564 
PHYSICS: C. BARVS 
When the spectrum elHpses are centered, N = Nc, a condition neces- 
sary for the occurrence of achromatic fringes, where, 
2No = 6 (m cos r + 25/X2 cos r)/cos i (10) 
if \dfx/d\ = IBj^ is adequate. Equation (10) may now be inserted in 
equation (9) and the coefficient of e, viz., the long parenthesis contain- 
ing circular functions evaluated for i = 45°, X = 6 X 10 \i = 1.55, 
IBjV^ = .026. Its value is shghtly greater than 1. Hence we may 
write approximately but with much greater convenience 
Acp = \/e (11) 
and we thus obtain the breadth of the fringes for different values of the 
parameter e, roughly. It would, of course, be easy to compute the 
accurate value of i. This equation placed in the above equations (3), 
(5), (6) gives in succession, 
2l^ip AN cos i ^ cos i 
Ad=— = 2 — AN (12) 
X e 
Ad = — AipAa = — Aa (13) 
X e 
, M bR ^^^^ 
2ANcosi eAd 
so that the measurement of the long distance d depends ultimately on 
the area, 2bR, of the ray parallelogram, the differential thickness of 
paired glass plates, e, and the displacement Ad of the achromatic fringes. 
From equation (14) we obtain the sensitiveness by differentiation, or 
d^e 
dd = —d(iAe) (15) 
bR 
Let the angle or its variation be measured in a telescope of length L, 
and provided with an ocular micrometer, so that the angle = x/L, x 
being the Hnear magnitude measured on this micrometer. Hence, 
d^e ,^ 
hd = bx (16) 
bRL 
and if we introduce moderate estimates, d = kilometer = 10^ cm., 
e = 10-2 cm., h = 200 cm., = 10 cm., L = 50 cm., dx = 10"^ cm., 
then 8d = 10 cm., or d should be measurable to 10 cm. at a kilometer, 
so far as the interferometer only is concerned. It may be noticed that 
in equations (11) to (14), e is variable and equal to \/A(p. If the plate 
halfsilvers traversed by the interfering beams are not equally thick 
