138 BELL SYSTF.M TECHXIC.-IL JOURNAL 



\apor, the caili()(k'-f;ill assuniL's tlie value 4.9 \oIts which is the first 

 resonance-potential of the mercury atom and therefore, as we have 

 seen, is effecli\ely the ionizing-potential of the free mercury atom when 

 the electron-stream is as dense as it is in the arc. This suggests a 

 delightfully simple theory of the whole process: the electrons stream 

 from the cathode, they acquire 4.9 volts of energy from the cathode- 

 fall, they ionixe mercury atoms at the outward edge of the region of 

 high field strength, the positive ions so created fall backward across 

 the cathode-fall and strike the cathode, surrender their energ>' to it 

 and so keep it hot, more electrons pour out, and so forth ad infinitum. 

 It remains to be seen whether so simple a theory can be modified, 

 by statistical considerations or otherwise, to explain the values of 

 the cathode-fall in mixed and diatomic gases. 



We do not know a priori what is the ratio of the number of electrons 

 flowing outward across the cathode-fall in a second to the number 

 of ions flowing inward. It might, however, be very great, and still 

 the number of ions within the region of the cathode-fall at any instant 

 could far surpass the number of electrons within it — the electron 

 moves so much more rapidK' than the ion, and has so much better a 

 chance of crossing the region in one free flight without a collision. 

 Even in hydrogen, in which the ions are the lightest of all ions, the 

 electron current would have to be 350 times as great as the ion- 

 current if the electrons just balanced the ions in unit volume. It is 

 therefore legitimate to try out the assumption that the region of 

 cath(xle-fall is a region of purely positive space-charge, in which some 

 such ecitiation as (IG), (17),f>r (IS) gives the current of positive ions as a 

 function of the cathode-fall and the width of the region. K. T. Comp- 

 ton selected (18). Unfortunately the width of the cathode-fall region 

 has not been measured, but he assumed it equal to the mean free 

 path of an electron in the gas. The value which he thus calculated 

 for the current of jiositive ions was about 1% of the observed total 

 current; the remaining OlC^'f consists of the electrons. 



From the cathode region onward to the anode, the gas traversed 

 i)y the arc is dazzingly brilliant. In the long c\lindrical tubes which 

 enclose the mercur\- arcs so commonh' seen in laboratories and studios, 

 the \apor shines everywhere except near the ends with a cold and 

 rather ghastly white light tinged with bluish-green. This is the 

 positive coliMiin of the mercury arc. The potential-gradient along 

 it is uniform, suggesting the flow of electricity down a wire; but here 

 the resemblance stops, for when the current-density goes up the 

 («)tential-gr;idient goes down. The curve of voltage versus current, 

 which for a solid metal is as we all know an upward-slanting straight 



