Barns — Ionization of Water and Phosphorus Nuclei. 219 



fore, n = 2'3aC(r 2 — r^/16'7 e "Fas the approximate equation for 

 the nucleation at the influx pipe of the tubular condenser, 

 while 



n 't=n k/ TJ 



is equal to the datum found for plate and spherical condensers. 

 Hence if k = # 3 cm./sec. for the phosphorus emanation, a lower 

 limit of V, is 



U=kn /n Q '= -3X8/36 = "067 cm./sec. 



In other words, the velocity of the phosphorus nuclei in the 

 unit (volt/cm.) field is about *07 cm./sec. The radius of the 

 phosphorus nucleus will then be 



R=-125X10- 6 /* 06 ' 7 = l-9XlO- e cm., 

 i. e., about 4*5 times larger than the value obtained under the 

 assumption of U=k. 



4. The results thus found for phosphorus nuclei make it 

 necessary to reopen the computation of n for plate and spher- 

 ical condensers. The assumption formerly made was U=k, as 

 a normal case and in the absence of available guidance. It is 

 well, therefore, to summarize the equations used as follows : 



For plates, ~(dE/dt)/E= A TJn,e/Cxe ax / A , where A is the 

 area, x the distance apart, a the linear edge of the plates. 

 Herefrom, if TJ= 1 cm./sec. ?z =33xl0 4 . 



For tubes, -{dE/dt)/E= 16-7 VTTen (l -e~ a ) / (r-r,)hC, 

 whence if U=k, n =8XlO\ 



For spheres, — (dE/dt)/E=4:'ireUn 1 /OR, where R is the 

 radius, n x the nucleation for radius l cm . Herefrom, ^=39 XlO 4 , 

 if TJ— 1 cm./sec. 



The value of U for the phosphorus emanation has been esti- 

 mated anew in the preceding paragraph as about *07 cm./sec. 

 Consequently these equations all need corresponding correc- 

 tions. Since n varies as 1/ £7, the estimated diminution of U 

 increases n, l/'07 = 15 times. Thus the number of nuclei 

 computed for TJ — '07 cm./sec, and for complete saturation of 

 the phosphorus emanation will be 



from plates, n = 4*9 XlO 6 



tubes, n =5-4xl0 6 



spheres, n x ~ 5*8 XlO 6 



results which contain the most careful revision of the subject 

 which I have been able to make. Note that in computing U 

 for phosphorus, I the condenser length does not occur as the 

 exponential term vanishes. The datum k — '3 cm./sec. was 

 found by direct experiments with the steam tube (Exp. with 

 Ion. Air, Chap. 3). The ratio k/ TJ follows from comparison 

 of tube with plate and spherical condensers. The method here 



