transmitted through a Metal of a Current in the Metal. 381 



Suppose a corpuscle has mass m, charge e, and that an elastic 

 force p£ acts on it, where £ is its displacement in the direction of 

 the a; axis, k a frictional coefficient, then the equations of motion 

 for the corpuscle are 



m % = eX ~«%- P% etc -> E = ( X > F > Z \ 



For corpuscles which are not acted on by a harmonic force we 

 have 



m dt^ 6X - K aH' 



„ T . , . 2ttk 4nr' 2 m n 47r 2 e 2 iV 

 Writing 1 = a, ■ = a, = 7, 



O p p p 



where N is the number of charges e per unit volume, then we 

 obtain 



1 + S, / l — s \ + 2 2 



a + 1& = 



2tt/c 4tt 2 



fc r- m 



v T T- > 



where t is the period of the luminous waves and Sj refers to 

 corpuscles of the first type, £ 2 to corpuscles of the second type. 

 (Drude, loc. cit.) 



For the modification to be introduced when a current is flowing 

 in the metal we first consider 2 2 . This sum will be unaltered by 

 the constant external force since the equations are linear both for 

 the motion of the corpuscle due to the light field and the electric 

 force producing the current. There will then be no change 

 in 2 2 . 



We have mentioned the possibility of some of the corpuscles 

 of the first type changing character owing to the electric force 

 driving the current, and becoming corpuscles of the second type. 

 But as Ohm's Law holds very accurately we see that the number 

 of corpuscles passing over from one type to the other is small 

 compared to the whole numbers in the two types provided the 

 temperature of the metal does not change, so that there will not 

 be much change in the values of a and b and any variation in 

 these constants will be of the order of variations from Ohm's Law. 



If now E', H' represent the electric and magnetic forces due 

 to the light and E,H, the part due to the battery producing the 

 current, the total electric flux is 



(a + cb) d ^-+ (c + id) [E', H 2 + H'] + - 1 + - pBx, H x + H'], 

 at <t o" 



Ei being constant. 



