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VIII. Aberration in a Dispersive Medium. 

 By Lord Hayleigh, O.M., F,R.S* 



THE application of the theory of group-velocity to the case 

 of light was discussed in an early paper t in connexion 

 with some experimental results announced by Young and 

 Forbes J. It is now, I believe, generally agreed that, 

 whether the method be that of the toothed wheel or of the 

 revolving mirror, what is determined by the experiment is 

 not V, the wave-velocity, but U, the group-velocity, where 



U = d(kY)/dk, 



h being inversely as the wave length. In a dispersive 

 medium V and U are different. 



I proceeded : — " The evidence of the terrestrial methods 

 relating exclusively to U, we turn to consider the astro- 

 nomical methods. Of these there are two, depending 

 respectively upon aberration and upon the eclipses of 

 Jupiter's satellites. The latter evidently gives U. The 

 former does not depend upon observing the propagation 

 of a peculiarity impressed upon a train of waves, and 

 therefore has no relation to U. If we accept the usual 

 theory of aberration as satisfactory, the result of a com- 

 parison between the coefficient found by observation and 

 the solar parallax is V — the wave-velocity." 



The above assertion that stellar aberration gives V rather 

 than U has recently been called in question by Ehrenfest §, 

 and with good reason. He shows that the circumstances 

 do not differ materially from those of the toothed wheel 

 in Fizeau's method. The argument that he employs bears, 

 indeed, close affinity with the method used by me in a 

 later paper ||. "The explanation of stellar aberration, as 

 usually given, proceeds rather upon the basis of the 

 corpuscular than of the wave-theory. In order to adapt 

 it to the principles of the latter theory , Fresnel found it 

 necessary to follow Young in assuming that the aether 

 in any vacuous space connected with the earth (and 

 therefore practically in the atmosphere) is undisturbed 

 by the earth's motion of 19 miles per second. Consider, 

 for simplicity, the case in which the direction of the star 



* Communicated by the Author. 



t Nature, vols, xxiv., xxv., 1881 ; Scientific Papers, i. p. 537. 

 \ These observers concluded that blue light travels in vacuo 1*8 per 

 cent, faster than red light. 



§ Ann. d. Physik, Bd. xxxiii. p. 1571 (1910). 



|| Nature, vol. xlv. p. 499 (1892) ; Scientific Papers, iii. p. 542. 



