OCEAN TEMPEBATUBES 413 



Let 



flf.^ + AS, 



and 



8 4 = l3i + St (217) 



where $! is the constant mean salinity for the prismatic volume from 

 the surface to the depth y^ and A$ 3 and A$ 4 are variable increments. 

 Then equation (216) becomes 



r.W^A + 8 A fVtdA t fv s dA 3 I 



0, (218) 



and substituting the value of 



from equation (215) we have 



W 1 = ^ 1 = (219) 



where (AS') is defined on page 411, and finally, substituting for V 

 the value given by equation (208) 



V f(z) 



j (Aflf' 



r 1 (8 2 8 l ) r l (S 2 S 1 ) (220) 



If the depth of the upper section is at the level y 2 we must sub- 

 stitute j/ 2 for y t and r 2 for r x in equation (220), which then becomes 

 identical with equation (211). But in equation (220) y l can have 

 any value between the limits, zero and j/ 2 , where y 2 is the depth of 

 minimum salinity, and estimates of the velocity based on different 

 values of y 1 should give the same result. Some divergence of these 

 values in any actual case is to be expected, since the different esti- 

 mates are based on different observations that are subject to errors 

 of measurement and since the actual relation of the velocity to depth 

 may differ from the theoretical relation (p. 403). 



In table 18, where V = 324000 (p. 404) and E for the latitude 

 of San Diego is .0754 meters per month (Schmidt, 1915, p. 121) are 

 presented the results based upon the mean value of (AS'), that is, 

 half the value entered in table 17, the mean annual salinities as shown 

 by plate 11 and table 3 (McEwen, 1916) and the values of r x and 

 /(10) from tables 13 and 14. 



