Ionized Phosjihorus Emanation in Tubes. 47 



Let ¥ be the number of particles decaying by mutual 

 destruction, &c., per cubic centim. per second, if n = 1, so that 

 Jc'n 2 is the number vanishing for the density of distribution n. 



wicv. h»> 



Hence the number of particles accumulating per second in 

 the element is —7rr 2 v(dn/cLv)dx; the number absorbed per 

 second by the walls of the tube, krclirr . dx\ the number de- 

 caying per second within the element, k'rfirr^dx. Thus 



- (v/k')(dn/dx) = 2kn/k'r + n*. 



This equation is integrable in finite form, and putting n as 

 the concentration at ,v , the equation becomes 



n = 2*w /(€ 2 ^-^ lrv {2k + kfm ) - k'rn Q ) . 



The direct discussion of this equation is cumbersome. Its 

 bearing on the present results is best shown by evaluating 

 the two special cases in which k = and &'=0, respectively. 

 The former case is incompatible with the observations, and 

 may be dismissed. 



Let then kf=0, so that decay within the element from any 

 causes whatever is absent. The only loss of nuclei is at the 

 surface of the absorption-tube. 



Hence n = n e~ 2kx t ro ^ 



if n is the concentration at .''0 = 0, i. e. in the absence of the 

 absorption-tube. But r = 1000 V/607r>' 2 , if V litres per minute 

 produce the velocity v centims./sec. 



Hence n = n 6- krl2 ' 6 '° y . 



The total number of nuclei injected into the colour-tube is 

 thus nV. Let these produce the fiducial clear blue field. In 

 the same manner let n'V nuclei produce the same field when 

 the dimensions of the absorption-tube are r' and a/ } and the 

 air passing V litres per minute. Then, since nY=nfV f , 



y € -Icrx/2-6bV _ y/g-irV, 2*65 V 



If V be the volume per minute when the tube-length is a/=0 

 and the field the identical blue, 



&=2-65(V/™)log(V/Y ) s 



