as applied to Micrometric Observations. -449 



difference of phase are 



MP + PQ + QR + RS + TU for one stream, 



M'P' + PQ' + R'S' + S'T' + T'U' for the other stream. 



Produce PQ, P'Q' to meet it in V and V and let N, N' be 

 the feet of the perpendiculars from R and S' on PQ, T'U' 

 respectively. 



Thus we may take the change of phase as due to the 

 retardation 



(MP + PV)+(NQ + QR) 

 for diffraction at one slit, and to the retardation 

 (M'P + P V) + (ST + T'N') 



for rays proceeding from the other slit. 



The terms in the first brackets give us the expression which 

 we had before, viz. : — 



As to the other terms 



NQ + QR = QR (l + cos26)==«^i^ r ?^=2acosW), 



v T COS (p 



where a is the distance between the mirrors a, b and <£> is the 

 angle of incidence of any ray on these mirrors. 



Similarly S'F + T'N' = 2/3 cos i/r, where /3 is the distance 

 between e and c and ty the angle of incidence of any ray 

 upon e and c. 



Now if the mirrors a and b are inclined to the plane of the 

 diaphragm at an angle 0, c, d, e at an angle ( — &), then 



, q sin + b cos 

 cos <p — 



cos yjr- 



— q sin & + b cos 0' 



\/p 2 + q 2 + tf 

 To find the disturbance at Z we have 



a + k + h 



Ci Cy A . 27r/\t p + u , q + v _ , \ 



a — k —h 

 -a+k +h 



, ( \i Cj A . 27r / Xt p + u q + v rt ~ ,\ 



■a-k 



