978 Prof. A. M. Tyndall on the forces acting 



At the other end of its path each ion imparts this momentum 

 to the electrode in coming to rest, and the latter is therefore 

 also thrust back, the forces on the two electrodes being thus 

 equal but opposite in direction. 



Hence, in so far as a horizontal arc may be regarded as 

 symmetrica], we should expect its carbons to be thrust apart 

 with forces which are equal both to one another and to the 

 sum of the momenta imparted per second to the ions starting 

 at the two electrodes ; this is on the assumption (justified 

 by the present experiments) that the amount of lateral loss 

 of momentum from the arc to the surrounding air is 

 inappreciable. 



The above applies to the case of ions which start from rest 

 in the gas ; but the conclusion is the same if they. have been 

 projected with high velocity from the electrode and have 

 then slowed down near the latter to the steady velocity of 

 viscous motion ; for the recoil felt by the electrode is now 

 in excess of the suction due to the slowing down, and by an 

 amount which is equal to the momentum left in the ions. 



It thus seems to be generally true that, provided the ions 

 reach the velocity of viscous motion close to the electrode 

 from which they start, the two electrodes will be thrust 

 apart by forces equal to the momentum put into the ions 

 per second in reaching that velocity. 



Now we may obtain some idea of the magnitude of these 

 forces by applying Langevin's original formula for the 

 mobility of an ion. In this the average velocity "v" of 

 ions moving viscously in a field of intensity "X 5 ' is 

 given by 



e X v 



where m is the mass of the ion, and \ its mean free path 

 and U its velocity of molecular agitation. 



In estimating the mean free path we may follow Wellisch, 

 who found an expression for the influence of the charge on 

 the ion on its mean free path. According to him, 



i* 777^ *{,_l_ 2R °\ 



V m \ mur/ 



where 



b - 5=- x t . 



b7rn <j* 



n is the number of molecules per c.c, " u " their velocity of 

 molecular agitation, M and m the mass of molecule and ion 

 respectively, a the sum of the radii of molecule and ion,' 



