The Velocity of Light

FIFTY years ago in the summer of 1879 a young instructor in the Department of Physics and Chemistry at the Naval Academy read a report before the Saratoga meeting of the American Association for the Advancement of Science on the “Experimental Determination of the Velocity of Light.” This instructor, who then held the rank of master, U. S. Navy, was Albert A. Michelson who in the succeeding half century has made a niche for himself through his brilliant researches as the dean of American physicists.

During the same year Thomas A. Edison in his laboratory at Menlo Park, New Jersey, perfected the first electric light globe, the golden jubliee of which has recently been held throughout the world. The one research was in the realm of pure science, the other in the field of invention. Which of these solutions of important problems was of the more value need not be discussed, as one has revolutionized modern living and the other has changed the trend of modern scientific thought.

Why should the speed of light be an important constant? Why should it be necessary to measure it to any great accuracy? The entire answers to these questions were not known in 1879, but the following years have shown that Michelson’s first research along this line was even more important than was then thought. The speed of light is the measuring stick that is used in dealing with the enormous distances that the astronomers measure, the billions of miles to the distant stars and nebulae, and this measuring rod should be as accurate as that “distance between two parallel marks on a platinum- iridium bar kept in the archives of the International Bureau of Weights and Measures at Sevres”—the standard meter. And now in later years with Einstein and his interpretation of the Michelson-Morley experiment, the speed of light assumes a new significance, as he postulates that this speed is the only physical entity which is absolutely constant in the universe, being independent of the motion of the vibrating system which created the light. The length, the mass, and the energy of a moving system is assumed to change with the motion, but the speed of light remains the same, constant and unchangeable. Also the speed of light is the maximum of all speed—absolute, supreme, —the asymptote that others may approach in value, but neither equal nor surpass.

With the study in later years of Maxwell and his electromagnetic vibrations through the postulated ether we have found that visible light is merely one of a family of waves whose sizes vary from that of the infinitesimal cosmic rays, reported on during the past year by Professor Millikan, to the longest of what were originally known as Hertzian rays—our modern radio waves—transmitted by the highest powered transatlantic stations. In this electromagnetic spectrum all of the rays, no matter what their source or what their effect, have the same velocity through the ether or interplanetary space. This speed is that of the visible waves—light. In this family we have the aforementioned cosmic rays, X-rays, ultra-violet, infra-red, radio waves, and many others between these, not so well known, but maybe some day to be of paramount importance. The only common family characteristic that all of these have, except that they are the combination of a variation in an electrical and a magnetic field, is that they travel with the same speed. Hence the speed of light is also the speed of radio, of ultra-violet, or of X- rays.

We may suppose that the ancients, as they watched the stars in the heavens and the flashes of the powerful lightning, believed that the speed of light was infinite, and that the light traveled instantaneously. Galileo is given credit for the first scientific experiment to determine this speed, but his apparatus was crude and his results were negative. Even though Galileo may be regarded as the greatest exposer of philosophical fallacies of all time, and the one man who started the science of physics on an accurate experimental basis, yet the speed of light was too great for the apparatus of the laboratory of the early seventeenth century. As velocity is the ratio of distance and time, for such a stupendous speed we must have either an enormous distance as in astronomy, or else have an accurate way of measuring extremely small intervals of time, as small as a millionth of a second. These requirements are the basis of the division of the four methods for the determination of this constant into the astronomical, as illustrated by the methods of Römer and Bradley, and the terrestrial or laboratory methods as used by Fizeau and Foucault.

Römer’s Method

Galileo, with the help of the negative telescope which he introduced to the savants of the age, had discovered in 1610 the satellites of Jupiter. During the next century observatories and telescopes were built and the astronomers of the time made many measurements on these moons, their periodicity, which varied from forty-two hours to sixteen days, and their eclipses. Ole Römer, a Danish astronomer, when occupied at the Royal Observatory at Paris in 1675, noticed that there was an anomaly in the periods of the eclipses of the same satellite. When the earth was approaching Jupiter the interval between successive eclipses was shorter, and when the earth was receding from Jupiter the period was longer. He gave this observation what we now know is the correct interpretation—that the light has a finite velocity. As the earth approached, the distance, and therefore the time, was shortened, and when going away the distance of travel of the light and therefore the time was lengthened. Römer discovered that the light took eighteen minutes to cross the diameter of the earth’s orbit, 186,000,000 miles in 1,000 seconds. But Römer did not arrive at the correct value of the velocity, because in order to secure this it was necessary to know the parallax of the sun, that is the angle subtended by the earth’s radius at the sun, and the distance of the sun from the earth, and at that time neither of these was known with any degree of accuracy. But to Römer must go the credit of stating that the velocity of light was finite and that it could be determined. His method is now used rather for determining the sun’s parallax and distance rather than the speed of light, this latter having been determined more accurately by other methods.

