-*^ 



FKESNEL ON DOUBLE REFRACTION. 263 



How Transversal Vibrations are extinguished at the extremity 

 of the Waves. 



Hitherto we have only considered indefinite waves; let us 

 suppose them limited, and examine what happens at their ex- 

 tremities, admitting the aether to be sensibly incompressible. 



I suppose that a part YW. 3. 



ofthewaveAE(fig.3.) \' 



has been arrested by a j 



screen EC; let M be I 



• A. E' C 



a point situated behind "- rT 

 the screen at a di- ; \ 



stance very great rela- 'r~ ^\ 



tive to the length of an 



undulation. However ^ 



small may be the sen- ^" 



sible magnitude of the y-- 



angle T E M which the "]^^ | 



straight lineEMmakes i 



with the direct ray E T, 



the light sent to M will be very little, as we know by experience, 

 and as may be easily concluded from the theory of diffraction. 

 If therefore the angle T E M is rather large, the point M will 

 be nearly at rest, w'hilst the point T and all the rest of the wave 

 S T will undergo sensible oscillations along the plane S T M. It 

 would seem that there ought to result from this alternate con- 

 densations and dilatations of the aether between T and M; but 

 remark, in the first place, that at the same instant when the face 

 (c e) of the small parallelopiped cdef is pushed towards M by 

 the semi-undulation whose middle corresponds to S T, the homo- 

 logous faces c k, eg of the two contiguous parallelopipeds move off 

 from M by the contrary movements of the two semi-undula- 

 tions whose middle points correspond to the lines s t, s' t' ; so 

 that whilst the volume ofcd ef diminishes, those of the two 

 similar parallelopipeds between which it is situated increase by 

 the same quantitj'^, and so on in succession in the direction kg. 

 If then the aether strongly resists compression, it is possible that 

 the equilibrium of tension may continually re-establish itself, and 

 almost instantaneously, between the neighbouring elements 

 parallel to gk. Moreover, the points which remain at rest during 

 the oscillations of the extremities of the waves, arc sufficiently 



VOL. V. PART XVIII. T 



