Prof. Challis on the Dispersion of Light. 499 



(pp. 475, 476), if 8 be the density of the medium and yu, 2 — 1 = HS, 

 the atoms being supposed fixed, the mobility of the atoms is 

 taken into account by multiplying the right-hand side of this 

 equation by the factor that multiplies m in the above expression 

 for M. Thus we have 



**->**+ zv~w 



This equation to the first power of e 2 may be put under the form 



//*-l = A-Be 2 , 



A and B being positive quantities. Hence the equation I have 

 employed in my theory of Double Refraction (Phil. Mag. for 

 December 1863, p. 479) is verified by this new investigation. 



In all the foregoing reasoning X has been supposed to have a 

 given value. To apply the equation (77) in accounting for the 

 phenomenon of Dispersion, it is necessary to discuss the cha- 

 racter of the factor a, this being the only quantity in it which 

 can contain A, explicitly. Now it was found that the velocity (W) 

 of the sether along the second half of the spherical atom is given 

 generally by the equation 



W = T sin0 + aTsin0 cos 0. 



If the same kind of reasoning were applied to the case of a uni- 

 form stream encountering the atom, which may be regarded as a 

 case of vibratory motion for which X is indefinitely great, the 

 second term of the value of W would be found to disappear. 

 (See Phil. Mag. for November 1859, p. 324.) Hence a is a 

 function of X which decreases as X increases. In general that 

 term expresses the difference between the effect of a stream and 

 that of a series of vibrations, which difference is owing to the 

 prevention of lateral spreading by the state of vibration. I have 

 remarked in the preceding paper on Dispersion (p. 460), that in 

 consequence of waves being compounded of separate vibrations 

 parallel and perpendicular to rectilinear axes, lateral spreading 

 may be counteracted in such manner that the whole motion, 

 direct and transverse, may be included in a cylindrical space of 

 small transverse section. The same cause must operate in a 

 degree to check the lateral spreading by which the portion of 

 the incident waves that passes the atom tends to supply the 

 place of the portion which the atom intercepts. In the paper 

 " On Double Refraction " (p. 468), an expression is given for 

 the function / which defines the law of the diminution trans- 

 versely of the vibrations parallel to a single axis. From this 

 expression it may be inferred that at a given position the diminu- 

 tion for any number of component vibrations, whether or not 



