( 674 ) 



if, after liavinji- )iiiilti|»lie(i (JG) l»y e, avc perform tlic (avo summations. 



indicated in llu- Ibriimla 



/< e T 



-l"" I mw/ //, ^' //, I (17) 



We have in the tirst i)Iace to take the sum of all the valncs 



of ".,■ foi' the svstem of eleeti'i>ns, at a |)arlienlar instant //,, and 



then lo add together all the results obtained in this way for the 

 instants f^, f.^, ele. 



§ 8. If \ve wish to lind -Zi" //,, foi- a gixcn time, we nnist keep 

 in mind that the velocities // of the electrons have at that instant 

 vei'v diifei'cnt directions. Wc may represent all these velocities hy 

 Acctors drawn from a fixed point ( '. The ends />) of all these vectors 

 will lie on a s))liere with i-adins //, and if we let fall from each of 

 these |»oints a per|»endicnlar /) I)' on the diameter of this sphere 

 that is parallel to U A', the di>lances of the projections from 6' will 

 ,iri\e the values of //.,. The sum of all these values may therefore 

 he represented hy 



if ^ is the posilixe or ne,uati\e distance at which the centre of gravity 

 of the points I)' , considered as e(pial to each other, is situated from 

 the centre ('. 



Of conrse. on account of the large nnmher of the points, this 

 distance will he \ery much smaller than the radius ii, and, if we 

 repeat the construction of the diagram of \elocities for each of the 

 instants t^. t...... the small \alne that is found for ^ will he positix o 



in one case and negative in another, ll i> to he reniarlve<l iji this 

 resj>ecl that there is no connexion at all hel ween the values of |, 

 which we shall tind for two succeeding instants in the series /j, /^ .. . 

 Indeed, between any t\\(» such insiants. e\cry electron \\\\\ have 

 undergone a collision, and it may safely be assumed that, Nvhatever 

 be the direction of motion of an electron before the im|)act, all 

 directions will be equally jirobahie after the impact ^). 



Xow, in order to determine (/^,^ , we have to lake the s(piare of 

 the sum denoted bv -i in the formula (17). This s(piare consists of 



A- 



terms of \\\o kinds, some having the form 



co.r ]it^\2: nf z=i<f ro.r 11 1 ^\ (18) 



1) This is easily shown, as has been done by Maxwell in liLs first [iaper on the 

 kinetic theory of gases, if botli the electrons and the particles ot the metal are sup- 

 posed to be perfectly elastic spheres. 



