110 DIRECT PROPERTIES OF MOLECULES 301 



The numbers express in square centimetres the sum of 

 the diametral sections for the molecules contained in one 

 cubic centimetre of the gas under the pressure of one atmo- 

 sphere, or, more correctly, for their molecular spheres of 

 action. What is noticeable in the table at the first glance 

 is the large value of these numbers, which seems to be out 

 of harmony with the assumptions made on the nature of 

 gases. The tabulated number for air, for example, tells us 

 that, if all the molecules contained in a cubic centimetre of 

 air under ordinary pressure could be ranged close together 

 in a plane, they would cover an area of T84 square metres 

 with their spheres of action. This large value seems to 

 suggest a rather dense packing of space with the air 

 particles and the assumption that the molecules of bodies 

 cannot be of small size. 



It requires, however, but little consideration to see the 

 error in this conclusion. The sum Q of the sections may also 

 attain its value by reason of the largeness of the number N of 

 the molecules, and in this case we should at once be able to 

 conclude that the value of the section of a molecule is really 

 small ; for if we consider the number of molecules N to 

 increase by division of the molecules, so that the section of 

 any one molecule becomes correspondingly smaller, yet the 

 sum of the sections will thereby increase. This is easily 

 perceived when we recall the mathematical formulae for the 

 section and volume of spheres. If, for instance, a sphere is 

 divided into two equal parts, the sum of the sections of the 

 two smaller spheres is greater than the section of the ori- 

 ginal sphere in the ratio 



2(i) : 1 = 2* : 1 = 1-26 : 1. 



But without mathematical calculation this is easily 

 seen. Suppose we pound a bit of a solid substance to 

 powder, then a larger surface can be strewn with the powder 

 so obtained the finer the powder. We may analogously 

 suppose the molecules of air, which in spite of their light 

 weight can cover so much area as is given above, to form 

 an extremely fine dust, like grains that are very small but 

 of enormous number. 



