SHEWING IT TO BELONG TO PHYSICAL OPTICS. I47 



line cc being the ray which has the minimum deviation and an asvmp 

 tote to the two branches. 



The section of the luminiferous surface at any position will be 



Fig. 2. 



similar to ege', the branch e'g being an involute of the caustic Bb, 

 and eg of the caustic Aa, or more accurately the part of eg as far as 

 the asymptote is the involute of the virtual branch Aa, and the re- 

 mainder of the other branch. 



For want of knowing the equation of the curve ege', I have used 

 this approximation of considering the two branches near g for the 

 small angular distances which we employ as coinciding with their os- 

 culating circles, at the given points. 



Then finding p and (p, which correspond to this angular distance, 

 and taking rectangular co-ordinates parallel and perpendicular to cc, we 

 easily get the values of the co-ordinates («, b) (a, b') of the centres of 



T2 



