172 The Rev. J. Challis on the different Refrangibility 



— n 



Suppose that — — = cot <p. It will be found that — 



A. 



= — m sin <p cos (— h <p). Hence if <r = the quantity 



of condensation reflected, 



w a t d x 



a <r = m sin 



dt 



/ t at \ 



m cos <J> sin ( \- $ \ 



We thus learn that when the reflecting plane is moveable 

 in a small degree, in the manner above supposed, the reflected 

 waves will be similar to the incident, but the condensations of 

 the former will have to the corresponding condensations of 

 the latter, a ratio cos <p, which depends on the breadth of the 

 waves, but is independent of the degree of condensation. 



To apply the preceding result to the action of the waves of 

 the aether on the particles of a me'dium through which they 

 are propagated, it will be necessary to make some hypotheses 

 respecting the constitution of the medium, and the state of the 

 aether in its interior. I suppose, after M. Poisson, that the 

 medium consists of exceedingly minute but finite atoms; so 

 minute that the space they occupy is very small compared to 

 the intervening spaces free of atoms, and yet so near each 

 other that an immense number are disposed along a linear 

 space equal to the mean value of X for luminous waves, which is 

 a 50,000dth part of an inch. Also for the sake of precision of 

 idea I conceive the medium to be homogeneous, so as to 

 contain a given number of atoms all of the same size and mass 

 in a given space, and the atoms to be spherical in shape. 

 With respect to the state of the aether in mediums, Dr. Young 

 says, " It is simplest to consider the aethereal medium which 

 pervades any transparent substance, together with the mate- 

 rial atoms of the substance, as constituting together a com^ 

 pound medium denser than the pure aether, but not more 

 elastic." At the same time he admits that "the phaenomenon 

 of aberration is not easily reconcileable with the theory of 

 undulations, if the aether be carried along before the medium 

 it pervades, and partake materially of its motion." This 

 phaenomenon seems to leave us at no liberty to suppose that 

 the density of the aether is at all different in the interior 

 of mediums from what it is in free space. For admitting that 

 a medium in motion does not carry any portion of aether along 

 with it, it is difficult to conceive how the spaces into which it 

 is successively transported should receive a sudden accession 

 of aethereal matter, and that too without any sensible effect 



being 



