120 DIRECT PROPERTIES OF MOLECULES 333 



covering spheres, in addition to the area covered, it is easy 

 to calculate the number of spheres which we wish to find. 



In this calculation I shall content myself again with an 

 approximate estimate. If the area of a molecule is about 

 3 x 10~ 16 sq. cm., while the molecules contained in 1 cubic 

 centimetre of air can cover an area of 18400 sq. cm., their 

 number is 



N = 18400/(3 x 10~ 16 ) = 61 x 10 18 , 



or in 1 cubic centimetre of air under atmospheric pressure 

 there are about 60 trillion molecules. This number holds 

 not only for air, but also, by Avogadro's law, for all gases 

 under the pressure of one atmosphere. 



From this number we at once obtain also the value of 

 the mean distance apart X of two neighbouring molecules 

 by means of the formula 



N\ 3 = 1, 

 whence 



X = 2-6 x 10~ 7 cm. = 2*6 millionths of a millimetre ; 



and this number, too, is the same for all gases under 

 atmospheric pressure. 



The values we have found confirm in a remarkable way 

 a conjecture which Clausius made so early as 1858 in 

 his celebrated memoir on the molecular free path. In 

 this paper, which has formed the starting-point for the 

 investigations now occupying our attention, Clausius l 

 estimates the fraction of the space, enclosing a gas which 

 is actually filled by the spheres of action when the pressure 

 is that of one atmosphere, as about one-thousandth, this 

 estimate being given for the explanation of his ideas by a 

 numerical example. Clausius, therefore, puts X 3 = 1000. f Try 3 , 

 whence it follows that X = 16 s- ; and he further finds 

 L = 61 X from his formula for the free path. 2 



If we find the corresponding relations with the values 

 that we have now obtained from observations, we have 

 in round numbers for air L = 0*00001 cm., and therefore 



1 Fogg. Ann. 1858, cv. p. 250 ; Abhandl 2. Abth. 1867, p. 273. 



2 Compare 65. 



