352 
PHYSICS: C. BARUS 
the achromatic fringes, should be placed at right angles to them, with the 
ocular micrometer so placed as to read from end to end of the slit image. 
A very fine wire beam across the slit gives the fiducial line relative to the ocu- 
lar micrometer. Figure 3 shows the general arrangement, SS f being the 
oblique wide slit image, ff the achromatic fringes, w the image of the fiducial 
wire across the slit, and ss' the ocular scale. Of course the fringes may be 
made horizontal or vertical; but this requires much adjustment (or else com- 
pensators) and is therefore an unnecessary complication of the work. With 
this fiducial mark at the collimator which is permanently out of reach, if the 
telescope is accidentally shifted, or it is temporarily removed, it may be re- 
placed without difficulty. It is the telescope, however, which contains the 
ultimately fiducial scale, and it like the collimator should be held on a stand- 
ard, t" , suitably attached to the interferometer and the pier. Similarly, the 
mirrors M and M f , N and N' fixed in pairs to slides or carriages F, F' are 
clamped to two parallel horizontal tubes E, E f (3/8 inch gas pipe smoothed, for 
instance) anchored in the pier. The highest attainable rigidity in the place- 
ment of the mirrors M, M' ', N, N', and of the telescope is essential. At the 
outset of the work the viscous yielding of standards and braces is quite 
apparent. 
3. Equations. — In figure 4 let pBd denote the horizontal pendulum in the 
plane of the diagram and dpe the line of pivots prolonged, terminating in e 
vertically above the center of gravity G. Let the inclination of de to the ver- 
tical be <pj a constant of the apparatus, and suppose a perpendicular h! is 
let fall from e to the vertical df through d. If in consequence of a change in 
the inclination of the pier the line of pivots passes to de f , over a nearly vertical 
angle a, h! will pass into h" over a horizontal angle 0. Thus the measurement 
consists in finding a in terms of the interferometer angle 6. Since these angles 
are all very small we may write (A being a differential symbol) as in the pre- 
ceding paper. 
In the rectangular interferometer with an auxiliary mirror, if the distance 
apart of the rays a and c, Fig. 1, be 2R 
where i — 45°, AN the displacement of micrometer to bring the achromatic 
fringes back to the fiducial line and n the number of fringes which pass that 
line. Hence 
Aa = (pA6 
(i) 
4RA0 = 2AiVcosi = »X 
(2) 
Aa = <p 
AN cost 
(3) 
2R 
The smallest angle Aa which can thus be measured depends essentially on 2R 
the breadth of the ray parallelogram. There would be no difficulty in making 
this as long as the line from tt' to B of the horizontal pendulum, i.e. over a meter; 
