AGGREGATE EFFECT OF INTERFERENCE. 165 



Let b be the radius of the sphere = BO, AO =f, AM = p, AE = x, 



EB = y + f, BE being perpendicular to AC. Then the vibration at the 

 point M due to a vibration C at B is 



c sin ~ (vt t BM). 



A 



But #M* = (p-f- y y + x 2 



= (p-JJ- s(p-/)y + « , + y 2 



.-. I?il!f = 1? - £ ~^ . y nearly. 



Hence the vibration at M produced by the upper mirror, as far as its 

 projection on the plane of the paper is concerned, is 



2cfy sin — {vt - (p -/*) - ¥ + 2(p -/) - y\. 



Also, if B be not in the plane of the paper, BM 2 becomes 



(p -/- yf + ** + **> or (p -fj -2(p-f)y + b\ 

 as before. 



