306 Mr. W. Sutherland on the 



He found this to hold for a large number of liquids ; and also 

 that water, the alcohols, and the fatty acids are exceptional at 

 the lower ranges of temperature. The theoretical grounds on 

 which he founds the law are, in the present state of physics, 

 somewhat transcendental ; but as they illustrate the power of 

 the idea of " correspondence,^'' which Van der Waals has deve- 

 loped so brilliantly, they can be reproduced herewith advantage. 

 Let V be the domain of a molecule when it is part of a mass 

 of liquid, and u when part of a mass of gas at the same tem- 

 perature as the liquid ; then, if the temperatures Tj and Tg 

 for two substances are chosen so that Vi/ui = V2fi(2, the con- 

 ditions of the molecules are considered by Eotvos to " corre- 

 spond." This equation may be written 



v,p,/T, = v,p,/%; (1) 



where jOj and p2 are the pressures of saturation at the tempe- 

 ratures Ti and Tjj, if we consider the vapours of the liquids as 

 approximately perfect gases. Then, according to the method 

 of " correspondence," it is stated that the forces acting on the 

 two molecules and the energies of the two molecules corre- 

 spond. Consider a plane area over which n molecules are 

 distributed. The pressure on it is npiVi^^; the tension across 

 a line in the surface-film on which I molecules lies is Ivi^a.^, 

 where a^ is the surface-tension or surface-energy. Then, 

 from the assumption as to complete correspondence in the 

 states of the two molecules, we have 



Iviidi lv2^a.2 «! a.2 ,r,^ 



5"=' o-> or r = r- • • • (^) 



npiv-^i np^v^t piVxi p^v^i 



Arguing in a similar manner as to correspondence in the 

 change of energy of the two molecules to their surface-energy 

 when they evaporate with absorption of latent heats ?WiLi, 

 W2L2 respectively, m^ and m^ being the molecular weights, 

 Eotvos writes ^^^^^ ^^^2 



2- = 2 (^) 



U]Vis a.2V2^ ^ ^ 



This last result is known as Waterston's law (Phil. Mag, 1857, 

 vol. xiv.), announced by him without reference to the idea of 

 correspondence; but, according to Eotvos, the quantities L^, 

 «!, ■^1, L2, &c. must be taken only for corresponding states of 

 the two bodies. We shall see afterwards that Waterston^s law 

 cannot be regarded as an accurate physical law when tested 

 by the available experimental material ; but that, as a rough 

 statement of a connexion between surface-tension and latent 

 heat, it can be deduced from the law of the inverse fourth 

 power. 



