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BELL SYSTEM TECHNICAL JOURNAL 



unchanged.* If K remains the same, then the increment of capacity 

 due to the ionization should vary as F''*; its logarithm should be a 

 linear function of the logarithm of V, the line having slope — 3/4. 

 This inference was tested by Appleton and Childs, with the favorable 

 result displayed in Fig. 4. 



The space-charge sheaths thus furnish an explanation for the 

 unexpected sign of the change in capacity occurring when the gas is 

 suddenly filled with ions — an explanation releasing us from having 

 to assume that the dielectric constant of the gas rises above unity, 

 in contradiction to the simple theory. 



V >- 



1.50 



Fig. 4 — Alteration in capacity of a stratum of ionized gas, ascribed to the for- 

 mation of positive-ion space-charge-sheaths along the surfaces of the electrodes 

 bounding the stratum. The slope of the line is — ^i. (E. V. Appleton & E. C. 

 Childs; Philosophical Magazine.) 



Could the sheaths be eliminated? If x is allowed to increase 



indefinitely, several things happen; in particular, the assumption that 



the thickness varies as F^'* and the assumption that K/Gtx is much 



larger than l/Awd depart further and further from the truth, and 



" "Electrical Phenomena in Gases," equation (182), page 360. The equation is 

 the familiar "three-halves-power equation," which derives its usual name from the 

 relation between voltage and current-density with which we are not here concerned. 

 It is valid only if the ions mostly cross the sheath without collisions, an important 

 restriction. 



