SECONDARY UXDULATIOXS OF OCEANIC TIDES. 65 



dimensions of the basins, we may assnme that the rise and fall 

 of the level is uniform for eacli basin, and that in the canal 

 the level is invariable, the motion of tlie water being chieflj^ 

 horizontal. Then, denoting the areas of the basins by S and 

 S', the breadth, the depth and tlie length of the canal by 

 b, h and / respectively, the displacemeiit of water in the canal 

 along its length by ç, and the vertical displacement of the 

 surface of S and S' by -^ and 7^ respectively, the kinetic and 

 potential energies are given by 



K.E. = £^r, P.E. = ^(Sf + Sr). 



Again, the correction to tlie kinetic energy on each end of the 

 canal is nearly 



phi)-/ 3 , nb 



7t\2, ' ^ IP' 



in which ; is the wave length, if the basins are infinitely 

 wide, and may be considered nearly equal to four times the 

 leno-th of tlio basin in the direction of oscillation. 



Since S-rj=-S'fj' a nd S-fj = bh ?, 



we obtain, in the usual manner, for the period of oscillation 



/SI (, '26/ 3 , 7tb w 



(5: 



In order to test the validity of the result, several tanks 

 were made of zinc plates, two circular basins communicating 

 with each other by a canal of uniform rectangular section. 

 These were filled with water to a suitable depth and set into 

 oscillation ; the results of experiment were found to agree well 

 with the above theory. 



