3^4 PROFESSOR KELLAND ON FRESNEL'S FORMULAE FOR THE 



ly opposed to that of M. Fresnel. How these philosophers have succeeded in the 

 more complex case of crystalline reflexion, it concerns us not to inquire, until the 

 principles which guide their hypotheses shall be shewn to be sound and mecha- 

 nical. 



It appears, however, that M. Cauchy has actually inferred, from mechanical 

 principles, that the vibrations of polarized light are the opposite to those assumed 

 by M. Fresnel. Of the amount of evidence which M. Cauchy adduces I am al- 

 together ignorant ; but it ought to be overpowering indeed to shake our faith in 

 an hypothesis which has so successfully overcome all difficulties, and brought the 

 apparently complex phenomena of double refraction to the level of common optics. 



However this be, the matter is not yet set at rest, for a paper has just been 

 printed for the next part of the Cambridge Transactions, in which M. Fresnel's 

 hypothesis as to the direction of vibration is assumed to hold, and his formulae 

 corresponding to light polarized in the plane of incidence are established, whilst 

 an approximate demonstration is offered for those corresponding to the perpendi- 

 cular plane. 



My primary object in drawing up the present memoir has been to remove 

 from the molecular theory some difficulties in which Mr Green's researches seem 

 to involve it. As a preliminary step, I will therefore point out the most import- 

 ant of these, and endeavour to shew that the arguments which naturally arise 

 out of them are such as can be answered without compromising any of the prin- 

 ciples on which the molecular hypothesis is based. Having done this, I shall ap- 

 ply the equations of motion deduced from molecular forces, to shew that the for- 

 mulae result in the most satisfactory manner from the state which such forces 

 induce. 



To effect my pui-pose of explaining the difficulties which Mr Green's memoir 

 opposes to the molecular theory, it will be requisite that I point out in few words 

 the nature and results of that theory. 



Almost all mathematicians have admitted the idea of discrete molecules to 

 be philosophical ; but very few have attached any weight to the results to which 

 this hypothesis leads. Laplace, in his Mecan-ique Celeste, supposes the atoms of 

 matter to be permeated by the molecules of caloric ; but he assigns forces to the 

 molecules, which are conceived to diminish with great rapidity as the distance 

 fi'om the molecule is increased, and actually to vanish at all appreciable distances. 

 By a similar hypothesis, in the same great worJc, he solves the problem of Capil- 

 lary Attraction. 



PoissoN also, in his Memoir on the Equilibrium and Motion of Fluids, as well 

 as in his Capillary Attraction and Theory of Heat, conceives the particles to be 

 separated by finite intervals, and makes use of a force which results fi-om this 

 circumstance ; but neither he nor Laplace appears to have investigated the com- 

 plex arrangement of actions and their counteracting opposites, to which this force 



