in reference to the Theory of Ocean Currents, 195 



for the present problem 



d to __ ~d w 



~di~~l$t 

 cannot be neglected. 



The problem now is, consequently, so to define the function 

 w that, within a space bounded by two planes perpendicular to 

 the X-axis and at the distance h from each other, it satisfies 

 the differential equation 



dw "d 2 io 



S7=°§^' •■•■ W 



and the equations 



(for^ = 0)-||+^=^(0,. .-:■■■(*) 

 (fora? = /i) io = 0, (3) 



and, finally, at the time £ = takes a given initial value — thus, 



for *=0, w=f{x) (4) 



k \ 



For simplification, - is supposed = a, and j- =p. 



Hereby, however, the problem is reduced to a well-known 

 thermal problem — to the determination of the temperature in 

 a partition, of which one boundary-plane is kept at the tempe- 

 rature 0, while the other radiates freely into a medium of a 

 temperature given as a function of the time. The long-known 

 solution of this problem shall be considered in what follows, 

 in its relation to some important phenomena of ocean-currents. 



The simplest case for calculation, but practically the most 

 important, occurs when the velocity iv x of the medium in con- 

 tact is independent of the time, and the motion has become a 

 stationary one and is consequently likewise independent of the 

 time. In this case the differential equation becomes 



and is therefore free from the coefficient of friction. Its solu- 

 tion has the form 



w = a + bx ; 



and the constants are determined by the two conditions for 

 x = and x=.h ; so that w becomes 



p(h-x) f 



O 2 



=^- ph + 1 



