five seconds, which is equivalent to assuming that the periodic displacements of the fringes take place with respect to an inclined axis. A compensation for the shift is made by adding to the sum of the seventeenth column such a number as will make it equal to the sum of the first column and by adding one-sixteenth, two-sixteenths, etc. of this compensating number to the second, third, etc. columns; this renders the axis of reference horizontal. These compensated sums of the sixteen columns of readings are divided by twenty, the number of turns of recordings, giving the average positions of the central black interference fringe for each of the sixteen azimuths of one complete turn around the horizon. The mean ordinate is now subtracted from the ordinate of each point and these points, plotted, will give the curve of fringe displacement referred to its own time axis.
In the definitive study of the ether-drift effect, this set of sixteen average readings for the position of the interference fringes is plotted to a large scale and is subjected to mechanical harmonic analysis to evaluate precisely the second harmonic component, which represents the second-order, half-period ether-drift effect; this process is illustrated in Fig. 21 in a later section. For the purpose of a preliminary study of the observations, it is convenient to obtain an approximate graphic representation of the effect by the following procedure. The second half of the line of sixteen average readings is placed under the first half and the mean of the two numbers in each column is obtained; by this addition any periodic full-period effect is eliminated and also any effect of all higher odd harmonic components. The final line of eight numbers represents the mean values of the ordinates of the half-period effect, together with higher even harmonics which may be present, obtained from forty sets of readings of this second-order effect. At the bottom of the chart, Fig. 8, are plotted the readings for the full turn of the interferometer, which contain all the effects observed and below this the readings for the half-period effects.
The set of readings here illustrated is not exceptional; it is a fair sample as to magnitude and periodicity of the ether-drift effect. This particular displacement corresponds to an ether-
drift velocity of 9.3 kilometers per second. Every set of readings shows a very definite periodicity which varies both as to magnitude and phase in a systematic manner.
The method of reducing the observations is further illustrated by the graphic representation of Fig. 9 which shows the complete process as applied to the first five turns of the record given in Fig. 8. The readings for the five turns are plotted to scale at the top of the figure. Below this at the left is shown the summation of the five turns for the sixteen azimuths of one complete turn in which the periodic displacements clearly oscillate about the downwardly inclined axis; below this are the linear compensations for the shift and next below this the sums of the readings with the shift eliminated. The mean of the sixteen ordinates is subtracted from each ordinate, giving the curve referred to its own true axis, as shown at the right. Below this are shown the two halves of the full-turn curve, one below the other; still lower is the half sum of the two curves, from which the full-period effect is now eliminated. This is the average effect for the half period obtained from the sum of the five turns; for final evaluation the ordinates are to be divided by five; this is indicated by a change of scale in the figure. It is interesting to note that the full-turn and the half-turn curves obtained from the readings for five turns are almost identical with the corresponding curves obtained from the full set of readings for twenty turns shown in Fig. 8.
Stability of the interferometer
The steel cross which forms the base of the interferometer has proved to be remarkably stable and dependable. The length of the light path, going and returning, is about 112,000,000 wave-lengths and, for the production of the interference fringes in white light, the two light paths, which are at right angles to each other and each of which consists of sixteen separate parts, must be exactly equal to the fraction of a wavelength. A difference in length of from five to ten wave-lengths displaces the white-light interference system so much that it is no longer visible in the telescope when the adjustment is made for wide fringes. The screws used for the adjustment of the end mirror, No. 8, have
threads 0.635 millimeter apart, and a turn of the screw through 16° causes a change of 100 wavelengths in the light path. These screws are turned by means of capstan pins in order to secure sensitive adjustment. Usually the final adjustment of the central fringe to the fiducial point is secured by means of small weights placed on the end of the arm of the cross, causing a change of length by flexure.
Tests have been made at various times to determine the rigidity of the steel cross; these show that the four arms are about equally rigid and that a weight of 282 grams placed on the end of one arm produces an elongation in the multiple light-path sufficient to displace the fringe system one fringe-width, which is less than one hundred-millionth part of the light path. Similar tests made on the concrete base used for the interferometer in December, 1924, showed that 30 grams on the end of the arm produce a displacement of one fringe-width; the concrete base was therefore nearly ten times as sensitive to distortion as is the steel.
A change in temperature of the apparatus as a whole causes a slight change in the relative lengths of the arms. The white-light fringes having been adjusted to the center of the field of view, a change in temperature causes the fringes to be displaced out of view; however, the change is quite reversible and a return to the first temperature brings the fringes again into view. It has occurred repeatedly that at the close of a day’s work the fringes would be in the field of view and upon returning the next day, after the drop and rise in temperature of the night, the fringes would be in the field without any readjustment. The temperature influence on the apparatus is so consistent that a scale of temperature is provided for the capstan pin of the adjusting screws. A change of 10° in temperature requires a change of about 18° in the turning of the screw, corresponding to a displacement of 112 wave-lengths in the double light-path.
The sodium light is used in making the adjustments when the apparatus is first assembled at the beginning of a series of observations. After the white-light fringes have been found these are rarely lost and it is not necessary to resort to the monochromatic light again during the entire period of observations, unless the
apparatus is disassembled for some cause. The white-light fringes have been kept in adjustment during a period of two weeks or more. Upon the completion of observations at Mount Wilson in September, 1925, the mirrors and other optical parts were removed and packed for safekeeping. When observations were resumed in February, 1926, the mirrors were repolished and all parts were reassembled; the fringes in white-light were found in less than one minute without the use of the sodium light.
Since 1927, the interferometer has been mounted on the campus of Case School of Applied Science, about 330 feet from Euclid Avenue; the passage of street cars and the motor traffic of the city thoroughfare do not interfere with the making of observations. However, it is interesting to note that the sound of the imperfectly muffled exhaust of a motor-truck or a motorcycle, which may be a thousand feet or more distant, will cause the fringes to disappear completely without the slightest tremor. When observations were being made on the Fourth of July, 1904, the discharge of large fire crackers twelve hundred feet distant, produced the same effect. This is due not to mechanical vibration, but to the passage of the sound waves through the air in the light path of the interferometer. On several occasions in the observations made at Mount Wilson, there were minute but very distinct seismic disturbances which for a few seconds completely obliterated the fringes. After one such "earthquake" or micro-seismism, it was necessary to readjust the end mirror through a distance of twenty wave-lengths. A man chopping a stump of wood, several hundred feet away, disturbed the fringes, as also did workmen on a highway three miles distant; the passing of an airplane overhead caused the disappearance of the fringes.
Observations by Morley and Miller in 1904
The interferometer with the steel-girder base was first used by Morley and Miller in a continuance of the test of the Lorentz-FitzGerald contraction hypothesis. For this purpose the mirrors were so mounted that the distances between them could be made to depend upon the lengths of rods of pine wood. On two ends of the cross, S and T, Fig. 6, are two upright frames of
