EVAPORATION OF ATOMS 361 



Case I. Retarding field for ions. Under these conditions the ions which 

 evaporate must all be brought back to the filament surface by the field so 

 that if there is no external source of ions, 



apHp=Vp (28) 



and therefore Eq. (27) becomes 



da/dt = aaiia-Va- (^9) 



Under steady conditions we then have 



Case II. Accelerating field for ions. In this case |Xp = o so that 



d(r/dt = aaP-a—Va — Vp. (31) 



In a steady state we have 



Determination of aa\.ia from the ion current 



According to Eq. (32), the value aa\ia can be calculated from the 

 positive ion saturation current density Ip by the relation 



a.l,. = {Ip/e){\ + v,Jv,). ■ (33) 



At high filament temperatures 6 becomes very small and v„/vp ap- 

 proaches a limiting value which may readily be obtained from Eq. (20) 

 by putting Vc ,= o. Inserting numerical values of Vw and Vi we thus find 



• log,o(u„/2v,) = -3770/T. ^34) 



The value of v^ in this equation is that corresponding to zero field. In 

 experimental determinations of Ip to measure aa,[Xa we usually employed a 

 potential of —45 volts on the cylinders. Such fields (about 3000 volts per 

 cm at the cathode) have been shown (at constant^) to increase Vp about 

 7-fold without having any effect on v„. Thus the ratio Vg/vp corresponding 

 to experirnental conditions should be 1/7 of that given by Eq. (34). We 

 thus calculate that Va/vp in Eq. (33) should have values that range from 

 2.1 X 10"^ at T = 1200° to 5.8 X 10"^ at 1400°. The errors involved in 

 neglecting v„/vp in Eq. (33) are therefore negligible. 



The experimental data given in Table IV were obtained to test this 

 conclusion. The 2nd column gives the galvanometer deflection (300 = 0.027 

 microampere) produced by the ion current obtained with 45 volts on the 

 cylinder, with the filament temperatures given in the first column. 



