428 Mr. O'BRIEN, ON THE PROPAGATION OF LUMINOUS WAVES 



§ 36. In like manner it is easy to shew that if there be two plane 

 refracting surfaces, MB, MC, forming a a^ 



prism, and if r denote the time in 

 which a disturbance travels from A to 

 D by the path A BCD, (p, £ the an- 

 gles which AB and BC make with 

 the perpendicular to MB, and \}s, ^' 

 those which CD and BC make with 

 the perpendicular to MC, MB = z 

 MC = s& ; then we have 





/sin \|/ sin \|/ 



**', 



where fl is the velocity at B, v at C, and »" at D. 



Hence, to determine the course of a ray, we have, (putting St = 

 independently of tz and oz') 



sin sin 0' sin >// sin \| / _ 



S 37. I shall now apply these formula? to determine 4he course of a 

 homogeneous ray passing from vacuum into a prism and emerging into 

 vacuum again. 



In such a case v is constant, and v" = v, and we have 



sin <p = — sin , 

 t? 



sin 4r * -j sin 4r . 



v 



and the common equation <p' + \j,' = i, i being the angle of the prism. 



v is in general a function of BC and the time t, for it is the velocity 

 of propagation of a spherical wave originating at B when it arrives 

 at C, which I have shewn to be variable except when the vibrations 



are cycloidal ; also BC — 



zs\m 



j7 -; hence — , is a function of d> and t: 

 cos (i — <p)' v' r ' 



let us therefore put — =f(<p't). It is evident that in general f is a re- 



