OCEAN TEMPERATUBES 339 



or downward. That is, at the same time, some portions of the water 

 are moving upward and others downward, thus tending to mix up the 

 water at different levels. In this problem the resultant of the upward 

 and downward flow will be assumed to be zero. 



4. This "mixing process" is most intense in the layers nearest 

 the surface, owing to wave motion and other surface disturbances due 

 to wind, but is present in some degree at all depths (Gehrke, 1909, 

 p. 12, Murray, 1898, p. 127). 



5. The amount of heat transferred from one level to another by 

 conduction through the water is a negligible fraction of that carried 

 by the water particles themselves as a result of the mixing process 

 (Gehrke, 1909, p. 12). 



6. The mean annual rate of change of temperature with respect 

 to latitude is practically independent of the depth within the upper 

 hundred meters. This is revealed by a study of the average tempera- 

 tures of the North Pacific, tabulated with respect to latitude, longitude, 

 and depth (Schott, 1910, p. 14). 



7. At the time of year when the surface temperature is a minimum 

 there is practically no variation of the temperature with respect to 

 depth in the upper thirty meters (McEwen, 1916, p. 272). 



Statement of assumptions; mathematical formulation of the problem 



and its solution. 



Let K l /! (L, t] equaZ Q^ the amount of radiant energy available 

 per month per unit area of horizontal surface at the latitude L and 

 time t, where K l is proportional to the solar constant and f l (L,t) 

 is a function of the latitude L and the time t. Let Q equal the amount 

 of radiant energy used directly in heating the water, that is, the 

 amount passing into the water. Also let 



y equal the distance in meters from the surface of the water, the 



positive direction being downwards, 

 a equal the specific heat of sea water per unit volume, 

 & equal the temperature, centigrade. 



t equal the time, the unit being 1 month, and t equal 1 for January, 

 1 equal a temperature assumed to depend only on the latitude and 



depth y, and 

 /?! equal the average transmission coefficient of sea water for the 



solar radiation, that is, the proportion of radiation at any level 



that passes through unit thickness of water measured from that 



level. 



