484 Prof. C. Barus on the Ionization 



where n is the number of particles at the right section l 

 of the condenser, and n the number at /. Thus n depends 

 essentially on k, and is not, as in the preceding and following 

 papers, independent of it. Moreover, k is to be replaced by 

 3k, as already intimated, the latter being nearly identical, 

 in order of numerical value, with U of the next paragraph. 



8. Effect of an Electric Field. — Supposing this number of 

 particles to be actually conveying electric current, or, from 

 a different point of view, supposing that one ion is sepa- 

 rated in case of the phosphorus emanation from each of 

 these nuclei by the stress of the electric field, the current may 

 be found as usual. Or the other theory developed in my 

 last paper may be applied, remembering that the effect of 

 the presence or absence of the electric field on the number of 

 nuclei is inappreciable when tested by the colour-tube. 



LetE be the difference of potential of the faces of the con- 

 denser (potential of the inner rod, since the metallic envelope 

 is continually earthed), U the velocity of the positive ions 

 relative to the negative ions in the unit field, Q the charge of 

 the condenser, C its capacity. Then the charge lost per 

 second at the element dl is 



27rEUwe(r s + r 1 ) . dl/fa-r^, 



in consequence of radial conduction across the ionized air- 

 space. The total loss of charge per second is 



dQ/dt = CdE/dt, 

 whence 



(Jl 





If now the value of n = n e~ 2k ^' Io ^ v ^~ r ^ just found for A/ = 

 is inserted and the integration completed, the result will be 



- (dE/dt)/E = ^ (r2 ~^ Um ° (1 - e -2*(z->o)Mr 2 -n)). 



It is next necessary to evaluate the velocity v (cm ./sec.) in 

 terms of the volume V (litres/minute), taken out of the gaso- 

 meter and passed through the condenser into the colour-tube. 

 ►Since 



Yl000/60=7r(r 2 2 -r 1 2 )v, 



the datum V, if inserted into the last equation, reduces it 

 eventually to 



- (dEldt)/® = 1G ' 7VU fr,° (1 - e -' 376 ^-^-M-i)/v) 



