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LII. On the Propagation of Waves in a Resisted Fluid ; >voith a 

 neiso Explanation qf the Dispersion atid Absorption of Lights 

 and other Optical Phccnomena. By the Rev. M. O'Brien, 

 Professor qf Natural Philosophy and Astronomy in King's 

 College^ London^ and late Fellow of Caius College, Cam- 

 bridge^. 



1. T^WO different hypotheses may be made respecting the 

 ^ mode of action of the particles of a transparent sub- 

 stance upon the vibrations of the aethereal fluid within it. The 

 first is this : that the transparent substance exerts upon each 

 element of the aethereal fluid forces which depend simply upon 

 the displacements of that element relatively to the contiguous 

 particles of matter. This will be the case when the amplitudes 

 of the aethereal vibrations (/. e. the maximum excursions of the 

 elements from their positions of equilibrium) are extremely 

 small compared with the intervals between the particles of the 

 transparent substance, but not otherwise. The second hypo- 

 thesis is this : that the forces exerted by the transparent sub- 

 stance upon any element of the aethereal fluid are of the same 

 nature as the resistances experienced by a set of particles 

 moving through a resisting medium, depending, not upon the 

 displacements of the element relatively to the contiguous par- 

 ticles of matter, but upon the velocity, or rather the state of 

 motion of the element. This will be the case when the am- 

 plitudes of the aethereal vibrations are large compared with the 

 intervals between the ])articles of the transparent substance. 



2. The equations employed by M. Cauchy, in investigating 

 the vibratory motion of two mutually penetrating systems of 

 particles, are obtained by assuming that the relative motion of 

 any two contiguous particles is extremely small compared with 

 the distance between them. Now, as we must suppose that 

 the displacements of the particles of a transparent substance 

 caused by the vibrations of the aether are always extremely 

 small compared with the amplitudes of the aethereal vibra- 

 tions f, the motion of any aethereal particle relatively to a conti- 

 guous material particle will be very nearly the same thing as the 

 actual motion of the former particle in space. Hence, in order 

 that M. Cauchy's assumption may be true, the displacements 

 of each particle of aether from its equilibrium position must be 

 extremely small compared with its distance from any conti- 

 guous particle of matter; which cannot be the case unless the 

 amplitudes of the aethereal vibrations be very small compared 



♦■ Communicated by the Author. 



•|- The truth of this statement is shown by a result obtained from 

 M. Cauchy's equations, namely the relation between «,, and a, at the bottom 

 of page 214 of the 20th volume of the Philosophical Magazine, S. 3. 



