OCEAN TEMPERATURES 357 



where g, K 2 , A^ and B : are constants having the following values : 



A, = =^= and B, = =^= 



\nl 



Substituting the above value of- in equation (50) gives 



00 



Art" 



' " ' - [1 (^coirf-f^ana*)] [n 



(53) 



remembering that k equals k 1 e~ bl(y ' 3) and for depths between zero and 

 six meters the constant value y equals 6 is to be used for ?/, while for 

 other depths the actual value of the depth is to be used for y (p. 343). 

 H, the horizontal velocity, may be any function of the time, but it 

 is assumed to be independent of z and y. Having in mind a numerical 

 application to be made later it will be convenient to let H equal the 

 periodic function of the time 



H = H! ( 1 -f- 4 sin at -)- a 5 cos at) 



where H^ a 4 and a 5 are constants. Equation (53) then becomes the 

 ordinary linear differential equation of the first order in 6" and t 



# 2 r [1 



X (1 H- a t smat + a g cosaO (54) 



Solving by the corresponding standard formula we have 



X [1 + a 4 sin at -f- a 5 cos at] e kt + C \ dt (55) 



where C is arbitrary but independent of t and z. Under these con- 

 ditions Ce~ kt will evidently be included in a general solution of equa- 

 tion (51), and will therefore be neglected in the expression for 6". 

 Equation (55) can be directly integrated with the aid of well known 

 standard forms and the result for H equal to a constant velocity H l is 



H,n 



]- 



X [2ak sin a* + (A; 2 a 2 ) cos at] (56) 



