|529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564|
the retardation which a ray experiences on account of having to traverse a dense medium instead of a vacuum. Let us calculate this retardation.
Let there be a transparent medium whose thickness is a, and let it be supposed fixed. Let the luminiferous ether be supposed to move with velocity v in air, and with velocity v' within the medium. Let light be propagated through the ether with velocity Y in air and with velocity V' within the medium. Then the absolute velocity of the light will be v-f-V in air and t/+V' within the medium, and the retardation, or difference of time in traversing a thickness a of the medium, and an equal thickness of air, will be
and the retardation in distance reckoned as at the velocity, V will be JV v\ «ra/V3 v2\ ]
VIJ "t"V2\\ls t>,2y j’
Now, according to every form of the theory, y,=/a, the index of refraction, and according to Fresnel’s form of the theory, in which the density of the medium varies
as /K/2, the equation of continuity requires that In this case the second term dis-
appears and the retardation is a((t—1)+terms in which may be neglected, as Y is
more than 10000 times v.
Hence, on Fresnel’s theory, the retardation due to the prism is not sensibly affected by the motion of the earth. The same would be true on the hypothesis that the luminiferous ether near the earth’s surface moves along with the earth, whatever the form of the theory of the medium.
Since the deviation of light by the prism depends entirely on the retardation of the rays within the glass, no effect of the earth’s motion on the refrangibility of light is to be expected. Professor Stokes (Phil. Mag. 1846, p. 63) has also given a direct proof of this statement, and the experiment of Arago confirms it to a certain degree of exactness.
In order to test the equality of the index of refraction for light moving in opposite directions through a prism, I employed in 1864 the following arrangement.
I made use of a spectroscope constructed by Mr. Becker, and provided with a tube at right angles to the axis of the observing-telescope, carrying a transparent plate of parallel glass placed between the object-glass and its focus, so as to reflect the light which enters the tube along the axis of the telescope towards the object-glass. In this tube is placed a screen with a vertical slit, in the middle of which is a vertical spider-line so arranged that its virtual image formed by the first surface of the glass plate coincides with the crossing of the spider-lines of the telescope at the principal focus of the object-glass. This coincidence is tested by observing the cross lines through the other telescope, with the two telescopes facing each other. The eyepiece of the second telescope is then removed, and a plane mirror is placed at the focus of the object-glass, perpendicular to the axis, and the telescopes are so adjusted that light entering by the side tube is
reflected down the axis of the first telescope, traverses the prisms in succession, enters the second telescope, is reflected by the mirror at its focus, and emerges from the telescope parallel to its direction at incidence; it then traverses the prisms in the reverse order, and is brought to a focus at the cross lines of the first telescope.
If the deviation of the rays in passing through the prisms from east to west differs from that produced during their passage from west to east, the image of the vertical spider-line formed by the rays which have traversed the prisms twice will not coincide with the intersection of the spider-lines as before.
I have found, however, that when the instrument is properly adjusted, the coincidence is so perfect with respect to rays of all refrangibilities, that the image of the vertical spider-line is seen with perfect distinctness, though the rays which form it have passed twice through three prisms of 60°.
If we observe the coincidence of this image with the intersection of the spider-lines at the focus when the rays pass through the prisms first in the direction of the earth’s motion and return in the opposite direction, we may then reverse the whole instrument, so that the rays pursue an opposite path with respect to the earth’s motion. I have tried this experiment at various times of the year since the.year 1864, and have never detected the slightest effect due to the earth’s motion. If the image of the spider-line is hid by the intersection of the cross lines in one position, it remains hid in precisely the same way in the other position, though a deviation corresponding to one-twentieth of the distance of the components of the line D could be easily detected.
On the other hand, M. Fizeau* has observed a difference in the rotation of the plane of polarization according as the ray travels in the direction of the earth’s motion or in
# t o
the contrary direction, and M. Angstrom has observed a similar difference in phenomena of diffraction. I am not aware that either of these very difficult observations has been confirmed by repetition.
In another experiment of M. Fizeau, which seems entitled to greater confidence, he has observed that the propagation of light in a stream of water takes place with greater velocity in the direction in which the water moves than in the opposite direction, but that the acceleration is less than that which would be due to the actual velocity of the water, and that the phenomenon does not occur when air is substituted for water. This experiment seems rather to verify Fresnel’s theory of the ether; but the whole question of the state of luminiferous medium near the earth, and of its connexion with gross matter, is very far as yet from being settled by experiment.
June 10,1867. James Clerk Maxwell.
§ II. Description of Apparatus.
All the experiments were made with my refractor by Alvan Clark, of 8 inches aperture and 10 feet focal length, which is mounted equatorially, and carried very smoothly
* Ann. de Chimie et de Physique, Feb. 1860,
MDCCCLXVIII. 4 E