STABILITY OF THE PEAR-SHAPED FIGURE OF EQUILIBRIUM. 
15 
The series of values °A 0 2 " were also computed independently from the series given 
on p. 537 of “ Harmonics.” 
A little consideration will show that the differences of the series of functions Q A 2 , 2n , 
with the signs of the odd differences changed, gives the series of functions 2p A 2 J n . 
Stated analytically 
(— ) r A'' °A 2m 2p ~ 2r = 2r A 2 , 2p ~ 2r . 
A table of the natural numbers °A 2m 2il is given, but the table of differences is not 
reproduced. 
The following is the result of the recomputation :— 
Table of the A Functions (Natural Numbers). 
n. 
0 A 0 «. 
°A 2 n . 
°A 4 m . 
°A g A 
0 
' 2-7024906 
8•034600 
30-53878 
132-38251 
2 
■ 9505345 
1-4779482 
2-866414 
7-149917 
4 
• 6559354 
•8294118 
U1590804 
1-8826818 
6 
• 5285432 
•6160958 
•7537022 
•9929042 
8 
•4543269 
•5084364 
•5844941 
•6987687 
10 
•4044492 
•4419004 
•4909693 
•5582507 
12 
•3680175 
•3958484 
•4306317 
•4755180 
14 
•3399181 
•3616261 
•3878603 
•4203234 
16 
•3173978 
•3349328 
•3556021 
18 
•2988272 
•3133708 
•3295135 
20 
•2831734 
22 
•2697454 
Table of Logarithms of the O Functions. 
n. 
log % n . 
log R 2 ”. 
log 
log Sl 6 n . 
0 
•2047610 
1-0302912 
1-8667641 
2-7138144 
2 
9-8993673 
•7715375 
D6492558 
2-5319084 
4 
9-7729862 
•6613000 
1-5528790 
2-4473549 
6 
9-6930884 
•5897701 
1-4886134 
2-3893880 
8 
9•6346685 
•5365117 
1-4398970 
2-3446714 
10 
9-5886267 
•4939849 
1-4005014 
2-3080689 
12 
9•5506357 
•4585472 
1-3673618 
2-2769972 
14 
9-5182995 
•4281522 
1-3387296 
2-2499642 
16 
9-4901531 
•4015325 
1-3135070 
18 
9-4652355 
•3778480 
1-2909612 
20 
9-4428427 
•3565096 
1-2705764 
22 
9-4226147 
The results in the original paper were not so accurate as I had thought they were. 
There was a mistake in the differences which give the H 6 series, affecting the values 
from n = 10 onwards, but as no use was made of the series as published, the 
mistake did not affect the final result. 
