Page:Scientific Papers of Josiah Willard Gibbs - Volume 2.djvu/227

This page has been proofread, but needs to be validated.

XIII.

ON THE GENERAL EQUATIONS OF MONOCHROMATIC LIGHT IN MEDIA OF EVERY DEGREE OF TRANSPARENCY.

[American Journal of Science, ser 3, vol. xxv, pp. 107–118, February, 1883.]

I. The last April and June numbers of this Journal^[1] contain an investigation of the velocity of plane waves of light, in which they are regarded as consisting of solenoidal electrical fluxes in an indefinitely extended medium of uniform and very fine-grained structure. It was also supposed that the medium was perfectly transparent, although without discussion of the physical properties on which transparency depends, and that the electrical motions were not complicated by any distinctively magnetic phenomena.

In the present paper^[2] the subject will be treated with more generality, so as to obtain the general equations of monochromatic light for media of every degree of transparency, whether sensibly homogeneous or otherwise, which have a very fine-grained molecular structure as measured by a wave-length of light. There will be no restriction with respect to magnetic influence, except that an oscillating magnetization of the medium will be excluded.^[3]

In order to conform as much as possible to the ordinary view of

↑ See pages 182–194 and 195–210 of this volume.
↑ This paper contains, with some additional developments, the substance of a communication to the National Academy of Sciences in November, 1882.
↑ Where a body capable of magnetization is subjected to the influence of light (as when light is reflected from the surface of iron), there are two simple hypotheses which present themselves with respect to the magnetic state of the body. One is that the magnetic forces due to the light are not of sufficient duration to allow the molecular volumes which constitute magnetization to take place to any sensible extent. The other is that the magnetization has a constant ratio to the magnetic force without regard to its duration. We might easily make a more general hypothesis which would embrace both of those mentioned as extreme cases, and which would be irreproachable from a theoretical stand-point; but it would complicate our equations to a degree which would not be compensated by their greater generality, since no phenomena depending on such magnetization have been observed, so far as the writer is aware, or are likely to be, except in a very limited class of cases.
For the purposes of this paper, therefore, it has seemed better to exclude media capable of magnetization, except so far as the first mentioned hypothesis may be applicable. But it does not appear that this requires us to exclude cases in which the medium is subject to the influence of a permanent magnetic force, such as produces the phenomenon of the magnetic rotation of the plane of polarization.

[1] See pages 182–194 and 195–210 of this volume.

[2] This paper contains, with some additional developments, the substance of a communication to the National Academy of Sciences in November, 1882.

[3] Where a body capable of magnetization is subjected to the influence of light (as when light is reflected from the surface of iron), there are two simple hypotheses which present themselves with respect to the magnetic state of the body. One is that the magnetic forces due to the light are not of sufficient duration to allow the molecular volumes which constitute magnetization to take place to any sensible extent. The other is that the magnetization has a constant ratio to the magnetic force without regard to its duration. We might easily make a more general hypothesis which would embrace both of those mentioned as extreme cases, and which would be irreproachable from a theoretical stand-point; but it would complicate our equations to a degree which would not be compensated by their greater generality, since no phenomena depending on such magnetization have been observed, so far as the writer is aware, or are likely to be, except in a very limited class of cases.
For the purposes of this paper, therefore, it has seemed better to exclude media capable of magnetization, except so far as the first mentioned hypothesis may be applicable. But it does not appear that this requires us to exclude cases in which the medium is subject to the influence of a permanent magnetic force, such as produces the phenomenon of the magnetic rotation of the plane of polarization.

[1]

[2]

[3]