OCEAN TEMPEEATUEES 373 



Let 



a = a 1 ~b- L i or a? = a^ & X 2 2a 1 & 1 i (HO) 



then 



Oi^iT W]t ^sinat (HI) 



the arbitrary constant of equation (109) being so chosen, that when 

 r equals zero, equation (111) reduces to equation (82) derived for a 

 constant velocity. 



Rearranging the terms in the exponent of e in equation (111) gives 



(112) 

 Let 



I> 1 (2fji z a 1 w 1 )=a 1 (113) 



and 



2/2 7i 2 \ / * A / "1 "1 A \ 



as before (p. 370). Substituting in equation (112) and making use of 

 the properties of imaginary exponents gives 



= M e iy ailj/t =*= sin at -sin a t 



(aj + 6^ ^^sin a#) I 



+ B cos [ajt + b,y i^-sin at) Y (115) 



where a t and &, have the values given on page 370 and A lt B l and a l 

 are arbitrary. The values 



6 t = a x = and a l = or A 



are also consistent with equations (113) and (114) and lead to the 

 solution 



D c(l e-~^r- 



IT 



where C and Z> are arbitrary constants and \ has the value 



' 



