EXCESi; SKMJCO.XDL CTOK IIOI.I-: IKA.WSl'URT 41)5 



Since the neutrality condition requires -— = — -", subtractingf 1 )anclf2)and 



at ot 



integralinj^ f^ives the equation of conservation of total current: 



Eififii, + M/i"/') — J(l)c = const, indep. of .v 



where of course 7 = ^6 = (j„ + /,) when < .v < 6 and when conditions 

 are such that all currents flow from left to right. Putting the neutrality con- 

 dition ;/, = Hh + "(1 , into the equation gives the following relation between 

 E and »;. : 



E[(iJic + Hh)nn + Me«nl = j/c (3) 



This can ])e used to eliminate cither E or m, from (1). Tf E is eliminated 

 we have 



d>lh _ _ HelJ-h'hj dNn _ _y( \ ^'^ (a\ 



dt e[{ne + fJih)nh + He nof dx dx 



where V(tih) is an abbreviation for the coefficient shown. If, instead, «/, is 

 eliminated from (1) a similar equation results: 



^ = |f-F(£)££ (5) 



dt J at ox 



where 



V{E) = cE-iihficno/j = E^JLh(E/Eo) (6) 



where 



Eo = j/<ro (7) 



i.e., the field necessary to maintain the total current by electronic conduction 

 in the normal state of the specimen. The velocity V{E) is of course numeri- 

 cally the same as the V(nh) occurring in (4) when E and ;/;, are related 

 by (3). 



The solution can be based on either (4) or (5). We shall use (4), as ;//. 

 is the most interesting quantity for direct measurement, and as the differen- 

 tial equation to be given below for the case where diffusion terms are in- 

 cluded is simpler when )ih is chosen as the dependent variable. 



Equation (4) (or (5)) describes a wave ])ropagated with the variable 

 velocity V. If > « 7',, , so that E is never greatly dilTerenl from E^, , 

 (4) (or (5)) and (6) indicate that ///, (or E) is propagated with the constant 

 velocity £0 ma , as is of course to be expected. More interesting is the case 

 where 7,. and ja are comparable, so that V departs significantly from con- 

 stancy. It is tempting to sui)i)ose that, for this case also, the curve of ni, 

 against x at any time / can l)e constructed by taking the graj)h of ;/;. against 

 .V at / = and moving each point of the curve horizontally to the right a 



