14 
PHYSICS: C. BARUS 
auxiliary mirror mm, capable of rotation (angle a) about a vertical axis A. 
The mirrors M-N' in their original position are conveniently at 45° to the 
rays of light,, while mm is normal to them. Light arriving at L is thus separated 
by the half silver N at 1, into the two components 1, 2,1. 9,3, T and 1,6,7,6,3, T, 
interfering in the telescope at T. 
When mm is rotated over a small angle a, these paths are modified to 
l,2,2 / ,4,4 / ,5,r 2 and 1,6,7',8,jTi. T\ and T 2 enter the telescope in parallel and 
produce interferences visible in the principal focal plane, provided the rays 
Ti and T 2 are not too far apart, in practice not more than l or 2 mm. In- 
terference fringes therefore will always disappear if the angle a is excessive, 
but the limits are adequately wide for all purposes. The essential constants 
of the apparatus are to be 
(9,1) = (6,3) = b; (1,2) = (6,7) = c; (9,3) = (1,6) = 2R, 
R being the radius of rotation. 
When the mirror mm is rotated to mm' over the angle a, the new upper 
path will be 
c + R tan a + d + e + g, 
where 
(2',4) = d, (4,40 = e, (4',5) = g, 
the plane (8,5) = q normal to 7\ and T 2 being the final wave front. The 
lower path is similarly 2 R + (c — R tan a) + d' to the same wave front 
(8,5) where (7^8) = d' . Hence (apart from glass paths which have been 
treated, the path difference w\ (n being the order of interference) should be 
n\= 2R (tan a - l) + d - d' + e + g. 
The figure in view of the laws of reflection then gives us in succession 
d = (b + c + R tan a)/(cos 2a + sin 2a), 
d' = (b + c - R tan a)/(cos 2a + sin 2a), 
e = 2 R/(cos 2a + sin 2a), 
g = 2 R sin 2a (1 + tan a) (cos 2a — sin 2a)/ (cos 2a + sin 2a), 
q = 2R sin 2a (1 + tana). 
