36 A CONTINUOUS RECORD OF ATMOSPHERIC NUCLEATION. 



The successive values of the table (one minute apart) correspond on the average 

 to about 16 per cent, per minute. In the present installation this jet was 

 unable to charge the condenser, the charging cun-ent being less than 10'" 

 amperes, about of the same order as the leakage. 



One may conclude, therefore, that the loss of charge per minute, i. e., the 

 electrical cuiTent radially traversing the condenser, is practically independent of 

 its length if the latter exceeds a few centimeters, for the air current and width 

 given. All but a few per cent, of the charge are lost in the first few centimeters 

 ahead of the influx tube of the condenser. The experiments are thus in keeping 

 with the surmise of the preceding paragraphs. 



SUMMARY AND INFERENCES. 



18. Working hypothesis. — In conclusion a brief summary of the working hy- 

 pothesis from which most of my work has proceeded may be added for reference. 



Let the ions be regarded as charged nuclei, and let there be an average of 

 q electrons per nucleus. Let the loss of ions be due merely to absorption of the 

 charges at the boundar}- of the region. This is virtually stating that the loss is 

 as the first power of the number n, per cubic centimeter. Whether the charge 

 travels with the nucleus, or whether it travels from nucleus to nticleus along a 

 highway of nuclei, as it were, is left open, but the charges are lost at the bound- 

 ary at a more rapid rate than the nuclei. 



To fix the ideas, let a tube condenser of radii r, > r,, and length, /, be given, 

 and let v (cm. /sec.) be the velocity of the air current bearing charged nuclei 

 longitudinally through the condenser. If V is the volume of this air in liter/min. 

 entering the condenser at one end, tt (r; — r J) z;= 16.7 V. 



The loss of nuclear charges is then due to two causes: (i) These charges 

 have a specific velocity, k (absorption velocity in a given cardinal direction) in 

 the absence of the electric field. Charges are lost in pairs by this non-directed 

 motion without producing current. (2) The nuclei have a second velocity, 

 U', in the same direction per electron carried and per volt/cm. of the field. 

 Hence the number of nuclei, n, at the section / cm. from the influx end, where 

 n = n^, is given per unit of length by 



M = n,f^^''- '"<'■'+'■) = «„?-*' . . . (i) 



where K = k + qEU'/{r,-r,) and a=.377 IK {r, + r,) /V. 



The radial current at the same section, if the potential difference between 

 the surfaces r, and r, of the tube condenser is E, will not depend on k, but on 



U', so that 



-di = 27t{r, + r,)neU'q'{E/{r,-r,)) dl 

 or eventually 



^jir/j^ 16.7 yM„eg-(/-f-») ,, 



- ^ ^^/^^= q+k/iU'E/ir,-r.)) " " " ^'^ 



where C is the capacity of the condenser and e the charge of one electron, while 

 q such charges travel per nucleus. 



