Crystalline Reflexion and Refraction. 167 



SECT. V. CONDITIONS TO BE SATISFIED WHEN LIGHT PASSES 

 OUT OF ONE MEDIUM INTO ANOTHER. EEMARKABLE CIRCUM- 

 STANCES CONNECTED WITH THEM. RELATIONS AMONG THE 



TRANSVERSALS OF THE INCIDENT, REFLECTED, AND RE- 

 FRACTED RAYS. 



Now let light pass out of one medium into another sup- 

 pose out of an ordinary into a doubly-refracting medium ; and 

 taking the origin of rectangular co-ordinates # fl , y n , z at a point 

 on the surface which separates the two media, let this surface 

 be the plane of # y*> Then if the components of the displace- 

 ment of a particle whose initial co-ordinates are # , ^o, %o be 

 denoted by ' , TJ' O , ?'o when the particle is in the first medium, 

 and by ", rj " 5 o" when it is in the second, the equation (1), 

 adapted to the present case, will be 



?' /7 2 */ AW 



* Z' , a ^ $ ' , a * s> 



S + - 8.1. + - 8 



= Iff dx Q dy dz Q 8V + Iff dx, dy, dz SV" ; (17) 



wherein 8V and 8 V are the respective values of SV for the two 

 media, which are conceived to extend indefinitely on each side 

 of the plane of X Q y Q ; that plane being an upper limit of the 

 integrations relative to one medium, and a lower limit of the 

 integrations relative to the other. Each medium is conceived 

 to be occupied by systems of plane waves the first by incident 

 and reflected waves, the second by refracted waves ; and, except 

 where they are bounded by the plane of X Q y , these waves are 

 regarded as unlimited in extent. 



For the ordinary medium, if we put 



dz dy^ dx Q dz^ r/// dx Q J 



