ACTION OF ENZYMES AND CELLS 179 



Nos. 1 and 2. Where a single substance undergoes change into 

 either one or two others: 1 



In words, this means that the velocity of reaction is proportional 

 to the molecular concentration, at the moment, of the substance 

 undergoing change. 



The above equation can be written 



dx 



a -x 



= kdl; 



this when integrated gives -log nat. (a - x) = kt + const., and sinco 

 when x is 0, t is 0, the constant is -log nat. a = const. Subtracting, 

 we get log nat. a - log nat. (a - x) = kt, 



a 



or log =fct, 



a - x 



and, for the value of the constant of reaction, 



1 jir 



t ct x 



The curve showing the quantity of substance changed in different 

 t tines, for such reactions in which only one substance undergoes change, 

 is accordingly a logarithmic curve. 



Such reactions are termed mono -molecular, and include all those 

 reactions induced by enzymes, in which a single substance breaks up 

 into two or more, and the quantity of ferment active throughout the 

 reaction remains constant. 



No. 3. Where two substances on the left-hand side of the equation 

 of reaction react to form two (or more) 2 substances on the right-hand 

 side. 



Here the velocity equation becomes 



1 Or indeed any number of others; the same equation would hold, for 

 example, for a triglyceride, breaking up into three molecules of fatty acid and 

 one of glycerine. This arises because there is only one substance chang- 

 ing on the left-hand side, and the back action of those on the right side is 

 negligible. 



2 As before, the number of substances on the right-hand side has no 

 effect if these do not react back on the progress of the reaction from left 

 to right. 



