of Air by Phosphorus. 485 



or 



- (dE/dt)/E = K V(l - €- L / v ) , 

 where 



K = 16'7JJen /kC{r 2 —r 1 ) and L=^7 6k{l—-l )(r s -hr 1 ) n 



[). Numerical Comparison. — Case of TJ=k. Instead of 

 computing the current i = C(dE/dt), I have considered it pre- 

 ferable to deduce 



— (dE/dt)/Vj= -log 108 (log E)/&=log 10^/60, 



in paragraph 4, Table I., seeing that x there is referred to 

 minutes ; for this result is almost at once given by the 

 observations, Thus 



tf=KV(l-e- L/v ) x 60 x log e. 



On consulting the chart (fig. 3), however, oojY is seen to be 

 constant in one and the same series, to the extent in which 

 the observations are trustworthy. Hence finally 



.iyV = 26K(l-e- L / v ) 

 is the convenient quantity * for a general survey. 



Moreover 3 it will at the outset be expedient to assume U = & 

 for the saturated emanation, where U, the ion velocity in the 

 unit field, may be taken as 1*5 centim./sec, and where k is 

 equivalent to 3k, admitting roughly that ra/3 ions travel in a 

 given cardinal direction. In my second paper & = *9cm./sec. 

 was directly found in the absence of an electric field for the 

 emanation not quite saturated, however. In my first paper I 

 gave experimental evidence showing that k may be looked 

 upon as decreasing with the degree of saturation n. Indeed 

 it will appear presently that if U = k, it makes little difference 

 within certain limits, what its absolute value is ; for in such a 

 case it practically vanishes from the equation. Thus either 

 of the values given for U and for k will suffice for the dis- 

 cussion ; and in the absence of detailed knowledge as to the 

 nature of the phosphorus emanation, whether ionized air or 

 not, the stated premise is a convenience. 



Hence the following values make up the constants K 

 and L : — 



U = &=1*5 cm./sec, r 2 — r 1 = , 14 cm., I— Z = 50 cm., 

 E=40 volts, ,', + ^ = -46 cm., C = l*l/10 10 farads, 



c =2-3 x 10-' 9 (J. J. Thomson), 

 ti = 4x10 4 (J J. Thomson). 



* 26K=434Uc» /A;C(r a — rj. All data might have been left in terms 

 of minutes as found, but for convenience in other deductions. The colour 

 of the steam-tube should depend on Vw=Vw e- L /v. 



Phil. Mag. S. 6. Vol. 2. No, 11. Nov. 1901. 2 K 



