DISCHARGE OF ELECTRICITY FROM HOT PLATINUM. 
255 
When X/p is greater than about 200, ajj) is given (as Townsend shows) by the 
formula aj-p = where N = 15-2 and E = 25 volts. The values of 
are oiven in the third column of the above table, and it can be seen that they agree with 
the experimentally determined values of a/^j. X is measured in volts per centimetre 
and p in millimetres of mercury. Thus when X/j:) is large, ctj'p is nearly ecjual to 15-2. 
If V is the P.D. between the wire loop and cylinder, and r the distance from the 
V 
near the wire X = —j-, wliere h is the 
r log b/a 
radius of the cylinder and a that of the wire. In the experiments just described 
5 = 07 centim. and a = 0’005 centim., so that loghja — 4‘94 and X = V/4'94r. 
Hence X at the surface of the wire is equal to 40 V. 
Let n, denote the number of negative ions, crossing a cylinder of radius r coaxial 
with the hot wire, per second. Then we have 
dur = UrOL dr ; also a = Nand X = . , so that dn,. = -^^^,]SI'^e-(NEWV)iogz-/« 
r log b/a 
centre of the wire, then approximately 
Integrating, we get log ni/Ua = 
V 
E log h/a 
|g-(NEixt/V)log?V« _ g-(NEi)&/V)log6/«j. 
This equation 
should therefore be capable of approximately representing the variations of the 
current with the pressure and P.D. at constant temperature, when the P.D. is large 
enough to drag all the corpuscles which escape away from the wire. The value of N 
or the maximum number of negative ions produced l)y a corpuscle in going 1 ceJitim. 
in air at 1 millim. pressure is equal, according to Townsend’s res\dts (Joe. cit.), to tlie 
number of collisions with air molecules made Ijy the corpuscle. N sliould, therefore, 
he proportional to the numljer of molecules present at I millim. pressure, that is, it 
should be inversely proportlon'al to tlie absolute temperature of the air. 
The following talde contains valnes of n^/na taken from the curve in fig. 2 at 
27 millims. pressure and tliose calculated by the formula taking N = 3’04 and 
E = 177, which values were olfiained from the ol)served values of at 150 and 
300 volts. 
V. 
nd'na found 
= 5). 
iihl'n-a (calcnlaled). 
100 
2 * 2 
2-5 
1.50 
3-9 
4-0 
200 
G-8 
G-4 
2.50 
11-7 
11-0 
300 
21 -2 
21-0 
320 
26-1 
27-2 
If N varies inversely as the absolute temperature, then, the value of N being 15 at 
20 ° C., N at 1648° 0. should be 2‘3. The nuinljer 3 obtained is rather larger than 
this, as was to be expected, because the air near the wire must be cooler than the 
