MORLEY AND MILLER. — THE FITZGERALD-LORENTZ EFFECT. 325
diameter; each pair of tubes is joined together in a vertical truss, as shown in Plate 1. Against the farther end of these rods there rest the frames which hold the two sets of mirrors, I and II, Figure 1. Each of the latter frames is freely suspended by two thin steel ribbons and is held firmly against the pine rods, and through these against one of the two fixed mirror holders ; the pressure is applied by means of adjustable spiral springs. Thus the distance between the opposite systems of mirrors depends upon the pine rods only. This construction permits the convenient substitution of distance rods of other material, so that experiments might be easily made to test the theory that the dimensions of different materials are differently affected by motion of translation through the ether. The diagonal mirrors are carried by adjustable supports bolted to the steel frame near its centre.
The observing telescope of an inch and a half aperture with a magnifying power of thirty-five is attached to a support bolted to the steel frame. The acetylene lamp and the four-inch condensing lens stand on a wooden shelf as far as convenient from the mirrors, which are protected by asbestos screens with air spaces. The whole path of light through the apparatus is enclosed by a wooden cover made of pine seven eighths of an inch thick, having doors and glass windows where these are required. The observer’s eyes are protected from extraneous light by a dark cloth.
The entire apparatus, weighing about nineteen hundred pounds, rests upon a circular wooden platform about five feet in diameter. An annular projection on the under side of the platform is immersed in mercury of such depth as to float the platform and the apparatus. The mercury is contained in an annular cast-iron trough of such dimensions as to leave a clearance of about half an inch between the iron and the wooden float. A small pin at the centre of the iron trough enters a socket in the wooden float, so as to keep the float from touching the sides of the trough.
Plate 1 shows the steel framework and float, together with the trusses which are to support the distance pieces. The mirror frames and the telescope are in position, but lamp and lens are not in position. Plate 2 shows the apparatus as it appeared at the time of the observations.
With this apparatus, fringes adjusted on a certain Monday remained in adjustment throughout the whole of the week during which our observations continued. Observations were made in precisely the same manner as with the previous apparatus.
We obtained 260 complete observations, consisting each of readings at
320
PROCEEDINGS OF THE AMERICAN ACADEMY.
sixteen azimuths around a circumference. At the date of the observations, the annual motion of the earth, together with the motion of the solar system, may be taken as 33.5 kilometers a second. It is assumed that the solar system is moving towards a point whose right ascension is 277.5°, and whose north declination is 35°, with a velocity of eleven miles a second. The velocity of light being 300,000 kilometers a second, the ratio of the squares of the velocities is 0.72 × 108. The length of path of a ray in our apparatus was 3224 centimeters, in which distance there are contained 5.5 × 107 wave lengths of sodium light. The expected effect being doubled by rotation through 90, the displacement of fringes expected on the simple kinematic theory will be 11 × 107 ÷ 0.72 × 108. This is 1.5 wave length.
As was indicated, there were two times in the day when observation was advisable. The direction of the motion with reference to a fixed line on the floor of the room being computed for the two hours, we were able to superimpose those observations which coincided with the line of drift for the two hours of observation. Doing this, and subtracting a constant so as to make the algebraic sum of the observations equal to zero, we get a certain result. Then adding the first term to the ninth, and so on, since the effect repeats itself in a circumference, we get our final result, as follows : —
Result of observations at various azimuths.
Azimuths 87654321
Wave lengths+0.0075 + 0.0088 + 0.0113 - 0.0102 - 0.0123 + 0.0027 - 0.0021 - 0.0062
Azimuth mark 1 denotes that the telescope of the apparatus was directed N. 29° E. ; 3, N. 16° W. ; 5, N. 61° W., &c.
These numbers may be confidently pronounced to be due to errors of observation. We computed from them several curves of the theoretical form, having their origin at sixteen equidistant points in the half circumference ; this was done by the method of least squares. The most probable of these curves had an amplitude of 0.0073 wave lengths, and its zero was half-way between the azimuths marked 4 and 5. The average of the given observations is 0.0076 wave lengths; after subtracting the ordinates of the computed curve, the mean residual was 0.0066 wave lengths. The sum of the squares of the residuals before was 565 × 10–4 ; afterwards, it was 329 × 10–4.
We may therefore declare that the experiment shows that if there is any effect of the nature expected, it is not more than the hundredth part