368 MISCELLANEOUS STUDIES 



However, observation shows that there is a seasonal variation of 5 

 at 40 meters and exceeding 1 at 100 meters (Murray, 1898, p. 127; 

 McEwen, 1916, p. 268) ; thus something other than the direct absorp- 

 tion of solar radiation must be the main factor in heating the water 

 of these lower levels. 



These facts show that there must be a transfer of heat between 

 the upper and lower level, but the ordinary process of heat conduc- 

 tivity, as illustrated by laboratory experiments on still water, is 

 wholly inadequate to effect this transfer at a sufficiently rapid rate 

 (Wegemann, 1905<z, 1905&). It is now generally recognized that this 

 transfer of heat results from an alternating vertical (p. 338) circula- 

 tion of the water (Helland-Hansen, 1911-12, pp. 68, 69), in which at 

 any given instant certain portions of the water are moving upward 

 while others are moving downward. The resultant flow of a given 

 column of water may be either upward or downward, or may be zero. 

 Without analyzing the complicated process by which heat is trans- 

 ferred from one level to another in the ocean, it will be assumed to 

 be similar to ordinary conduction. But the coefficient of conductivity 

 corresponding to conditions in the ocean will depend mainly on the 

 intensity of the circulation or mixing process (Gehrke, 1910. p. 68; 

 Jacobsen, 1913. p. 71), and might be called the "coefficient of con- 

 vective conductivity" to distinguish it from the ordinary laboratory 

 coefficient. In the following investigation this coefficient of conduc- 

 tivity will be used and the direct effect of solar radiation will be 

 neglected. If the resultant vertical flow is zero, the well known partial 

 differential equation 



=" 2 < 79) 



applies, where 6 is the temperature, t is the time, y is the distance 

 below the surface, and /t 2 is the diffusivity, a constant proportional 

 to conductivity. If the resultant vertical flow is w it follows, as on 

 pages 354-355 that the time rate of change of temperature due to this 



flow is ( w -] and the temperature equation then becomes 



M 9 6-e 66 , ftm 



= jr -T-T w-7- (80) 



dt dy dy 



Equation (80) is a special case of the general equation of the conduc- 

 tivity in a moving medium ("Winkelmann, 1906, p. 444). Equation 

 (79), a special case of Fourtier's equation of the flow of heat in a 



