The light from the moving mirror was concentrated on the fixed mirror by a lens 8 inches in diameter, with a focal length of 150 feet. These improvements on Foucault’s arrangement were so advantageous that Mr. Michelson obtained, even with a smaller speed in the revolving mirror, an angle of separation between the outgoing and returning rays of light so great that the inclined plate of glass in front of the micrometer was not necessary; the head of the observer not shutting off the light. The mean result of one hundred observations taken on eighteen different days made the velocity of light 186,313 miles per second, with a probable error of 30 miles.
In 1882, at the request of Professor Newcomb, Mr. Michelson made a redetermination of the velocity of light at the Case Institute, in Cleveland, Ohio, by the method already described, with some modifications. The space traversed by the light in going and returning between the two mirrors was 4,099 feet. Two slight errors in the reduction of his former work were corrected in this. The velocity deduced from five hundred and sixty-three new observations was 186,278 miles, with a probable error of 37 miles.
In March, 1879, Congress had voted an appropriation of $5,000 for experiments on the velocity of light, to be made under the direction of Professor Newcomb. All the delicacy of instrumental construction, all the skill of scientific observation, and all the resources of mathematical discussion were enlisted in this service. The method adopted was that of the revolving mirror. The movable mirror was mounted at Fort Myer. Two different locations were selected for the fixed mirror, viz, the Naval Observatory and the Washington Monument. In one case the distance was 2,550.95 meters, or about 8,367.12 feet; in the second case, 3,721 meters, or about 12,205.57 feet. Mr. Michelson assisted in the observations until his removal to Cleveland, in the autumn of 1880. The observations began in the summer of 1880, and were continued into the autumn of 1882, the most favorable days in spring, summer, and autumn, being selected. In all five hundred and four sets of measurements were made, viz, two hundred and seventy-six by Professor Newcomb, one hundred and forty by Professor Michelson, and eighty-eight by Mr. Holcombe. After a full discussion of all the observations and the possible sources of error, Professor Newcomb decided to rest the final result on the one hundred and thirty-two sets of observations made in 1882 over the long distance between Fort Myer and the Washington Monument. The velocity then obtained was 186,282 miles. The velocity deduced from the three sets of observations was 186,251 miles. The probable error of the first result was about 19 miles.
For some future attack upon this problem Professor Newcomb suggested a prism for the reflector with a pentagonal section, and placed at such a distance that it could revolve through an arc of 36° while the light was going and returning; five hundred turns a second and a distance of 19 miles would fulfill this condition. In the Rocky Mountains,
or the Sierra Nevada, stations from 20 to 30 miles distant could be found, and with no greater loss of light from absorption than is produced by 2 or 3 miles of common air.
The first experiments made in Great Britain for the measurement of the velocity of light were published by James Young and Prof. G. Forbes in the Philosophical Transactions of 1882. They adopted the method of Fizeau. In 1878, between six and seven hundred observations were made; but the number of teeth in the rotating wheel was insufficient. New experiments were made in 1880-’81 across the river Clyde. Two reflectors were used at unequal distances, and the time was noted when an electric light after the two reflections was at its maximum. The corrected distances for the two mirrors were 18, 212. 2 and 16, 835 feet. After an elaborate mathematical discussion of the theory of this method, the velocity of light was placed at 187, 221 miles. This value exceeded those obtained by Cornu or Michelson; but this might be explained by the color of the light used in the different experiments. Mr. Young and Professor Forbes made some experiments with lights of different colors, in confirmation of this view. But Professor Michelson compared his three hundred and eighteen observations with sunlight and two hundred and sixty-seven observations with electric light, and found that the difference was in the opposite direction; and in a differential experiment, when half the slit was covered with red glass, he found no displacement. Young and Forbes were attracted to their experiments on the velocity of light by Maxwell’s speculations on the electro-magnetic theory of light, and also as promising the most accurate method of obtaining the parallax and distance of the sun. Their velocity of light combined with Struve’s constant of aberration made the sun’s parallax 20″. 445, and its distance 93, 223, 000 miles.
When Arago, in 1838, suggested to the French Academy an experiment on the velocity of light, and explained his method of making it, which was essentially the one afterwards adopted by Foucault, he had in view the settlement of the long controversy between the advocates of the corpuscular and undulatory theories. Almost all of the different classes of phenomena in geometrical optics can be explained by either one of these theories, though even here the undulatory has the advantage of greater simplicity. But in one respect the two theories are antagonistic. According to the corpuscular theory, light should move faster in glass or water than in air, for example. The undulatory theory reversed this proposition. Here was an experimentum crucis. In 1850, Fizeau and Foucault made the experiment, each in his own way, and in both experiments the result was in favor of the theory of undulations. It has been shown that in the case of air alone lengths of many thousand feet are practicable. But the absorbing power of water prevents the use of greater lengths than about 10 feet. Light would pass through 10 feet of air in less time than one eighteen-thousandth of a second;