CONTEMPORARY ADVANCES IN PHYSICS 501 



when X passes d/2 the sheaths overlap and the conditions change 

 entirely. Other things being equal, x increases as the number of ions 

 per unit volume of the gas outside the sheath decreases; and it is 

 actually found that as the direct current maintaining the ionization is 

 reduced, the increase of capacity due to the ionization is also reduced, 

 passes through zero, and becomes a diminution as the simple theory 

 indicates. 



One might on the other hand get rid of the sheaths altogether, by 

 adjusting the (mean) potential of the plates to so low a value that 

 X vanishes, instead of leaving it to seek its own level. This has 

 recently been done by Childs, though for some reason he chose to 

 study not the dielectric constant, but the conductivity of the ionized 

 air. A galvanometer w-as coupled into the high-frequency circuit, 

 which was tuned to resonance when the mean potential of the plates 

 had been so adjusted that the visible sheaths had just vanished. 

 The reading of the galvanometer was taken; the current maintaining 

 the ionization (it was 300-cycle A.C., instead of D.C.) was discon- 

 tinued, and various high resistances were connected in parallel with 

 the condenser plates, until the galvanometer resumed its former 

 reading; the value of resistance then existing was taken as that of the 

 ionized air between the condenser-plates. The edge-correction of the 

 condenser was determined by filling the tube with alcohol of known 

 conductivity; it was found that the conductance of the condenser had 

 to be multiplied by 0.57 to be converted into conductivity of the 

 medium between the plates. The values of conductivity (I will 

 presently state the conditions more precisely) were of the order of 

 10-1^ E.M.U. 



A value of conductivity by itself, obtained at a single frequency, 

 is theoretically the value of a combination of N and g; to determine 

 either, without the aid of a simultaneous measurement of dielectric 

 constant, one must have an independent value of the other. Childs 

 evaluated N by the Langmuir probe-method.^ Working with air at 

 1 mm. pressure and a frequency about one million, for three values 

 of the 300-cycle A.C. maintaining the ionization (5 ma., 10 ma., 

 15 ma.) he obtained three values of the electron-concentration N 

 (they were 9.6, 24 and 36 times 10'^ per cc), and substituted them, 

 not into the general equation (7) for a, but into an approximate form 

 thereof : 



<T=Ne'/g, (11) 



believing g to be so large that mn is small by comparison. The 

 values of g thus obtained w^ere 2.5, 3.1 and 2.5 times 10~^^ Despite 

 * "Electrical Phenomena in Gases," pp. 351-352. 



