Nature of Dielectric Capacity. 15 



H 2 and 2 applies to the monatomic inert gases. It is given 

 under " Fourth method of finding the virial constant/' on 

 p. 247 o£ " The Laws of Molecular Force " (Phil. Mag. [5] 

 xxxv. 1893), namely, Z=27R 2 T e 2 /64p ( ,, for in this case I is 

 identical with a of Van der Waals, so that M 2 Z depends only 

 upon T c 2 /p c . The values of 10~ 6 (M 2 Z)i with the dyne as 

 unit of force are given for three of the inert gases in the last 

 row of the following table : — 



A. Kr. X. 



T c abs 156 210 288 



i? c atmos 52-9 54-3 57*2 



1-15 1-53 2-05 



These values of 10" 6 (M 2 /)» stand to one another nearly as 3 

 to 4 to 5. According to the theory of corresponding states the 

 critical volumes of substances are proportional to T c /p e , if 

 the molecules of the substances form similar dynamical 

 systems, but the constant of proportionality for elements is 

 different from that for compounds, and it varies somewhat in 

 compounds according to type. The values of T c /p c from the 

 above table are 2*94, 3'88, and 5*03, which are again nearly 

 as 3 to 4 to 5. If both (M 2 l)h and the critical volume were 

 strictly as 3 to 4 to 5, p c would need to be the same for the 

 three gases, as it nearly is. According to the equation of 

 Van der Waals the critical volume is proportional to the 

 limiting volume of the molecules. But even though that 

 equation is not of general application, it gives valuable ap- 

 proximate generalizations like those concerning corresponding 

 states. So we shall assume the limiting volumes in A, Kr, 

 and X to be as 3 to 4 to 5. But the diameter of the mole- 

 cule of A is 2'66 x 10 ~ 8 cm., whence 



B = 2-77xl0 19 x 2 x 11215(2-60 xl0- 8 ) 3 = 11-7. 



Now for He 2a = 1-92 x 10~ s , whence B = 4'42. Since 4*42 

 is to 11' 7 nearly as 1 to 3, I shall assume that for the family 

 B = 4*0(1, 2, 3, 4, 5). To complete the knowledge of 

 (M 2 Z)* obtainable from existing data we can use the result 

 (Phil. Mag. [5] xxxvi. 1893, p. 507) that C in the formula 

 for the viscosity of a gas is connected with M 2 / by the rela- 

 tion that M 2 / is proportional to OB. Now for He and A the 

 values of O are 76 and 160, so that the values of (M 2 /)* are 

 as (76 x 1)* to (160 x 3)*=1 to 2'5. 



I shall assume that the relation is 1 to 3, and that the last 

 table can be extended to give the formula 10 _6 (M 2 Z)5 = 

 0*4(1, 2, 3, 4, 5). One of the assumptions used above would 

 lead to an absurdity if applied directly to the case of helium. 