The French astronomer Jean Baptiste Delambre, from a computational study of the satellites of Jupiter in 1792, gave the speed of light as 193,350 miles per second.

Bradley’s Aberration Method

The second of the astronomical methods is based upon the phenomenon of the aberration of the stars, that is that any star describes annually an elliptical orbit such that at any time it is apparently displaced from its true position. Dr. James Bradley, the astronomer royal of England, made this discovery at Kew in 1725 when he observed that y Draconis in March was in a position twenty seconds more southerly than in December (see Fig. I) and then that it proceeded northwards until in September it was forty seconds more northerly than in March The explanation, which we now know illustrates the difference between apparent and relative motion, a problem in vector differences, came to Dr. Bradley while sailing on the Thames. As his boat changed its course the vane on the boat also changed. If the speed of the ship were AE, Fig. II, and the true speed of the wind were BA, then the apparent speed of the wind is the vector sum of AB and DB (the negative of AE), and the wind has apparently shifted due to the speed of the boat by an angle a in the direction of motion of the boat, such that tan a=AE/BA.

Transferring this analogy to that of the aberration, Bradley concluded that the telescope was shifted a maximum of twenty seconds away from the true star position in the direction of motion of the earth due to the compounding of the speed of the earth and the speed of light. If we know the linear speed of the earth in its orbit and the “constant of aberration,’’ the speed of light is readily calculated. With the value of 20".445 Struve calculated the velocity of light as 191,513 miles per second, a value several per cent too high due to an error in the assumption of the distance from the earth to the sun.

Both of the astronomical methods depend for their accuracy upon knowing the exact values of the astronomical constants. In recent years the following values have been computed:

Constant of aberration = 20".4962± 0".006

Time taken by light to traverse the mean radius of the earth’s orbit=498".82±0".1

Mean distance from earth to sun = 92,900,000 miles

Velocity of light= 186,330 miles per second

Velocity of light=299,870±30 kilometers per second

Fizeau’s Method

Over a century went by before the first terrestrial method of determining the velocity of light was successfully made in Paris by Armand Fizeau, a French physicist. The method may be thought of as a variation of that of Galileo, of successively shutting off and exposing a beam of light, and measuring the time of travel over a known distance. In 1849 Fizeau had constructed a disk with 720 teeth and slots of equal size, the disk being rotated at a constant speed by a train of wheels and weights.

 

A beam of light from the source L is brought to a focus at the slot S of the toothed disk D by means of a lens and mirror (see Fig. III). The light is then made parallel by a lens O and travels over a long distance to another lens O' and is brought to a focus on the surface of the concave mirror M. The light is then reflected back over its original path and once more falls on the slots or teeth of the disk. If the disk is moving slowly the eye sees a flickering image of L, but if the images succeed each other faster than twenty per second a steady image appears due to the persistence of vision. The brightness of this image depends upon how much of the light is stopped by the teeth on the disk. If the speed of the wheel is increased so that a tooth has moved into the position of a slot in the time of travel, the light is intercepted by the tooth and the image vanishes. At twice this speed the light would again appear at its brightest, at three times dark, at four times bright, and so on.

With 720 teeth and a distance from S to M of 8.6 kilometers, with w the angular speed of the wheel, and V the velocity of light, then for the first disappearance:

 t = (2 X 8.6)/V = 27? /2 X 720 X w

 or for the nth disappearance:

t= (2 X 8.6)/V = (2n — 1)/2 X (2 ?)/720 X 1/w

from which V was computed by Fizeau as 195,741 miles per second.

Fizeau’s method has been used to determine the velocity of light by Cornu in 1873, by Young and Forbes in 1881, and by Perrotin in 1900. Cornu increased the distance to twenty-three kilometers, and kept the speed of the wheel under the control of the observer and measured its speed by a hundredth-second chronometer. These refinements gave him a speed in vacuo of 300,400 kilometers per second. Perrotin increased the distance to forty kilometers at the Nice Observatory and obtained a velocity in vacuo of 299,860 kilometers per second.

