( 225 ) 



The simplifications relating to the case that one of' the two 

 coexisting phases as compared with the other has a very small 

 density, will be considered in the sections 7 and 8 of this Commu- 

 nication. 



§ 2. Empirical reduced equation of state. As to the supposition 

 mentioned in § 1, we are now under much more favourable circum- 

 stances than at the time when Comm. N". 59a was wj'itten. 



The beauty of van der Waals' theor}' lies above all in the fact 

 that it brings under one point of view phenomena in mixtures w4iicli are 

 distributed over a large range of temperatures and densities. Hence 

 for a satisfactory illustration of this theory we require tirst of all 

 an equation of state which holds true over a large range of tempe- 

 ratures and densities. Now most of the equations of state — this has 

 been made clear especially by D. Berthelot — hold only for a limited 

 range. For considerations as are meant here probably only those 

 equations of state can serve wiiich are developed in series and made 

 to agree with the observations over a very large range. Such equa- 

 tions of state which are very suitable for the calculation have been 

 obtained in Comms. W. 71 (June '01) and N". 74 (Livre jubil. 

 Bosscha p. 874) by combining as well as possible the known pieces 

 of reduced equations of state for substances with difterent critical 

 temperatures. As now we neglect the deviations from the law of 

 corresponding states in the different substances and in their mixtures, 

 we may without more base our considerations on a similar empirical 

 reduced equation of state. 



We have used a form which does not differ much from the more 

 preliminary one given in Comm. N". 74, which was indicated by 

 r2. We obtained it by making it agree with hydrogen 0° C. ^), oxygen 

 and nitrogen 0° C. (all of Amagat) and ether 0" C, 100° C, 195° C. 

 (Amagat, Ramsay and Young). This polynomial, which contains for 

 instance all the reduced temperatures which occur on the if'-surface 

 for ether and hydrogen at 0' C, will be designated by VI Ï. As in 

 Comms. N". 71 and 74 we have for a substance wntli the critical 

 temperature 7\ and pressure i^k, if v is expressed in the theoretical 

 normal volume, 



B C D E F 



pv = A + -^--\--^---^- (I) 



V 17 t" V V 



where at an absolute temperature of ^ above freezing-point 



.1 =z 1 -f 0.0036625 t 



1) For hydrogen tlie critical quantities of Olszfavski arc still used in llie calculalion. 

 ~) Gomp. Gomm. No. 71 form. (10). 



