18 
SIR G. H. DARWIN: FURTHER CONSIDERATION OF THE 
If allowance be made for the difference of definition adopted in this paper from that 
used in “Harmonics” as regards the second zonal harmonic, it will be found that 
a> 2 , &j ti , a> 8 , oj 10 , when set out graphically, fall into an evenly flowing curve. The 
corresponding test for the p’s is not quite so convincing, hut there is nothing which 
implies a mistake. The values of p 0 , p 2 , p 4 , p 6 fall well into line, and so do p 4 , p ti , p 8 , p m 
hut there is a gentle elevation in the neighbourhood of p 6 . In consequence of this 
slight waviness of the curve I recomputed the whole again independently, after it had 
been recomputed and verified once, and special attention was paid to and p 6 . 
§ 5. Final Synthesis of Numerical Results , and Conclusion. 
The several numerical values are combined just as in the original paper, but the 
numbers, of course, differ a little from those obtained before. The following table 
gives the final stage, inclusive of the additional terms now computed :— 
. 
6*. 
(1) 
b, 4 
(4 
BfjCf. 
2 0 
+-000138868 
- -000219736 
- •000080868 
- -12382 
2 4 
•000000717 
+ -000000970 
+ -000001687 
- •0S056 
4 0 
•000092542 
•000154732 
•000247274 
+ -06273 
4 2 
•000001908 
•000001190 
•000003098 
- •000355 
4 4 
•000000012 
• 000000000 
■000000012 
+-0000017 
6 0 
•000031204 
•000031146 
• 000062350 
+-019564 
6 2 
•000003422 
•000002107 
•000005529 
--000229 
6 4 
•000000014 
•ooooooooo 
•000000014 
+ -0000003 
8 0 
+-000012905 
•000006671 
•000019576 
+-007505 
10 0 
- -000001030 
+ -000007358 
+ •000006328 
- -00667 
Sum = 
•000265000 
a 3 [A(cr 2 ) 2 + 2<: 4 ]-i<r 4 = 
- -000500513 
Numerator = 
- -000235513 
I then find log D = 9 - 9840165, log L = ’6454565, log M— ‘9591963. From these 
we find c = L6 2 , t) = Mf ?; whence 
B, , 
- -0553908 
C 
It? „ 
•0008037 
t) = 
•0316007 
Denominator = 
- -0229864 
