JOHN H. NORTHROP 251 



Solving this equation for Q we find that 



-V( 



and since it is assumed that the velocity of the reaction is proportional 



toQ 



dx ^X I ^ , Ti Qi 



—r oc — - oc — oc y and v;r « -S- 

 dt AT T ^ Ti Qi 



All the values in the above equations are known (in arbitrary units) 

 except d and K. If more than one experiment is made it is therefore 

 possible to solve for these two values, and then compare the calculated 

 and observed values for Q. When this is done it is found that below 

 a certain value for d, K is negative while above a certain limit the 



value of — becomes constant owing to the fact that one of the terms 

 d 



of the equation becomes negHgible when d is too large. It is also 

 found that the constancy of K is very sensitive to experimental error 

 (as was to be expected since it depends on the difference between 

 two experimental values), so that a comparison of the observed and 

 calculated values of Q is a better test of the formula than the constancy 

 of K. Between the two limits for the values of d there are several 

 values all of which give values of K which permit the calculation of the 

 experimental results. The smallest of these has been taken. This 

 gives a value for K of 0.1 and for P (in the particular inhibiting 

 solution studied) of 10, both expressed in the same arbitrary units 

 (cf. Euler and Svanberg* for a discussion of the same equilibrium with 

 invertase, and Northrop-' in the case of pepsin). It will be noted 

 that the expression for the equilibrium as used in this form contains 

 two arbitrary constants; i.e., it is necessary to make two determina- 

 tions before the others can be calculated. The agreement between 

 the calculated and observed values is close enough to leave little 

 doubt that the formula correctly expresses the facts, but the presence 

 of two constants renders it possible that the agreement is accidental. 

 If this were the case we should expect to find that it was necessary 

 to use different values for K and d in each set of experiments. This 

 is, however, not the case. All the experiments were found to agree 



* von Eulcr, H., and Svanberg, O., Fermeniforschimg, 1920, iii, 330; 1921, iv, 142. 



