474 Mr. J. Walker on the Admissible Width of 



Let t be the distance of the flat face of the prism from its 

 edge, and z — a-\-b the equation to the screen of observation, 

 then if the ray from the point f, 77 of the slit to the point 

 a?, y of the screen meet the faces of the half of the prism on 

 the side of positive x in the poinfs # 1? y lt a — t and a? 2 > 3/2? z 2 

 respectively, the undulatory time of passage of the light that 

 passes through this half of the prism is 



=a—t+fi(z2~a + t) + (a + b—z 2 ) 



, 1 r fa-ft'+Cyi-g)' , >,-*i) a +(y 8 -yi) 8 



" t 2l a-t "^ £ 2 -a + £ 



+ a + b-z 2 J 



= a + b+ (/i — l)t— (>L6 — 1) tana 3 . # 2 



. 1/ fa-fl'+fo-iy) 8 , , >,-*i) 8 +(y,-yi) a 



+ 



with the conditions 



afoi a — £ £ ? 



(0-g2) 8 +(y-ys) 8 l 



dy Y a — t *~ t 



fY = ^Z5 + /t ^=^ = , 



_ =_(^-l) tana 1 -^- r - + -j 0. 



whence 

 Y 1= =a + 6+ (ft— 1) * — (/Lt — 1) tan a x . # 2 



= a + 6 + (/a — 1) * + i?> (/*-l) 2 tan 2 «!+^5 (/a— 1) tan^. (# x — # 2 ) 



-O-i) tan « x .^+^{/* (a+6)-o»- i)M{to-* 2 ) 2 +(yi--ys) 2 }, 



