soMi: coxri-.MroK.th')- .ii>r.ixci-.s ix rinsns r m? 



is i;i\fil li\ llir <li'j;ri'i' <il ili»<ui,ili(>n, wliicli In itiiii -IhhiIiI \,irv 

 will) ihf liMii|KT.ilurr in .< in,iiiiu-r |>r»-s(rilnM| ,ili(ii;ii lu-r li\ the .iiiiu.iiii 

 tif work iu'iH"s>.iry lo n'ni<»\t- ,in fln-lmn lioiii ,iii .iinni into ilu' 

 (prrsuiiifih iiitrrs|).u r wlu-ri- it pliiys iilxiiil frt'i'K . \U\\ \\v >li(Hil<l 

 ftTUiiiily i-\|KTl tli.il this wiirk woultl Ik- positivt-. .i> ii is lor ilic 

 eMrartiiMi of «.'li-rin>iis from frei- atoms; in which lasi- tlie dt'^rff of 

 (liss(K-iation and thi- ium)l)(.T of free electrons should increase with 

 teni[K'rature. The theor\ is therefore adapted to explain a resistance 

 which decreases steadily with increasinj; temperature, as do the 

 resistances of some non-metallic elements; it is adapted to explain 

 a resistance which at first diminishes and then, as the temperature 

 increases further, goes through a minimum and rises, for the decrease 

 in the factor / V 7" finally predominates over the increase in the factor 

 «; it is not adapted to explain a resistance increasing with temperature 

 over the whole range, as do those of the metals. One might assume 

 that the work of extracting an electron from an atom inside the 

 metal is negati\-e. This is essentially the alternati\e embraced !)>■ 

 Waterman, who postulates that the work in question is a function of 

 temperature, of the form ]V=\Vo — cT, c>0. For metals H',, is to 

 1h' chosen negative or zero, so that W shall be negative throughout; 

 for non-metallic elements ll'„ is to be given some jxisitive value, so 

 that W shall change in sign at some point in the temperature-range. 

 This unusual theory must be judged by its efTecti\eness; that it 

 should reduce conduction in all elements, metallic and non-metallic 

 alike, to a phenomenon of a single type is a feature appealing strongly 

 in its faxor; but No\es" curves of resistance versus temiKrature for 

 graphite did not agree with its demands in a satisfactory manner. 



The a.ssumption underlying (4) has however involved us in a col- 

 lateral difHcultv'. If we believe that the n free electrons per cc. of 



the metal have an average encrgv' 'kT and a total kinetic energy 

 -—nkT, we are certainK- forced to admit thai wlu-n the imit cube of 



metal is heated through 1° the electrons must take their share " nk 



of the heat imparted to it; but the specific heat of most metals is 

 such that it seems that the atoms must take it all and leave none 

 f>ver for the electrons. If we evade this difficulty by assuming n 

 to be quite small compared with the number of atoms per cc a few 

 per cent, of it or less, we lose certain numerical agreements which 

 will be mentioned later, and we have also to make / c|uite large, 

 amounting to several times the distance between adjacent atoms; 



