OCEAN TEMPERATURES 343 



Corresponding to the time of year t when the surface temperature 

 has the minimum value equation (13) becomes 



P O = 1- 6 l j- T- \- - (18) 



Since the coefficient of cos (at e) is negative (see p. 341) cos (oi e) 

 must equal plus 1 ; therefore from the seventh general statement 

 (p. 339) 



1= * t _:*^dbd^ (19) 



Vo. + " 



where 3 is a constant. 



Making use of the results just found equation (13) becomes 



[cOs(a*-e)-l]+^+r +*3 (20) 



where 



The small variation in temperature with respect to depth in the upper 

 six meters indicates that these upper water layers are very thoroughly 

 mixed (Michael and McEwen, 1915, 1916). Accordingly temperatures 

 in this 6 meter interval will be computed by using 3 meters, the 

 average value of the depth. That is, (y 3) will be substituted for 

 y when the depth exceeds 6 meters and the constant value (6 3) =3 

 for all depths between and 6 meters. From equation (20) it follows 

 that at the time of minimum temperature the temperature is inde- 

 pendent of the depth y in accordance with the seventh general state- 

 ment (p. 339). But the latitude gradient which is the part of the 

 coefficient of x in equation (20) not involving the time is 



Bo,* e~^ lV Ba, 



. - _ _ I 7 ' 



This is not in accordance with the observed fact that the latitude 

 gradient is independent of y; but the relative error will depend upon 

 the ratio of the first term to the second term, and may not be important. 

 As will be seen later (p. 345) it proves to be a negligible error if we 

 add to $t of equation (19) the term Boxe- 



Therefore equation (20) with this modification and the use of (y 3) 

 for the depth y gives the approximate form of the relation between 



