1190 



also : 



i~i 



"' ^ 7 fix «o' + ^ ^^ _ ^ (^ _ (/_5) )' . dr, 



u 



when the two paths covered .<; =: to / — s, and x=^l — 5 to / — 5' 



are considered as one. Over the first range s must be always 



taken as =0, whereas over the second we must put f = 0. The 



above integration may now also be split up into two parts, and the 



following equation may be put : 



i- 

 _ 1 



-Si 



l-s 



in which ^ = ^^ -|- ^^ may be put (see (c)). In the second integral x* 

 has become constant and equal to {l—aY for the part referring to 

 the attraction, and it does not increase any further in consequence 

 of the elimination of the attiactive force. ^) 



The importance of this last relation is very great. ¥oy\{^I^ Nmu* 

 {K is the total number of molecules, e.g. in i Gr. mol.) is a mea- 

 sure for the temperature of the system, then ' , jS^mii^'^ will be a 

 measure for the Energy of that system. For only the velocity w/, 

 with which a molecule passes the neutral position in J/, can be 

 arbitrarily increased or decreased by addition or diminution of energy 

 (heat). What is added to 7, Nmu^\ in the term Nf{l—sy e.g. till 

 the collision, in consequence of the attractive action of the molecules, 

 can never be modified by supply or removal of energy. This 



When we assume that the attractive action still continues to exist during 



e 



2/ 



— (L—s)^ at the second integration in (c) and [d). But then the results become 



m 



much more intricate, while the difference is after all exceedingly slight, because e 



is so many times greater than f. The already very short period of time of the 



collision would only become somewhat longer, while also the mean square of 



velocity would be subjected to only a slight modification in its value. Hence we 



have relinquished the idea of working out this entirely unnecessary complication, 



the more so as the supposition concerning the mode of action of the attractive 



forces made by us (i.e. in direct ratio to the distance of the centre of the moving 



molecule to the edge of the sphere of attraction of one of the two other molecules 



between which it moves to and fro), should only be esteemed an approximation. 



2/ 

 the collision (which would even be plausible), — x^ should again be substituted for 



m 



