524 Mr. A. Griffiths on the Source of 



If we make the hypothesis that S 1? S 2 , and S are constants, 

 then 



= S^?! -f <7 2 / 2 ) ti — d^ Si^o — d 2 l 2 S 2 ^o» 



This equation indicates that (£ — ^), the fall in temperature, 

 depends in some way on the height through which the dis- 

 solved substance diffuses. The preceding was worked out 

 long before I published my paper. In what follows, the 

 influence of Prof. Fitz Gerald will perhaps be shown. 



If we wish to study the fall of temperature due to the rise 

 of matter by diffusion in a theoretical manner, we may assume 

 that the capacity for heat of the mixture is the sum of ihe 

 capacities for heat of the components, and that there is no heat 

 of combination. 



Let m = total mass of the two liquids. 



,<? = thermal capacity of unit mass of mixture. 

 h = rise of C.G. 

 (/ = acceleration due to gravity. 

 f = the fall of temperature. 

 Then, since the potential energy gained equals the capacity 

 of the liquids multiplied by the fall of temperature, 



mgh = msf. 



Hence ,_ gh 



' s ' 



It may be pointed out that this equation indicates a limit 

 to the height to which diffusion (with ultimate uniform dis- 

 tribution) can spread. Thus if s be a constant, the above 

 equation holds whatever the fall in temperature ; and if the 

 temperature be initially 0° C, /cannot be greater than 273° C, 

 and h cannot be greater than 273 s/g. 



Let 5 = 42,350 xg (the capacity of a gram of water), then 

 h cannot be greater than 273x42,350 cms.; that is 115 

 kilometres approximately. It may be noted that h is not the 

 height at which diffusion occurs, but the rise in the centre of 

 gravity. In a given case the height at which diffusion occurs can 

 readily be expressed in terms of h. 



The Absorption of Heat in a simple case ivhen there is a 

 combination of Diffusion and Motion. 



In the figure there is a representation of a vertical tube of 

 length L. 



Let us suppose that the lower end is continuously in contact 



