300 



DIRECT PROPERTIES OF MOLECULES 



109 



then two in 1870 by Lord Kelvin, 1 and in 1873 one by 

 Maxwell. 2 



In the formula found earlier ( 68) for the free path, 



= A,/7rs> 



V2, 



its value is expressed in terms of the size of the elemental 

 cube whose edge has length X, and of the diametral section 

 of the sphere of action ( 44, 63) whose diameter is s. If 

 we use the relation between the size of this cube and the 

 number of molecules contained in unit volume, which is 

 given by JW = 1, 



the former formula may be written in the shape 



which shows that, if the free path L is known in absolute 

 measure, the magnitude 



or the sum of the diametral sections of the spheres of all 

 the molecules contained in unit volume, can be also ex- 

 pressed in absolute measure. 



110. Numerical Values 



From the values of the molecular free paths as obtained 

 from the observations on viscosity carried out by Graham 

 and by Kundt and Warburg, which are tabulated in 79, 

 I have calculated the following values of the magnitude Q 



by the above formula. 



Values of Q. 



1 Silliman's Amer. Journ. 1870, 1. pp. 38, 258 ; Ann. Chem. Pharm. 

 1871, clvii. p. 54 ; Nature, 1883, xxviii. p. 203 ; Exner's Eepert. 1885, xxi. 

 pp. 182, 217. 



2 Phil. Mag. 1873 [4] xlvi. p. 453 ; Ency. Brit. 9 ed. iii. p. 36 ; Scient. 

 Papers, ii. pp. 361, 445. 



