OCEAN TEMPEBATUEES 369 



stationary medium, has been applied to the problem of temperature 

 distribution in the ocean by Wegemann (1905a, 1905&), using the 

 laboratory value of ft 2 , but the theoretical results were of an entirely 

 different order of magnitude from those given by observation. 



Jacobsen (1913, p. 71) has successfully applied the equation of 

 the form (79) to some data on the distribution of salinity and cur- 

 rents in the sea near Denmark. He determined /*, 2 , the Mischungs- 

 intensitdt from field observations, using the idea that salt content, 

 quantity of motion, temperature, and other properties of sea water 

 vary because of the alternating changes in the position of the water 

 particles. The writer is, however, not aware of any application of 

 equation (80) to oceanographic problems. 



Solution for the case in which the vertical flow is constant. 



If the vertical velocity has the constant value w t then we have 

 (p. 368) to find a solution of the following linear partial differential 

 equation with constant coefficients 



69 ,6 2 . 60 



f ^--\-w 1 -=0 (81) 



dt 6y 2 a 6y 



satisfying certain boundary conditions. To determine the temperature 

 at any depth, having given that at the upper level y = y 2 , we must 

 have a solution reducing to the given function of the time t (in this 

 paper it will be a periodic function of t) at the upper level and having 

 a given constant value at the lower boundary. A convenient method 

 of solution is to assume 



e==Me a V +bt (82) 



and substitute in equation (81). The result is 



& -f WJL fa 2 = 0. (83) 



Therefore e av + bt is a solution of equation (81) for all values of the 

 constant M and for all values of a and & satisfying equation (83) . Let 



a = a 1 & t i (84) 



where a i and & x are real, then from equation (83) we have 



b = [n*(a 1 * l> l *) w l a l ] [(2a lA i 2 wO&Ji (85) 



