68 Mr. Mac Cullagh on the Laws of 



be simpler than the laws of double refraction, as they were delivered by Fresnel ; 

 yet the properties of his wave surface still continue to furnish the geometer 

 with beautiful and curious relations. So we may hope that a little more time, 

 devoted to the laws of reflexion, will not be spent in vain. They promise to 

 supply many other theorems, not undeserving of attention, though pei'haps not as 

 simple and comprehensive as those that have already been made known. 



If we are asked what reasons can be assigned for the hypotheses on which the 

 preceding theory is founded, we are far from being able to give a satisfactory 

 answer. We are obliged to confess that, with the exception of the law of vis 

 viva, the hypotheses are nothing more than fortunate conjectures. These conjec- 

 tures are very probably right, since they have led to elegant laws which are fully 

 borne out by experiments ; but this is all that we can assert respecting them. We 

 cannot attempt to deduce them from first principles ; because, in the theory of light, 

 such principles are still to be sought for. It is certain. Indeed, that light is pro- 

 duced by undulations, propagated, with transversal vibrations, through a highly 

 elastic ether ; but the constitution of this ether, and the laws of its connexion (if 

 it has any connexion) with the particles of bodies, are utterly unknown. The 

 peculiar mechanism of light is a secret that we have not yet been able to penetrate. 

 As a proof of this, we might observe, that some of the simplest and most familiar 

 phenomena have never been explained. Not to mention dispersion, about which 

 so much has been fruitlessly written, we may remark, that the very cause of ordi- 

 nary refraction, or of the retardation which light undergoes upon entering a 

 transparent medium, is not at all understood. Much less can it be said that 

 double refraction has been rigorously explained ; its laws alone have been clearly 

 developed by Fresnel. In short, the whole amount of our knowledge, with 

 regard to the propagation of light, is confined to the Zai6"s of phenomena ; scarcely 

 any approach has been made to a mechanical theory of those laws. And if the 



tans=^'^^— ij sin(£o— a;,)sin|,;', 

 tan£,=^ (- — i- j sin (tu-f a;,) cosi-i|/, 



(xi.) 



where r and r,.are the two radii of the wave surface which are in the direction of the ray ; the 

 spherical triangle P, AA, , of which the sides and contained angle are expressed by the same letters as 

 before, being now formed by producing the ray and the two nodal diameters of the wave suiface, 

 until they intersect the sphere in the points P,, A, A^. 



