10 Mr. A. A. Michelson on the Application of 



LetOC =GB=DC 1 =C 1 E=7». 

 001=2*, OP =w, VQ=y. 

 Then the intensity of the interference-fringes will be 



2ttA\ 



= j ?/( 1 + cos 





da 



as in (1). 



where 

 and 



Integrating- from to B and from D to E, we have 

 1=1 */^l + cos— J^+l y B fl + cos-^J<fcr;(ll) 



yi=/ (*-*•) and y»=/.[>— (2«+» i )] 



A = j3a;—yh. 

 In the first integral put Wi=(«?— r*). 

 „ second „ w 2 =.£— (2s + r). 

 Then we obtain 



I 



f + /Oi) [l + cos ^■(ffw 1 + fir-yb)^dw 1 



•s —r -> 



Expanding the first of these integrals we obtain : — 



(12) 



f{w l ) dw 1 + cos —(Pr — yb) I f{w Y ) cos -^ /^ dw, 



•sin-£(Pr—yb) I , 



/(^j)sin 



2tt 



V«'i; 



in which the first term is half the area of the aperture, and the 

 last term (since f(io{) is a symmetrical function) is 0. The 

 same is also true of the expansion of the second integral. If, 

 then, we put 



J". 



f(io)dw=±Q, 



f(iv) cos ~/3wdw=±QA, 



equation (12) becomes 



