Miller D.C. The Ether-Drift Experiment and the Determination of the Absolute Motion of the Earth // Reviews of modern physics, Vol.5, July 1933

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of the positions of the interference fringes corresponding to the sixteen equidistant azimuths of one complete turn of the interferometer when the instrument is turning at the rate of one turn in about fifty seconds. A set of readings which corresponds to a single observation, represented by one point on the charts of the original observations, usually consists of twenty turns, involving three hundred and twenty readings, made in about eighteen minutes. The time midway between the beginning and ending of the set of readings is taken as the time of the observation. The twenty turns are ordinarily observed in continuous succession; however, if a single reading at any one azimuth is lost, due to vibration of the support or other cause, the entire turn is cancelled. The adjustments are maintained so that the central fringe of the field of view, Fig. 7, is never more than two fringe-widths from the fiducial point. Often the temperature drift is such that the fringes shift more than this before a set of twenty turns is completed. When this occurs, the fringe system is restored to its central position simply by placing a small weight of two or three hundred grams on the end of the arm or by removing a weight from the arm. This is done without stopping the uniform turning of the apparatus and usually without interrupting the readings; if a reading is lost, the entire turn is cancelled and the observations are continued until twenty complete turns of readings have been secured. Only rarely is it necessary to readjust the fringes by means of the screws against which the end mirror rests. On some occasions the temperature conditions are so steady that no adjustment of fringes is required through several sets, which may cover an interval of an hour or more. Such sets of observations are repeated continuously during the several hours of the working period.

It is considered very important that the interferometer should not be enclosed in a metallic casing, nor even in an opaque covering; also that it should not be placed inside a room with heavy walls such as are required for a constant-temperature room. The apparatus should be, as nearly as possible, in the open so that there is no possibility of entrainment of the ether in massive materials surrounding it. The instrument is very sensitive to changes of

temperature and to vibration of the support and the quantity to be measured is extremely small. When the apparatus is used with the least possible covering, it is subjected to greater temperature disturbances than when fully protected, which results in greater dispersion among the separate readings; it is therefore necessary to accumulate a larger number of readings as rapidly as possible under these conditions and to arrange and combine them in such a manner that the systematic ether-drift effect will be fully preserved while the temperature changes which proceed more slowly will be eliminated in the final average. As the readings are taken at intervals of about three seconds, the position of the maximum displacement is dependent upon readings covering an interval of less than ten seconds. A complete period of the displacement takes place in about twenty-five seconds. Any temperature effect or other disturbing cause which is not strictly periodic in every twenty-five seconds over an interval of fifteen minutes would largely be cancelled out in the process of averaging, while a real periodic effect persists. Thus the observations for the direction of the absolute motion are largely independent of ordinary temperature variations. The observation is a differential one and can be made with considerable certainty under all conditions. Disturbances, due to temperature or other causes lasting for a few seconds or for a few minutes, might affect the actual amount of the observed displacement and give less certain values for the velocity of the ether-drift while, at the same time, the position of maximum displacement is not altered.

Previous to 1925, the time of actual readings had been confined to one or two hours at a predetermined time of day; the time required for preparation and preliminary adjustments would perhaps be two hours more. The procedure adopted in 1925 makes it necessary to have observations equally distributed over the twenty-four hours of the day to determine the curve of diurnal variation. Allowing a few minutes for reading thermometers and for making readjustments of fringes and also a few minutes for relaxation, two sets of readings may be made in each hour through a working day, or night, of eight hours. The accumulation of a hundred sets

of readings, distributed over the twenty-four hours of the day will, under favorable weather conditions, occupy a period of six or eight days. Such a series of observations is finally reduced to one group, corresponding to the mean date of the epoch; several series of this extent are represented in Fig. 22.

The observer has only one single thing to do, that is to note and announce the position of the central black fringe with respect to the fiducial point, plus or minus, in units of a tenth of a fringe width, at the instant of the click of the electric sounder. An assistant records these readings in order, on a prepared form, starting with the reading corresponding to the north or other noted azimuth, as shown in Fig. 8, which is the

Fig. 8. Form of record of ether-drift observations.

record of actual observations made at Mount Wilson on September 23, 1925. The observer gives no attention to the azimuth. The reading is determined by instantaneous visual estimation; it is quite impracticable to use any kind of a scale in the field of view because the width of the fringes is subject to slight variation. That this

Fig. 9. Interferometer readings and the process of reducing them for the ether-drift effect.

method is sufficient is shown by the uniformly consistent and systematic periodic curves representing the observations. The numerical quantity used as the result of a single observation is the average of forty such readings (the function being periodic in each half-turn) and it approaches an accuracy of a hundredth of a fringe.

While readings are being taken, neither the observer nor the recorder can form the slightest opinion as to whether any periodicity is present, much less as to the amount or direction of any periodic effect; the taking of observations is quite unprejudiced and is simply mechanical. That this must be true will be evident from an inspection of the numbers representing the readings as recorded in the chart, Fig. 8, and shown graphically in Fig. 9.

Reduction of the interferometer observations

The numerical reduction of a set of readings is a simple arithmetical process. In the record, Fig. 8, the horizontal lines give the sixteen readings for one turn of the interferometer, the first reading being that when the telescope points to the north; the readings for twenty turns are shown. The seventeenth number at the end of each line is the first reading of the next succeeding line or turn; if an adjustment of fringes is made, this number is for the beginning of the next turn, before the adjustment is made. The twenty numbers in each column are added with respect to the plus and minus values. Under ideal conditions, all the numbers in column one (and in column seventeen) should be the same integer but actually there is always some shift of the fringe system with respect to the fiducial point. This shift is assumed to be steady, or linear, throughout the time of one turn, about twenty-



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