32 Mr. Mac Cullagh on the Laws of 



briefly, I will take leave to introduce a new term for expressing a right line 

 drawn parallel to the plane of polarisation of a ray, and perpendicular to the 

 direction of the ray itself. Calling such a right line the transversal of the pola- 

 rised ray, I found, from the formulae of Fresnel, that when polarised light falls 

 tipon a singly refi'acting medium, the transversals of the incident, of the reflected, 

 and of the refracted rays are all parallel to the same plane, which is the plane of 

 polarisation of the refracted ray; and that the magnitudes of the vibrations, or the 

 greatest excursions of the ethereal molecules, in the incident and the reflected 

 rays, are to each other inversely as the sines of the angles which the respective 

 transversals of those rays make with the transversal of the refracted ray. I was 

 struck by the strong analogy which these relations among the transversals bore to 

 the composition of forces or of small vibrations in mechanics ; but it happened 

 unfortunately, that, in the theory of Fresnel, the vibrations of light were supposed 

 to take place, not in the direction of the transversals, but perpendicular to them, 

 so that there was no physical circumstance to support the analogy, there being no 

 motion in the direction of the transversals ; while, on the other hand, no such 

 analogy existed among the vibrations themselves in the directions which Fresnel 

 had assigned to them. It was therefore with some interest that I afterwards 

 learned, upon the publication of the tenth volume of the Memoirs of the Institute, 

 that M. Cauchy* had actually inferred, from mechanical principles, that the 

 vibrations of polarised light are in the direction of the transversals ; but this 

 inference was to be received with caution, as being contrary to the hypothesis of 

 Fresnel ; and besides, I had in the mean time contrived a way of adapting my 

 analogy, in some degree, to that hypothesis, by supposing areas to be com- 

 pounded instead of vibrations ; so that I hesitated which of the two opinions to 

 prefer. Taking, however, the opinion of M. Cauchy as that which fell in more 

 naturally with the aforesaid analogy, I was led to the conclusion, that the vibra- 

 tion in the refracted ray is probably the resultant of the incident and reflected 

 vibrations ; and I saw that if this principle were true for singly refracting media, it 

 should also, from its very nature, be true, when properly generalised, for doubly 

 refracting crystals ; so that in such crystals the resultant of the two refracted 

 vibrations would be the same, both in length and direction, as the resultant of 

 the incident and reflected vibrations. 



* Memoires de I'Institut, tome x. p. 304. 



