300 Mr. W. C. Unwin on the Relations of Pressure, 



the density or specific volume ought to be expressed in terms 

 of the formulae for latent heat and pressure and temperature. 



dp 

 But there being no simple expression for — - it is more com- 

 mon to resort to the quite independent empirical formula of 

 Zeuner. 



For purely scientific purposes no absolute difficulty or in- 

 accuracy is caused, and no advance can be hoped for till 

 rational expressions are found. When such expressions are 

 found, also, it may probably prove, as Hirn surmises, that 

 they will not have the simplicity which some people expect 

 in all natural laws. The practical difficulty, again, can be 



surmounted by means of the tabulated values of p, t, -—, 



calculated with great care and labour by Prof. Zeuner and 

 Prof. Cotterill. Nevertheless the author thinks that some 

 clearness would be introduced into the teaching of thermo- 

 dynamics, and possibly some facility gained in practical cal- 

 culations, if only amongst empirical expressions to which 

 recourse must be had, one could be found accurate enough 

 and yet so simple that all the related functions could be derived 

 from it. The paper of Messrs. Ramsay and Young suggested 

 an attempt in that direction. 



It might be expected that the approximate relations stated 

 by Profs. Ramsay and Young could be deduced from some 

 of the empirical relations already established. This, however, 

 is not strictly the case. 



It is known for instance that the expression 

 p = AT 5 ' 5 , 

 where A is a constant and T is reckoned from an arbitrary 

 zero, approximately satisfies the law connecting the pressure 

 and temperature of saturated vapours. 



Differentiating, 



So that 



Consequently 



J|=5-5AT** 



T J| = 5-5AT 5 - 5 = 5-5p. 



T t=5-5: 



p dT 



a relation which should be approximately satisfied for dif- 

 ferent vapours. 



Thus, for instance, reckoning from the zeros given below 



