36 Prof. J. H. Poynting on 



above 0°, if ice can exist at such a temperature. Prof. J. 

 Thomson has subsequently (Brit. Assoc. Report, 1872, p. 24; 

 Proc. Roy. Soc. 1873; 'Nature,' ix. p. 392) arrived at a similar 

 conclusion independently. A proof differing in arrangement 

 from Kirchhoff's, and following out rather the line indicated 

 by Thomson, will be given below. 



In a mixture, then, of ice and water below 0°, since the 

 water has the greater vapour-tension, more molecules will 

 cross the surface from the water to the ice than in the opposite 

 direction. The ice will therefore gain, while the water loses. 

 At the same time the molecules will possess less energy when 

 arranged as ice. Hence the temperature of the whole will 

 rise, and this rise will go on till 0° is reached, when there is 

 once more equilibrium — or till the whole is converted to ice, 

 if that condition be previously reached. This seems sufficiently 

 to explain the action of a small piece of ice dropped into water 

 below 0°; and the fact that the change of state is a surface 

 phenomenon seems to show that the presence of some ice is 

 necessary to commence change of state. 



If a mixture of ice and water at 0° be supplied with heat, 

 as soon as the temperature rises ever so little above 0° the 

 equilibrium of exchange is destroyed : for the vapour-tension 

 of ice becomes greater than that of water, and therefore the 

 number of molecules entering the water from the ice is greater 

 than the number going in the opposite direction. But since 

 the water arrangement requires more energy, heat is absorbed, 

 and the mixture has a tendency to fall back to 0°. 



Before going on to discuss the effect of pressure on the 

 melting-point, I give a proof, with a somewhat more general 

 result, of Kirchhoff's formula, 



—r jr = '044 millim. of mercury, 



where <&' is the maximum vapour-tension of ice, and ot that of 

 water. 



Start with a volume v of water at temperature — f. Let it 

 evaporate, always at the temperature — 1°, in a cylinder which 

 it does not wet, at its maximum vapour-tension «r, which we 

 suppose to be maintained by a piston. Let the ultimate 

 volume of the water-vapour be V. Then the external work done 

 in the expansion is «r (V — v). 



Now let the vapour further expand, always at the same 

 temperature and in equilibrium with the pressure, till we have 

 reached a volume V' at the maximum vapour-tension «*■' of 

 ice. Assuming Boyle's law to hold, the work done in this 



expansion is w'V'log— -, ; and this would be if co^w'. 



