376 Proceedings of the Royal Society 
Operating now on this in the usual manner we find 
4 y> -P -o 
a L 
> 7 O J 
w 
Q 8 
P’ a » ~ 9 
• • ( 10 ) ; 
whence by expanding the determinant and removing the superfluous 
factor 8, we have 
which gives 
J!_ + ^ + £! + r? = 0 . 
aWtif a 2 6 2 c 2 
; 2 / 
where t denotes J -l. 
And from the second and third of (9) we have 
9 
which gives 
S 2 , 2 “ a 8 “ o 8 
^2 + a a ^ + 7^2 
o , s n 8 
a^ + y_ 
^ = £— p , and^ = £ 
6 2 c 2 
+ or 
8 2 
5 2 c 2 
(ii), 
| (12); 
• (13), 
• (14). 
+ a^ 
In virtue of (12) we may take as the solution for any one of the 
coordinates, £ for example, as follows — 
£ = A cos wt \ 
where <0 = 2 
and from this (14) gives 
2 / p N2 
c 2 + a 2 
H„7Tf)] 
(15); 
a/3 COS co£ — -A a) sin coif 
9 = a- 
ycr COS (at + co Sin oo£ 
6 2 C 2 
/? 
r (16)- 
S = A- 
»2 — 
6 2 C 2 
