independent of the various pressures.* Since practically, jSq = -2/3^, the response time t 

 for oxygen may be taken to be one-half that for nitrogen. Consequently, fitting a response 

 function of the prescribed form to experimental data involves the determination of a single 

 parameter only. In the discussion which follows, the observed response will be characterized 

 by giving the response time t^. for nitrogen thus inferred. 



It would be incorrect to interpret the preceding discussion as implying that the instru- 

 ment can give a significant indication only when the equilibrium condition exists. Consider 

 first the behavior where the inflowing sample contains only one dissolved gas whose concen- 

 tration is changing with time. Rearrangement of terms in Equation [1] gives the instantaneous 

 relation between the pressure P, corresponding to the instantaneous gas content of the in- 

 flowing sample, and the indicated pressure p corresponding to the instantaneous gas pressure 

 in the chamber: 



dp 

 P^p+T-£ [la] 



at 



Ideally, then, the instantaneous value of the gas content of the inflowing sample may be de- 

 termined without delay even though its value may be fluctuating in an arbitrary manner. In 

 practice, however, there is a limitation: Equation [1] assumes that the gas-space volume is 

 constant. If fluctuations in gas-space volume occur, corresponding fluctuations in the gas 

 pressure p will accompany them. Whether the extrapolation procedure indicated by Equation 

 [la] is made by the observer or by an automatic device incorporated in the indicating or record- 

 ing instrument, spurious fluctuations proportional to the time derivative of the volume fluc- 

 tuations will appear in the indication of the meter. The extent to which the lag inherent in 

 the response may be compensated depends, therefore, upon the accuracy with which the 

 volume of the gas space can be maintained constant. A reduction by a factor of 2 or 3 in the 

 response time is probably the most that can be obtained with the simple type of level control 

 contemplated for the Model Basin installation. 



♦Neither of these assumptions is strictly correct; the evolution or absorption of the two gases at rates result- 

 ing in unequal net velocities of flow into or out from the liquid surface results in concentration gradients in a 

 thin gas film adjacent to the liquid with a consequent interaction between the rates of absorption or evolution. 

 However, because of the low solubility of oxygen and nitrogen, the gradients in the gas film may be considered 

 negligible and the rates of absorption or evolution are determined principally by the liquid film. In the liquid, 

 rates of diffusion of the two gases are determined near the surface by molecular diffusion and in the interior of 

 the liquid by a combination of molecular diffusion and convection. The molecular diffusivity of oxygen in water 

 is about 10 percent greater than that of nitrogen. The convective diffusivity, if such obtains, is of course the 

 same for both dissolved substances. The assumed relation (Bt))/-. = 2(,BT))f,^ represents, then, the 



limiting condition in which molecular diffusion plays a negligible role in the "mixing" as contrasted with "tur- 

 bulent" diffusion occurring in the agitated upper portion of the film. The opposite extreme condition in which 

 molecular diffusivity accounts for the major portion of the distribution of the dissolved substance within the 

 liquid would accordingly result in the relation (BT])f-, = 2.2 (^r/).,,. . While the former condition is be- 



lieved to correspond more closely to that actually realized in the tests (except Run 1), Equation [3] should be 

 considered as a convenient empirical form rather than as one having a strict theoretical basis. 



