VELOCITY OF REACTION 195 



that is, it shows a stage when x is small where the reaction is linear, 

 a stage where the reaction is more rapid than the simple logarithmic 

 law demands, as in Henri's own experiments, a stage showing a falling 

 off from the logarithmic values, as in the later stages of the experiments 

 of Armstrong and of Bayliss, a zero stage at the equilibrium point, a 

 reversed velocity, which also at the very end tends to become linear. 



To make the investigation of the equation easier, 1 we may suppose, 

 since Henri found experimentally that the value of e was approxi- 

 mately unity, that e = e 1 = l, when the equation becomes 



dx 



This may be written 



and in this form we may now investigate how the velocity that is, the 

 value of ^ will vary at different stages of the reaction. 



First, let the value of x be small compared with a as in the earlier 

 stages of the reaction, then x 2 and higher powers of x may be neglected 

 as small magnitudes of the second or higher orders and the equation 

 reduces to 



dx 7 . 



,- = k (a -x)+x.k 1 = ak v 



That is, the velocity of reaction is constant, and the curve expressing 

 it is linear. 



Secondly, for higher values of x (that is, later in the reaction), but 

 where x is not yet large compared to (a - x), since k 2 is small com- 

 pared to /q, k 2 x 2 is small compared to k^a - x) and may be neglected 

 when the formula becomes 



This may be written 



dx 



x\ 



) [d, 



a) v 



which is Henri's formula that is to say, during this period when k 2 x 2 

 is small compared to k^(a - x), or, in other words, when reversion may 

 still be neglected, Henri's formula holds. The curve of velocity shows 

 a greater value than is given by the simple logarithmic law, and the 



1 The same results follow with the formula as it stands, only the expressions 

 are more complicated. 



