384 MISCELLANEOUS STUDIES 



where R is the constant average reduction. A variation of the velocity 

 from its minimum to its maximum value, that is, from to 2u\ as at 

 varies from to 2* produces a variation of temperature reduction from 



to 



l 



that is, as the velocity varies from to 2w l the temperature reduction 

 increases by the amount 



n \,.f X>) 



= CeMe e 



from which the temperature reduction due to the velocity w l is 



(133) 



The approximate temperature reduction deduced by two inde- 

 pendent methods is given by equations (132) and (133), respectively. 

 Equating these two values and using equation (127) gives 



(134) 



Solving for the unknown function / t (A) gives 



A(y yj 



y-r 

 f ^il 



(135) 



Since A is assumed to be independent of y, the variation of the 

 right-hand member of equation (135) with respect to y is a measure 

 of the error in the two expressions for A<. Also a comparison of the 



AC 



theoretical temperature gradient, '=: ^--^-- (equation 126), which 



/i(A) 



would be expected in case of no upwelling with observations of deep 

 water temperature in such regions affords an additional test of the 

 theory. The following values of the constants of equations (125) and 



