PHYSICS: C. BARUS 
353 
but this would necessitate two mirrors m one at each end. For the present 
purposes, I preferred to use apparatus which I had at hand in which 2R was 
but 10 cm. and a single mirror could be used at m. Nevertheless if n = 1, 
the limit of angle measurable, if <p = 0.0175 or one degree is Aa = 5 X 10 -8 
radian per fringe; i.e. about 0.01 second of arc. With an ocular micrometer 
and well produced achromatic fringes there is no difficulty in estimating 1/10 
fringe, so that the limiting angle here is to be a few thousandths of a second, 
even if <p — 1°, which may also be reduced. By making 2R — 100 cm. one 
should therefore be able to reach 0.0001 second per tenth fringe breadth, if 
(p is 1°. 
Finally on using the ocular micrometer for moderately sized fringes of say 
one scale part (0. 1 millimeter fringes in the ocular) the case is equally promis- 
ing. A comparison of the two displacements AN at M' and Ae of the fringes 
in the ocular, showed Ae/AN = 265. Hence 
Aa = <pAe cos Z/265 X 2R 
If Ae/AN = 10 -2 (one scale part) and 2R = 10 cm. etc., as above, 
Aa = 2.7 X 10- 8 
or 0.005 " per scale part of the ocular micrometer. A few tenths of this may 
be estimated on the scale. The sensitiveness will be ten times greater if 2R 
is a meter. 
4. Observations. — The interferometer was installed with rather smaller fringes 
than instanced above and therefore with less sensitiveness, as the inclination 
of the pier in a heated laboratory would probably run into seconds of arc 
in the lapse of time. For this reason R was also satisfactory at its small value 
of 2R = 10 cm. The angle <p was directly measureable, as the inclination of 
the line joining the points of the pivots to the plumb line. Under these cir- 
cumstances Aa — 0.9 Ae seconds, roughly, the tenth millimeters of the ocular 
scale are about 1/100 second of arc in relation to Aa and the fringes were of 
about the same size. There would have been no difficulty in making them 
much larger and therefore more sensitive as they were clear and strong. The 
end of the compound pendulum was damped in lubricating oil. 
The earlier observations were discarded; but even after January 14 (after 
which time the apparatus worked smoothly), there are instances of displace- 
ment within the apparatus requiring readjustment. These betray themselves 
in a lack of coincidence of the two wide slit images, Fig. 3, or of the cross wire 
w (the slit is really superfluous and the collimator lens may be so placed as to 
widen the illuminated field). 
Though observations were made continuously since January, I can here 
only give the graphs for the days of August and September, just passed. In 
figure 5, the lower curve shows the apparent change of inclination of the pier 
in seconds of arc; the upper curve the corresponding temperature (in degrees 
centigrade) of the basement laboratory room. Observations were usually 
made at 10 a.m. and 6 p.m. Between August 1 and 21, the resemblance of 
