638 BELL SYSTEM TECHNICAL JOURNAL 



llic >,imc \\a\. At lr.i>l ,i> iiuirli. ll M•^m^, ^luuild In- iKin.inilcd 

 frnm .m\ llicorv ol ciiiKliiilinii olUrcd in ((impel ilion with llic "cl.is- 

 >-i( ,il" (inc. 



riu- ((ini rplidn (il Irci.' ili-(lr(in> in nu'lals also j;i\fs a luMiniliil 

 ciualilalivc explanation ot llu- lIurmoL-lLTtric effects, alth()iii;li un- 

 fortunately it does not do \er\- well as a quantitati\-e theorN'. If 

 in two metals at a certain tempera iiirt' the densities of free electrons 

 are different — «i free electrons ])er ec. in one and «2 in the other — 

 and these two metals are brought into contact with one another, 

 electrons will flow from the one where the density is greater into the 

 one where it is less; and this llow will continue until arrested 1)\- a 

 countcr-electromotive-force 1', ol which the eciuilibrium-value can 

 I)e shown, in an\' one of a \ariety of ways, to he 



V= — ln{tii/ni) 

 c 



Sncli ,m cleclroindliv e force would .iccouni for the Peltier effect ; 

 and con\ersel\', il tile liie(ir\- wvw correct, measurements of the 

 Peltier effect between two mi'tals at a given temperature and pres- 

 sure would give the ratio between the densities of free electrons in 

 the two metals under the specifietl conditions. Such data, combined 

 with data on conducti\-ity interjireted by such an equation as (4), 

 should give information al)out the free paths !, and l< in the inelals. 

 The Thomson etTect is more difhcult to deal with, as ihernial e(|ui- 

 libriutn does not pre\,iil; howi'\er il can be seen that there will be 

 a coiuiter K.M.I'', in .ui une\ enl\-lie,iled nul.il. Measureineni> on 

 the I'eltier and Thomson coetificienis lor ni,ni\ inetal>. over wide 

 ranges of tem|)eiature and pressuiH', would be \er\' x.iluable; bill 

 they are so exlremeh- hard to make even under the best of conditions, 

 that the outlook for obtaining a reall\- extensi\e set is unpromising. 

 Possibly there is a better chance with the indirect method (detei min- 

 ing the first and second derivatives of llu- curM- of therm. il electro- 

 motive force versus temi)erature). .Such d.il.i of the ■riioni-nn elTecl 

 as exist are not helpful to the simple iheors . 



Another phenomenon which lends itself very readily to explana- 

 tion by the theory, and so contributes a certain amount of support 

 to it, is the thermionic etTect — the spontaneous outflow of electrons 

 through the surfaces of hot metals. (But carbon likewise exhibits 

 it very efficiently, and we must beware of formulating an\' theory of 

 it which reposes on specific properties of metals not shared by carbon!) 

 ■|"o interpret the thermionic effect only one new feature need be added 

 to the theory, and (his a feature which in fact was all the time latent 



