^T¥A"a"73 + 5f A-Ba/3 - + lgA-Ca/3y + 2ff-AB-/3'' 
+ ffACfV + ifABGAy] dX 
+ 
AAB 3 
[ffA 2 (L [3 + 2 no) + 2f f B 2 M (3 +(N/3 + 2Zy) 
AAB 3 
+ lfAB (Ma + 2n/3) + §AC (Za + m/3 + ?iy) + §BC (My + 2Z/3)] rix 
.(60) 
1 3 [f An + f Bi« -pf-CI] + r -^L dX 
AAB 2 
The value of C 33 can be written down from symmetry. 
^23 — 
1 
AAB 2 C 2 
[3f A 2 a/3y + 2fAB/3 2 y + 2fAC/3y 2 
1 
AAB 2 C 
—fA (Za+m/3+ny)— fB (My+ 2Z/3) —fC (N/3 + 2/y)+fl] dX 
- [6yf AV|8 + 5|A 2 Ba/3 2 + if A 2 Ca/3y + 2ff AB 2 /3 3 
+ x TAC 2 /3y 2 + fABC/3 2 y] dX 
1 
+ 
AA ^[( 6 ^ A3a V+ il-A^a^y + 5f A 2 C a y 2 + ^AB^y 
+ 2ffACy+|ABC/3y 2 ] dX 
1 [f j] A 2 (L/3 + 2na) + 2ffB 2 M/3 + *C 2 (N/3 + 2 ly) 
+ f AB (Ma + 271/3)+ f AC (/a + w/3 + wy) + fBC (My + 2^/3)] dX 
AAIO 
1 
A ABO 
i[If A 2 ( Ly + 2wa) + yf B 2 (My+ 2//3) + 2ff C 2 Ny 
+ fAB (/!a+m/3+?iy) + §AC (Na + 2ny)+fBC (N/3 + 2Zy)] dX 
- £^HAm+iW+ICM] dK- £ ^[fA„ + |BJ« + iCl] dx 
G 
o AABG 
dX. 
• ( 61 ) 
