470 Prof. Challis on the Theorij of Double Refraction 



as composed of motions obeying the law of the circular sine, and 

 the above reasoning, being applicable to the motions taken sepa- 

 rately, applies also, on the principle of the coexistence of small 

 vibrations, to the total motion. On this account, in the subse- 

 quent reasoning the initial waves will be supposed to constitute 

 a single series defined by the law of the sine of a circular arc, 

 and having a constant value of \. 



Let now a series of waves, generated as above supposed, be 

 intromitted within a refracting substance, the surface on which 

 they are incident being a plane parallel to the front of the waves. 

 It may here be stated at once that, with the view of simplifying 

 the present inquiry, I shall not enter upon the theories of re- 

 flexion and refraction at the surfaces of diaphanous bodies, these 

 being questions which may be treated apart from that of the 

 laws of transmission within the bodies. For the same reason I 

 shall disregard the small difference between the intensities of the 

 light before and after intromittence, caused by reflexion at the 

 surface. This being understood, it will be assumed to be a ne- 

 cessary condition of diaphaneity, that the effect of the presence 

 of the atoms of the body is simply to diminish in a constant 

 ratio the accelerative force due to the actual gradations of the 

 density of the sether. That is, dp being the change of the den- 

 sity p corresponding to the change ds of a line s drawn in the 

 positive direction of the motion, if the accelerative force without 



the body be A the force within is j- for the same 



J pds pas 



values of p, dp, and ds, the ratio of b to a being constant and 

 less than unity. 



In the present state of physical science we do not know by 

 what difference of atomic constitution, or arrangement, a dia- 

 phanous body is distinguished from an opake one. It is only 

 known that the condition of diaphaneity is of a very critical 

 nature, and that the complete opacity of a substance, or its opa- 

 city to certain rays, appears in many cases dependent on ingre- 

 dients in its composition which bear a very small proportion to 

 the rest of the components. With respect, however, to the 

 movement and condensation of the sether, it is certain that the 

 above-stated condition must be fulfilled ; and I shall now endea- 

 vour to show, by taking account of the spherical form of the 

 atoms, in what manner it may be fulfilled. Conceive, at first, a 

 series of waves after intromittence within the diaphanous body, 

 to impinge upon one of its atoms supposed fixed. What under 

 these circumstances will be the distribution of condensation about 

 the surface of the atom, and the amount and law of variation of 

 the reflected velocity ? Respecting the distribution of conden- 

 sation (which is the subject of express treatment in the "Mathe- 



