Vapour- Temperatures at Equal Pressures. 337 



by Ramsay and Young shows that the absolute temperature 

 of mercury vapour is rather more than double that of ether 

 vapour at the same pressure. The scale for mercury might 

 therefore be conveniently taken double of that for ether. 



The best general formula that has been propounded for 

 the relation between t and p is Rankine's, which is dis- 

 cussed in the first of his ; Collected Papers/ and shown to 

 give good results for very various substances. His tables 

 of steam-pressure were calculated by it. It is 



l°gp = *- f-£ (3) 



the second and third terms being in practice always negative. 

 If we omit the third term, as Rankine does in cases 

 where the data are not very accurate, we have, for two 

 vapours 



£= '-£ 



t a t 1 



whence 



t t' 



b<rP = *-? = *'-£, (4) 



indicating that the line X Y passes through the fixed point 



x= :j3 /3 



^?' V" 



Ramsay and Young's law is thus deducible from Rankine's 

 shortened formula. 



Treating Rankine's full formula in the same way, we get 



0+7/* P' + y'/t' 



—t r~ = "-*' 



showing that the ultimate intersection of two consecutive 

 positions of X Y is 



,_fi±# ,— £±^. ... (5) 



As t and t' increase, the absolute magnitudes of x and y 

 diminish. Instead of strictly meeting in a point P. as in 

 fig. 1, the lines X Y will accordingly touch a curve with its 

 concavity turned away from the origin, like the dotted curve 

 PPPinfig. 2 (p. 338). 



