A.A.Michelson, Henry G.Gale. The effect of the earth’s rotation on the velocity of light. Part I, II

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THE EFFECT OF THE EARTH'S ROTATION ON THE VELOCITY OF LIGHT

PART I By A. A. MICHELSON ABSTRACT

Theory of the effect of the rotation of the earth on the velocity of light as derived on the hypothesis of a fixed ether.

Historical Remarks.—The theory was given originally in 1904. The experiment was undertaken at the urgent instance of Dr. L. Silberstein. A preliminary experiment at Mount Wilson in 1923 showed that it was necessary to resort to an exhausted pipeline.

In the Philosophical Magazine, (6) 8, 716, 1904, a plan was proposed for testing the effect of the earth’s rotation on the velocity of light. The expression for the difference in path between two interfering pencils, one of which travels in a clockwise, and the other in a counterclockwise direction, may be deduced on the hypothesis of a fixed ether as follows:

If l1 is the length of path at latitude φ1 and l2 that at latitude φ2, v1 and v2 the corresponding linear velocities of the earth’s rotation, and V the velocity of light, the difference in time required for the two pencils to return to the starting-point will be

or with sufficient approximation

or if

and

(R—earth’s radius), the resulting difference in phase of the two pencils will be

in which ω is the earth’s angular velocity, and λ the effective wavelength of the light employed.

The experiment remained in abeyance for many years, until, at the urgent instance of Dr. L. Silberstein, the writer was convinced of the importance of the work, notwithstanding serious difficulties which were anticipated in the way of raising the necessary funds. The greatest expense would be in arranging a pipe line a mile long and a foot in diameter, such as would be required for the work. In the hope that this device might not be necessary, however, it was decided to attempt the experiment in the open air at Mount Wilson.

The work was undertaken at Mount Wilson during the summer of 1923, with a circuit over one mile in length. The interference fringes between the two pencils, one of which traversed the circuit clockwise, and the other counterclockwise, were observed most clearly during the half-hour before and after sunset. But even under the best conditions, the interference fringes were so unsteady that it was found impossible to make any reliable measurements.

A doubt had been raised concerning the possibility of referring

1 In the original article, Δ was erroneously given as half of this value. Dr. L. Silberstein (Journal of the Optical Society, 5, 291, 1921) deduced the expression equivalent to the above, which was confirmed by Dr. A. C. Lunn, ibid., 6, 112, 1922, except that the area inclosed is substituted for the product lh.