through Oxygen and Hydrogen at Low Pressures. 231 
dps fi & 
the tables, — =H 5). ter Ae ao Ua) 
Before proceeding, it is necessary to find an expression for 
the number of molecules of water, the formation of which is 
associated with the passage to the electrodes of each pair of ions. 
Let N be the number of molecules in a c.c. of gas at 
a dp F 
(60 mm. pressure. Let A, = — - the fall of pressure per 
(gy 
| ‘ Ap : 
coulomb-passed ; -so that A, is nearly equal to AQ? varying 
with p. > 
Then the number of molecules of hydrogen and oxygen 
lost per coulomb is, since the capacity of the apparatus 
was 970 c.c., 
N x90, 3N\ 
<4 gee Wa 
io Pee 4 “? 
Let e be the charge in electrostatic units on an icn. 
Then from experiments on the diffusion of ions (J.S. Townsend, 
Phil. Trans. 1899), 
Ne=12x 10". 
Now one coulomb is equal to 3x 10° electrostatic units. 
Therefore when one coulomb passes round the circuit, the 
number of negative ions which reach the anode (or of positive 


ions which reach the cathode) is 
3 * 10? 
en 
which 3x10°xN 3x10°xN  N 
c Ne ek bY At ae hs 
Therefore, when the pressure is p mm. it follows that the 
arrival of — negative ions at the anode involves the dis- 
ay aN 
rope 
appearance of 7 molecules of hydrogen and oxygen. 
That is, the passage of each negative ion to the anode is 
accompanied by the formation of 
2h 
molecules of water. 
On referring to the Table VII., by way of illustration, it 
will be found that <i, =2°2 when p=1°8, this being one of 
the lowest pressures recorded in the tables. 
Therefore, as each pair of ions reached the electrodes at this 
pressure, 4:4 molecules of water were formed. 
_ Next, on taking the highest recorded pressure 6°5 (Table 
V.), it will be found that 8°83 molecules of water were formed 
as each pair of ions reached the electrodes. And on all 
