50 K. D. Kraevitch on an Approximate Law of the 



equation (5) we have just considered, because they do not 

 refer to actual vapours but only to imaginary ones such as do 

 not really exist. 



4. I will now pass to the applications of equation (5) and 

 to proving that its theoretical bases are confirmed by experi- 

 ment. The fundamental proposition upon which equation (5) 

 is based is that at a certain temperature a vapour in a state 

 of saturation has the properties of a perfect gas. Above and 

 below this temperature it diverges from these properties, but 

 for the present investigation it does not matter in which 

 direction. It follows from the calculations given below that 

 such a temperature does actually exist for the majority of 

 substances yet experimented upon, and which are liquids at 

 the ordinary temperature and pressure. The vapours of 

 other liquids are not subject to the laws of Boyle and 

 Gay-Lussac within the limits of the observations made by us. 

 Without fresh observations it is impossible to say if these 

 vapours are able to exist in the state of a perfect gas outside 

 the temperatures observed. Equation (5) is naturally as yet 

 inapplicable to such vapours. Our theory should not be 

 applied to gases which are able to take the form of liquid only 

 under very high pressures, because the volume of the resultant 

 liquid would then be somewhat considerable compared with 

 the volume of the gas and could not, therefore, be taken as 

 zero, as our theory demands. 



5. Suppose that in equation (5) 



c ~ G i — v r o _ 

 AD ~*' AD~ y ' 



we shall have 



log £ = ~ [ log % ~ m ^r 5 ] x + (t - %h- • < 7 > 



If x and y be regarded as arbitrary constants, then they might 

 be determined, if any vapour-pressures p, p 0j and p ± were 

 known corresponding to temperatures T lf T , and T'. If, 

 moreover, vapours in a state of saturation followed Boyle's 

 and Gay-Lussac's laws, and if in general the propositions 

 which served for the deduction of equations (5) or (7) 

 were unimpeachable and perfectly accurate, then the pair of 

 unknown quantities x and y would be the same whatever 

 were the temperatures T 1? T , and T', and their corresponding 

 tensions p lf p , and p 1 . In reality just the contrary occurs. 

 Every three observations, taken at random, give in general 

 different magnitudes for x and y, so that not unfrequently 



