502 
the ions could have been destroyed by the 
electric transfer; otherwise the steam tube 
would have shown perceptible variation of 
color, ; 
In connection with this result I have 
questioned whether the importance of the 
mutual destruction or decay of the ions has 
not been overestimated ; whether the phe- 
nomenon of leakage in a plate condenser 
may not be very fully explained * by taking 
account of the ions which wander laterally 
out of the field of force. Let A be the area 
of the condenser of air space x, and let ax 
be the circumferential area terminating in 
the edges of the condenser (mantel of the 
cylinder of air). If one of the plates is a 
phosphorus grid (thin pellets of phosphsrus 
secured between appressed dises of wire 
gauze), let n be the number of particles per 
cubic centimeter at a normal distance x 
from the grid. Let & be the (absorption) 
velocity of the ions in the absence of an 
electrical field when passing from a satur- 
ated region either into free air or normally 
to an absorbing surface, and k’n” the number 
decaying per cubic centimeter per second. 
Remembering that in such a condenser 
there is lateral loss of ions escaping from 
between the plates, as well as the loss upon 
the plates whether the (phosphorus) con- 
denser be charged electrically or not, the 
differential equation meeting the case is 
— dn/dx = n(a/A + nk’/k). This is integ- 
rable in finite form, and if n, be the number 
of ions per cubic centimeter at the phos- 
phorus plate (saturation), the equation be- 
comes n/n, =(a/A)/((a/A + nk’ /k) el? — 
n,k'/k). If k’ = 0, decay within the ionized 
space is ignoredand n = n,/<“/*. Thus n is 
independent of the absorption velocity k, 
depending for a given initial saturation n, 
only upon the mantel (ax) and the base 
(A) areas of the condenser air space. 
Now let the condenser be charged, re- 
*See my paper in the Physical Review, X., p. 257, 
1900, whence the data of this paper are taken. 
SCIENCE. 
[N. S. Von. XIIL No. 326, 
membering that the additional loss from 
this cause alone is insignificant. Let V be 
the potential difference at the time ¢, C the 
effective capacity, U the relative or mutual 
velocity of the ions, ¢ the charge of each. 
Then —dV/dt= AUVne/Ox, or from the 
value of n, —dV/dt =(AUVn,e/ C)/xe“. 
In my data given in the Physical Review 
(1. c., Table III.) I put, as usual for leak- 
ages, V=V,10-“, whence ¢ was computed. 
Substituting this in the preceding equation, 
it reduces to ¢=(AUn,e/Cln10)(1/ae"!*), 
ras 
>) 
oh 
In the annexed diagram I have drawn this 
curve and distributed the observations with 
reference to it by so determining the con- 
stant AUn,e/Cln10, that the first observa- 
tions coincide (c= .200, e=1.7). The 
agreement of the theoretical curve and the 
observations is so striking as to give great 
probability to the hypothesis that decay * is 
here relatively insignificant. 
It is even possible to make an approach 
toward computing the constant, which 
since ¢ in my observations is taken rela- 
*How much importance is to be attached to this 
decay (k’) I shall show in experiments with spher- 
ical condensers in which the ions can not escape. 
These results, while giving no evidence of decay 
show that dilution (since saturation must fall off at 
“increasing distances from a central phosphorus ema- 
nator) is accompanied by additional ionization; i. e., 
there is relatively too much current, cxf. par., when 
the spherical condenser is larger. 
