(2) 



in a new Form of Ref Tactometer. 239 



It is proposed to find such a distance P that, with a given 

 aperture, these differences shall be as small as possible, which 

 is equivalent to finding the distance from the mirrors at which 

 the phenomena of interference are most distinct. 



The change of A for a change in is 



-r. , , , -\ tan 



2(t + F tan 6 tan i) — ^y. 

 dA_ v r J cos 2 6 



W~~ (1 + tan 2 i + tan 2 0) f 



The change of A for a change of i is 



^ (l + tan 2 i + tan^)^-(. Q + Ftan^tanO^ 



"di (l-+tan s t+tan 2 0)i ' ^ } 



For ^-5-= we have 



d# = (or A=0). 



For ir=0we have 



(1 + tan 2 i + tan 2 0)P tan <£ = (* + P tan </> tan i) tan z, 

 or 



(1 + tan 2 6) P tan $=t Q tan z, 

 whence 



P=-\tanicos 2 0. 

 tan $ 



Hence the fringes will be most distinct when 0=0 and 



Pa-A-tani (4) 



tan$ v ' 



This condition coincides nearly with that found by Feussner. 



If the thickness of the film is zero, or if the angle of inci- 

 dence is zero, the fringes are formed at the surface of the 

 mirrors. If the film is of uniform thickness, the fringes appear 

 at infinity. If at the same time ^> = and £ =0, or <£ = and 

 t=0, the position of the fringes is indeterminate. If i and <£ 

 have the same sign, the fringes appear in front of the mirrors; 

 if i and <jb have opposite signs, the fringes appear behind the 

 mirrors. 



To find the form of the curves as viewed by the eye at E, 

 call T the distance between the surfaces at E', the projection 

 of E. From P draw PR parallel to DP', and RS parallel to 

 CP', let RS = c, and let SE = D. We have then t = T + ctan <£, 

 whence, since c= D tan i, 



. T + (D + P)tan<fttan^ 



\/l + tan 2 ;+tan 2 0~' * ' 



