ELECTRICAL CONDUCTIVITY OF AIR AND SALT VAPOURS. 
417 
the E.M.F. is small it is allowable to apply Professor Thomson’s theory to flames. 
It is consequently necessary to consider the arguments brought forward by Dr. Marx 
in favour of his view. 
His main reason for concluding that the ionization is nearly uniformly distributed 
is the existence of a point of inflexion in some of the curves showing the fiill of 
potential between the electrodes, which, as he points out, can only occur theoretically 
when there is some volume ionization. 
It is easy to calculate the variation of the electric intensity between two electrodes 
when only surface ionization occurs and a saturating P.D. is applied. We have 
then 
dX/dx = 477 ( 72 ^ — Uo) <?.(I), 
(d/dx) (/-pbX) = 0.(2), 
(d/dx) {kjLX) = 0 .(3), 
db "p Xe = t.(l)’ 
If qi is the number of positive ions coming in unit time from unit area of the 
jDositive, electrode (2) gives 
/.•p/qX 
and in the same way 
Hence substituting in (l) 
= A- 
ilX 1 
— 477 ( 
lU \ 
dpX /,,x, 
or 
2X'^ = 877| 
(l\ _ a'\ 
(U ' 
d’l 
Integrating we get 
I 
0 
00 
II 
'M 
- 
If we measure x from a point where the intensity is X,,, then X/ C, so that 
X~ - X 2 = 8 
77 
X . 
Therefore in this case the intensity should inci'ease regulaily from one electrode to 
the other unless qi/k-^ = iii which case X = X,j everywhere. 
The fall of potential in the flame when the upper electrode is negative is like that 
indicated by the above calculation (‘Phil. Trans.,’ A, voL 192, 1899, p. 508), and so 
agrees with the view that the ionization nearly all occurs on the electrodes. 
In Dr. Marx’s experiments the upper electrode appears to liave always been 
positively charged, in which case, as I have shown, the curves show a rapid fall of 
potential near both the electrodes witli a nearly uniform intensity in the intervening * 
space, and this form of curve is obtained even when very large voltages are applied. 
VOL. CXCVII. 3 H 
