EXPERIMENTS WITil IONIZED AIR. 85 



ever, iiijiy he done more julvantageuusly aftei' tlie data of tlie next section, in whicli 

 i2 is constant and V variable, have been sijnilaily broiiglit forward. Tlie values 

 for table 1, in which for highei' temperatures and i-emarkably stronger ionization, 

 the values n^/vahow a [)ractically linear and relatively rapid increase with 7/, must 

 be left without comment. Cf. fiirure (>. 



10. C(fxe of (1i fusion. — The next case with a bearing on the piesent lesults and 

 desei'ving a statement is that of diffusion. Since liiit a small part of the ions are 

 utilized as electrical carriers, as repeatedly evidenced, the effect of curi-ent may be 

 neglected. This facilitates integration. 



The motion is now subject to the concentration gi'adieut dii/<li\ and a new 

 constant is thus needed. Let a be the number of [)articles flowing across a stjuai'e 

 centira. per second when the gradient {dii/dr) is a unit. Thus a{dn./dr)/i). is the 

 velocity of the flux. If influx into the spherical element, drxlca, be positive, the accu- 

 mulation within the element is, per second at a given instant, ard'^^rv) / di^.drdoo. 

 The decay in the same element is k'n'drdai. Hent'e, if the effect of current is neg- 

 lected, d~(rv)/dr = k'lr/u./: This equation is not integrable in finite form, being 

 virtually y" = ^'[f/''- It is ecjuivalent to the series 



y = C+ C'(r - a) + fi{CV2a){r - .,)' + fi{C/3a'){,rC - C/2){r - af + 



where Cand C", a and /> are constants. Thus if a = /• 



n = C/r + C'{r - R)/,- + hC'-{r - RY/iRr + bC{RC' - C/2){r - Ry/:,R'r + 



If at r = R the concentration ii vanishes, oi' ii. = 0, then 6'= and 



n - C'{r - R)/r + bC\r - RYh-Rr + /'(y?=C' - (C - RCj){r - RY/2 X T^R'r + 



Hence, veiy near the surface the gi'adient is dit/dr =. C'li/r, and at the surface 

 d„/<lr = C'/R, so that C is negative. Thus uAn R' C'/R = i7ra OR is the number 

 of pai'ticles available per second, at the boundary, increasing with R^ while aC/nR 

 is their velocity, decreasing with R. 



If all pai'ticles were here used to cany electric curi'ent {(l(^./dt), d(^/dt^ 

 01 V/dt = 4:7taC'Re^ where 6" is negative. Hence the curi-eiit would be greater as 

 R increases and constant as to time which is not compatible with the observations 

 as a whole. Thus e must be an avei'age charge and a function of V /R, so that the 

 case does not admit of immediate numerical computation and is therefore of minor 

 intei'est in promoting the piesent inquiiy. 



In the preceding instance the effect of current is ignoied. If this is not done 

 and the presence of current is a destruction of particles in each shell, the conditions 

 are as follows. The accumulation per second in the shell of radius /• will be 

 4i7Tard~(^ri!^/d/--.dr, the decay per second h' ir-^n r'~di\ the number per second de 

 stroyed by the current C(dV/dt)e.dr/R. Thus 



d-(ni)/dr = k'r-;r/ar + C{dV/dt)/^TteaRr 



or simply ?/"= (^''y -f- ^'")/''- '^^^^ integral if obtained in a way similar to the 

 above gives 

 „ = A'(r-R)/r^k'{r~RY/x X 2/?/- + //(;■- /?)72 X3^V+(/C".4'^y?=+ /&")(;•- i?)V3X4A'V 



+ 



supposing that 7i = at /■ = R. 



