334 DIRECT PROPERTIES OF MOLECULES 120 



L = 40 X about. We further find, since s- = 2 x 10~ 8 cm., 

 the relation X = 13 s, and, finally, we obtain for the volume 

 actually filled by the molecules contained in 1 cubic 

 centimetre under atmospheric pressure, 



N.7Ts 3 = 2-5 x 10~ 4 ccm. = cubic millimetre ; 



the molecules themselves therefore fill only about a 4,000th 

 part of the whole space containing them. The spheres of 

 action of Clausius, of which s is the radius and not the 

 diameter, occupy a volume eight times larger than the 

 molecules, and therefore about a 500th part of the whole 

 volume. 



The agreement with the numbers assumed by Clausius 

 is so close that the good fortune with which he chose his 

 example would appear wonderful if we had not rather to 

 see in it a testimony to his sure and clear vision into things. 



If we calculate the values of these magnitudes for very 

 small pressures such as occur in Geissler's tubes, i.e. for 

 a pressure of about 1 mm. of mercury, the number of 

 molecules in 1 cubic centimetre will be 760 times less, 

 or N = 80000 billions about ; it thus remains still very 

 large, and we see again that a space containing gas which is 

 so extremely rarefied is still very far indeed from being 

 completely empty. 1 In this case the mean distance apart 

 of two neighbouring molecules is X = 23 millionths of a 

 millimetre about. 



We can also raise the question as to how these relations 

 alter when the gas is very highly compressed. At a pressure 

 of 1,000 atmospheres the distance between neighbouring 

 molecules would become X = 0-26 millionths of a millimetre, 

 so that the molecular spheres must then be nearly in contact 

 with each other. But, as we have several times remarked, 

 we must not leave out of account the fact that our numbers 

 represent only limiting values ; s may very well be less than 

 we have calculated it, and in this case N would have to be 

 taken still larger, while X on the contrary would diminish, 

 though not so much as s, since the value of the free path L 

 is not altered by such change of s. 



1 Compare 84 and 110. 



