some Thermodynamical Relations. 257 



Their paper, published in the December number of the 

 Philosophical Magazine and in our i Proceedings/ is devoted 

 to the illustration of these three laws, and it is the record of 

 an extraordinarily large amount of calculation. 



IV. Ramsay and Young's law : 



-=- It -4-\ is nearly constant for all stable substances 

 dp\ dt ) J 



at the same pressure. 



One of us pointed out in the discussion on the paper, that 



to measure -~ by drawing a tangent to a plotted curve was 



usually an inexact method ; and that much greater accuracy 

 would have been obtained by the authors if they had, for each 

 substance, found the values of the constants a, /3, and 7 in 

 Rankine's well-known formula 



8 y 

 logp = u—j-±+&G.; (1) 



and that probably the best way of making a comparison 

 between two substances and observing changes due to dissocia- 

 tion would be by remarking that, for the substances examined 

 by Regnault, 



■-f-J+Ao.=a-J-£ + 4o., ... (2) 



if t and 6 are the absolute temperatures of two saturated 

 vapours at the same pressure. It is unlikely that any person 

 will discover an improvement on Rankine's formula just given. 

 It cannot merely be looked upon as an empirical formula 

 being based on Rankine's molecular theory. The exactness 

 with which Rankine has reproduced Regnanlt's numbers, 

 using only three constants, is exceedingly remarkable. Ran- 

 kine in his paper refers to the formula 



logjp=«-|, (3) 



which is the same formula but with two constants only, and 

 is inexact for calculations of pressure. 



To show that Messrs. Ramsay and Young might have em- 

 ployed a less laborious method of testing, we may first point 

 out that it would have reduced the labour by something like 

 75 per cent, to have recognized the fact that I., II., III., and 

 IV. are all identical. If any one of them is true, they must 



