OCEAN TEMPERATURES 383 



Substituting in equation (125) gives 



>'/ 2 (A) (129) 



where the forms of the functions / t (A) and / 2 (A) are to be deter- 

 mined. At the greatest depth, y l for which the theory is valid, assume 

 the temperature to have the constant value ^ for all values of A. 

 What effect will a vertical velocity have on the temperature above this 

 level? The right-hand members of the equations (126) and (129) are 

 equal for y = y 1 , since <f> 1 is assumed to be independent of A at that 

 depth, that is, 



X)=B'y 1 + D'+C' (130) 



A 



Therefore from equations (129) and (130) 



^. (131) 



Subtracting the general value of <j> given by equation (131) from 

 the particular value <f>' corresponding to the case of no upwelling 

 given by equation (126) gives 



4>'_ + = B'(y yj f/ 1 (A)(^_ e x, l)=A</) (132) 



A 



the reduction in temperature due to the upwelling velocity w r = /x 2 A. 

 It remains to determine B' and the form of the function / t (A). 



The temperature change due to the variation of velocity with the 

 time was found to be approximately 



(equation 116), where the velocity is 



w=w 1 (l -\- r'cosat) 



and the value of r in the remaining terms is neglected, for the fol- 

 lowing reasons. The values of the constants A^ and B l depend mainly 

 on the seasonal variation in temperature due to radiation; if there 

 were no such variation they would be zero, in which case the variation 

 in temperature with respect to time would be due entirely to that of 

 the wind. The temperature reduction is therefore approximately 



,_ t^lL 8 in at 



R + e^cl e 



