106 



MATHEMATICAL AND PHYSICAL SCIENCE. 



[Diss. VI. 



using it. Such Fresnel possessed, though he always 

 refers with great modesty to his limited facility of em- 

 ploying the higher mathematics. 



C488 ) Transverse Vibrations Young and Fresnel. 



Transverse Considerable obscurity hangs over the first publi- 

 vibrations ca ti n of this important discovery. A clear and 

 andFref- impartial abstract of the facts will be found in 

 nel. the second volume of Dr Whewell's History of the 



Inductive Sciences, and some further documentary 

 evidence, including interesting letters which passed 

 between Young and Fresnel, have more recently 

 been published in the Life and Works of the for- 

 mer, edited by Dr Peacock. The difficulty of appor- 

 tioning the credit between Young and Fresnel partly 

 arises from the unfortunate system of imperfect pub- 

 lication, or non -publication, adopted on professional 

 grounds by the former, and partly from the grievous 

 delays imposed upon the latter by the opposition with 

 which his opinions and experiments were received at 

 the French Academy of Sciences. This continued to 

 the very close of Fresnel' s career. His greatest work 

 was not published in the Memoirs of the Institute 

 until six years after date ; another was mislaid for 

 above twenty years, and even the hardy friendship of 

 Arago sometimes almost recoiled before the storm of 

 opposition which the novelties of his associate were 

 sure to excite in the minds of the dominant mathe- 

 matical section. It is quite impossible to say pre- 

 cisely at what period Young first imagined that the 

 differences of oppositely polarized rays of light might 

 be explained by perpendicularity in the directions of 

 vibration of the ethereal molecules, which he compared 

 to the vibrations of a cord in which the elementary 

 movements are at right angles to the direction of wave- 

 propagation. It seems evident that Young was not 

 possessed of this idea in 1814, when he partly explained 

 depolarization in a few pages of an article in the 

 Quarterly Review. It is equally certain that he an- 

 nounced it to Arago (with whom he became person- 

 ally acquainted in 1816) in January, 1817; and that 

 he then speaks of it as an idea which apparently had 

 recently occurred to him, most probably since their 

 interview. 1 Arago and Fresnel had already, in 1816, 

 made experiments demonstrating that rays oppositely 

 polarized do not produce dark bands by their inter- 

 ference, a memorable discovery, requiring very great 

 nicety for its satisfactory proof, which, however, 

 was completely attained. It was this observa- 

 tion which (naturally) gave Fresnel the first idea 

 of transverse vibrations, and it is much more than 

 probable that Young worked out a similar solution 

 of the great problem, in consequence of the account 

 of these experiments which he received from Arago 

 in the summer of 18 16. 2 Be this as it may, Young 



and Fresnel unquestionably imagined the theory se- 

 parately, but Young first announced it, Fresnel being 

 discouraged by the doubts of Arago, and by his 

 awe of the Institute. As clearly, the experiment of 

 non-interference was the first which gave a colour to 

 so bold an assumption, and in the details of its ap- 

 plication to double refraction Fresnel had the undi- 

 vided merit. What is not least worthy of notice in 

 the affair, is that neither of the amiable rivals (Young 

 and Fresnel) ever published a word in disparagement 

 of the other, nor a single unfriendly reclamation of 

 priority. 



The doctrine of transverse vibrations being allowed, (489.) 

 its applications and severest tests were twofold, 1st, 

 To the phenomena of ordinary reflection and refrac- 

 tion including the polarization produced by these ope- 

 rations; and 2dly,to double refraction and the univer- 

 sally concomitant polarization. In these bold specu- 

 lations and laborious inductions, Fresnel was nearly 

 alone. Young did not appear as a competitor ; even 

 his friend Arago, though sympathizing with and 

 proud of his success, was not associated with him. 



Laws of Reflection and Refraction. With re- ( 490 -' 

 gard to the reflection and refraction of light, its in- $*?* 

 tensity has to be defined, and also its condition as to an d refi 

 polarization. The fundamental laws of the direction tion 

 of the rays are not affected by this theory. Rigorous ^ resnel 

 mathematicians who then doubted the possibility 

 of transverse vibrations having more than a transi- 

 tory existence, if they existed at all, could not be ex- 

 pected to supply the theory of their reflection and re- 

 fraction at the bounding surfaces of different media. 

 Fresnel, however, guided by probable mechanical 

 analogies, with an intuitive insight worthy of Newton 

 himself, gave a formula for the intensity of reflected 

 transverse vibrations, both when the plane of vibration 

 of the molecules is in the plane of reflection, and when 

 it is perpendicular to it ; and he conceived common 

 light to act as if equally composed of both sets of 

 vibrations. His formulae embrace the non-reflection 

 of polarized light at the critical angle, under the 

 circumstances explained in the last section. It is a 

 most remarkable fact that these inferences by Fresnel 

 as to the numerical relations of the intensity of the re- 

 flected to the incident light through all angles of inci- 

 dence, anticipated almost every trustworthy photo- 

 metrical measure; and from their singular though 

 indirect accordance with many phenomena, they have 

 been generally accepted as an expression of a natural 

 law of great complexity, even by those who were not 

 favourable to the theoretical views on which they are 

 based. 



The modifications of the state of polarization of 

 light which takes place by reflection, was equally 



1 " I have also been reflecting on the possibility of giving an imperfect explanation of the affection of light which constitutes 

 polarization, without departing from the genuine doctrine of undulation." He then refers to " a transverse vibration propagated 

 in the direction of the radius, the motion of the particles being in a certain constant direction with respect to that radius j and 

 this," he adds, " is a polarization." Young's Miscell. Works, vol. i., p. 383. 



2 Peacock's Life of Young, p. 390. 



