Oscillations of Rotating Water. 113 



zero. Hence the oscillations of water in a rotating rectangular 

 trough are not of the simple harmonic type in respect to form, 

 and the problem of finding them remains unsolved. 



If <» = 0, we fall on the well-known solution for waves in a 

 non-rotating trough, which are of the simple harmonic type. 



I b. Waves or Oscillations in an endless Canal with straight 

 parallel sides. 



For waves in a canal parallel to a } the solution is 



7i =H€-^ cos (m#—<rt); .... (12) 



where I, m, a- satisfy the equation 



2 , 2 O- 2 — 4ft) 2 /1QX 



m gB ' < 13) 



in virtue of (9) or (11). 



Using these in (7), we find that v vanishes throughout if 

 we make 



l= 2 -^; . . . (14) 



and with this value for I in (12) we find, by (7), 



M=H^e-^cos(mo; — at); . . . (15) 

 and using (14) and (13) we find 



m *=£>> ( 16 ) 



from which we infer that the velocity of propagation of waves 

 is the same for the same period as in a fixed canal. Thus the 

 influence of rotation is confined to the effect of the factor 

 e- 2(aml<r -y. Many interesting results follow from the interpre- 

 tation of this factor with different particular suppositions as to 



— ), the 



period of the rotation ( — J, and the time required to travel at 



the velocity — across the canal. The more approximately 



nodal character of the tides on the north coast of the English 

 Channel than on the south or French coast, and of the tides 

 on the west or Irish side of the Irish Channel than on the east 

 or English side, is probably to be accounted for on the prin- 

 ciple represented by this factor, taken into account along with 

 frictional resistance, in virtue of which the tides of the English 

 Channel may be roughly represented by more powerful waves 

 travelling from west to east, combined with less powerful waves 



