G INTRODUCTION 



only So per cent of So, i.e. the quantity 64 per cent, 

 remains ; after the time 3^ (3 hours) So per cent of 64, 

 i.e. the quantity 51-2, remains of the sugar; after the 

 time 4/ (4 hours) So per cent of 5 1 -2, i.e. the quantity 

 40-96, and so forth. We say then that when time 

 increases in an arithmetic series, the quantity of 

 cane-sugar decreases in a geometric series. If the 

 quantity of cane-sugar is called z and the quantity 

 at the beginning of the experiment r (we have in 

 this case put = IO ), tnen tne sa id ^ aw regarding 

 the progress of the inversion of the cane-sugar with 

 time, /, is expressed by means of the formula 



log z Q log z = bt. 



For the time / = o, i.e. when the sulphuric acid 

 is added to the solution of cane-sugar we have 

 log ZQ = log 2, i.e. z = z^= 100. 



Now if we translate the said law into a graphical 

 expression, we get the r-curve as a function of the 

 time / (Fig. 2, the lower curve). This --curve is a 

 so-called exponential curve. Even to an eye ac- 

 customed to curves it is rather difficult to distinguish 

 this exponential r-curve from another curve indicat- 

 ing a regular decrease of the quantity of cane-sugar, 

 z, with increasing time, /. The curve does not tell 

 us very much in its general character ; only if we 

 measure special points on it, and determine cor- 

 responding values of .~ and /, do we get a real 

 representation of the meaning of the curve. In 

 this case a table giving the comparison of calculated 



