468 Prof. Challis on the Theory of Double Refraction 



their motion relative to the motion of the sether. Hence the se- 

 cond principal requisite in a theory of double refraction is to 

 determine in what manner the setherial undulations are modified 

 by these circumstances. But here it must be remarked that 

 such data cannot be had in the present state of physical science, 

 so far as regards the magnitudes and arrangement of the atoms, 

 and the number in a given space. We must therefore com- 

 mence with a general and initiatory solution, not requiring these 

 particular data, — and the rather so because there is reason to 

 expect that such a solution may be one means of gaining an in- 

 sight into the interior constitution of crystalline bodies, and thus 

 obtaining eventually the more precise data. 



Before proceeding to the theory of the changes which light 

 undergoes after intromittence into a refracting medium, it will 

 be proper to state briefly those characteristics of setherial rays 

 and waves which have been ascertained by mathematical investi- 

 gation. For more complete information on this head, recourse 

 may be had to the before-mentioned article in the Number of the 

 Philosophical Magazine for December 1862. The principal 

 results bearing on the present question are the following. Pre- 

 vious to the supposition of any instance of disturbance of the 

 fluid, it is found that the differential equations of hydrodynamics 

 are satisfied to the first order of approximation by vibratory mo- 

 tion having these characteristics : — The motion is symmetrically 

 disposed about a rectilinear axis, so as to be at each instant a 

 function of the distance from the axis in any plane cutting it at 

 right angles. This axis of the motion being taken for the axis 

 of z, let V be the velocity transverse to the axis, and w the ve- 

 locity parallel to it, at a point distant from it by r, and let the 

 pressure at the same point be « 2 (l + (r). Then the values of V, 

 w, and cr, to the first approximation, are determined by the equa- 

 tions 



*_i AY 4- 1 AV_ 1 AY 



J - i \xJ ^vw'Kxj i 2 .2 2 .3 2 'Uy + ' 



XT JlW M f # 



r dr J ds a? dt 



As these results were obtained independently of any specific 

 disturbance, we may conclude that they apply in all cases of 

 arbitrary disturbance, and that every instance of vibratory mo- 

 tion is "initially composed of motions defined by the foregoing 

 equations. Since, also, they were deduced from linear differen- 

 tial equations with constant coefficients, to satisfy this condition 

 we have at disposal an unlimited number of such motions, with 



