Experimental Determination of the Velocity of Light Part 1

Experimental Determination of the Velocity of Light.

by Albert A. Michelson.

Note.

The probability that the most accurate method of determining the solar parallax now available is that resting on the measurement of the velocity of light, has led to the acceptance of the following paper as one of the series having in view the increase of our knowledge of the celestial motions. The researches described in it, having been made at the United States Naval Academy, though at private expense, were reported to the Honorable Secretary of the Navy, and referred by him to this Office. At the suggestion of the writer, the paper was reconstructed with a fuller general discussion of the processes, and with the omission of some of the details of individual experiments.

To prevent a possible confusion of this determination of the velocity of light with another now in progress under official auspices, it may be stated that the credit and responsibility for the present paper rests with Master Michelson.

Simon Newcomb, _Professor, U.S. Navy_, _Superintendent Nautical Almanac_.

Nautical Almanac Office, Bureau of Navigation, Navy Department, _Was.h.i.+ngton, February 20, 1880._

Introduction.

In Cornu's elaborate memoir upon the determination of the velocity of light, several objections are made to the plan followed by Foucault, which will be considered in the latter part of this work. It may, however, be stated that the most important among these was that the deflection was too small to be measured with the required degree of accuracy. In order to employ this method, therefore, it was absolutely necessary that the deflection should be increased.

In November, 1877, a modification of Foucault's arrangement suggested itself, by which this result could be accomplished. Between this time and March of the following year a number of preliminary experiments were performed in order to familiarize myself with the optical arrangements.

The first experiment tried with the revolving mirror produced a deflection considerably greater than that obtained by Foucault. Thus far the only apparatus used was such as could be adapted from the apparatus in the laboratory of the Naval Academy.

At the expense of $10 a revolving mirror was made, which could execute 128 turns per second. The apparatus was installed in May, 1878, at the laboratory. The distance used was 500 feet, and the deflection was about twenty times that obtained by Foucault.[1]

[Footnote 1: See Proc. Am. a.s.soc. Adv. Science, Saint Louis meeting.]

These experiments, made with very crude apparatus and under great difficulties, gave the following table of results for the velocity of light in miles per second:

186730 188820 186330 185330 187900 184500 186770 185000 185800 187940 ------ Mean 186500 300 miles per second, or 300140 kilometers per second.

In the following July the sum of $2,000 was placed at my disposal by a private gentleman for carrying out these experiments on a large scale.

Before ordering any of the instruments, however, it was necessary to find whether or not it was practicable to use a large distance. With a distance (between the revolving and the fixed mirror) of 500 feet, in the preliminary experiments, the field of light in the eye-piece was somewhat limited, and there was considerable indistinctness in the image, due to atmospheric disturbances.

Accordingly, the same lens (39 feet focus) was employed, being placed, together with the other pieces of apparatus, along the north sea-wall of the Academy grounds, the distance being about 2,000 feet. The image of the slit, at noon, was so confused as not to be recognizable, but toward sunset it became clear and steady, and measurements were made of its position, which agreed within one one-hundredth of a millimeter. It was thus demonstrated that with this distance and a deflection of 100 millimeters this measurement could be made within the ten-thousandth part.

In order to obtain this deflection, it was sufficient to make the mirror revolve 250 times per second and to use a "radius" of about 30 feet. In order to use this large radius (distance from slit to revolving mirror), it was necessary that the mirror should be large and optically true; also, that the lens should be large and of great focal length. Accordingly the mirror was made 1 inches in diameter, and a new lens, 8 inches in diameter, with a focal length of 150 feet was procured.

In January, 1879, an observation was taken, using the old lens, the mirror making 128 turns per second. The deflection was about 43 millimeters. The micrometer eye-piece used was substantially the same as Foucault's, except that part of the inclined plate of gla.s.s was silvered, thus securing a much greater quant.i.ty of light. The deflection having reached 43 millimeters, the inclined plate of gla.s.s could be dispensed with, the light going past the observer's head through the slit, and returning 43 millimeters to the left of the slit, where it could be easily observed.

Thus the micrometer eye-piece is much simplified, and many possible sources of error are removed.

The field was quite limited, the diameter being, in fact, but little greater than the width of the slit. This would have proved a most serious objection to the new arrangement. With the new lens, however, this difficulty disappeared, the field being about twenty times the width of the slit. It was expected that, with the new lens, the image would be less distinct; but the difference, if any, was small, and was fully compensated by the greater size of the field.

