446 Dr. J. J. Hood on Retardation 



solution, caused the oxidation to progress at a rate 10 per cent, 

 less than when no such salt was added ; an effect which might 

 be produced even to a much greater extent by the products 

 gradually formed during the course of any chemical change, 

 especially where the quantities of material in unit volume are 

 comparatively large, as, for instance, in the many cases of 

 etherification that have been studied dynamically during the 

 last few years, and might consequently vitiate somewhat the 

 inferences drawn from such experiments. 



As it was found in the experiments alluded to that the 

 amount of retardation was proportional to the amount of the 

 sulphate added, it would naturally be supposed that the pro- 

 ducts formed during a reaction would produce a retarding 

 or accelerating effect (for the latter is possible, as these 

 experiments show) proportional to their quantity ; and it is 

 easy on this hypothesis to introduce this effect into the 

 equations. 



Suppose in a chemical system undergoing change there are 

 n different bodies taking part in the reactions, and the mea- 

 surements that are made of the progress of the change relate 

 to one of these n bodies. Let A x , A 2 , . . . A n be the initial 

 quantities of the active substances, and at time t from the 

 commencement of the change u u a 2 , • • • a ni the quantities of 

 these that have become chemically inactive members of the 

 system, and let the measurements that are made relate to the 

 body A K . At time £ the quantities of these substances that are 

 still capable of reacting one with the other will be A x — a u 

 A 2 — a 2 , . . . A w — ot n ; and the inactive products resulting from 

 the changes that have taken place will be a x + « 2 + . . . * n . Then, 

 on the usual hypothesis that the amount of change that takes 

 place in unit of time with regard to any one of these bodies, 

 A K , is proportional to the product of the active substances, and 

 that the retardation- or acceleration-effect of the products of 

 the reaction is proportional to their amount, the equation 

 representing this would be written 



d"* — ,. ( A i" g i)( A 2"«i) • • • (A w —* n ) f 



dt~~^ B±(\ / * 1 + \"* 2 ...\ n cc n ) ' • ' V } 



where X / , X", &c. are the coefficients of retardation or accele- 

 ration of «i, a 2j &c, and + is taken according as these 

 effects are all of the first or of the second character. The 

 nature of the effect of each individual product a ly a 2 , &c, 

 whether ±, could be determined experimentally by adding a 

 considerable quantity, and noting the difference in the rate of 



