516 



PROFESSOR CHRYSTAL 



Then 

 where 



4(7, -j 3a = U cos fj>-Y sin <f> , 



We find 



U = \ dw w dt n x sin n-^t sin (mt - Xw), \ 



r r 



V = I dw w I dt ?<! sin ii-yf cos (mt - Xw) 

 U = 



v= 



(55). 



sin A. cos A\4 sin 2 tt 



A 2 + ' A 



1 -0 2 



1 7T0 COS TrO I 

 T^P J 



where 6 = m/^ = T/T . 

 Hence 



dk v 



sin A cos A\4 sin 

 '~XT + ~X 



, /sin A cos A\2 sin ttO ■ . A lN 



(56), 



(57). 



The function sin A/A 2 - cos A/A has already been considered above. Its maximum 

 value (for #<7r) is "436. Also, as we have seen, the maximum value of 2 sin ttBJ{\ —6 2 ) 

 is 3-273. 



Hence the maximum possible value of dk x is given approximately by 



d\ = 2' 14a ...... (58). 



The methods of calculation which we have used for a symmetric parabolic lake are, 

 of course, applicable to any lake for which the normal modes of motion can be found. 

 All we have to do is to use, instead of the Legendrian functions, the general Seiche 

 functions, Bessel's functions, or other functions appropriate to the special form of lake- 

 basin in question. 



