IN THE INTERIOR OF TRANSPARENT BODIES. 427 



the same time to travel from B to D, and from B' to C, for the 

 paths BD and B'C become ultimately similar in all circumstances when 

 BB' is indefinitely diminished; hence, if t be the time in which a 

 disturbance travels over the path ABC, r + time of describing EB' 

 — time of describing DC will be the time in which a disturbance 

 travels over the course AB'C; now if v be the velocity of propagation 

 of a wave spreading from A when it arrives at B, v the velocity of 

 propagation of a wave spreading from B when it arrives at C, it is 

 evident that we have ultimately, 



time of describing EB' = = ™, 



. , ... nri DC BC'-BC 3zsin0 

 time of describing DC = — p- = ; — . — = — *- , 



where and <p' are the angles made by AB and BC respectively with 

 the perpendicular to the refracting surface MBB', 



and % = MB, in = BB'. 



Hence the time in which a disturbance travels over the course AB'C 

 is ultimately 



t /rinj> _ rings 

 \ e v J 



and therefore 3x = [ £ ^-1 ^ss. 



v » » y 



If we suppose ABB' to be a small pencil originating at ^4, we de- 

 termine its direction after refraction by putting St — independently of 

 3« (by a well-known principle in Physical Optics): hence the law of 

 refraction of a small pencil is expressed by the formula, 



sin cp sin <p' 



v v 



and this does not suppose that v or v' is constant. 



