OCEAN TEMPERATURES 415 



Except for the first two values of y^ near the surface, where the 

 water is most disturbed, and for the largest value of t/ 15 where the 

 difference (S 2 SJ is so small that it is subject to the largest pro- 

 portional error, the computed values of the velocity W x shown in the 

 last column are in good agreement. And the mean of the central 

 values, which are subject to the least error, is about 35, which is 

 the best estimate from the available data and agrees well with the 

 values 31 and 53 found before, page 408. 



CONCLUSION 



In the case of no average flow of the water the form of a function 

 giving the rate of gain of heat and of another giving the rate of loss 

 of heat from a small volume of water at a given latitude and depth, 

 was developed from a few simple assumptions, suggested by laboratory 

 experiments as well as field observations. Equating the sum of these 

 two expressions to the product of the specific heat by the volume by 

 the rate of change of temperature resulted in a differential equation 

 whose solution gave the temperature from the surface to a depth of 

 ten meters as a known function of time, depth, latitude, and certain 

 physical constants, under the conditions of no average flow of water. 



From observations on the relation to latitude of the mean annual 

 surface temperature and the annual temperature range and the relation 

 to latitude of the mean annual solar radiation and its annual range, all 

 of the physical constants of the formula were computed. 



The lag between the time of the temperature maxima and minima 

 and the time of the maximum and minimum values of the solar radia- 

 tion deduced from these constants agreed well with the observed value. 

 Also the mean monthly temperature at a region whose mean annual 

 temperatures agree well with the normal value for the latitude, that 

 is, the value corresponding to no average flow, would be expected to 

 agree with those computed from the formula for normal temperature. 

 A comparison of such computed and observed temperatures for a 

 series of latitudes from 20 N to 40 N indicated a very satisfactory 

 agreement. 



If the rate of change of temperature due to some factor not in- 

 cluded in the above reasoning is known this quantity can be added 

 to the differential equation already derived. Since all of the constants 

 of the original differential equation are known the solution of the 

 modified equation will give the temperature due to the new factor. 



