190 
MR. G. H. BRYAN ON THE WAVES ON A ROTATING 
where 
0U 
dt 
- 2coV == 
0V 
dt 
0W 
0^ 
-}- 2(»XJ — 
h?; i 
d-yjr 
( 1 ). 
(Si)- 
We have also the equation of continuity, 
0U 0V 0W _ 
0.r 0y dz ~ 
(3). 
Eliminating U, V, W from equations (1), (3), we obtain the differential equation 
02 
0^2 
vV + = 0 
(i), 
where, as usual, stands for Laplace’s operator d'^jdx^ + 
3. Let us now consider separately the simple harmonic oscillations of’one particular 
period. Assume that U, V, W, and xfj all vary as so that the ratio of the period 
of oscillation to the time of a complete revolution of the liquid mass about its axis is 
i/2/c. The equations (1), (4) reduce to 
2a; (ikU - V) 
2a; (lkV -h U) 
2colkW 
B-yfr 
dx 
0 ^ I 
0y ’ r 
d\Jr 
87 
( 5 ). 
0h|/ ^ / _ 1 \ ^ 
0;c2 df 022 “ 
Put 
and 
Equation (6) now becomes 
T 2 
1 — , = T- 
K“ 
Z — TZ 
02'v^ , d~\Jr I 
( 6 ). 
("). 
(8). 
