8 INTRODUCTION 



of the cane-sugar, the greater is the velocity of 

 reaction. 1 



In this case we get immediately, by means of the 

 log 2-curve, a general view of the progress of the 

 reaction, and we see at once how well the law, 

 represented graphically, agrees with experience (the 

 dots in Fig. 2 represent some experiments of WIL- 

 HELMY carried out in 1850 ; the unit of time is here 

 72 min.). Another example we find in the repre- 

 sentation of SCHUTZ'S rule, which says that at constant 

 temperature the digestion of egg-albumen by the 

 aid of pepsin proceeds so that if the quantity a is 

 digested in one hour, it takes four hours to digest 

 the double quantity 20, nine hours for the threefold 

 quantity 30, sixteen hours for the fourfold quantity 

 40, and in general 1? hours for digesting the n-fo\d 

 quantity na. If we take the time, counted from the 

 beginning of the experiment as abscissa, and the 

 digested quantity y as ordinate, we get a curve (a 

 parabola) expressing that the square of y is pro- 

 portional to time, i.e. y i a"t. This curve does not 

 give a good representation to the eye. To begin 

 with, it rises extremely rapidly its tangent is vertical 

 in the point ^ = o, then it increases more slowly, 

 and at higher values of t so slowly that it seems 

 to reach a certain maximum value asymptotically, 

 which is not true. But if instead of plotting y as a 



1 It would be more exact to use natural logarithms instead of the common 

 ones. With natural logarithms the value of b (the velocity of reaction) is 

 2-3 times greater than with common logarithms, which are still generally 

 used on account of their convenience. In the following we always use common 

 logarithms. 



