382 MISCELLANEOUS STUDIES 



Comparison of theoretical and observed monthly temperatures at 



depths from 40 to 600 meters in the San Diego region. 

 The values computed from equation (124) and entered under the 

 observed temperatures given in table 6 are seen to agree well with the 

 mean of the observed values, thus proving the approximate correctness 

 of the form of the function deduced from theory. These computed 

 values and those from table 12 for the surface are also shown graph- 

 ically by figures 4 to 15, on which are entered a number of points 

 corresponding to actual observations (Michael and McEwen, 1915, 

 1916). 



Solution of the problem of temperature reduction due to upwelling 

 with application relative to the 40 meter level in 



the San Diego region. 

 In the relation of mean annual temperature to depth 



D =--<!> (125) 



deduced from the differential equation (80), A = -4 equals the 



velocity divided by the diffusivity, but C and D are constants of 

 integration. From observations of the mean annual temperature at 

 a series of depths these constants can be determined as was done on 

 pages 372 to 376, and they correspond to the particular physical con- 

 ditions under which the observations were made. For the same value 

 of D, the deep water temperature, but a different value of one of the 

 physical conditions, say the velocity w^ what will the temperature < 

 be? To answer this question it is necessary to know the relation of 

 each constant to the velocity w^. The relation of A to w l is known 

 and it remains to find the relation of C to u\. 



In the limiting case in which A = 0, denote the new value of the 

 constants by C", D' and A'; then expanding the exponential gives 



1 ' (126) 



where B' = C'\ r is the constant temperature gradient corresponding 

 to zero vertical velocit. 



C=-/ 1 (A) (127) 



A 



A) (128) 



where A(0) =/ 2 (0) = 1, since, as A = 0. C = C" and D= D'. 



