THE 



LONDON, EDINBURGH and DUBLIN 



PHILOSOPHICAL MAGAZINE 



AND 



JOURNAL OF SCIENCE. 



SUPPLEMENT to VOL. XXVIII. FOURTH SERIES. 



LXI. Continuation of a Theory of the Dispersion of Light. 

 By Professor Challis, M.A., F.R.S., F.R.A.S* 



HAVING been much occupied with preparing for publication 

 a volume of astronomical observations, I have been 

 hindered from proceeding with the researches relating to the 

 Dispersion of Light, which were commenced in a communication 

 to the Number of the Philosophical Magazine for last June. 

 On account of this interruption, it will be expedient, before 

 advancing beyond the point to which the investigation was 

 brought in that communication, to mention briefly the principal 

 steps of the antecedent reasoning. It was assumed that an 

 aethereal wave within a transparent medium obeys the same laws 

 as one without, but is propagated with less velocity in consequence 

 of being acted upon by an extraneous force always opposite in 

 direction, and proportional in magnitude, to the accelerative 

 force due to the aether. The density of the aether was supposed to 

 be the same within the medium as without, and the extraneous 

 retarding force was considered to be the mean effect of the re- 

 flexion of the motion of the aether from the atoms of the 

 medium, a vast number of atoms being supposed to be contained 

 in a portion of space the linear dimensions of which are ex- 

 tremely small compared to the breadth (X) of a wave. The 

 amount of retardation depending not only on the number of 

 atoms in a given space and their arrangement, but also on their 

 mobility, it is necessary, in order to calculate the rate of pro- 

 pagation in the medium, to determine the motion of an individual 

 atom as resulting both from the dynamical action of the waves 

 and the molecular forces of the medium. The form of the atom 

 being assumed to be spherical, the determination of the accelera- 

 tion due to the waves was shown to depend on the solution of a 

 hydrodynamical problem of which this is the enunciation : — A 

 series of waves defined by the equations 



T = Kau = m sin— - [teat— x-\-c) 

 A, 



* Communicated by the Author. 

 Phil. Mag. S. 4. No. 192. Suppl. Vol. 28. 2 K 