The first observation with the new lens was made January 30, 1879. The deflection was 70 millimeters. The image was sufficiently bright to be observed without the slightest effort. The first observation with the new micrometer eye-piece was made April 2, the deflection being 115 millimeters.

The first of the final series of observations was made on June 5. All the observations previous to this, thirty sets in all, were rejected. After this time, no set of observations nor any single observation was omitted.

Theory of New Method.

[Ill.u.s.tration: FIG. 1.]

Let S, Fig. 1, be a slit, through which light pa.s.ses, falling on R, a mirror free to rotate about an axis at right angles to the plane of the paper; L, a lens of great focal length, upon which the light falls which is reflected from R. Let M be a plane mirror whose surface is perpendicular to the line R, M, pa.s.sing through the centers of R, L, and M, respectively. If L be so placed that an image of S is formed on the surface of M, then, this image acting as the object, its image will be formed at S, and will coincide, point for point, with S.

If, now, R be turned about the axis, so long as the light falls upon the lens, an image of the slit will still be formed on the surface of the mirror, though on a different part, and as long as the returning light falls on the lens an image of this image will be formed at S, notwithstanding the change of position of the first image at M. This result, namely, the production of a stationary image of an image in motion, is absolutely necessary in this method of experiment. It was first accomplished by Foucault, and in a manner differing apparently but little from the foregoing.

[Ill.u.s.tration: FIG. 2.]

In his experiments L, Fig. 2, served simply to form the image of S at M, and M, the returning mirror, was spherical, the center coinciding with the axis of R. The lens L was placed as near as possible to R. The light forming the return image lasts, in this case, while the first image is sweeping over the face of the mirror, M. Hence, the greater the distance RM, the larger must be the mirror in order that the same amount of light may be preserved, and its dimensions would soon become inordinate. The difficulty was partly met by Foucault, by using five concave reflectors instead of one, but even then the greatest distance he found it practicable to use was only 20 meters.

Returning to Fig. 1, suppose that R is in the princ.i.p.al focus of the lens L; then, if the plane mirror M have the same diameter as the lens, the first, or moving image, will remain upon M as long as the axis of the pencil of light remains on the lens, and _this will be the case no matter what the distance may be_.

When the rotation of the mirror R becomes sufficiently rapid, then the flashes of light which produce the second or stationary image become blended, so that the image appears to be continuous. But now it no longer coincides with the slit, but is _deflected_ in the direction of rotation, and through twice the angular distance described by the mirror, during the time required for light to travel twice the distance between the mirrors. This displacement is measured by the tangent of the arc it subtends. To make this as large as possible, the distance between the mirrors, the radius, and the speed of rotation should be made as great as possible.

The second condition conflicts with the first, for the radius is the difference between the focal length for parallel rays, and that for rays at the distance of the fixed mirror. The greater the distance, therefore, the smaller will be the radius.

There are two ways of solving the difficulty: first, by using a lens of great focal length; and secondly, by placing the revolving mirror within the princ.i.p.al focus of the lens. Both means were employed. The focal length of the lens was 150 feet, and the mirror was placed about 15 feet within the princ.i.p.al focus. A limit is soon reached, however, for the quant.i.ty of light received diminishes very rapidly as the revolving mirror approaches the lens.

Arrangement and Description of Apparatus.

Site and Plan.

The site selected for the experiments was a clear, almost level, stretch along the north sea-wall of the Naval Academy. A frame building was erected at the western end of the line, a plan of which is represented in Fig. 3.

[Ill.u.s.tration: FIG. 3.]

The building was 45 feet long and 14 feet wide, and raised so that the line along which the light traveled was about 11 feet above the ground. A heliostat at H reflected the sun's rays through the slit at S to the revolving mirror R, thence through a hole in the shutter, through the lens, and to the distant mirror.

The Heliostat.

The heliostat was one kindly furnished by Dr. Woodward, of the Army Medical Museum, and was a modification of Foucault's form, designed by Keith. It was found to be accurate and easy to adjust. The light was reflected from the heliostat to a plane mirror, M, Fig. 3, so that the former need not be disturbed after being once adjusted.

The Revolving Mirror.