Chemical Attraction between Atoms from Physical Data. 85 



given substance at the temperature Ti, where L denotes the 

 internal latent heat, and let B x B 2 denote the graph for the 

 temperature T 2 , &c. Let the abscissa? of! the points a x , 6 l9 c 1? 

 . . ., denote the densities of the substance in the liquid state 

 in contact with its saturated vapour at the temperatures 

 Ti, T 2 , . . ., aud the abscissae of the points a 2 , b 2 , c 2 , . . . ., 

 denote the corresponding densities of the saturated vapour. 

 The internal latent heat of evaporation of the liquid at the 

 temperature T L is then the difference between the ordinates 

 of the points a l and a 2 , and so on for the other temperatures. 

 Now the finding of a formula for the latent heat consists in 

 finding an equation for a series of curves X l5 X 2 , . ., 

 which pass through the points a u a 2 . b l9 b%, . . ., as shown in 

 the figure, but which need not coincide with any other 

 points or parts of the curves A l A 2 , B x B 2 , .... It is 

 obvious, then, that an infinite number of sets of such curves 

 can be found to each of which corresponds a formula for the 

 latent heat. And since each formula corresponds to some 

 law of attraction between the molecules (for given a law of 

 attraction and w T e can at once deduce a formula for the latent 

 heat), an infinite number of laws can be obtained in this way, 

 but we cannot be sure that any one of them represents the 

 true law of attraction without further evidence. It follows, 

 therefore, that the law deduced from latent heat data should 

 contain an arbitrary function. 



We have considered the most general cnse in latent heat 

 in assuming that it is a function of the temperature as well 

 as of z or p. But the same conclusions hold if we could 

 prove that the attraction between two molecules a given 

 distance apart is independent of the temperature. Let the 

 equation of the latent heat of evaporation of a substance 

 into a vacuum in this case be L = ^ 2 (/°)? where p denotes its 

 density, and the curve A/ A 2 ' in fig. I its graph. Let the 

 difference between the ordinates Cj a 2 , &,, b 2 , . . ., denote the 

 latent heat of a liquid corresponding to the temperatures T l5 

 T 2 , . . . Let the curve N 1? N 2 , possess the property that the 

 difference between the ordinates of c x and a 2 is equal to the 

 difference of the ordinates of c 2 and a 2 in the curve A/, A 2 \ 

 and the difference between the ordinates of b { b 2 in the curve 

 Nj N 2 is equal to the difference of the corresponding ordinates 

 in curve A/ A 2 ', and so on. It is obvious that the curve 

 N] N 2 subject to these conditions may have an infinite variety 

 of shapes. Now the equation of the curve Nj N 2 gives the 

 latent heat in terms of p, and as the curve may have an 

 infinite variety of shapes there are an infinite number of such 

 equations. If the curve is expressed by a single equation it 

 must contain an arbitrary function : and the law of attraction 



