is co})U)wnly te/'uied a '* Vacnuni.'" Ill 



tence to do more than apply the matluMnatical results of 

 others to a special case; and I shall be glad if the result 

 obtained is of any service, or may induce others to pursue the 

 subject further. 



2. It has been deduced by Professor Maxwell (Phil. Mag. 

 Dec. 1873) that the number of molecules contained in a cubic 

 centimetre of any gas at normal density may be estimated, 

 in round numbers, at 19 million billions. This is carefully 

 given by Professor Maxwell as uprohable or approximative re- 

 sult. But, on the other hand, it should be kept in view that 

 the result is estimated on the basis of experimental data ; and 

 other results predicted by mathematics in connexion with the 

 kinetic theory, and which admit of direct test by experiment, 

 have (as is well known) been confirmed in a striking manner. 

 Also it is needless to add that mathematics is not less cer- 

 tain because the dimensions dealt with are small. Sir William 

 Thomson in a paper on ''Atoms," published in ' Nature ' 

 (March 31st, 1870), by four distinct lines of argument arrives 

 at accordant results as limiting values for dimensions of mole- 

 cular structure ; and these results agree very well with the 

 above estimate of Professor Maxwell. Sir William Thomson 

 finally remarks that the results may be considered as estab- 

 lished with "a very high degree of probability." 



3. Taking, therefore. Professor Maxwell's result in refer- 

 ence to a o-as, if we take the cube root of the number of mo- 

 lecules contained in a cubic centimetre, or ^1^ x 10^^, we 

 have the number of molecules which (placed at their mean 

 distances) would reach the length of a linear centimetre, or 

 we have 2,668,400. The mean distance of the molecules of 

 a gas at normal density is therefore ^ "^ of a centimetre, 

 about one seven-millionth of an inch — which, it may be re- 

 marked, is about one seventh of the distance capable of being 

 measured by a Whitworth machine. We have new to con- 

 sider what the effect is on rarefying the gas. To clear the 

 ideas, suppose all the molecules in a given space (such as an 

 air-pump receiver) to be placed regularly ; i. e., suppose the 

 given space to be subdivided up into a number of imaginary 

 cubes of such a size that, when molecules are placed at the 

 corners of all these cubes, exactly the whole number of mo- 

 lecules is thus taken up. Then the side of one of these cubes 

 wdll be one seven-millionth of an inch long, representing the 

 mean distance of the molecules. Rarefying a gas to a given 

 degree is of course equivalent to increasing the space in which 

 the gas is to that same degree. The side of a cube being as 

 the cube root of its volume, it follows that when the gas is 



