68 EXPERHIEXTS WITH lOXIZED AIR. 



- ((lE/dt)/E= Jj;':^ (1 - f -««>^^'-'o)(r, + r.,/P) 



..!• - {dE/dt)/E= KV{\ - f'-^/''), where K= 16.7 UenJhC{r^ - /■,) 

 and L = .376 h (l-I,,) C/-, + /\). 



V). yiii/urical comparison. — Case of ^ = 1c. — Instead of computing tlif cnnvnt 

 / = C {<IE/dt), I have considered it pi'eferable to deduce 



- {dE/dt)/E= - In 10 <y(log E)/6i = In 10 x/m, 

 in i)aiagra])h 4, table 1, seeing that ■/' there is referred to minutes: for this result is 

 almost at once given V)y the observations. Thus ./' ^ KV ( 1 —e -'-/'') x GO x log f. 

 Oil consulting the chart, figure 8, however, a/Kis seen to be constant in one and 

 the same series, to the extent in which the observations are trustworthy. Hence 

 finally x/ V= 26 K (l — f -'- ') is the convenient quantity ' for a general .survey. 



Moreover it will at the outset be expedient to assume U = k, for the saturated 

 emanation, where C^, the ion velocity in the unit field, may be taken as 1.5 

 centim./sec, and where k is eiiuivaleiit to 3^', admitting I'oughly that n/'3 ions 

 travel in a given cardinal direction. In my second paper ^=.9 cm/sec was directly 

 found in the absence of an electric field for the emanation iiof quite saturated how- 

 ever. In my first paper I gave experimental evidence showing that /■ may be 

 looked upon as decreasing \vith the degree of saturation 7i. Indeed it will appear 

 presently that if U = k, \t makes little difference within certain limits what its 

 al)solute value is; for in such a case it practically vanishes from the equation. 

 Thus either of the values given for ZZand foi- I will suffice for the discussion, 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 /iTaud L: 

 U^ k = 1.5 cm/sec, ^g - r^ =z .14 cm, ^— ^o ^^ ^^ ^™' 



E= 40 volts, '•2+'"i = -46 cm, C= 1.1/10'" farads, 



e = 2.3/1 0-'» (J. J. Thomson)", 



«y = 4 X 10^ (J. J. Thomson ; together these values follow also from the 

 present sei'ies of experiments, but fi'om different hypotheses). Thus 



26 K= 434 X 16.7 X 2.3 X lO"'-' X 4 x lO'/l.l X lO"'" x .14 = .260, 

 since Z7= k cancels out ; 



L = .376 X 1.5 X 50 X .46 =: 13.0. 



The following table is thus computed from // V==: 26/i'(l — f -'-"') : 

 V 1 2 3 4 5 litres/minute 



x/V= .26x1.00 .26X1.00 .26 X .99 .26 X .96 .26x93 

 = .26 =.26 =.257 =.250 =.242 



Hence within the limits of observation (F" <4 litres 'mi n), x/ V is appreciably 

 linear, compatibly with the evidence of the four series contained in the chart, 

 fifjure 3. 



10. Slopes of the loci. — The slope, x/ V, of the computed values is, however, in 

 every case definitely above the slopes found by experiment, wiiidi as taken from 

 the chart are, 



' 26 A' = 434 Uen^/kC (r, — ^, ). The electric conductions, x. might have been left referring to 

 minutes, like the volumes V, but for convenience in other computations. 



