SOMI-: COM F.Mi'iU^'.iKy .inr.ixcrs /.v I'livsus it \y? 



If \vi' siipiMisi' lli.it the corpiisili-s .u'(|iiiii' llirii s|hc(1 ii .iI iIr- ili>l.iiu»' 

 ■v ill frir llii;lil Inmi ilir i-lrctrndr wlicir llu-\ si.irl, \vc li>ivr \inir=e\', 

 .iiul 



{Va-V.)"^=^=yj'^id\ (16) 



This is till- t(|u,iliiii .ul.ipted to ok-rtrons or other ions llowing acrAss 

 olht-nvisf enipt\ sp.ur. 



If wo supposr that the corpuscles have at each point a speed propor- 

 tional to tin- titid -trenyjth at that point, we have u= ±k dV/dx, nm\ 



I'd- V»= .^-^ 



This equation would be adapted to ions drifting in so dense a gas, 

 or so weak a field, that they acquire very Utile energy from the field 

 (in comparison with their average energy of thermal agitation in the 

 gas) Ix'tween one collision and the next, and lose it all at the next.'^ 

 If we conceive of ions which acquire much energy from the field 

 between one collision and the next (much, that is, in coinparison 

 with their average energ>' of thermal agitation) and lose it all at 

 the next collision, we have u- = {irel/2m) dV,'dx and 



{V4-Vof = Cid^'^ (18) 



the constant C being equal to vm'El multiplied by a certain numer- 

 ical factor, and / standing for the mean distance traveled by the ion 

 between one collision and the next. 



The theory- just given is too simple; it is an essential fact of the 

 actual physical case that the ions emerge, at the surface of the electrode 

 whence they start, with forward velocities which are distributed 

 in some way or other about a mean value. These initial forward 

 velocities, though often small compared with the velocities which the 

 ions may acquire as they cross to the other electrode, are large 

 enough so that all of the ions would shoot across the gap if the field 

 strength were really zero at the emitting electrode and assisted them 

 ever>where beyond it. In fact the space-charge creates a retarding 

 field at the surface of the emitting electrode, and a potential minimum 

 (if the ions are negative; a potential maximum, if the ions are positi\e) 

 at a certain distance in front of it. Here, and not at the emitting 

 electrode as we previously assumed, the field strength is zero. Equa- 

 tion (10) is often valid in practice, because this locus of zero field- 

 strength is often very close to the emitting electrode. In fact, by 



'* .As in electrical conduction in solid metals (cf. my preceding article). 



