452 



LXX. Researches in Hydrodynamics, with reference to a Theory 

 of the Dispersion of Light. By Professor Challis, M.A., 

 F.R.S., F.R.A.S.* 



THE theory of Double Refraction on the hypothesis of undu- 

 lations, given in the Number of the Philosophical Maga- 

 zine for last December, involved the theory of Dispersion on the 

 same hypothesis ; but for the purpose I had there in view it was 

 not necessary to discuss fully the results obtained relative to the 

 latter theory. On subsequently testing by numerical examples 

 the equation (a), which gives the law of dependence of the re- 

 fractive index (p) on the breadth of the wave (X), I met with an 

 incompatibility which proved that the true formula for disper- 

 sion had not been discovered. Either, therefore, the hypotheses of 

 the theory were false and must be given up, or, if true, I had 

 reasoned from them erroneously. In a difficult investigation of 

 this kind, involving necessarily definite hypotheses respecting the 

 elementary composition of the refractive medium, failure might 

 be attributable to error in these hypotheses, while at the same 

 time the antecedent hypotheses respecting the properties of the 

 sether, and the laws of its motion and pressure deduced therefrom 

 mathematically, might still be true. In order to be able to decide 

 whether or not the failure was due to erroneous reasoning from 

 the supposed constitution of the refractive medium, I reconsidered 

 the mathematical argument, and found, in fact, that a step in it 

 had been omitted, which it will be the object of this and a suc- 

 ceeding communication to point out and to supply. I disco- 



vered also that the expressions for -r- and — j — had been incor- 

 1 dfju dfi 



rectly deduced from the equation (a) ; but as the correct expres- 

 sions would have led to the same results, and as that equation 

 itself requires modification, it is needless to rectify the error. 



According to the theory, the diminution of the rate of propa- 

 gation of an sethereal wave after entrance into a medium, is pro- 

 duced by the mean retarding effect of reflexions of the motion 

 from the atoms, an extremely large number of atoms being sup- 

 posed to be contained in a space the linear dimensions of which 

 are extremely small compared with X. The amount of the re- 

 tardation depends in part on the mobility of the atoms, which 

 may be conceived to be in positions of equilibrium by reason of 

 the action of attractive and repulsive molecular forces, and con- 

 sequently to be moveable by any extraneous action, such as that 

 of the setherial waves. Both the theory of double refraction and 

 that of dispersion require a mathematical investigation of the 

 modifying effect of the motion of the atoms; and for this pur- 

 * Communicated by the Author. 



