Law of Molecular Force. 321 



CClsCOH {Q,-K,),G,0, (CH3CO)20 QzB.,0^ QJ^.O, 

 5-3 4-4 6-7 5-5 5-4 



Mean. Mean. 



C5H10O2 C6H12O2 C7H14O2 C8H16O2 



5-3 6-0 6-5 6-9 



Mean. Mean. Mean. Mean. 



The previous numbers show that Waterston^s law, while 

 representing a remarkable attempt at the time it was an- 

 nounced to connect latent heat, surface-tension, and molecular 

 volume, is far from being verified by experimental data; and 

 they show the danger of pushing the idea of " correspond- 

 ence " too far. In fact, it would appear that the manner in 

 which Eotvos deduces his law theoretically from the principle 

 of " correspondence " only happens by chance to give a rigo- 

 rous law, as the same principle applied to latent heats and sur- 

 face-energy leads to a law so far from rigorous as Waterston's 

 has been shown to be. 



In the preceding pages we have argued from Eotvos's 

 empirical law as basis ; but probably, when the dynamical 

 rreaning of temperature in liquids has been made clear, 

 Eotvos's law will be deduced in the following manner. 



The temperature of a liquid subjected to small constant 

 pressure is such a property of the molecule of the liquid, that 

 its rate of variation with the translatory kinetic energy of the 

 molecule is the same for all molecules; but as external virial 

 is negligible under these circumstances, we have the rate of 

 variation with temperature of internal virial multiplied by 

 molecular mass proportional to the rate of variation of the 

 translatory kinetic energy of the molecule, which is the same 

 for all molecules. But according to the law of the inverse 

 fourth power, internal virial multiplied by the mass of the 

 molecule is proportional to surface-tension multiplied by the 

 two-thirds power of the molecular domain, whence Eotvos^s 

 law follows, that the rate of variation with temperature of 

 the product of surface-tension and the two-thirds power of 

 the molecular domain is the same for nearly all liquids. 



In the present paper we have been occupied only with 

 attractions between similar molecules; and there is too little 

 experimental material to allow of our testing any hypothesis 

 as to the parameter of molecular attraction in the case of dis- 

 similar ones ; but it seems probable that the parameter will 

 be inversely proportional to the product of the square roots 

 of the surfaces of the two molecules. 



Phil. Mag. S. 5. Vol. 27. No. 167. April 1889. Y 



