CONFERENCE ON MICHELSON-MORLEY EXPERIMENT 359
complete periods in each rotation of the instrument. Beginning when the telescope points north, the position of the fringes is noted at sixteen equidistant points around the horizon. The azimuth of the line of sight when the displacement is a maximum having been noted at two different times of day, it is a simple operation to calculate the right ascension and declination, or the “apex” of the presumed “absolute” motion of the earth in space. The determination of the direction of the earth’s motion is dependent only upon the direction in which the telescope points when the observed displacement of the fringes is a maximum; it is in no way dependent upon the amount of this displacement or upon the adjustment of the fringes to any particular zero position. As the readings are taken at intervals of about three seconds, the position of the maximum is dependent upon observations covering an interval of less than ten seconds. A whole period of the displacement extends over only about twenty-five seconds. Thus the observations for the direction of the absolute motion are largely independent of ordinary temperature disturbances. The observation is a differential one, and can be made with considerable certainty under all conditions. A set of readings usually consists of twenty turns of the interferometer made in about fifteen minutes’ time; this gives forty determinations of the periodic effect. The forty values are simply averaged to give one “observation.” Any temperature effect, or other disturbing cause, which is not regularly periodic in each twenty seconds over an interval of fifteen minutes would largely be canceled out in the process of averaging. The periodic effect remaining in the final average must be real.
The position of the fringe system is noted in units of a tenth of a fringe-width. The actual velocity of the earth’s motion is determined by the amplitude of the periodic displacement, which is proportional to the square of the relative velocity of the earth and thé ether and to the length of the light-path in the interferometer. A relative motion of 30 km/sec., equal to the velocity of the earth in its orbit, would produce a displacement of the fringes from one extreme to the other, of 1.1 fringes. 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
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DAYTON C. MILLER
thus give less certain values for the velocity of relative motion, while at the same time the position of maximum displacement is not disturbed. Thus it is to be expected that the observations for the velocity of motion will not be as precise as the observations for the direction of motion. The two things, magnitude and azimuth of observed relative motion, are quite independent of each other.
It is desirable to have observations equally distributed over the twenty-four hours of the day; since one set requires about fifteen minutes of time, ninety-six sets, properly distributed, will suffice. The making of such a series usually occupies a period of ten days. The observations are finally reduced to one group, and the mean date is considered the date of the epoch. The observations made at Mount Wilson in 1925 correspond to the three epochs, April 1, August i, and September 15, and are more than twice as numerous as all the other ether-drift observations made since 1881. The total number of observations made at Cleveland represents about one thousand turns of the interferometer, while all the observations made at Mount Wilson previous to 1925 correspond to 1200 turns. The 1925 observations consist of 4400 turns of the interferometer, in which over 100,000 readings were made. A group of eight readings gives a value for the magnitude and direction of the ether-drift function, so that 12,500 single measures of the drift were obtained. This required that the observer should walk, in the dark, in a small circle, for a total distance of one hundred miles, while making the readings. Throughout these observations the conditions were exceptionally good. At times there was a fog which rendered the temperature very uniform. Four precision thermometers were hung on the outside walls of the house; often the extreme variation of temperature was not more than one-tenth of a degree, and usually it was less than four-tenths of a degree. Such variations did not at all affect the periodic displacement of the fringes. It may be added that while the 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 hundred thousand readings are added in groups of twenty, are averaged, and then plotted in curves. These curves are subjected