50 horse-power motor, reduced the pressure in the pipe to about a half-inch in three hours. Most of the measurements were made when the residual air in the pipes had been reduced to a pressure of about half an inch to one inch of mercury. At these pressures the fringes were perfectly steady, and as sharply defined as could be desired.
Fig. 2.—Details of comer box and mirror mounting
The fringes to be measured were those formed by the beams going in opposite directions about the circuit ADEF. As a fiducial mark from which to measure the displacement, a second set of fringes was formed by the mirror system ABCD. The area inclosed by this circuit was much too small to give a measurable displacement of the fringes, and the shifts actually recorded were those between the central fringes of the two sets.
In general the two sets of fringes will not coincide in position, entirely aside from any question of ether drift or the earth’s rotation, unless the two direct images and the two reflected images of the source are exactly superposed. The central fringes of the set formed by the mirrors of the short circuit will be halfway between the direct and reflected images of the source, and the central fringe of the long line would be halfway between the direct and reflected images if there were no difference due to the earth’s rotation.
To correct for any lack of superposition of the two sets of rays, the observing telescope (a six-inch achromatic objective, and two-inch micrometer eyepiece) was focused on the images of the source (arc or slit) and the apparent displacement of the central fringe of the long circuit, compared with the central fringe of the short circuit, was corrected by an amount equal to the difference in the mean positions of the two images for the two light circuits. The fringes are most conveniently observed in the overlapping cones of light an inch or so inside or outside of the focal plane.
About half of the determinations were made with the arc placed directly in front of the window at A, and about half with a condensing lens, slit, and collimating lens. The second arrangement gave much more light than the first, but there was no apparent difference in the measured displacements.
The calculated value of the displacement on the assumption of a stationary ether as well as in accordance with relativity is
where A is the displacement in fringes, A the area in square kilometers, φ the latitude (41°46′), V the velocity of light, ω the angular velocity of the earth, and X the effective wave-length of the light used. Measurements were made in the laboratory, comparing the fringes produced by the same set of mirrors and the same 20-ampere alternating-current arc, with fringes produced by sodium light from a bit of glass in an oxyhydrogen flame. The light from the arc was reduced to approximately the same intensity as in the experiment at Clearing, by transmitting it through a rather narrow slit in a