402 MISCELLANEOUS STUDIES 



where C 2 is a constant of integration corresponding to a given stream 

 line. From equation (185) the upward flux through a horizontal area 

 of unit width and length z measured perpendicularly to the coast is 



r W dz=^ 



Jo 



[cos A e" ay cos (az -f -, u \~, i ngo) 



Rembering that /(O) =0 and /()=! as z = 



\ 



I/O 



[cosA e-^cos (ay + A)]/() 



jy^ 2 __ L ^^_ vv> (190) 



and that the maximum numerical value for a given value of y is 



I 



Wdz = - V [C S A ~ e '" V e (191) 



which approaches the value - ( ^) as V increases, the ratio R 



of the upward flux through a horizontal area at the depth y of unit 

 width and length z measured perpendicularly to the coast to the total 

 upward flux is 



I 



J 



Wdz 



[cosA 



V cos A cos A 



Therefore the parameter C 2 in the equation of the stream line (equa- 

 tion 188) equals the ratio R multiplied by cos A, and the flux between 

 any two adjacent stream lines of a series in which the increments of 

 C 2 are equal is constant. 



The mean w r ind velocity of the 5 degrees square of the U. S. Coast 

 Pilot Charts (Moore, 1908-11) west of San Diego was found to be 

 about fifteen miles per hour in a southeasterly direction, approxi- 

 mately parallel to the coast. Therefore for the San Diego region the 

 angle A in equation (185) is zero, and the vertical velocity at the 

 depth y is, from equation (185), proportional to [1 e-" v cosay] 



where a= ^ = ^ (p. 398). The values of this function are tabu- 

 D 75 



lated with respect to depth in table 13. 



