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PHYSICS: C. BARUS 
per vanishing fringe. As the change of glass path of one beam would 
have to be deducted from 2R, a somewhat larger value would be antici- 
pated. Testing the complementary fringes (white light) the passage of 
about 25 fringes completed the phenomenon after which it paled to white- 
ness. These 25 fringes passed within Aa = 0.75', or per fringe about 
0.03' or 1.8'' of arc. Of course this is merely an estimate from the small 
angles of turn involved. 
The complementary fringes with sodium light are available indefi- 
nitely. I counted about 100 fringes for an angle of 2.7', i.e., 1.6" per 
fringe. 
Finally using the spectrum fringes of the spectroscope, about 120 
fringes were counted within 3', i.e., 1.5" per fringe. All of these values 
are larger than the computed value \/2R without correction, but in view 
of the large number of fringes within exceedingly small angle Aa, sharp 
agreement is not to be expected. 
[This note is from a Report to the Carnegie Institution of Washing- 
ton, now in preparation.] 
THE DISPLACEMENT INTERFEROMETRY OF LONG 
DISTANCES 
By Carl Barus 
DEPARTMENT 0F:PHYSICS. BROWN UNIVERSITY 
Communicated, May 22, 1917 
1. Small Angles. — In my preceding notes I suggested two methods 
for the measurement of small angles. The first used an auxiliary mirror 
and apart from corrections the angle over which the auxiliary mirror 
turns is 
Aa = AiVcos i/2R (1) 
where AiV is the displacement of one of the plane mirrors parallel to 
itself necessary to restore the achromatic fringes to their former posi- 
tion in the field of the telescope, i the angle of incidence (conveniently 
45°), 2R the normal distance apart of the (parallel) interfering pencils 
in the fore and aft direction of the incident beam. In the second method 
the auxiliary mirror is dispensed with and the rotation of a rigid system 
of paired mirrors is used. The sensitiveness is half the preceding. 
2. Distances. — Suppose now that the paired mirrors near the tele- 
scope confront but a part of the area of the objective and that the tele- 
scope can therefore look over the mirrors directly into the region be- 
yond. (A series of small mirrors or reflecting prisms may be employed 
