CONTENTS 



PAGE 



Introduction. The place of mathematical methods in researches on oceano- 

 graphic problems 337 



Solar radiation and surface temperature, assuming the average rate of flow of 

 the water to be zero : 338 



Preliminary discussion, and statement of certain generally accepted 

 conclusions as to the process by which the water gains and loses heat 338 



Statement of assumptions, mathematical formulation of the problem and 

 its solution 339 



Determination of the numerical values of the constants in the solution.... 344 



Observed and theoretical lag of temperature maxima and minima behind 

 the radiation maxima and minima; comparison of computed and 

 observed normal temperatures 348 



Numerical estimates of the coefficient of absorption of solar radiation 

 in sea water 350 



Deduction of the change in surface temperature produced by a horizontal flow 

 of water 352 



Preliminary discussion, statement of assumptions, and mathematical 

 formulation of the problem 352 



Solution for the case in which the flow is constant 356 



Solution for the case in which the flow is a periodic function of the time.... 359 



Solution for the particular case in which the time interval is so small 

 that the solar radiation may be assumed to depend only upon the 

 ' latitude 360 



The rate of horizontal flow in the North Pacific off the California coast from 

 latitude 40 N to 30 N and in the North Atlantic off the west coast of Africa 

 from latitude 30 N to 20 N 362 



The rate of flow off the coast of California deduced from surface tem- 

 peratures 362 



The rate of flow deduced from temperature data compared with that ex- 

 pected from the empirically ascertained relation of winds to currents 

 and with direct observations on currents \ 363 



The surface current prevailing for a short time interval near the north- 

 west coast of Africa, estimated from surface temperatures, com- 

 pared with direct observations and with results deduced from the 

 empirically ascertained relation of winds to currents 364 



