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PHYSICS: C. BARUS 
NOTE ON COMPLEMENTARY FRESNELLIAN FRINGES 
By Carl Barus 
DEPARTMENT OF PHYSICS. BROWN UNIVERSITY 
Communicated May 9. 1917 
Measurement of Small Angles without Auxiliary Mirror. — This method 
makes use of the original apparatus heretofore described, but the two 
mirrors M and M' or N and N' , figure 1, are rotated together as a rigid 
system around a vertical axis, at A for instance. In view of the absence 
of auxiliary reflection, the method will be but half as sensitive as the 
preceding one, so that the equation 
RAa = AN cos i 
is sufficient to approximately express the results. But on the other 
hand, if spectrum fringes are to be observed, there is greater abundance 
of light since the half silver film is penetrated but once by each compon- 
ent, ac or bd. When the achromatic fringes are used however the light 
is always superabundant and must be reduced in intensity. To try this 
method the mirrors N and were mounted on a good divided circle so 
as to rotate together on a rigid arm over a small angle a. The achromatic 
fringes displaced in this way were restored by advancing the mirror M^ 
over the distance AN along the normal micrometer screw at n\ The 
following is an example of the results of corresponding values of AiV^ 
and Aa, when the distance apart of the rays ac and bd was 2R = 7 cm. 
a = 0.0° O.r 0.2° 0.3° 0.4° O.S'' 0.6° 0.7° 0.8° 0.9° 1.0° 
AiVXl03 = 0.0 8.0 16.6 35.6 34.9 42.7 50.7 61.7 70.5 78.5 90.6 cm. 
These results as a whole are much smoother than the earlier ones, 
for incidental reasons. From a graphic construction the mean rate 
AN /Aa = 0.088 cm /degree or 5.0 cm/radian may be obtained. Hence 
since 2R = 7 cm., {AN/Aa)2/R = 0.013 in terms of degrees or 0.72 in 
tenns of radians. This result is roughly half that in the preceding 
paper, if incidental errors be disregarded. From the above equation 
since i = 45° nearly, 
Aa 2 cos i 1.41 
agrees closely with the experimental result. 
Complementary Fringes — Attention was now given to the hyperbolic 
fringes of a fine slit and white Hght, observed in the telescope at T when 
the ocular is drawn outward or to the rear of its position for the principal 
