Probabilities of Molecular Configurations. 53 



among all elements is the most probable event*. Thus the 

 arrangement of a given number of molecules in a given 

 volume, the probability of which is greatest, is found to coin- 

 cide with what would actually take place in the case of a 

 homogeneous fluid not acted on by external forces. 



If in a given volume molecules of different kinds are present, 

 the ultimate arrangement is easily seen to coincide again with 

 that the probability of which is greatest. 



To interpret such results, observe that the calculation of 

 probability wholly depends upon the assumption that the pro- 

 bability of a molecule being in a definite element is not 

 affected by the fact of other molecules being there at the same 

 time. The conclusion then we have to draw every time the 

 actual arrangement of molecules coincides with that the pro- 

 bability of which is greatest, is clearly that in such cases no 

 disturbing forces are operative, the effect of which would be 

 to influence the chances of some elements or of certain mole- 

 cules and thus to affect pure probabilities hitherto considered. 



In many and various cases, however, the actual ultimate 

 arrangement of molecules is found to differ immensely from 

 what we should have expected on grounds of purely geo- 

 metrical probability ; and the same may be said with respect 

 to chemical or elementary atoms, their arrangement being in 

 all cases (except when total dissociation occurs) of a kind 

 which we should have expected to be highly improbable. 



It would seem therefore that these are the cases in which 

 it is right to introduce the idea of molecular and atomic forces. 

 Let us admit, as a general principle in molecular theory, that 

 atoms and molecules, unless they are subjected to mutual or 

 external forces, tend to assume that kind of ultimate arrange- 

 ment the [pure) probability of which is greatest. This principle 



* Highly instructive from this point of view is Joule's celebrated ex- 

 periment of 1844, in which air compressed in a vessel (A) was allowed 

 to rush into another equal vessel (B) which was previously exhausted. 

 Take every one of the vessels as an " element/' as defined above ; the two 

 taken together will represent what has been called " Volume V." Con- 

 sider the state of things in the moment when the stopcock is suddenly 

 opened and the first molecule is about to escape from A into B. In that 

 initial (artificially produced) configuration the arrangement of molecules 

 is exactly that which in this case is the most improbable (n being here 

 = 2). In the final condition of uniform density and temperature, on the 

 other hand, the arrangement is reached the probability of which is 

 greatest. 



Thus, in this case, 



9L-1 AN 



Q" 2>V 2' 



and N being of the order of 10 24 , the initial distribution is seen to be 

 exceedingly important if compared with the final. 



