SECT. 1] THE INFLUENCE OF ORGANISMS ON THE COMPOSITION OF SEA-WATER 59 



horizontal advection in either layer is given by V-dN/dx, where V is the 

 velocity of flow and dN/dx is the gradient in mean concentration along the x- 

 axis. Under steady-state conditions the combined effect of the vertical ex- 

 changes balances the effect of advection in each layer so that 



Tr dN v D AdN 



for the upper layer, and 



dN L AdN 



VL '~dx~ = E ~~h~dz (5b) 



for the lower layer. The subscripts U and L designate the properties peculiar 

 to the upper and lower layers respectively. 



Combining these equations to eliminate the right-hand term, 



dN L _ V v dN v 



dx V l dx 



This states that under steady-state conditions the mean concentration of N in 

 the lower layer will increase along the #-axis as that in the upper layer de- 

 creases, and at a rate which is proportional to their relative velocities. In the 

 case under consideration the layers are taken to be of equal depth and con- 

 sequently the quantity of N present is proportional to the concentration in 

 the respective volume units. It follows that if Vu=Vl the quantity of N in 

 the lower layer increases along the x-axis at exactly the same rate that it 

 decreases in the upper layer. Consequently there will be no change in the total 

 quantity of N along the x-axis. If, as is usually the case, V u> V l, the quantity 

 of N in the lower layer will increase more rapidly than it decreases in the upper 

 layer and the total quantity present in the two layers will increase in the 

 direction of flow. 



If the flow of the lower layer is in the opposite direction to that of the upper 

 layer, V l is negative and the right-hand term of equation (5) becomes positive. 

 In these circumstances the quantities of N will change in both layers in the 

 same way and will decrease in the direction in which the upper layer is flowing. 

 Consequently countercurrent systems are particularly effective in producing 

 changes in the distribution of nutrients along the direction of flow and lead to 

 accumulation in the direction from which the surface current is flowing. 



More complete expressions of the relations of the several factors involved in the effect 

 of differential advection on the distribution of nonconservative properties along the axis 

 of flow may be derived from equations (5a) and (5b). Substituting dQ/h for dN and dQn/h 

 for R to express changes in the quantities of N rather than concentrations, the rate of 

 change along the x-axis of the total quantity of N in both layers is obtained by adding the 

 equations and rearranging the terms. Thus 



dQL + d Qy 



dx 



! -iV(tH-C¥-'-S> 



