22 
MR. J. H. JEANS ON THE INSTABILITY OF THE PEAR-SHAPED 
The values obtained were 
C I2 = — 0 ’ 00027991 L— 0 ' 0093206 JH + 0‘010377 5 N 
-0'0045815l -0'0016151m +0-0040268II+0-0042388, . . (91) 
C 13 = — 0 " 00035031 L+ 0 ' 0035301 JH — 0 ' 0295936 K 
- 0-00242841 + 0 ' 0074994 m - 0 ' 0010296 n+ 0 ' 0044353 , . . ( 92 ) 
C 22 = 0 - 0001010 lL+ 0 - 0126532 fl + 0 - 0153304 N 
-0-02508191 +0 - 0010344m -0-0017407H-0-0015791, . . (93) 
C 33 = 0 - 00013611 L + 0 - 0062287 J 1 + 0 - 0353141 N 
-0-02615751 -0-0035230m +0'0007874n-0-0016798. . . (94) 
Two values of C 23 can now be deduced from equations (69) and (70) respectively. 
These are found to be 
1-23 
+ 0-0002337 
-0-047957 
-0-123015 
IL 
m 
+ 0-0002343 
-0-047962 
-0-123004 
+ 0-16424 
-0-001361 
-0-001636 
I 
m 
+ 0-16420 
-0-001360 
-0-001636 
0-003242 
0-003227. 
The agreement of these values provides a check on the computations of the 
coefficients C 12 , ..., and of the integrals from which they have been calculated. 
In virtue of relations (73), equations (68)-(70) become 
5 
JL 
« 4 
(95) 
, 1^311 
^ 74 * 4 
o a 
(96) 
3 
N 
c 4 
M + JL = 0 
« 4 6 4 
(97) 
while relations (73) and (74), of which only 
represented by 
12 2 M 
. _ i ^ 
13 2 « 6 c 4 
n 
m 
three are now independent, may be 
= 0.(98) 
= 0, 
(99) 
r _1 
l 22 4 
a 2 b 8 
m = o. 
( 100 ) 
On substituting for C 12 , C 13; and r 22 from equations (9l)-(98), these become sis linear 
equations for IL, UK, W, l, lit, and It. 
