354 FOURTH REPORT 1834. 



propagation will depend on the magnitude of the force developed 

 by the displacement. To account for the fact that there are no 

 sensible vibrations in a direction normal to the wave, we have 

 only to suppose the repulsive force between the molecules to be 

 very great, or the resistance to compression very considerable ; 

 for in this case, it will be seen, the force which resists the ap- 

 proach of two strata of the fluid is much greater than that which 

 opposes their sliding on one another. Fresnel's views on this 

 subject are contained in a short paper, entitled, " Considera- 

 tions M(^caniques sur la Polarisation de la Lumiere *," and in 

 his celebrated memoir on double refraction f. 



The principle of transversal vibrations, however, has not 

 been received without much discussion; and even to this hour, 

 the opinion of the mathematical world is not entirely at rest 

 upon the subject. In a memoir on the propagation of motion 

 in elastic fluids, read before the Academy of Sciences in the 

 year 1823, M. Poisson arrived at the conclusion that the vi- 

 bratory motions of the particles finally become normal to the 

 wave, whatever be the direction of the original disturbance |. 

 To this Fresnel replied that the equations of motion of elastic 

 fluids employed by M. Poisson are but a mathematical abstrac- 

 tion, which do not apply to an}i;hing actually existing. That 

 in fact these fluids are assumed to be composed of contiguous 

 elements, capable of compression in a degree proportionate to the 

 pressure exerted ; that this hypothesis is mitrue ; and that al- 

 though it may accord with the statical properties of these fluids, 

 it can never lead to the discovery of their dynamical laws§. 



M. Poisson seems to have felt the full force of this objection; 

 for in his memoirs on the same subject, read to the Academy in 

 the years 1828 and 1830, he has resumed the Avhole theory, and 

 reared it upon its firmer basis. In the former of these memoirs 

 he has formed the differential equations of equilibrium and 

 motion of elastic bodies, these bodies being supposed to consist 

 of molecules attracting or repelling one another according to 

 some function of the distance ||. In the latter he proceeds to 

 integrate these equations generally, and to deduce the laws of 

 propagation of waves at a considerable distance from the origin 

 of disturbance ^. In the case of fluids he arrives at the con- 

 many instances the elementary motions of the molecules of bodies which trans- 

 mit soiind are transverse to the direction of the propagation. 



* Bulletin de la Soc.Philom. 1824. f Mhnoires de I'Institut, torn. vii. 



X ylnnales de C/iimie, torn. xxii. § Ibid., torn, xxiii. 



II " Memoire sur I'Etjuilibre et le Mouvement des Coqis Elastiques," Me?n. 

 Inst., torn. viii. 



^ " Memoire sur la Propagation du Mouvement dansles Milieux Elastiques," 

 Mim. Inst., torn. x> 



