of Oceanic Tides, 265 



guous one at a. given time. The variation (-4r)& would give 



the change of p Xi in passing to a contiguous surface of equal 

 pressure, when the change due to variation of position of the 

 surfaces in a given soiall time is taken into account. If the 

 value of jOj be the same for the two contiguous surfaces, we shall 



have ( -j± ) = 0. Now this is the case with respect to the exterior 



surface of the ocean, which is always a surface of equal pressure, 

 and of the same pressure at all times, the pressure being that of 

 the atmosphere. Consequently an equation for determining C 



should be obtained by equating to zero (-4r )> ana * putting a for 



r in the result. 



In the expression for IQ), those terms containing -rt -j-> 



and -r, which would introduce terms of the second order with 

 at 



respect to m, are to be omitted. Hence 

 Putting now for -r-, or -^-, its value 



2C ( r ~ pc) cos2 x sin 2(0-f*O> 



substituting a for r, and equating the result to zero, we get the 

 following equation for calculating C : 



or 



C = 



Smajj, 

 4R3G 



a b G 



-/, 2br>\ 



By numerical calculation made on the suppositions that a— b, 



79 



the depth of the ocean, is 3 miles, a = 3956 miles, //,= — x the 



earth's rotation in one second, 



u?a ma __m a s 1 1 



G 311-4 GR 3 E B» 70 (603) 3 



