124 EEPOET ON PHYSICAL OPTICS. 



surface touched by them all at any instant.* Hence the problem 

 is reduced to the determination of the law of propagation of a 

 plane wave. 



M. Cauchy then shows that a disturbance, confined originally 

 to a given plane, will in general give rise to three pairs of plane 

 waves parallel to the original plane, and propagated with uniform 

 velocities, the two waves of each pair moving with equal velocities 

 in opposite directions. The velocities of propagation of the separate 

 pairs, he proves, may be represented by the reciprocals of the axes 

 of a certain ellipsoid, whose form depends upon the position of the 

 plane wave and upon the nature of the system ; and the absolute 

 displacements of the molecules will be parallel to the directions of 

 these axes. Accordingly, a system of plane waves, superposed at 

 first at the point of original disturbance, will be subdivided into 

 three corresponding systems; and these, by their superposition, 

 will generate a curved surface of three sheets, each sheet being 

 touched by all the plane waves of the same system. From these 

 principles it follows that a single ray of light will be, in general, 

 subdivided into three polarized rays; a ray being said, in this 

 theory, to be polarized parallel to a certain line or plane, when the 

 vibrations of the ethereal molecules are parallel to that line or 

 plane. M. Cauchy does not state the precise physical condition 

 on which the existence of the third ray depends. It would seem, 

 however, that it must arise from the circumstance that the vibration 

 normal to the wave is not absolutely insensible, or that the actual 

 vibrations are not accurately in the plane of the wave. He states 

 that the intensity of this ray will be in all cases very small, and 

 that its observation therefore will be a matter of difficulty ; and he 

 promises in a future communication to point out the means of 

 manifesting its existence. 



The formulae, on which the solution of the general problem 

 depends, may be reduced to contain nine constant coefficients 

 depending on the law of distribution of the molecules in space. 

 Three of these represent the pressures sustained in the natural 

 condition of the medium by any three planes parallel to those of 

 the three coordinates ; and these (M. Cauchy afterwards concludes) 



* M. Poisson does not admit the legitimacy of this conception of the wave-surface : 

 id he thinks that an assemblage of indefinite plane waves, having a small part in 

 common at the origin of the motion, cannot represent the initial condition of a medium 

 disturbed at that point. 



