polarization was 18° 40′ and 24° 58′ for the two bundles. By Fresnel's hypothesis the change in the velocity of light from the motion of the
medium is ±((μ–1)/μ2)v. The greatest available velocity for the medium
is that of the earth in its orbit, viz, 101,708 feet per second (31,000 meters). At the time of the solstices this motion is horizontal, and from east to west at noon. If the incident light comes from the west, the velocity of light is diminished by Fresnel's fraction of the velocity of the earth. If the light comes from the east, its velocity is increased by
the same amount. The change in the index of refraction (or δμ/μ) is
equal to (v′/v) (μ2–1); this for an index of 1.513 amounts to 1/11740. Measurements show that in glass, the index increasing by a certain fraction, the rotation increases by a fraction four and one-half times greater, and the consequent change in the plane of polarization would be 1/2500. The
total change on reversing the direction from which the light came would be 1/1250. If the incidence is 70°, and allowance is made for the change
of direction inside of the glass, the fraction becomes 1/1500. When a ray of light falls on a single plate of glass at an angle of 70°, if its plane of primitive polarization makes an angle of 20° with the plane of refraction, this plane is changed by 6° 40′. This multiplied by gives sixteen seconds for the probable effect of the earth’s motion. With forty such plates the effect would be increased to ten and two-third minutes. Two mirrors were used, one to the east and the other to the west, and light could be sent by a heliostat upon either one. The apparatus was easily turned through 180° so as to receive successively the light which travelled with or against the earth’s motion.
With a single pile of plates highly inclined and a second pile less inclined, of more highly tempered glass and in the opposite azimuth, a rotation of 50° could be produced, while the tendencies to elliptical polarization were exactly balanced. The motion of the earth could modify this result to the extent of only two minutes; which is too small for accurate observation. Fizeau then resorted to a device already indicated by Botzenhart for amplifying this effect. A small variation in the primitive plane of polarization produces a greater effect the smaller the azimuth of this plane. If the original azimuth is only 5°, a small change in the azimuth trebles the value of the rotation. A large rotation is first produced on a ray whose azimuth is large, and then this rotation is largely changed by another pile so placed that the ray enters it under a small azimuth. More than two thousand measurements were made under various conditions. For noon observations at the time of solstice the rotation was always greater when the light came from the west, and was less at other times of day. The excess in the value of the rotation when the light came from the west varied between 30′ and 155′, according to the different ways in which the piles of plates were
combined. The difference in the values of the rotation according as the light came from the west or east was consistent with a change in the index of refraction corresponding to Fresnel's hypothesis. Fizeau indicated his intention of renewing the research with improved apparatus, but no further publication on the subject by him can be found.
Faye has criticised this investigation of Fizeau, on the ground that he has taken no account of the motion of the solar system towards the constellation Hercules. This motion, recognized by astronomers on substantial evidence, amounts to 25,889 feet per second (7,894 meters) at its maximum. Its influence is almost zero at noon of the solstices. But it increases after noonday. Faye examines Fizeau's observations at 4 P. M., and finds discrepancies of 12′ or 15′ between the results of theory and observation. By neglecting the term which corresponds to the motion of the solar system, Fizeau's observations accord better at all hours of the day. Must the inference be, Faye asks, that the solar system does not move? Tessan, in reply to Faye, says that the sun, from which Fizeau derived the light used in his experiments, moves with the rest of the solar system; and that therefore Fizeau was justified in neglecting the term which expresses this motion, as of no effect on his calculations. Fizeau's theory depends only on the relative velocity between the source of light and the body which receives it; that is, the velocity of revolution and rotation of the earth.
In 1881, Professor Michelson published the results of his investigation on this delicate problem. He first calculates the probable difference of time taken by the light in going and returning over a given distance, according as that distance lies in the direction of the earth’s motion or at right angles to it. If the distance were 1,200 millimeters, the difference of time translated into space would be equal to one-twenty-fifth of a wave-length of yellow light. The apparatus was ingeniously devised so as to bring about fringes of interference between the two rays which have travelled on rectangular paths. The whole apparatus was then turned round bodily through 90°, so as to exchange the conditions of the two interfering rays. Special apparatus was made for this experiment by Schmidt and Haensch of Berlin, and was mounted on a stone pier at the Physical Institute of Berlin. It was so sensitive to accidental vibrations that it could not be used in the day-time, nor indeed earlier than midnight. To secure greater stability the apparatus was moved to the Astrophysikalisches Observatorium in Potsdam, in charge of Professor Vogel. But even here the stone piers did not give sufficient protection against vibration. The apparatus was then placed in the cellar, the walls of which formed the foundation for an equatorial. But stamping with the feet, though at a distance of 100 meters, made the fringes disappear.
The experiments were made in April, 1881. At this time of the year, the earth’s motion in its orbit coincides roughly with the motion of the solar system, viz, towards constellation Hercules. This direction is in-