SECT. 1] THE INFLUENCE OF ORGANISMS ON THE COMPOSITION OF SEA-WATER 67 



such a case is much more complicated, but it has been attempted in one case, 

 that of the distribution of oxygen, phosphate and nitrate in the Atlantic Ocean 

 by Riley (1951). This remarkable paper, which requires and deserves careful 

 study, develops as well a comprehensive account of the physical circulation. 



Riley's procedure is to construct a mathematical model to which equation (1) 

 can be applied. 



Equation (1) is converted to finite difference form to read: 



1 (A x AX X A. x AN- X \ . I (A u AN U A- v AN- 



8N t 



R] L A X 4JS X A-i/W-A l_ U y AN y A- y AN- y x 



Ax \ p Ax p Ax J Ay ' p An p Ay j 



1 (A, AN Z A- z AN- Z \ l / AN X AN- X \ 



+ Az\ P ' Az" P ' Az J 2V x "A~x~^ [ - x '~Ax~) 



1 (r ANy i r AN -y\ l (v AN *+v AN ~*\ 



Nq is the concentration at the center of some specified volume unit, N + AN is the con- 

 centration at the center of the adjoining volume unit and Ax, Ay and Az are the distances 

 separating the centers along the specified axes. When the centers on any axis are equi- 

 distant, AN x jAx, etc. represent the gradients and A x , V x , etc. represent average values 

 of the physical coefficients between successive centers. A steady state is assumed, in which 

 case the array of terms on the right-hand side of the equation equals zero. 



The surface of the ocean between 63°N and 36°S is divided into rectangular areas 

 1000 km on a side and the water column under each area is subdivided into unit volumes 

 separated by surfaces at intervals of 0.2 at units. To the center of each of these volumes 

 representative values of the items — temperature, salinity, oxygen, phosphate and nitrate 

 — are assigned, based on oceanographic data. The result is an array of data, distributed 

 geometrically in the horizontal and so that each vertical series lies between the same at 

 surfaces, which defines the values of the gradients AN X /Ax, etc. 



The physical coefficients A x , V x , etc. are evaluated from the data on temperature and 

 salinity. Relative values for the velocity of flow in each at surface are obtained by applying 

 standard procedures of dynamic oceanography to the distribution of temperature and 

 salinity. From these the relative transport between the at surfaces is then derived by 

 taking account of the difference in their depths. These relative values are adjusted to 

 accord with the principle of continuity to give absolute transports such that the total 

 flow across the southern boundary of the array as a whole is zero. Reversing the pro- 

 cedure the absolute values for the velocity of flow, V x , etc., are obtained. From these 

 values the advective terms of the equation may be evaluated for each volume unit. 



The coefficients of eddy diffusion, defining the exchange of water across the boundaries 

 of the unit volumes, are obtained by applying the relaxation method to the salinity 

 distribution. It is assumed that a steady state exists, in which case the quantity of salt 

 entering each unit volume must equal that leaving. The boundary conditions require that, 

 in the array as a whole, this equality shall apply also to the exchange across the southern 

 boundary. Provisional values are assigned to the coefficients of vertical and horizontal 

 diffusion until this condition is met within each unit volume when the advective terms 

 are taken into account. Certain simplifying assumptions are made, including the effect 

 of stability and shear on the vertical diffusivity, for which the original paper may be 

 consulted. 



Average values for the coefficients of horizontal and vertical diffusivity obtained are 

 given in Table XI. These coefficients vary somewhat from one area to another. 



By these procedures all the terms defining the motion of the water are determined and 



