﻿the Kinetics of the Process of Coagulation. 311 



total number of particles of all categories, which varies 

 continually with the progress of coalescence. Let us 

 assume that at the times " ^ " and " £ 2 " both electrolytes 

 have reached a state at which the total number of particles 

 is the same. From equation (1) we have, therefore, 



l+rp 1 + rlT 



or 



t "~ r r * 



(9) 



The general equation (3) may be written as 



n 



(i + i) 



<\* +i 



(10) 



Since n and k are constants, if ^ is constant, n k has a 



fixed value — that is, the condition -J- =J- , which is deduced 



l-i 1-2 



from the condition that ^n has a fixed value, also implies 

 that the values of n u n 2 , ft3, ... n^ are the same in both cases. 

 This means, in other words, that a definite value of %n fixes 

 unequivocally the stage of coalescence. Therefore, from 

 the deduction that the successive stages of coalescence are 

 always the same and depend only on the time, any property 

 of the sol that varies continuously can be utilized to re- 

 present a fixed value of %n or n x or a definite stage of 

 coalescence. A definite value of this property is thus 

 characteristic of the stage of coalescence. It also follows 

 from the above considerations that all curves showing a 

 variation of this property with time should be similar. A 

 deviation from this similarity, in itself, would mean that 

 equations (1) to (3) do not represent the facts. 



The absorption coefficients of gold sols for different wave- 

 lengths change on addition of an electrolyte in a complex 

 manner. The theories of the colour of these sols as 

 advanced by Maxwell Grarnett (Phil. Trans, vol. cciii. A, 

 p. 385, 1904; vol. ccv. A, p. 237, 1906) and by Mie 

 (Ann. der Phys. [4] vol. xxv. p. 377) would lead one 

 to expect that any change in the number and manner of 