Foucault’s Method

In 1834 Sir Charles Wheatstone, by an ingenious method making use of revolving mirrors, had succeeded in measuring the speed of electrical discharge between two spark gaps a quarter of a mile apart, the mirrors revolving at about eight hundred revolutions per second and the images from the different gaps being displaced horizontally. In 1838 Francois Arago communicated to the French Academy the details of an apparatus utilizing revolving mirrors for finding the speed of light. Due to the rise of Louis Napoleon in 1848 Arago was kept busy in the important post of minister of war and of marine where “he effected some salutary reforms, such as the improvement of rations in the navy and the abolition of flogging.” His eyesight failed in the spring of 1850 and the details of the method were turned over to J. B. L. Foucault. In 1850 by this method Foucault showed that the speed of light in a refracting medium, water, was less than that in air, but it was not until 1862 that he determined the absolute velocity of light.

In this true laboratory method Foucault allowed the light from a slit to fall upon a plane mirror which was revolving at about four hundred revolutions per second. This light was reflected successively to five other mirrors and returned over the same path to the revolving mirror after traveling a total distance of sixty-six feet. As the revolving mirror had moved in the interim the image would be displaced a fraction of a millimeter, as the time was only one fifteen-millionth of a second, and the speed of light was computed.

In this experiment the deflection was extremely small and of small intensity as it had to be turned aside to be observed, and even at its best was indistinct due to atmospheric disturbances, but it gave a value of 298,000 kilometers per second; with a probable error of at least 1 per cent.

Michelson—1878-79

Albert A. Michelson had graduated from the Naval Academy in 1873 where, according to Admiral Fiske in his Memoirs, he spent much of his time in the physics laboratory engaged in research rather than on the athletic field or engaged in distinctly naval pursuits. In 1875 he returned to the Academy as instructor with the rank of ensign and in May, 1878, made ten independent observations of the speed of light “under difficulties, and with apparatus adapted from the material found in the laboratory of the Naval School.” These measurements indicated the improvements that should be made in order that the desired accuracy would be secured. By use of a lens of long focal length (150 feet), Michelson was enabled to reflect light over a distance of 2,000 feet. The time intervals were measured by means of the revolving mirror whose speed was kept accurately constant by means of a hand control on an air turbine, the speed being measured by the stroboscopic effect with a tuning fork of known frequency. Thus time intervals of four-millionths of a second were measured to an accuracy of 1 part in 200,000. A final result of 299,740 kilometers per second in air, or 299,828 kilometers per second in vacuo was obtained, a result which agrees amazingly well with the present weighted mean of 299,800 kilometers per second in vacuo.

 

 

By reference to Fig. IV it is seen that light is reflected from the sun on a slit by means of a heliostat and mirror. The light from the slit which acts as an object falls upon a revolving mirror R at a distance of thirty feet where it is reflected through an opening in the building on to a lens of long focal length. It is there sent to a plane mirror M at a distance of about 2,000 feet where an image of the slit is formed. The light is then reflected back over its path and if the mirror R had not moved would be superimposed on the slit. But while the light was traveling twice the distance from the revolving mirror to the distant mirror, the revolving mirror had turned clockwise through an angle \delta ?/2, and the reflected light will therefore be turned through an angle 9 and the light will arrive at S' instead of S. With the mirror revolving at 257 revolutions per second a displacement SS' of 133 mm. was noted.

If D is twice the distance between the mirrors, r is the distance from the slit to the revolving mirror, d is the displacement of the image at the slit, ? is the angular displacement of the image, n is the speed of revolution of the mirror, and t is the time for the light to travel the distance D; and as there are 1,296,000 seconds of arc per revolution, then tan ? = d/r; V=D/t; t= ?"/1,296,000X n X2; and F=2,592,000XD X n /?", thus the velocity measured is proportional to D, to r, and n, and inversely proportional to d.

The measurement of D was made by a standard steel tape whose temperature and stretch coefficients had been carefully determined, and which had been compared with a standard meter. The speed of rotation of the revolving mirror was measured by counting the optical beats between the revolving mirror and an electrically maintained tuning fork, and this was maintained constant by regulation of the air blast that drove the turbine which rotated the mirror. The electrically driven fork was compared with a standard Koenig fork, its temperature coefficient being known, and the time was regarded as known to within 1 part in 200,000, giving a speed of light as 299,895 kilometers per second.

