SECT. 1] THE INFLUENCE OF ORGANISMS ON THE COMPOSITION OF SEA-WATER 51 



phosphate from sinking organic matter and the losses by eddy diffusion. The 

 steady-state equilibrium may be expressed by 



in which dQn\dt is the rate at which the quantity of phosphorus in the water 

 below unit area of the transition zone is increased by regeneration, A is the co- 

 efficient of diffusion and dNjdz is the gradient of phosphorus concentration in 

 the transition zone. 



Measurements of the assimilation of carbon in the euphotic zone over the 

 Cariaco Trench indicate that 0.48 g C/m 2 is absorbed per day. This is equivalent 

 to the production of organic matter containing 4.4 x 10 -10 mg atom/cm 2 of 

 phosphorus each second. How much of this organic matter sinks below sill 

 depth is unknown, but Riley (1951) estimates that in the sea only about one- 

 tenth of photosynthetic production sinks to decompose at depths greater than 

 200 m. Consequently we may assume for purposes of illustration that cQnjdt = 

 0.44 x 10~ 10 mg atom/cm 2 sec. The hydrographic data obtained by Richards 

 and Vaccaro show that at sill depth the gradient in total phosphorus concentra- 

 tion, dNjdz, is 0.75 x 10 -10 mg atom/cm 3 cm. Applying these values to equation 

 (2) the coefficient of eddy diffusion A is found to be approximately 0.6 g/cm/sec. 

 This estimate agrees well with values for intermediate depths in the Atlantic 

 Ocean obtained by Riley (1956) by procedures to be discussed in the following 

 section (Table XI). 



This example illustrates how a physical characteristic of the motion of water 

 may be evaluated by the use of biochemical information. 



b. The half-life period 



Estimates of the average time a constituent of the water remains below sill 

 depth in a stagnant basin may be made by dividing the content of the basin, x, by 

 the rate at which the content is changed by some measured process, dxjdt. 

 The time is appropriately expressed as the half-life period, r, which equals 

 0.693xj(dxjdt). The content of the basin is given by N -h, where N is the mean 

 concentration of N below sill depth and h is the depth of water below this level. 

 The content is changed at a rate given by dQ^dt or by A ■ dNjdz, which are equal 

 according to equation (2). Consequently, 



tjv = 0.693 ' , 7j or 0.693 



dQn/dt ' A-dNjdt 



In the case of the Cariaco Trench, N = 2.4 x 10 -6 mg atom P/cm 2 , h= 1.2 x 

 10 5 cm and dQRJdt = 0A4: x 10 -10 mg atom P/cm 2 sec. Consequently the half-life 

 period of phosphorus below sill depth, tn, is 0.45 x 10 10 sec or 142 years. This 

 estimate is subject to error in the assumption that one-tenth of the organic 

 matter produced in the euphotic zone sinks and decomposes below sill depth. 

 As an expression of the average for all depths in the water column, it un- 

 doubtedly overestimates greatly the rate of exchange of materials in the 



