﻿38 Messrs. W. J. Jones and J. R. Partington on a 



In this equation ex! is small compared with 7^-, and thence 



Jci may be neglected in comparison with Ic. Equation (12) 



then reads : 



r/T T 



= (13) 



lr kr*—! 



By integration of (13) we obtain the equation on which 

 the theory of supersaturation now proposed is based : 



T=( 'fi^) • < 14 > 



If X is positive, i.e. when heat is absorbed on dissolution 

 of the solid in a nearly saturated solution, then the expression 



., ^1. If r is diminished, the corresponding value of T 



is also diminished. If, on the contrary, X is negative (i. e. heat 



is evolved on dissolution), then — rr~ > 1? an d in this case T 



increases when r is diminished. 



Ordinary supersaturated solutions belong to the first type. 

 An example of the second type (X <z 0) is furnished by a 

 normally saturated solution of gypsum. 



The constant C in equation (14) denotes the temperature 

 at which the given concentration is equal to the concentration 

 of the normally saturated solution, since when r = 00, then 

 T=C. 



The spontaneous crystallization of supersaturated solutions 

 of the first type, when they are cooled below a certain tem- 

 perature, remains to be explained. In the sense of the 

 theory described above, the size of the particle required to 

 induce crystallization is smaller the lower the temperature. 

 It may therefore be assumed that at a sufficiently low tempe- 

 rature the necessary size is only a relatively small multiple of 

 the molecular size, an assumption which becomes more pro- 

 bable from the following considerations. In order that a 

 particle of this size may be produced in the solution itself, 

 it is obviously necessary that several molecules shall simul- 

 taneously collide inside a small element of volume. This 

 leads directly to the hypothesis of de Coppet *, according 

 to which the formation of crystals is dependent on a 

 " favourable collision " of the molecules concerned, and such 

 " favourable collisions " occur all the more frequently the 

 further the solution is removed from its state of normal 

 saturation. An estimate of the size of particle required can 



* Ann. ehbn.pliys. (5) vi. p. 275 (1875). 