To quote from Master Michelson’s paper before the American Association:

The site selected for the experiments was a clear, almost level stretch along the north sea wall of the Naval Academy. A frame building forty-five feet in length was erected at the western end of the line… It was found that the only time during the day when the atmosphere was sufficiently quiet to get a distinct image was during the hour after sunrise or during the hour before sunset. At other times the image was boiling, so as not to be recognizable.

Master Michelson resigned from the Navy and after several years of study in Europe at the University of Berlin, Heidelberg, and the École Polytechnique, was appointed professor of physics at the Case School of Applied Science. While there in 1882 and later at Clark University he continued his experiments, securing still more accurate values.

Simon Newcomb—1882

During the progress of Michelson’s research Simon Newcomb secured official support and, using essentially the same method, made a determination on a still larger scale. He placed the reflector at Fort Myer, Virginia, across the Potomac River from the Washington Monument and the Naval Observatory where the readings were taken, so that the light traveled a distance of about seven kilometers. He maintained the position of the returned image constant by control of the speed of the mirror and in a run of about two minutes counted by means of a chronograph the number of revolutions of the mirror. The mirror could also be turned in either direction so that no zero reading need be taken, but merely the two extremes. A revolving mirror made of nickel steel and having four vertical sides was used. The final result was concluded to be: velocity of light in vacuo = 299,860 kilometers per second.

Maxwell’s Electromagnetic Method

James Clerk Maxwell, after a study of Faraday’s scientific papers, published several mathematical treatises on the electromagnetic theory of light. The first paper was communicated to the Royal Society in 1867, but it was not until 1873 that the theory appeared in a fully developed form in his Electricity and Magnetism. Maxwell reduced all electric and magnetic phenomenon to stresses and motions of a material medium and proved that the velocity of an electromagnetic wave motion in a transmitting medium was v=c /√?k          . He pointed out that in the ether, where the magnetic permeability ? is unity in the electromagnetic system of units, and the dielectric constant k is unity in the electrostatic system of units, that the velocity of light c is that of an electromagnetic wave disturbance v, and that this velocity is the radio of the electromagnetic and the electrostatic units.

When the same electrical quantity is measured in both electromagnetic and electrostatic units the ratio of the result is always a power of c, the velocity of light. For example: 1 volt = 10⁸ abvolts= 1/300 stat volt, so that 1 stat volt=3X 10¹⁰=c abvolts; or 1 ohm=10⁹ abohms=l/9X10¹¹ stat ohms so that 1 stat ohm=9X10²⁰ abohms=c² abohms.

Thus the value of the speed of light may be determined by purely electrical methods, the mean of determinations by J. J. Thomson, Rowland, Rosa, Thomson and Searle, Pellat, Abraham, Hurmuzescu, Perot and Fabry, and Rosa and Dorsey, from 1883 to 1907 gave as a value 299,300 kilometers per second.

That this speed may be determined without measuring either time or distance, but merely the ratio of two units in electricity, is indeed remarkable, and much more than a strange coincidence.

Michelson—1925-1929

Simon Newcomb, in an article in the Encyclopedia Britannica makes the statement:

It seems remarkable that since these determinations were made (1882-3), a period during which great improvements have become possible in every part of the apparatus, no complete redeterminations of this fundamental physical constant has been carried out.

But during this period Dr. Michelson had been appointed head of the Department of Physics at the University of Chicago and had performed and directed much brilliant research. He had performed the Michelson- Morley experiment which showed that the speed of light was not changed by the motion of the transmitting body, and upon this experiment Einstein has based his theory of relativity. He measured the speeds of light in different media and showed that the index of refraction was inversely proportional to the speed of the light in the medium, a fact which killed the corpuscular theory and saw the rise of the undulatory or wave theory. He had invented the refractometer or interferometer which bears his name, and the echelon grating, and had measured the standard meter in terms of the wave-length of a standard light. Not until he was promoted to distinguished service professor of the University of Chicago and relieved of the arduous duties of supervision and teaching was he enabled to return to his first love, the accurate determination of the speed of light. During the summers of 1924 and 1925, again in 1926 and 1927, and now again in 1929, in California, Professor Michelson has and is determining this fundamental constant.

