ANALYSIS TO THE DYNAMICAL THEORY OF THE TIDES. 
285 
from these we deduce 
log (C. 2 /C 4 ) = 27505, 
log (Cj/Cu) = T'0414, 
log (CJCs) = T-.3653. 
whence, finally 
Cg/Cg = -0014, 
CVCg = -0255, 
ayCg = -2319, 
log (Cio/Cg) = 11 1-5822, 
log (Ci2/Cio)=n 1-1994, 
log (Cji/Cio) = 712-9636, 
log (^le/C^) = « 2-7885, 
log (C^g/C^e) = n 2-647 ; 
Cio/Cg = - -3821, 
Cjo/Cg = + -0605, 
CiVCg = - -0056, 
Cic/Cg = + -0003, 
Cig/Cg = - -00002 
Combining witli our solution a second, obtained by changing the sign of i wliere- 
ever it occurs, we obtain a solution in the real form 
^ = 08 cos {\t + e) 
-OOI 4 P 3 + -0255?^ + -2319Pc + Pg 
- -382lPio + -OOOoPij - -0056Pi^ + -OOOSPjo 
5 
where Cg, e are arbitrary constants. 
This determines the type of oscillation for that particular mode which is in question. 
It will be seen that the coefficient of Pg predominates, and that consequently the 
deformation of the surface will be similar in character to that which takes place when 
there is no rotation, in which case the height of the surface-waves is expressed by a 
single harmonic term. The nodal circles will however be displaced from their 
positions when the rotation is annulled. 
§ 10 . Numerical Expressions for the Height of the Surf ace-Waves. 
By the method illustrated in the preceding section I have computed the series 
which indicate the types of oscillation for each of the forty-eight cases for which the 
periods are tabulated in §§ 7, 8 ; these series are given in the following tables. To 
obtain the height of the surface-waves, the series here given must be multiplied by a 
simple harmonic function of the time of arbitrary amplitude and phase, but whose 
period is found from the corresponding entry in the preceding tables. 
2 H 2 
