29B 



gradient i.s zero part of the eiiieigcd elei'lioii.s nia> fall hack on 

 the katliorh;. This theory led Langmiih Io the fonnnla'): 



1= rV^ . . (2) 



Here / is the current as long as it remains below the satnration 

 ciiiient, r is the iujpressed voltage, (/ js a constant which depends 

 on the form and the distance of the electiodes. In the neighhonr- 

 hood of saturation, i approaches a constant value. 



This relation between the thernioionic current and ihe impressed 

 voltage will be foun<i in the characteristics of fig. 2 and 3. A com- 

 plication is here caused by the presence of the third electrode, the 

 grid, about which we may make the following observations. As a 

 ride the audion is used with tensions of sucii values that we 

 should have a saturation-current, if no grid were used. It is the 

 function of the grid to retard more or less the electrons emitted 

 bv the kathode. The potential of the grid is theiefore always 

 chosen lower than the potential which we should have at that 

 place, if the grid were removed. Tsiudly the grid-potential is not 

 much different from the average kathode-potential, in many cases 

 it is even a little hnver. Of the electrons, which I'each the? plane 

 wliich we can draw through the grid, by far the greater part will 

 e.seape between the grid-wires to the anode and but few will strike 

 the grid. The usually small surface of the wires also contributes to 

 this eftecl. Thus the grid current //, (see tig. 1) is in normal woi'king 

 t'onditions small as com[)ared to the anode-current /„. The latter not 

 only depends on the anode-potential e, but also on the grid-potential 

 r. We cannot go far wrong in taking as "driving force" of i„ the 

 mean potential in the plane of the grid. Denoting by ^ this mean 

 potential, fp is, as long as the anode-current has not yet reached 

 its maximum, a linear function of f' and /' 



(f= ((e 4- t^v . . . . . . , . . (3) 



At first therefore we get for the anode-current the following 

 relation : 



,,.^C{u.^^rf. ....... (4) 



An analogous empirical forniida is given by LAN(i.MUiK 'j for his 

 piiotron. 



In wii'eless telegraphy the audion is used as rectifier and as 



') An analogous formula had been given before by Child for the transport of 

 pos. ions. See Phys. Rev. (1911) p. 492. 



1) See HuNn: Jahrbucli f. Dr. Tel. (1916) 10 p. 521. 



