238 



Mr. William Sutherland on the 



pv 



20 25 T 

 "7 ' 13 T 



409^ c 



' 98 v 



One and the same law holds for compounds below the 

 critical volume only if B varies as the square root of the 

 critical temperature, and if j3 is proportional to the critical 

 volume : in the elements we have found the latter condition 

 to hold approximately, and so we are prepared to find it do so 

 for compounds. The following Table compares B with \/T c 

 and £ with k, which is 6vJ7 for the Hye compounds for which 

 we have as yet found k. The values of B and /3 for NH 3 and 

 N 2 were obtained from Andreeff's data for the expansion of 

 these bodies as liquids {Ann. Chem. Pharm, ex.) and for S0 2 

 from Jouk's (Wied. Beibl. vi.). 



Table XXI. 





Jc. /3. 



i 



2-9 

 30 

 3-6 

 36 

 3-1 



(0,H.) o 



4-066 1-11 

 1-76 -69 

 2-08 -55 



3-7 63 

 4-0 54 

 3-8 71 

 3-9 70 

 3-5 55 



CO, 



S0 o 



NH 3 



4-8 

 23 



1-22 

 •66 



N.O 





In these bodies we find a fair approximation to propor- 

 tionality between j3 and k on the one hand, and between 

 B and \/T c on the other ; to the same degree of approxi- 

 mation Yan der Waals's generalization can be applied to 

 compounds below the critical volume (excluding of course 

 such exceptional bodies as the alcohols and water). 



The accurate statement of the generalization ought then to 

 be as follows : — When the variables are expressed in terms of 

 their critical values as units, then down to the critical point 

 compound bodies with certain exceptions have all one and the 

 same characteristic equation, but below the critical point they 

 have closely similar but not identical equations. 



It is a remarkable fact that Yan der Waals should have 

 been led to his valuable generalization by means of a form of 

 equation which completely fails to apply to the substances 

 which are the subject of the generalization. As a point in the 

 history of this branch of molecular physics, it calls for mention 

 thatWaterston,in the Phil. Mag. vol.xxxv. (1868), had prac- 



