A.— MATHEMATICAL AND PHYSICAL SCIENCES. 



31 



heat of the solution in terms of the specific heats. For a substance like 

 water changing phase 



dTKTJ^ T 

 For the electrical case we obtained the equation 



The quantity L I have called the latent heat of dilution. It is con- 

 nected, however, with the latent heats of evaporation from the two metals 

 at the junction temperature. These latent heats of evaporation are those 

 that come into play in thermionic emission. Prof. 0. W. Richardson 

 has measured such latent heats, and concludes that they support the 

 existence of large thermionically excited voltages. Whatever their 

 magnitude it must not be forgotten that tt is a measure of the difierential 

 latent heat at a junction and tt is certainly very small.'' 



^ I am accustomed to put the matter thus : 



Assume that the emitted electrons behave as a perfect gas in the vapour state, 

 having pressure, volume, and temperature connected thus : 



V 



Now, any latent heat is given by 



L=T:{v.,-v,)^ (Clausius). 



The internal latent heat is 



But Vi (the volume in the solid) is exceedingly small compared with v; hence very 

 nearly 



Li T, T d fp\ d I p\ 



T^ = ^ ^ (iT\T j = ^ dT ^""^ \t) ' 

 whence, by integration 



or putting p = wRT (re = concentration in the vapour state) 



n = reJ»'^''' 



IT. 



If we consider a second metal in equilibrium with the first 



re' = re„J^^*'' 



But things which are in equilibrium with the same thing are in equilibrium with one 

 another ; therefore re = re' and 



Li — Li* is the internal latent heat of dilution. This equation is Kirchhoflf's equation. 

 Now though the latent heats may be large their difference is usually a small quantity, 

 and it is their difference which is nearly represented by tt. 