In the expression for the velocity by the revolving-mirror method the distance D between stations, and the speed of the mirror n, may be determined with great accuracy, but the angular displacement of the mirror, ?/2 cannot be measured with great enough accuracy. Newcomb suggested that a revolving mirror of prismatic form be used and the distance between stations be made so great that the return light be reflected at the same angle on the following face of the prism so that the object and the image would coincide. Between Mount Wilson and Mount San Antonio near Pasadena the experiment was tried over a distance of thirty-five kilometers, with a speed of rotation of 1060 turns per second and a four-sided mirror. With an octagonal mirror the speed of revolution could be reduced one-half. The faces of such a prism may be made accurate to within an error of one-millionth by means of interference fringes. The added accuracy of an audion circuit to maintain the tuning fork has been used.

In the summer of 1926 an assortment of mirrors of glass and steel having eight, twelve, and sixteen sides were tried and gave a weighted mean for the velocity of light in vacuo of 299,796±1 kilometers per second.

During the summer of 1929 Professor Michelson has been repeating the experiment at the Mount Wilson Observatory. A twelve-sided steel mirror driven by a small air turbine was formed by a single piece of steel. The flatness of each face is within one-sixth of the wave length of light and the mirror is vibrationless up to 47,000 revolutions per minute. The light is sent from Mount Wilson to Mount San Jacinto, a round trip of 165 miles, and hence must be of great intensity. This was obtained from the crater of a high-intensity searchlight lamp focused on a slit one-tenth millimeter in width.

A further refinement is to be tried at the Ross Flying Field, where permission has been secured to erect a pipe line three feet in diameter and half a mile in length. Dr. Michelson plans to pump the air from the pipe in order to get rid of the errors due to air resistance and to send the light back and forth several times in the pipe by special mirrors. An octagonal mirror will be used and adjustment of the speed be made until the returned image coincides with the object. Thus the velocity of light will be measured directly in vacuo, the dream of every physicist whose fetish is accuracy.

Fifty years have passed since Master Michelson measured the speed of light at Annapolis and started on his way to fame. The probable error of measurement in this time has decreased with the refinement of scientific apparatus until now it is no longer necessary to secure any greater accuracy than that obtained by the former master. In a reminiscent talk before a recent graduating class at the Naval Academy Dr. Michelson said: “When I resigned from the Navy my classmates, who are now admirals, prophesied many dour happenings for me, but now I would not be surprised, if in certain quarters of the globe, the experiments that I have performed would give me a rank almost equal to that of these same admirals.”

Rank is not always the essence of accomplishment, and perhaps Dr. Michelson’s statement is correct. After all the Navy lost a potential admiral, in order that the world would gain an eminent physicist, whose minuteness of detail, accuracy of determination, and brilliance of research have made him by popular consent the world’s greatest authority on light.

BIBLIOGRAPHY

Michelson, A. A. Light Waves and Their Uses, University of Chicago Press.

Michelson, A. A. Studies in Optics, University of Chicago Press, 1927.

Michelson, A. A. Original article on velocity of light was printed in Sittiman’s Journal, Vol. 15, p. 394, May, 1878.

Michelson, A. A. “Experimental Determination of the Velocity of Light”; Proceedings of the American Association for the Advancement of Science, 1878.

Michelson, A. A. Reprinted in Scientific Monthly, December, 1928, p. 562-565 with two pictures of Dr. Michelson.

Michelson, A. A. “Experimental Determination of the Velocity of Light,” a report of the August, 1879 meeting of the A.A.A.S., Scientific American Supplement, No. 193, September 13, 1879.

Encyclopedia Britannica: articles on “The Velocity of Light” by Samuel Newcomb; on "Aberration”; and on the following scientists: Galileo, Römer, Delambre, Bradley, Arago, Wheatstone, James Clerk Maxwell, Fizeau, Foucault, Young, Michelson, Newcomb, Cornu.

Houston, R. A. A Treatise on Light, Longmans, Green and Company.

Lovering, Joseph, President Am. Acad. A.S. Michelson’s Recent Researches on Light.

Annual Report of Smithsonian Institution, July, 1889, pp. 449-468.

Wood, Robert W. Physical Optics, MacMillan.

Brent, Silas, “Measuring the Speed of Light,” excerpt from Research—the Business Builder, reprinted in Sperryscope, Vol. 5, No. 11, April, 1929.

Associated Press, “Speed of Light Will Be Checked by Experiments,” Baltimore Evening Sun, July 12, 1929.

 

Artificial sunlight used for the light speed measurements was obtained from a Sperry high intensity searchlight lamp 

Revolving reflector with cover removed which Dr. Michelson used for his light speed measurements.