351 



From the values of Z^e' 361 given in table 3 it follows that & t > .12 

 or e~ bl = & < .887 where {S^ equals the proportion of incident light 

 that passes through one meter of sea water. Direct observations of 

 the proportion of solar radiation passing through samples of sea water 

 taken from the Nordlichen Ostsee and the Bottensee (Petersen, 1912, 

 p. 39) give values of & varying from .60 to .86, which are less than the 

 upper limit .887 deduced from theory. 



The variation with respect to depth of the heat absorbed by the 

 water tends to maintain a temperature gradient which would be 

 greater the smaller the transmission coefficient, and the mixing process 

 tends to reduce the gradient by transferring heat from warm to cooler 

 layers. That is, the rate at which heat is supplied to a given layer is 

 equal to that due to direct absorption of radiation plus the amount 

 due to the alternating vertical circulation of the water. But the rate 

 of gain of heat was assumed in the theory to be due entirely to the 

 absorption of radiation ; and therefore the estimate of the value of the 

 transmission coefficient deduced from observed temperatures at dif- 

 ferent depths would be larger than the true value. This conclusion is 

 confirmed by the following computation, based on temperature observa- 

 tions near San Diego (McEwen, 1916, pi. 26). The general equation 

 (22) (p. 344), is of the form 



= R 1 e-Mv-s) [ cos ( a j _ )_i] +R 2 



where R t and R 2 are constants, for a given latitude. Therefore, 

 Tj^g-Ms-a) e q lia i s the half range of temperature at the surface, 

 Tj^g-Mio-3) e q ua is the half range at the depth of 10 meters and 

 [E 1 e~ & i (6 - 3) R l e- bi(10 ~ 3 ' ) ] equals the difference between the mean 

 annual temperature at the surface and at the depth of 10 meters. If 

 there is a vertical flow (p. 374) the general temperature equation 

 reduces to the same form (equation 155, p. 390), and can therefore be 

 applied to temperatures in the San Diego region. 



Substituting the observed average values of these quantities 

 (McEwen, 1916, pi. 26) gives 



R^- 31 '! = 3.15 half range at surf ace (41) 



R l6 -^ = 2.70 half range at depth of 10 meters (42) 



R l [e~ a ^ 1 e~ 76 i]=.40 difference in mean annual tem- 

 perature at surface and at 10 meters. (43) 



