﻿310 Profs. J. N. Mukherjee and B. C. Papaconstantinou on 



and temperature — following each other by intervals of time 

 equal to "Si," they are each characterized by a definite 

 number and manner of distribution of particles of each 

 category (primary, secondary, etc.). Let us indicate the 

 stage of coalescence corresponding to the time " t " seconds 

 (since the sol and the electrolyte were mixed) under the 

 given conditions by the numbers 



2N, N x , N„ N ? „ . . . N* . . . , 



where the subscripts refer to the number of primary particles 

 by the union of which the aggregate is composed. Thus 

 Nfc denotes the number of aggregates, each of which is 

 composed of "&" primary particles. "A:" is evidently 

 an integer. 



Similarly let us denote the stage of coalescence corre- 

 sponding to the time t' ( = t + At) by 



, 2N', N,', i\Y, N 3 ', ... K,/ ... . 



These stages of coalescence are independent of external 

 conditions so long as equations (1) to (3) are valid. The 

 only change that external conditions can bring about is 

 a variation in the value of T — that is, if the external 

 conditions are varied the sol will always pass through the 

 same consecutive stages of coalescence and only the rapidity 

 of succession of these stages will be determined by them. 

 Any property which varies continuously with the progress of 

 coalescence without having any maxima or minima can be 

 utilized to characterize the stages of coalescence ; for each 

 value of this property is characteristic of the time that has 

 passed since the mixing of electrolyte and sol. According to 

 the equations of Smoluchowski, the times taken to reach any 

 particular stage depend only on the value of " T/' which is 

 constant under a definite set of conditions. Let us compare 

 two different electrolytes, A and B, of concentrations C\ 

 and C 2 . Let us suppose that after the time " t " the stage 

 of coalescence indicated by 



2 N, N,, N 2 , N 3 , . . . N t . . . 



has been reached when the electrolyte is u A " of con- 

 centration Ci. This stage of coalescence has a definite 

 value for the physical property we are considering, and 

 is independent of the value of T. Let us assum£ that " T l *'■ 

 and '"T 2 " are the corresponding values of "T" for the two 

 cases. To be definite, we shall consider the variation in the 



