by a Charged Metal Surface. 443 
of the charge be measurable, we have here a method of measur- 
ing the ratio — for the charged particles which are associated 
with the charge on a conductor. 
If we put the ratio of the amplitudes in the form Re L% , then 
the change of phase as a time is 
1 2 v (cf) + vk) 
p an 1 — v 2 + (<£ -f vk) 2 ' 
The change of phase when the metal is uncharged is 
1 2 v 2 k 
p l_^(l -tf)' 
Now 
_ 2cr e 
(f> ~pV m' 
V is 3 . 10 10 , p we may take as 3 . 10 15 , so that (f> is of the order 
2<r - . 10-“, 
m 
Q 
where e and cr are in electrostatic units. — is of the order 3 . 10 17 
m 
in electrostatic units, and <£ is therefore of the order a . 10 -8 . 
(j) may therefore be considered small compared with vk. 
The difference between the change of phase due to the 
charged metal and that due to the uncharged metal is to the 
first order in </>, 
1 2 v {1 - z ; 2 (1 + & 2 )} 
p ' 1 + 2v 2 (k 2 -l) + v* (k 2 + l) 2 
And so the fraction of the wave-length that the phase is 
changed due to the charge is 
4t tv {1 - v 2 (1+ k 2 )} 
1 + tv 2 (k 2 -l) + v* (k 2 4- l) 2 V’ 
= A(j>. 
For Silver A = — T27, 
Copper A = — *65, 
Bismuth A = — T26, 
Platinum A = — TO, f 
Potassium ...A = — T75, 
Mercury A — — *705. 
2cr e 
