132 Henry Riddell on 



proper values for a and C this equation gives a very 

 approximation to the experimental results, as long as the gaseous 

 condition is plainly present, but at very high pressures a small 

 error in a or F introduces so great a change in the results that it 

 is useless under such circumstances. 



c c 



Again, in the equation ^^ - -jir = Vo P" - Vj P^, representing 



the relation betM'een two points on the same isothermal, if P^ is 

 unity, and by the conditions of the experiments V.i, also unity, 



the equation becomes =\ + C ~ VP, but comparing this with 



previous results it is plain that 1 + C is sensibly equal to R, as 

 already defined, and an equation resembling Kankine's simple 



, R C ^ 



form appears ,-r - -j-j.., = s^. 

 \ V ' 



Again, this represents the results better if the first term 1)0 



assumed as -77 , where a has the value already mentioned. 



V — a 



-Thus Rankine's, Van der Waals', and also Clausius' equations are 

 very closely related to this simple approximation due to Andrews. 

 The connection between different temperatures was also investi- 

 gated, and valuable results obtained. In his later experiments 

 upon the behaviour of mixed gases under changes of temperature 

 and pressure, some results were obtained, the value of which was 

 not apparent until the liquefaction of air became an economic 

 success. 



It is impossible to follow Andrews' work further in such a 

 sketch as this. It is well, however, to remind the reader of the 

 very remarkable anticipation of the results of the experiment on 

 the critical condition, which is found in the hypothesis framed by 

 Mendeleeff' at the very time Andrews was completing his experi- 

 mental work. He predicates a condition in which, by combination 

 of temperature and pressure, a vapour becomes of the same 

 density as its liquid under the same circumstances, and concludes 



