79 VISCOSITY OF GASES 195 



the value of the free path of mercury vapour at 370 C. and 

 atmospheric pressure is 



L = 0-0000209 cm., 



and that of the collision-frequency under the same circum- 

 stances 



fl/Z, = 1245 x 10 6 per sec. 



An estimation of the values at can only be made with 

 great uncertainty, since the law of alteration of rj with 

 temperature at such low temperatures is not known. If we 

 employ the formula of interpolation determined by Koch 

 for high temperatures, according to which rj is proportional 

 to the l'6th power of the absolute temperature, and put fi 

 proportional to the square root of the same magnitude, we 

 have for mercury vapour at and atmospheric pressure 

 v = 0-000162, L = 0-00000344, fl/L = 7540 x 10 6 . 



We may expect that in the foregoing series of numbers 

 regular relations between the free paths and molecular 

 weights may be recognisable. For it can scarcely appear 

 doubtful that the area of the central section of the sphere 

 of action which is contained in the formula for the free path 

 is closely connected with the molecular volume ; and it is 

 just as probable that the molecular volume depends in like 

 manner on the molecular weight, as in chemically simple 

 bodies the atomic volume depends on the atomic weight. Bat 

 Lothar Meyer 1 has shown that, as the atomic weight in- 

 creases, the atomic volume now increases, now decreases, with 

 a peculiar kind of double periodicity ; and similar behaviour 

 has been shown, by the investigations of Mendelejeff, 

 Lothar Meyer, and other chemists, in the case of all 

 other physical properties of the chemical elements. Conse- 

 quently we may expect that the molecular free path and 

 collision-frequency will also be functions of the molecular 

 weight that regularly decrease and increase. 



Graham has already recognised the simplest relations 

 to the molecular weight. He noticed that substances of 

 equal molecular weight in many cases possess the same 



1 Ann. d. Chem. u. Pharm. 1870, Suppl.-Band vii. p. 354. 



o 2 



