SECONDARY UNDULATIONS OF OCEANIC TIDES. 67 



whence the equation of motion are at once written down ; 



X X-X' 



.V /X'-X X' 



Eliminating X', and putting X-—e'^'^, we have 



If we put S'-mS, c' = nc, then 



2.T l~(fc~ 



where ^ = l^n-\ — . (i^n)- + — + — ^ ^ ; 



my 111- m 



whence the vahie of T can be obtained. It m=n=l, (p=?j±i/5. 



The case, in which both ends of the dumb-bell shaped 



bay open to the sea, can also be treated in a similar manner. 



§ 7. THE METHOD AND THE RESULT OF 

 CALCULATION FOR THE PERIOD OF OSCILLATION. 



In the calculation of the period of oscillation in a bay by 

 the simplest formula, it is necessary to evaluate the length 

 and the mean depth of the bay from the charts ; the charts 

 used were those published by the Hydrographical Section of the 

 Naval Department. As the mean depth, we took the ratio of 



