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Full text of "Scientific Papers - Vi"

42                              ABERRATION  IN  A  DISPERSIVE  MEDIUM                           [3,{
explanation of stellar aberration, as usually given, proceeds rather upon tl basis of the corpuscular than of the wave-theory. In order to adapt it to tl principles of the latter theory, Fresnel found it necessary to follow Young assuming that the aether in any vacuous space connected with the earth (ar therefore practically in the atmosphere) is undisturbed by the earth's motii of 19 miles per second. Consider, for simplicity, the case in which tl direction of the star is at right angles to that of the earth's motion, ai replace the telescope, which would be used in practice, by a pair of perforate screens, on which the light falls perpendicularly. We may further iinagii the luminous disturbance to consist of a single plane pulse. When th reaches the anterior screen, so much of it as coincides with the momenta: position of the aperture is transmitted, and the remainder is stopped. Tl part transmitted proceeds upon its course through the aether independent of the motion of the screens. In order, therefore, that the pulse may 1 transmitted by,the aperture in the posterior screen, it is evident that tl line joining the centres of the apertures must not be perpendicular to tl screens and to the wave-front, as would be necessary in the case of res For, in consequence of the motion of the posterior screen in its own plar the aperture will be carried forward during the time of passage of the ligl: By the amount of this motion the second aperture must be drawn backwarc in order that it may be in the place required when the light reaches it. the velocity of light be V, and that of the earth be v, the line of aportur giving the apparent direction of the star must be directed forwards throuj an angle equal to v/V"
If the medium between the screens is dispersive, the question arises what sense the velocity of light is to be taken. Evidently in the sense of tl group-velocity; so that, in the previous notation, the aberration angle v/U. But to make the argument completely satisfactory, it is necessary this case to abandon the extreme supposition of a single pulse, replacing by a group of waves of approximately given wave-length.
While there can remain no doubt but that Ehrenfest is justified in I criticism, it does not quite appear from the above how my original argume: is met. There is indeed a peculiarity imposed upon the regular wave-mofcii constituting homogeneous light, but it would seem to be one imposed for tl purposes of the argument rather than inherent in the nature of the cm The following analytical solution, though it does not relate directly to tl case of a simply perforated screen, throws some light upon this question.
Let us suppose that homogeneous plane waves are incident upon "screen" at z = 0, and that the effect of the screen is to introduce a reducti' of the amplitude of vibration in a ratio which is slowly periodic both wi respect to the time and to a coordinate cc measured in the plane of the scree represented by the factor cos m (vt - as). Thus, when * = 0, there is no effe