CONTEMPORARY ADVANCES IN PHYSICS 589 



but the values computed from these curves for N and g are not very 

 plausible, as I will later stress. What is much more serious: the 

 capacity of the ionization-condenser is increased by ionizing the air; 

 the dielectric constant of the ionized air is greater than unity, instead 

 of less! The method therefore, adequate as it seems in principle, 

 suffers from some defect or defects, which it is important to discover. 

 One of these defects was recognized towards 1925 by Appleton, 

 who in previous work by the same sort of method had obtained the 

 same bothersome result: when the air was ionized, the capacity of the 

 ionization-condenser usually went up instead of down (although he, 

 and van der Pol before him, did have the satisfaction of observing a 

 decline of the capacity, when the strength of the direct current and 

 hence the degree of ionization were relatively low). This however 

 he explained by taking into account the space-charge sheaths of positive 

 ions which form upon plates immersed in a strongly-ionized gas, 

 or for that matter upon the walls of the tube containing the gas, 

 if they are allowed to assume the potential which they naturally seek.^ 



If each of the two plates of the ionization-condenser is overspread 

 by a positive-ion sheath of thickness x (x being less than half the 

 distance d between the two plates, otherwise the sheaths would 

 overlap) the system behaves not like a single condenser but like two 

 in series. The capacity of each of the two, according to Appleton 

 and Childs, varies inversely as x; their formula for each is AK/Sttx, 

 K standing for what they define as "the effective dielectric constant 

 of the sheath" and A for the area of the plate; it differs from the 

 customary formula for the capacity of a plane condenser — AK/Atx — 

 because of the distribution of charge in the volume between the 

 plate and the outer edge of the sheath. The capacity of the two in 

 series is AK/Gttx. If x is sufificiently small, this will be considerably 

 larger than the capacity A/^ird of the ionization-condenser as it was 

 when the gas was not yet ionized ; and the change in capacity occurring 

 when ionization is started will consist chiefly of the substitution of 

 the value AK/Gtx, for the value Aj^ird — even the influence of the 

 layer of ionized gas between the outer surfaces of the sheaths will 

 be minor. 



If these ideas are correct, then when x is small the change of capacity 

 of the ionization-condenser should vary inversely as x, provided we 

 can vary x without altering K. Now when the potential V of the 

 plates relative to the bulk of the ionized gas is varied, and the intensity 

 of the ionization in the gas remains the same, the thickness of the 

 sheath varies as V^'^ while the current-strength across it remains 



^ "Electrical Phenomena in Gases," pp. 355-371. 



