78 
PROF. It A. WILSON ON THE ELECTRICAL CONDUCTIVITY AND 
The following tables gives the conductivities of the flame containing different 
amounts of CsCl, deduced from the above results, taking that of the flame 
without salt equal to unity :— 
Solution sprayed 
(grammes CsCl per litre). 
Conductivity. 
0 
1 
0•0032 
2-88 
0 • 008 
5-72 
0-016 
8-9 
0 • 032 
13-5 
0-08 
22 • 7 
0-16 
32-8 
0-8 
85-2 
8-0 
282 
80 
883 
The ionic theory of the variation of the conductivity with the concentration will 
now be considered. 
Let S denote the number of salt molecules per cubic centimetre in the flame, 
ionised or not, and n the number of positive salt ions per cubic centimetre. Then 
S — n will be the number of lion-ionised salt molecules if we suppose one salt molecule 
gives one positive ion. 
Let F denote the number of flame molecules per cubic centimetre, which can be 
ionised, and m the number of flame-positive ions per cubic centimetre, F —m is then 
the number of non-ionised flame molecules per cubic centimetre. 
We then have 
S — n = an(n + m) .(l) 
F —m — (3m (n + m), .(2) 
where a and (3 are constants ; a is the ratio of the coefficient of recombination of the 
positive salt ions with the negative ions to the fraction of the non-ionised salt 
molecules which ionise per second ; (3 is the same thing for the flame-positive ions. 
F is very large compared with S, and m is usually small compared with n. 
Hence m must be extremely small compared with F, so that F—m may be replaced 
by F. 
The conductivity (c) of the flame is proportional to the total number of ions per 
cubic centimetre, so that 
where A is a constant. 
Ac = n + m, 
(3) 
