196 EXPERIMENTAL OBSERVATIONS ON 



"constant" calculated on the simple logarithmic basis will increase in 

 this stage of the reaction, while a " constant " calculated on the above 

 formula will remain approximately constant. 



As x goes on increasing, however, the value of k 2 x 2 will cease to be 

 negligible as compared with k^a - x), and in the end k(a - x) will 

 become less than k 2 x 2 , when the expression within the square brackets 

 will become negative in value. Just around the point where k 2 x 2 = 

 k^a -x), the simple logarithmic law will approximately hold, for then 

 the expression in square brackets will be almost zero and negligible in 



dx 

 comparison to k^a-x), so that the equation becomes jj=k 1 (a - x), 



which yields the simple logarithmic formula. But as x goes on increas- 

 ing, and a - x diminishing, it is obvious that the negative value of the 

 expression in square brackets will rapidly increase, and that the reaction 

 will proceed much more slowly with ever-increasing deviation from the 

 logarithmic law. 



Finally, the reaction will come into equilibrium, and beyond this 

 point will be reversed. 



For the reversed reaction near the end-point, since a - x is small 



compared to x and hence - = 1, the equation becomes j^ = k 2 a 2 } or the 

 x at 



velocity of reaction is constant and the curve expressing it a straight 

 line as at the beginning of the reaction. Since, however, the whole 

 of the reversed stage is short, and an appreciable amount of a - x 



dx 

 relatively to x is soon formed since the reaction runs -,. k 2 x 2 , and x 



is here large, the straight line portion on this side is infinitely short 

 and cannot be demonstrated experimentally. 



The equation given above hence serves to demonstrate that the 

 law governing the reaction is the same throughout, and that the 

 deviations from the logarithmic law arise from the assumptions having 

 been made in the derivation of that law (1) that reversibility can be 

 neglected, and (2) that the intensity of action of the enzyme, per 

 molecule of substratum, can be taken as constant throughout the 

 reaction. 



EFFECTS ON VELOCITY OF REACTION OF ALTERATIONS 

 IN THE CONCENTRATION OF ENZYME. 



The effects of variation in the amount of enzyme initially added 

 upon the velocity of reaction, in the case of the sucroclastic en- 

 zymes and of trypsin, have been already mentioned in describing 



