52 EXPERIMENTS 'WTrH lOXIZED AIR. 



TABLE 8.— SUMMARY : / = c' „ /( i + dx); c / c „ = «/«„ ; ,'„ 



.too ; /' ; 



.88. 



10. Working hypothesis. — It will be .seen in the ne.xt chapter tliat tin- 

 ciiirent removes a relatively insignificant number of particles. Hence in the 

 condenser, figure 2, the loss of ions is due either to their mutual destruction or 

 decav in the space .r between the plates, or to their escape latei'ally <>ut of this 

 space into the surrounding atmos[)here. 



Let n be the number of j^articles per cubic centini. at a distance x from 

 the phosphorus grid, /-*, figure 2. Let A be the area of the condenser of air 

 space X, and let ax be the circumferential area terminating in the edges of the 

 condenser (mantle of the cylinder of air). Let k be the al)sorj)tion velocity of the 

 ions in the absence of an electric field, when passing from a saturated legion eithei- 

 into free air or normally to an absorbing surface. Thus k is the nninbei' lost 

 under these conditions, per .square centim. per second, when 71=1. Let k'n^ 

 be the number decaying per cubic centim. per second. Then the accumulation 

 in the air plate Adx will be, per second, —{(ln/dT)Ahlx—anMx; the decay 

 in the element will be, per second, h'n'^ AcLv ; and when the flow is stationary 

 (ln/dt=^0; whence — (dn / dx) =z a?i, / A -{- k'n- / i\ If >i „ be the value of n 

 at ./•= 0, the position of the phosphorus plate,/', figure 2, this equation admits 

 of integration in finite form leading to n / n.^ = (a / A) / ({a / A -\- n^h'/ 1-) 

 ("''/^ — n^k'/ k). If A;' = 0, the decay within the element is ignored and the 

 equation takes the simple foi'in »/„ = fis"-'^^, which is specially interesting as n is 

 independent of the absor[)tion velocity also, depending for a given n and x merely 

 on the circumfei-ential area, a.i\ and the base area A of the cylinder of air space 

 between the plates. 



Thus far no reference has been made to the electric field. AVith the velocity, 

 k, moreover, it would not be practicable to approach the <juestion of electric con- 

 duction at once, for the other variables, // and ^, remain undetermined in relation 

 thereto. If?* were found by Aitken's method of nuclear condensation, e would 

 then be deducible by methods presently to be indicated ; but I have not yet done 

 this. 



11. Eledriad conHtderaiions iniroduced. — Suppose, however, in order to esti- 

 mate in how far the present argument is tenable, that the number « = h,,/*""^"^' just 

 found, is a correct value : The question is put whether this numl)er is in reason- 

 able acconl with the usual theory of electrolytic conduction. In other words, let 

 the condenser lie charged, remembering that the additional contribution of ions 

 from this cause is insignificant. Let V be the potential difference at the time t. 



