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CVIL The Propagation of a Fan-shaped Group of Waves in 

 a Dispersing Medium. By G. Breit, National Research 

 Fellow, U.S.A.* 



BY a Fan-shaped Group is meant a group of waves in 

 which the successive waves are plane, and have a 

 small constant inclination with respect to each other. It 

 may be produced by reflecting a plane wave-train in a 

 rotating mirror or by moving a source of light in the focal 

 plane of a lens. A picture of such a group is given in fig. 1. 



A 



H 



B 



The propagation of a fan-shaped group in a dispersing 

 medium has been discussed by Gribbs t- His calculation 

 shows that at a given point of the group (such as a maximum 

 of intensity) the orientation of the elementary waves is 

 constant in spite of the fact that each of the waves rotates 

 during its progress as a result of the dispersion. The im- 

 portant consequence of this result is that the image of a 

 fan-shaped group, which is first passed through a dispersing 

 medium and then through a lens, does not experience a dis- 

 placement on account of the dispersing action of the medium. 



Having recalled this result of Gribbs, Prof. Ehrenfest 

 showed that the experiment recently proposed by Einstein J 

 is not capable of settling Einstein's question, for the latter 

 incorrectly supposed that, according to the classical wave 

 theory, the image of a fan-shaped group formed by a lens is 

 displaced on account of the dispersing action of a medium 

 which is put in front of the lens. [Another criticism leading 

 to the same result has been published by Raman § ; and 

 Einstein also revised his views ||.] 



* Communicated by the Author. 



t W. Gibbs, « Collected Works/ vol. ii. p. 253 ; ' Nature,' vol. xxxiii. 

 p. 582, April 22, 1886. 



X A. Einstein, Sitz. Ber. d. Berliner Akad. p. 882 (1921). 



§ C. N. Raman, < Nature,' p. 477, April 15, 1922. 



|| A. Einstein, Sitz. Bsr. d. Berl. Akad. Feb. 2, 1922, pp. 18-22. 



