204 
Mr Gookson, The Oscillations of a Fluid 
These series are absolutely convergent but are not very con- 
venient for numerical work: it was necessary to include terms up 
to J . 
We have also 
n 
y ' — v V 
■*-71 — ■* 71—1 „ J ») 
an equation required in the calculation of B n (/ cr ). 
The formula 
T _ T T 
° 71 + 1 — ° 71 U 71 
oc 
was occasionally used as a check. 
Large-scaled graphs were drawn of J 1 (x) and of Yi (#) 
Y i \fcb) 
and the values of these functions read off them. The contour 
lines were traced by assigning a value to the constant C in the 
equation 
f(r) . cos nO = C, 
and by finding the values of 6 corresponding to an assumed r. 
Numerical Application. 
Let a the inner radius of the trough be 12 inches, 
„ h the outer „ „ „ 20 „ 
„ h the depth be \ inch. 
h 5 
Then P = ~ = o • 
r a 3 
The first thing to do is to find k from equation (9): the first 
two roots for the cases n = 0, n = 1 will suffice. 
I. n = 0 : 
II. n= 1: 
xfi = 4*758 : ^ 0 (2) = 9’449. 
= 4-824: xf ] = 9’481. 
We have therefore 
^ = 0-396: 
icq® = 0-787, 
rp (l) 
*,« = -i- = 0-402 : = 0-790. 
