344 MISCELLANEOUS STUDIES 



temperature, time, depth, and latitude, in accordance with the assump- 

 tions and general results of temperature observations already stated. 

 The modified equation is 



1 -- 2 r , Ba a B , Ba 2 xe- 3t ( 



6= *~ 2 -- [cos (atf )!]+- X + -T-+- +0-3 



22 * 2 



(22) 

 Also from equations (19) and (20) 



B , Ba.x , B(a 1 -\-a 2 x)e-^v- a) 



cos (at ~ } (23) 



where 



a a 



tan c=-=- 



k AV 



Determination of the numerical values of the constants in the solution. 



In applying mathematical methods to physical problems the 

 functional relation between the variables involves certain constants 

 which must be determined from observed values of these variables. 

 The constants in equation (22) are 



a x a 2 a z a k l 3 B and b^ 

 Also from equation (8) we have B = . The first four constants 



cr 



are found by fitting the function 



^i [ ( a i + a 2 x ) cos - 



(equation 5) to the estimated values of solar radiation, as given for 

 example by Angot's tables (Hann, 1915, p. 40). The next three 

 require observations on temperature. For example, they can be found 

 from the observed values of the normal annual range of temperature 

 at a series of latitudes and from the mean annual temperature at 

 these latitudes. 



The coefficient of absorption ~b^ can be estimated from direct meas- 

 urements of the intensity of radiation in the ocean at different depths 

 (Grein, 1913), or from observations on water samples taken to the 

 laboratory (Petersen, 1912. p. 39). Also an indirect estimate can be 

 made from temperature and solar radiation data (pp. 350-352) by 

 means of equation (22). However, in the problem of surface tem- 

 perature in which the vertical flow is neglected the value of b^ is not 

 required. 



