PHYSICS: C. BARUS 
563 
THEORETICAL RELATIONS IN THE INTERFEROMETRY OF 
SMALL ANGLESi 
By Carl Barus 
DEPARTMENT OF PHYSICS. BROWN UNIVERSITY2 
Communicated July 25, 1917 
In addition to the sides of the ray parallelogram (base, h) and the 
radius of rotation R, we shall have to consider the following angles or 
angular increment: Aa the angular rotation of the paired mirrors, 
the corresponding angular displacement of the fringes, A AT" the linear 
displacement of the micrometer mirror (in a direction normal to its 
face), and A(^ the angle subtended by two consecutive fringes. If n 
is the order of the fringe we may write 
A(^ = ^e/^n (l) 
Moreover if i is the angle of incidence (45°) of the impinging beams at 
the mirrors and X the wave length in question, 
2 cos i AN /An = X, (2) 
or on substitution. 
Ad /AN = A<p/(AN/An) = 2 cos i-A<p/\ (3) 
Again if ^ is the angle at the apex of the distance triangle on the base b. 
As = lAa (4) 
and 
Aa = AN cos i/R ' (5) 
and since the distance d = b/2As = b/2Aa, from (5) 
d = bR/2AN cos i = F/AN (6) 
so that the sensitiveness is from (6), 
dd = (2J2 cos i/bR) d (AN) = 8 (AN)/Fd' (7) 
If M is the index of refraction, e the effective thickness of the plates, 
i.e., the difference of effective thickness of the two half silvered plates 
through which the beams pass, we may write as in the colors of thin 
plates (since the respective beams pass each plate but once) 
nK = eiJL cos r — 2A^ cos i (8) 
if r is the angle of refraction corresponding to the incidence, i. If n, 
i, r, alone vary while e, n, X, N, are fixed and since sin i = m sin r, i.e., 
if the eye travels through the field of the telescope from left to right, 
A(p = di/dn = \/{2N sin i — e tan r cos i) (9) 
so that A(p depends inversely on e and N. 
