PHYSICS: C. BARUS 
437 
to the same purpose ; or the mirrors may both be half silvered and trans- 
parent.) The telescope now contains two images, the first due to rays 
{K) entering it directly, the second due to rays (L) reflected into it by 
the mirrors of the interferometer. Suppose the object seen lies at in- 
finity like a star, that its two images are made to coincide by adjusting 
the angle a, and that the achromatic fringes have been brought into the 
field by adjusting the micrometer displacement N. 
Now let the angle a be changed by Aa until the two images of an ob- 
ject If, at a measurable distance d, coincide. Displace the micrometer 
mirror by AiV until the achromatic fringes are restored to their former 
position. Let h be the effective distance apart of the paired mirrors 
in the direction right and left to the observer or transverse to the im- 
pinging rays {L) and finally 5 the angle at the apex of the triangle of 
sight on the base h; i.e. the small angle between the present rays KL. 
Then 
d = h cos g s = h cos g 2Aq; = Z)/2Aa (2) 
(nearly) by the laws of reflection. Hence from equation (1) 
d = hR/^N cos i (3) 
Here 2hR is the area of the ray parallelogram of the interferometer. Us- 
ing the constants of my apparatus, let i = 45°, = 10 cm., h = 200 cm., 
AiV = 10~^ cm., the latter being the smallest division on the micrometer. 
Hence 
J = 200 X 10/10-4 X 0.71 = 2.8 X 10^ cm. == 280 kilometers. 
or about 170 miles is the limit of measurement of the apparatus. 
3. Performance. — Again from equation (3) the sensitiveness b{^N)/bd, 
since 
hd = (6^2 cos i/bR)d{AN) (4) 
is inversely proportional to the square of the long distance d and the 
area of the ray parallelogram 2bR. Thus with the above constants, if 
dis2 kilometers, 5 (AiV) = 10"^ cm., then 
8d = (2 X 10^)2 X 0.71 X 10-7200 X 10 = 14 X 10^ cm. = 14 meters. 
Thus an object at about a mile should be located to about 30 feet. Per 
fringes of mean wave length X, moreover, 8d = \d'^/2bR, the placement 
should be about 6 meters at 2 kilometers. I have stated the case, of course, 
merely for the interferometer, not for subsidiary optical appurtenances. 
