238 Mr. A. A. Michelson on Interference Phenomena 

 order, and sin 2 ^ is a small quantity of the fourth order; con- 



Ar 

 sequently 2P/> . sin 2 -^ may be neglected. We have therefore, 



to a very close approximation, A =pp' cos •&, or, substituting 

 2t for pp, 2t being the distance between the images, at the 

 point where they are cut by the line P/>, 



A = 2£cos$. 



Fig. 3. 



r 



a 

 & 



J J 



Let c d ef, c' d' e' f (fig. 3) represent the two images, and 

 let their intersection be parallel with cf } and their inclination 

 be 2(f). Let P be the point considered; P'the projection of P 

 on the surface; and P B the line forming with P P' the 

 angle <&. Draw P' D parallel to cf, and P' C at right angles, 

 and complete the rectangle BDFC. Let P / PC = ?', and 

 DPF=^. Let PF = P; and call the distance between the 

 surfaces at the point P', 2t . We have then 



t = t + OP', tan $ = t + P tan <£ tan i, 

 and 



A = 2(t + P tan <£ tan i) cos S, 



A = 2 



(7 + Ptan<fttanf) 

 \/l+ tan 2 i+tan 2 0* 



(1) 



We see that in general A has all possible values ; and there- 

 fore all phenomena of interference would be obliterated. 



If, however, we observe the point P through a small aper- 

 ture ah (the pupil of the eye, for instance), the light which 

 enters the eye from the surfaces will be limited to the small 

 cone whose angle is h P a ; and if the aperture be sufficiently 

 small, the differences in A may be reduced to any required 

 degree. 



