SOME COSTEMl'OR.lin .//>/'. /.Vl/s /.V I'liySICS- r 64/ 

 .111(1 runiliini' ilu- i(iii.iti;in> im>« 



';+A.=i.7'';;'f^' .,18) 



which iiin-i;rali'(l. \ii'l(ls 



/, = .r/v' "-"". (ic) 





\\V still h.ivf lo make llu- hriilKf bclwcL-n tliis Idiimila. which 

 relates to the pressure of the eleitron-Ras in etiuilibriiim with the 

 metal, and the (luantity actually observed, which is the saturation- 

 current out ol the metal surface in an accelerating field. In the 

 equililmum-state. the number of electrons which issue Irom the 

 metal is equal to the number which, coining from the external electron- 

 gas, strike its boundary and do not rebound. This is indisputable: 

 to make it useful we have to make two new assumptions: one. that 

 the numl)er of electrons which issue from the metal is the same in an 

 accelerating field as in the eciuilibrium-siate; the other, that no 

 electrons rebound from the surface. The first assumption had to be 

 made in the preceding detluction- that is. we had to assunu- tacitly 

 that the uncompensated outflow of electrons through the surface of 

 the metal did not appreciably distort the Maxwell distribution within: 

 the second is a drawback peculiar to the thermodynamic method. 

 Accepting these two assumptions along with ail their predecessors, we 

 finally reach the expression for the number of electrons emitted per 

 unit area per unit time from the surface of the hot met.il : 



This is the equation for the thermionic saturaiion-curreni .ittained 

 bv the thermodynamical reasoning. 



Let us finally try some hypothe.ses about the variation ol with 

 temperature: for a first one. the hypothesis <> = constani. The 

 general equation liecomes 



I = Crie~kf, 



(21) 



which is |x-rfectly identical with (S) which was deduced from the 

 electron-theory with the additional assumption of a double-layer 

 independent of temperature. We cannot however freely make an 

 assumption like this, for our equati.m (17) shows that an assumption 

 about <l<t> HT implies, and conversely is implied by. an assumption 



