21)6 PROFESSOR G. 11. DAPOYIN ON THE STABILITY OF THE PEAR-SHAPED 
Table of Logarithms of the B integrals. 
1 i. 
i 
log 10. 
log 
2 0 
9-69312 
•09295 
2 2 
9-33300 
•40665 
1 3 0 
9-54617 
•20467 
4 0 
9-44928 
•28206 
4 2 
9-25987 
•41239 
4 4 
9-06489 
•44858 
6 0 
9-24383 
• 35876 
6 2 
9-16199 
•41249 
6 4 
9-02369 
•44195 
^19. Synthesis of Numerical Results; Stability of the Pear. 
In the following tables and remarks I collect together some of the results which 
occur in the course of the work. The final places of decimals as given have, perhaps, 
in many cases hut little significance :— 
/. .s. 
(1-) 
% - 
log {% - bi® = log Pi®. 
(3.) 
(^•) 
(■13 
(3) + (4). 
\ ' 2cos;8cosyP 
2 0 
- -141617 
(-) 8-1562926 - 10 
•0029865 
- -0011976 
•0017889 
2 2 
•136417 
6-1745705- 10 
- -0000247 
•0000127 
- -0000120 
4 0 
•07033 
8-53794 - 10 
•005214 
- -002555 
•002659 
4 2 
•16978 
•95653 
- -008965 
•004390 
- -004575 
4 4 
•23558 
3-18755 
•005594 
- -002664 
•002930 
6 0 
•17638 
8-95864 - 10 
•004067 
- -002384 
•001684 
6 2 
•20649 
1-52052 
- -019041 
•009820 
- -009221 
6 4 
•24609 
4-69108 
•032054 
- -015232 
•016822 
For all harmonics higher than those of the second degree '^3 — is the coetiicient 
of stability. Since in all these cases this expression is positive, the ellipsoid is stable 
for all such deformations. 
If UbU Ije the energy function for the pear, whose vai'iations for constant 
moment of momentum are considered by M. Poincare, we have in our notation 
£,' + 5 £7 = - 1 1 + j (A, - A,) + S<«=). 
