ox CEKTAIX Dli'FKACTJOX l'UEXOMEXA. 303 



/ t LP I'C \ ., _ 



\r / /, / 



Describe a sphere with D as centre, and jtassiu^- throuuii C ; tlieii the 

 time taken ]jy the ray U) go from the s|)]iericaJ surface to the eye will 

 he constant, provided D be siiüicientJy distant. I.et (his constant time 

 be denoted by " ; the vibration at T is thus ])roportional to 



an cos [ — TT, — ^ — ^- J 2 -. 



\ similar expressitjn holds for the light ])ropagated from every element 

 of tlie aperture, so that the total effect at T will be given l)y the 

 inteii'ral 



(1 



I <((7 COS I rn — ^ — — — : — ) 2 /T, 



./ \ i / / / 



where the integ'raiion extends (jver the whole aperture. 

 Taking any point near the :iperture, we may write 



PC = DC - DP, 



= DC + {DO - DP) - DO, 

 LP = LO - {LO - LP). 



Denoting the c(jnst;int distances LO, DU hy U and IÎ' res[)ec- 

 tively, let LO - LP -- JPi, and DO - DP = JPi! 



Introducing these syndjuls in the expressions for PC and LP, 

 we find 



PC - DC - R -{- JR\ 

 LP = R - JR. 



Substituting tliese in (1), we get for the vibration at T the integral 



,os r , n ~ - DC R- W JR - JR' \ ^ 

 (2) J da COS {-^^ . ^ + . )2.. 



Since r, DC, R — R' are all constant, we can put 



t - T DC R -- R' 

 -T J 1 ='^' 



