by a Charged Metal Surface. 



443 



of the charge be measurable, we have here a method of measur- 



e 

 ing the ratio — for the charged particles which are associated 

 m 



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 



tan" 



2v (p + vk) 



p 1 - i/» + (9 + vk) 2 ' 



The change of phase when the metal is uncharged is 



tan" 



2v 2 k 



Now 



p 1 — v 2 (1 — k 2 ) ' 



, 2a e 

 T pv m 



V is 3 . 10 10 , p we may take as 3 . 10 15 , so that p is of the order 



2<r - . 10- 26 , 

 m 



where e and a are in electrostatic units. 



is of the order 3 . 10 17 



m 



in electrostatic units, and is therefore of the order a . 10~ 8 . 

 <f> 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 2v {1 - v> (1 + ¥)\ 



p ' 1 + 2v 2 (k 2 -l) + v i (k 2 + l) 2 ^* 



And so the fraction of the wave-length that the phase is 

 changed due to the charge is 



4>7TV {1 - v 2 (1 + k 2 )} 



l + 2v 2 (k 2 -l) + v i (k 2 +l) 

 For Silver A=- 



2 9- 



--* \ 



Now 



Copper A = — "65, 



Bismuth A = - 1-26, 



Platinum A = — 10, 



Potassium ...A = — '175, 



Mercury A = - '705. 



2a e 



9 



pV in 



