54 THE ROYAL SOCIETY OF CANADA 
If the field is only slightly altered by the ions, we may write 
Pr = Fir, 6 (Er) 
where § (Fr) is a small quantity. 
Hence from (1) 
6 (Fr) = r6F = 279, @ — 2,7) 
where p, is the density of electrification at r,. 
If 6V denotes the change in the potential difference between the 
cylinders due to the ions, we have, when the inside cylinder is positive, 
ie ( lie ) 
| freee pp Et n 2 p 2 n 2 
ov fst dr = 7p,\r2 — rr? —2r} log — 
r r 
1 
where r, is the radius of the outer cylinder and r, that of the inner. 
Hence 
C To To 
V = ——— log — + rp, | r” — rr’ — 2r2 log — D... (2) 
2x0 ik Tr; Tr, 
In the same way, when the outside tube is positive— 
C 1 To 
V = —— log — + rp. 2r/ log — —r} +17 9... .- (3) 
2 «pk ie ne 
In the apparatus used r, was 0-375 cm. and r, was 0-15 cm. Sub- 
stituting these values in (3) we get 
01460 1 
Pat 
v= 
— + 0-436, 
which shows that there should be a linear relation between V and C, 
provided p, is constant and the P.D. sufficiently large for the electric 
field to be only slightly disturbed by the ions present. 
The figure shows the currents observed at the temperature 1,080° C. 
It will be seen that with the outside cylinder positive the relation 
between the P.D. and the current can be represented very well from 
200 to 800 volts by an equation of the form V = AC + B where A and B 
are constants. 
