42 
PHYSICS: C. BARUS 
In the figures the contact lever mme is horizontal. It may also be mounted 
vertically but in such a case it is less easy to mount the mirrors M, M\ iV, N\ 
when the system is to be exposed to tremors. 
2. Equations. — If the mirrors M, M\ etc., are set at an angle i, if the deflec- 
tion of the auxiliary mirror is 6, and if the breadth of the ray parallelogram 
MM' or NN' is we may write 
b Ad = AN cost (1) 
where A iV is the displacement at the micrometer at M\ If r is the length of 
the lever c figure 1 and A x the displacement of the pin e 
rAd = Ax (2) 
Hence 
Ax = (r cost/ b) AN (3) 
Thus the apparatus is more sensitive as r is smaller and b is larger. In the 
instrument used (adapted from an earlier apparatus) 
r = 11 cm.; b = 10 cm.; i = 45° 
so that 
Ax = .778AiV (4) 
But the main condition of sensitiveness is contained in the size of the 
fringes, and these may be made indefinitely large by suitable rotation of the 
mirrors M and M\ for instance, in like direction on a horizontal axis (local 
coincidence of rays on M'). Since 
2AiV cos i = nk 
in case of the passage of n fringes, equation (3) becomes 
Ax = nr\/2b (5) 
Hence the limiting sensitiveness {n = 10) would be (with the above data) 
Ax = 33 X 10-6 cm. (6) 
for a single fringe, a few tenths of which may be registered with certainty. 
When the achromatic fringes are used, it is however usually more convenient 
to standardize the ocular plate micrometer in the telescope, directly by aid of 
the screw micrometer at M\ figure 1. If the ocular plate is divided in tenth 
millimeters along a centimeter of length and the fringes are of moderate size, 
one may estimate that about 40 scale parts correspond to AN = 10"^ cm. so 
that a single scale part of displacement of the achromatics is equivalent to 
AN = 25 X 10-6 ^ while a few tenths of a scale part may here also be 
estimated. 
If the apparatus (fig. 3) is to be used as a spherometer, the ordinary method 
of measuring from a plate of glass is at once available. If r is the radius of 
the circle of the tripod and Ax the height of the central foot, we obtain as 
usual for the radius R required 
