On the Propagation of Waves in a Resisted Fluid. 327 



with the intervals between the material particles. Hence it 

 appears that M. Cauchy's equations are obtained, not only 

 upon the supposition that the relative motion of any two con- 

 tiguous particles of aether is extremely small compared with 

 the distance between them, but also upon the assumption that 

 the amplitudes of the aethereal vibrations are extremely small 

 compared with the intervals between the particles of transpa- 

 rent substances. 



When we consider that, in all probability, the intervals be- 

 tween the particles of matter are extremely minute compared 

 even with the length of a luminous wave, and that the amplitude 

 of a wave is not necessarily, nor even generally, extremely small 

 compared with its length, we are certainly not warranted in 

 assuming that the amplitudes of the sethereal vibrations are less 

 than the intervals between the particles of matter ; and I think 

 therefore that the correctness of the first of the above hypo- 

 theses may be fairly questioned on this ground, except in the 

 case of light of the weakest intensity. 



3. An explanation of the dispersion and absorption of light 

 has been deduced from M. Cauchy's equations* in the parti- 

 cular case where the number of aethereal particles in any space 

 is the same as that of the material. The explanation of di- 

 spersion appears to be satisfactory enough, but that of absorp- 

 tion is really fallacious for two reasons; namely, first, because it 

 is founded upon a perfectly gratuitous rejection of the positive 

 index in the expression for the disturbance, which is of the form 



a^^^^cos [nt—kz) 

 (see a paper in the Cambridge Transactions, vol. viii. p. 3); 

 and, secondly, because I think it has been proved, in the 

 paper just cited, that, in the case of light passing from vacuum 

 into a transparent substance, the equations of connection at 

 the surface of separation cannot be satisfied if we reject either 

 the positive or the negative index in the above expression, but 

 that the integral representing the disturbance within the trans- 

 parent substance must necessarily be of the form 



a {e^^ cos {Tit—kz + ui)-\- e~^^ cos {nt — kz-ui)], 



an integral which indicates the very reverse of absorption. 



4. M. Cauchy slates that his equations are capable of ac- 

 counting, not only for dispersion and absorption, but also for 

 several of the remarkable phaenomena exhibited by light when 

 it is transmitted through certain crystals and liquids; but 



* I may be allowed to mention here, that when I wrote a paper on this 

 subject in 1842, (Phil. Mag. S. 3. vol. xx. p. 201) I was not aware that 

 Prof. Lloyd had read one previously on Dispersion and Absorption before 

 the Royal Irist) Academy. 



