634 BELL SYSTEM TECHNICAL JOURNAL 



is a|)i)li(.'(l, and arc hroiij^hl to a full slnp at t'arli iiillisiiui. Ri'iirt-si-nl 

 li\' / tlu' a\i.Ta^c liislaiui.' lra\ersf(l hilwiiii i nlli>iiiri>. Tlu- pm- 

 |)ii>fi| a'-smiipiidn K-ail> In 7' = V2h;/;' cI\. Tlie ((hiiIihi i\ ii \ i lu-rrlOiT 

 wniild (k-piMi(l 111! i1r' lirUlstrcnglli, wliieii would xidlatr t )linr> law. 

 Ohm's law beinj; rigorniisly valid except uiukr ixirenu- rondiiioiis 

 (Bridgnian found llie first slight deviations from it, in i;(ild and siKer, 

 at current-densities of the order of 10''' amps/cm") we have to discard 

 the idea. The lesson is, that the electrons must be supposed to be 

 normalh- in motion at speeds enormously greater than the speed 

 imparted 1)>- the field during a free fall. Let u stand for the natural 

 a\erage speed f)f the electrons: we ha\e T = l u. and 



a — \ne-l mil, (3) 



provided always that ii^eET J m. 



This condition is abundantly fiillilled if we make the c)!)\iiius and 

 appealing assumption that the electrons are muxiiig with the same 

 a\eragc kinetic energy as atoms of a gas at the same temperature; 

 in fact, if the free path / is no longer than the average distance be- 

 tween atom-centres, the deviations from Ohm's law should not aj^pear 

 e\en under such extreme circumstances as those of Rridgman's ex- 

 l)eriments. Making tlicri-lore this .issuiiipiioii. which in sNiiibols is 



\nin- = -^ k'T. we lind 



' '' "^ (4) 



\(it nmcli attentidu >li(iuld be |)aid to the nunuTical factoi'. whiih would 

 be slightly dilTercnt if we should assume Maxwell's law of distribution 

 for the \el()cilies of the electrons; the essential factor is the last one, 

 nl; y/'J' . Kxamining (4) in the light of the fact that the conductivity 

 of most metals decreases distinctly more rapidly than 1 v 7" = in fact, 

 a.s rapidly as l/7"or still more so — as the temperature increases, we 

 sec that the product nl will ha\e to be supposed to \ary with temper- 

 ature. It seems natural to suppose that / depends altogether on the 

 distance between adjacent atoms, which \aries comijaratix el\ little 

 with temperature, and anyway \aries in the wrong direction Inr the 

 purpose of the theory; so that the burden of accounting for tin- pro- 

 portionality of a to the lirst or a higher power of 1 7 ntiisi Ik l.iid 

 upon w. 



Now il has occurred to a number of people that the free electrons 

 are dissociated from the atoms, and the number of free electrons 



