390 MISCELLANEOUS STUDIES 



From equation (147) 



/ s (y)=^ (150) 



and from equation (148) 



-- 5 - equals b^^-^v which gives 



(152) 



where ff z is a constant of integration. Substituting these values in 

 equation (149) gives 



(153) 

 As on page 343 



and since the change in temperature due to upwelling near the surface 



is due to the gradient- , only terms involving y should be functions 

 oy 



of w . Moreover, as w increases indefinitely the temperature at the 

 lower boundary of this upper layer should approach the constant value 



where 0' ^ \ f 



Therefore, as on page 344 



(155) 



7* 



which reduces to equation (22), (p. 344), when w = 0, except that 6. 2 

 takes the place of 0, and the average value of k 2 takes the place of 

 [&,e~ 6l<1 '~ 8) ] 2 . The latter quantities are small compared to a 2 and 

 therefore the difference between their values makes but little difference 

 in the result. This difference or error comes from the approximation 

 made in solving the differential equation (139), (p. 388). 6. 2 is found 

 by subtracting the temperature reduction due to upwelling at and 

 below the surface (3 meter level) from 3 , therefore in case of no 



