some Thermodynamical Relations. 33 



majority of cases), the relation of the ratios is expressed by 

 the equation 



W = ~R + c{t f -t) 



(where B/ is the ratio of the absolute temperatures of any two 

 bodies at a given pressure ; K the ratio at another pressure ; 

 t and t' the temperatures of one of the two bodies corresponding 

 to those vapour-pressures ; and c is a constant). Professors 

 Ayrton and Perry have based all their reasoning on the first 

 statement, which laid no claim to exactitude, and have in- 

 formed us, what we already knew, that Dalton's law gives 

 better results. The data given in our previous papers, how- 

 ever, show how nearly our generalization agrees with fact. 



To refute the accusation of having performed useless labour 

 would be really to repeat the substance of our previous papers; 

 but the members of the Physical Society would hardly thank 

 us were we to do so. There are, however, two or three 

 remarks made by our critics which call for special reply. 



1. It is suggested that our obvious course would have been 

 to employ Rankine's formula, which, our critics state, is not 

 empirical, but based on Rankine's molecular theory. We 

 have been informed that the formula deduced by Rankine 

 from his molecular theory was found by him not to agree 

 with the experimental results ; and that, in order to secure 

 agreement, an empirical term was added. We would ask if 

 this was not the case, and, if so, whether the whole formula is 

 not thereby rendered empirical ? 



2. We are told that our labours might have been reduced 

 by 75 per cent, had we recognized the fact that our four laws 

 are identical. Now we do not anywhere state that our 

 "laws" are absolute, in which case only would the identity 

 necessarily hold ; but indeed give methods for calculating 

 their deviation from constancy. It is moreover desirable to 

 test the truth of such statements in every possible way, inas- 

 much as different determinations by different observers are 

 thereby introduced. 



3. That it is by no means impossible to obtain with accu- 

 racy the specific volumes of saturated vapour will appear from 

 memoirs on the thermal behaviour of ethyl alcohol and ether, 

 which are in the hands of the Royal Society ; indeed such 

 measurements can be made at temperatures when a direct 

 determination of L would be extremely difficult, if not impos- 

 sible. To show the necessity of using determinations from 

 all sources, we may point out that if Regnault's values of L 



and of ~ for alcohol and for ether are employed, and the 

 Phil Mag. S. 5. Vol. 22. No. 134. July 1886. D 



