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 £-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 2a, nine hours for the threefold 

 quantity 3^, sixteen hours for the fourfold quantity 

 4#, and in general n" hours for digesting the ^-fold 

 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 2 = art. 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 t — o y 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 jy 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. 



