474 On the Laws of Connexion, fyc. [Nov. 16, 



stant, which depends upon the conditions under which the change takes 

 place. From this equation is derived dy ctydz, which expresses the fact 

 that the amount of change varies directly with the time and with the quan- 

 tity of substance. 



Cases of complex chemical change can be investigated by the application 

 of this general law. When two substances are reacting in proportional 

 quantities, the amount of change is proportional to the amount of each, and 

 the equation for determining the character of the reaction is dy <xy^dx, or 



- -- = -, where a is the quantity of substance present at the beginning of 



the change. If a is very large, the equation reduces to xy=b, i. e. the 

 quantity of substance remaining unchanged varies inversely as the time. 



It is shown that the complexity of the results obtained in the experiments 

 on the decomposition of potassic permanganate is probably due to the fact 

 that there are two substances undergoing change, and that one of these 

 substances is gradually formed from the other. The equations for deter- 

 mining the character of this reaction are 



From these equations are derived 



0)- 



(1) 



(3) 



where u is the quantity of one substance decomposed at the rate a, v the 

 quantity of the other substance formed from u at the rate ft and decomposed 

 at the rate y, y the whole quantity of substance capable of change, a the 

 quantity of substance present at the beginning of the change, and x the 

 time during which the change has been proceeding. Equation (3) admits 

 of the forms 



y = ( 



according as a is > = < y. By varying continuously one of the conditions 

 of the reaction, it is possible to obtain in succession values of a and y, such 

 that a is first > y, and then = y, and finally < y ; and thus these three forms 

 of curves may occur in an investigation on the effect of varying one of the 

 conditions of a reaction of this kind. 



