BETWEEN THE CONDITIONS OP A CHEMICAL CHANGE AND ITS AMOUNT. 219 



the time x. In the experiments to which this hypothesis is applicable (p. 204), the 

 value of u becomes inappreciable after the action has gone on for about six minutes, so 

 that after that time the course of the action satisfies the relation, 



or 



|(c-loga+i3a:)y=l, (15) 



{d+x)y=\ (16j 



An equation of the form (16) is satisfied by all the numbers recorded in page 203 



after ;r=6, the values of d and- being 0-1 and 167. Assuming for /3 the value "69, we 



obtain for c the value 4-68. Substituting these values in (14), we obtain the following 

 series of numbers for the values of y between 2 and 6. The earlier numbers are 

 omitted because the experimental values of y exhibit an irregularity, which is probably 

 due to errors of experiment which occur in short intervals of time less than one minute. 

 The numbers after x=&, obtained from the equation (a:+ -1)^=157, are given at p. 203. 



Considering the experimental evidence, and the fair agreement of the numbers in the 

 preceding Table, there seems to be sufficient ground for believing that in this case the 

 chemical change consists of the gradual formation of a substance which at the same 

 time slowly disappears by reason of its reaction with a proportional quantity of another 

 substance. 



The rate of formation of the substance, and the fraction (3 which is formed in a unit 

 of time, depend upon the conditions of the system, just in the same way as its rate of 

 decomposition depends upon these conditions. It would, however, be a hopeless task to 

 attempt to discover the relation between a, /3 and the conditions of the system, when we 

 have to deal with a series of complex equations like (14). This complexity explains the 

 failure to discover any simple relation in the case of the variation of sulphuric acid 

 referred to at p. 195. 



The next case to be considered is that of a system in which there are two substances 

 undergoing change in presence of a large excess of the other elements of the system. 

 If both substances are present in the system from the commencement of the change 

 and are independent of each other, the velocity of diminution of each is proportional 

 to its quantity, and their residues accord with the simple law y=ae~'" ; and if both 

 these residues are measured together, the equation of the reaction is 



y=a,e-''^'^a^e-'^, (17) 



2h2 



