the Slit in Interference Experiments. 475 



But 



x 2—g 7 — -jx — j- ztt— \fi (a — t) 4 t\, 



_%—x— (/jl—1) Han a, 



_ v — y 



yi ~ y2 ~ fi{a + b)-(fi-l) t'*' 



7 , 1V| f — #— (/a — 1)6 tan «]_ 

 + //,£> (At— 1)1 an a, . - — -. -f- — / — — i 



which becomes on reduction 



/*(a + &)— (/a — 1)£ 



/a P + ?y 2 + ^ 2 + z/ 2 _ rjy 



2^(a + 6)-(/*-l)« fl ' fi(a + b)-(fi-l)t 



_ jju%x + (fi — 1) tan ^i [/u6g + { /*a — (/a — 1) f }.*?] 

 /&(« + &) — (/* — l)t 



The undulatory time of passage Y 2 between the same two 

 points of the stream that passes through the other half of the 

 prism is obtained from V 1 by writing —tan a 2 for tan «j ; 

 hence the relative retardation of the streams, measured in 

 length in air, is 



v _ v _ 1 b\fia — (fi — T)t] {fi — l) 2 (tan 2 a 1 — tan 2 « 2 ) 

 A-\ 2 i— g /x^ + ^-^-l)^ 



(fi — l)(tan« 1 + tan a 2 )[fih^+{fia—(fi — l)t\ai] 

 fi(a + h)-(fi-l)t ' 



Billet's Divided Lens. — Suppose the slit placed sym- 

 metrically with respect to the two halves of the lens in a 

 direction perpendicular to the plane through their principal 

 axes : then an investigation similar to the above leads to the 

 result that at the point oc, y of the screen of observation, the 

 relative retardation of the two streams that emanate from the 



