( 595 ) 



cilv, llic ani|ililii(lo ot' llir vilnatidiis will lie pre\eiitcil from snrpas- 

 siiig a certain liinit. 



We should bc led into serions niallieniatical diflieullies. il', in 

 following n|) tliis id(>a, we were to consider the motions actually' 

 taking |)lace in a system of molecules. In order to simplify the 

 problem, without materially changing the circumstances of the case, 

 we shall suppose each molecule to remain in its place, the state of 

 vibration being disturbed over and over again by a large number of 

 blows, distributed in the system according to the laws of chance. 

 Let A be the number of blows that are given to N^ molecules per 

 unit of time. Then 



N 



Ti = ' 



may be said to be the mean length of time during which the vibra- 

 tion in a molecule is left undisturi^ed. It may further be shown 

 that, at a definite instant, there are 



iV -- 

 ~e ' do- 



T 



molecules for which the time that has elapsed since the last blow 

 lies between & and 0- -\- </{)■. 



§ 6. We have now to compare the influence of the just men- 

 tioned blows with that of a resistance whose intensity is determined 

 by the coeflicient (/. In order to do this, we shall consider a mole- 

 cule acted on by an external electric force 



ae''" 

 in the direction of the axis of x. 



If there is a resistance (/, the displacement x is given by the 

 equation 



m — = — fX — fj- ^ a e e'" ' , 



dt' ' -^ dt ^ 



80 that, if we confine ourselves to the particular solution in which 



X contains the factor <""', and if we use the relation (7), 



ae 



. -e'"' (15) 



m{7i,' - h') -(- 1710 



In the other case, if, between two successive blows, there is no 

 resistance, we must start from the equation of motion 



dt 

 whose general solution is 



d'x 



-z= — fX -\- aee">*. 



