G. Barus — Ionization of Water Nuclei. 109 



denser of length, Z, n the nucleation (number per cub. cm.), 

 Jc their effective velocity and e the charge on each. 



The value of w, for the case that decay of ions occurs merely 

 by absorption of the charge at the walls of the cylinders, is 

 n = n e— 2kl/v(r2 ~ ri ' ) where v is the velocity (cm. / sec.) of the 

 nuclei-laden air in the direction of the axis of the cylinder. 



Here, however, a sharp distinction must be made between 

 the fate of the nuclei and of their charges. The latter are 

 absorbed, producing current. The water nuclei, so far as 

 evidence from coronas goes, are not appreciably absorbed. 

 With phosphorus the absorption of nuclei could be independ- 

 ently proven for the fresh emanation. It failed, however, for 

 very wide tubes, implying stale emanation. Hence, after 

 integration, if the leakage of the condenser is dE / dt and its 

 capacity G, 



C(dJE/dt)=irevn {r\-r\) (l-r««/«MJ). 



Since, v = 16*7 Y /ir{r\— r\\ if V are the liters of nucleated 

 air fed into the condenser per minute, the equation becomes, 



dE/dt=z ;,° K (l — e --377M(r, + r 1 )/T). (1) 



The length of the condenser enters only into the exponential 

 quantity, and the results are the same if I / V is constant. 

 Hence so long as the exponential quantity vanishes, Jc may be 

 any function of the potential gradient, a result which gives 

 the equation much broader significance than appears from the 

 premises. 



To find the value of the parenthesis, it may be tested by 

 assuming k = l'5 cm. /sec, the value* for ionic velocities. 

 Hence the constants are as follows : 



I = 50 cm. y= 2 liters / min. 



2r 3 = 2*10cm. Jc =1*5 cm /sec. 



2r i= -64 cm. e = 2*3 / 10 19 coulombs, 



and therefore the exponential quantity here vanishes. The 

 equation now reduces to 



dE/dt = W7 n eV/ C, 



where n is the initial number of nuclei entering the condenser, 

 e the charge of each, V the liters of nucleated air supplied per 

 minute, G the capacity of the condenser. The current is 

 therefore independent of the length and radii of the condenser 

 and the velocity of the nuclei. This will still be true of h in 

 the two differential equations for di and dn above, is the same 



* Experiments with, ionized air, chapter iii. The value of k for water 

 nuclei is much smaller than the datum assumed, as will be specified below. 



