130 CONDENSATION OF VAPOR AS INDUCED BY NUCLEI AND IONS. 



77. The absorption of phosphorus nuclei.* The method of the pre- 

 ceding paragraph applied to the data obtained in the given paper with 

 phosphorus nuclei leads to striking results. It shows the possibility of 

 computing nucleation by passing a current of highly ionized air through 

 tubes of known length and section into the steam-jet apparatus there 

 developed. In these experiments, made a long time ago, the value of the 

 absorption velocity K was found to be 0.3 cm. per second, with the 

 condition that decay by the mutual destruction of phosphorus nuclei is 

 negligible. The equations here are 



where v is the velocity of the air current bearing phosphorus nuclei 

 and flowing through a tube of radius r, and where n and n are the 

 nucleations at the ends of the tube of length x. 



If V and V are the volumes of air in liters per minute of lengths 

 x and o, discharging equal numbers of nuclei per second into the steam 

 jet, 



If decay can not be ignored, as is now to be assumed, the equation is 

 more complicated; for 



-(v/K')dn/dx = 2 Kn/K'r + n 2 

 or 



n( 2K(x - Xo)/rv (2K + K'rn ) K'rn ) = 



where K' is the decay coefficient; or since ^ = 1000 



n 

 itR=K'/2K=b/2C. 



For the same clear blue field seen in the steam-jet apparatus, the incom- 

 ing volume per second of nucleation must be constant. Hence nV = 

 n'V', and if x = o, 



V 



If V = V corresponds to x f = o (or the absence of the tube) 



e Krx/ 2 .6 5 VlL + R r \_R r = 

 \ W / 



The equation therefore reduces to 



V /V +i 



e rX/2 ' 65V=: i+Rrn +I 

 whence 



i / V/V -i 



I T 



n -T-* ' z.-'*^- / A^T/ A 



* Experiments with Ionized Air, Smiths. Contrib., 1309, pp. 34-36, 1901. 



