Kinetic Theory of the Ideal Dilute Solution. f>21 



But taking v as a vector, the complete expression for accelerating 

 force is 



where the second term expresses v dm/dt. 



For transverse acceleration, m is constant because speed is 

 constant, the second term is zero, and the transverse inertia 

 is simplv as above. For longitudinal acceleration, however, we 

 must use the full expression, which writes itself algebraically 



- c - V(1-^)V l-v 2 Jdt 

 o - i dv 



and the coefficient of dv/dt represents the longitudinal inertia. 



But there is no such complication about momentum unresolved 

 into factors : that always has the value 



The following way of putting the matter has perhaps some 

 merits : — 



Let v=c sin )3 



then m=m sec 



and mv=m c t&n p 



while F = -t. (mv) = m Q c sec 2 (3 -jr 



dv 

 cU 

 which, read as mass-acceleration, gives the longitudinal inertia. 



m sec 3 /3 . 



i 



L. On the Kinetic Theory of the Ideal Dilute Solution. 



To the Editors of the Philosophical Magazine. 

 Gentlemen, — 



N a recent number of the Philosophical Magazine *, 

 Dr. F. Tinker puts forward a theory of the Binary 

 Liquid Mixture, deducing expressions for the partial vapour 

 pressures of the components, and obtaining in the case of a 

 dilute solution the relation expressing Raoult's law. jSTow a 

 direct kinetic explanation of Raoult's law would constitute 

 a very great advance in the theory of the Ideal Dilute 

 Solution. At present the only kinetic foundation for the 

 theory is the law of the proportionality between the partial 

 vapour pressure of the solute and its concentration (Henry's 

 law). Raoult's law and the " GJ-as law " of osmotic pressure 



* Mav 1917. 



