1881.] the Electromagnetic Theory of Light. 1G3 



Let Bff be parallel to this. Let BPB, BP X B', and BP'B be 



the sections of the sphere by planes parallel to the incident, the 

 reflected and the refracted waves, and let lines parallel to the 

 directions of electric disturbance in these waves cut the sphere 

 in P , P v P' and lines parallel to the directions of the magnetic 



77" 



disturbance in Q, Q X Q', PQ = P 1 Q 1 = P'Q' = ~ , and the direc- 



tions PQ, etc. are related to those in which the wave travels 

 as the directions of rotation and translation of a right-handed 

 screw. 



Let the normal to the surface drawn inwards meet the sphere 



in A and let B G = 5 . 

 2 



The surface conditions are, (1) That the magnetic and electric 

 displacements resolved normal to the surface should be the same 

 in the two media. (2) That the electric and magnetic forces parallel 

 to the surface should be the same. 



Thus the magnetic and electric displacements in the direction 

 A are to be the same. This gives two conditions, and the magnetic 

 and electric forces parallel to B and G are to be the same. This 

 gives four other conditions. Thus there are six conditions in all, 

 which, as we shall see, reduce to four. 



We treat the first medium as isotropic. Let K be the specific 

 inductive capacity, V the velocity of light in the incident wave, 

 <£ the angle of incidence, <£ t that of reflexion. We consider at first 

 only one refracted wave. Let V be the velocity of that wave, K' 

 the specific inductive capacity in the direction in which the dis- 

 placement in it takes place, % the angle between the refracted ray 

 and wave normal, <£' the angle of refraction. Also let 0, 6 X , 6' 

 be the angles which the directions of vibration make with B, B'. 

 Let S, S v S' be the electric displacements in the three waves. 



The electromotive forces are 



4tt ~ 4?r ~ 



K ' K ' 

 for the incident and reflected waves, and for the refracted, 



along the direction of displacement, 



and 



along the wave normal. 



and jp S' tan % 



