FRESNEL ON DOUBLE REFRACTION. 245 



Demonstration of the exclusive existence of Transversal 

 Vibrations in the Luminous Rays. 



It was in 1S16 that M. Arago and myself discovered tliat 

 t\A'o beams of light, polarized in planes at right angles to each 

 other, no longer exert any influence on each other, in the same 

 circumstances in which rays of ordinary light present the phae- 

 nomena of interference ; whilst, as soon as their planes of polar- 

 ization approach each other a little, the dark and bright bands 

 resulting from the concourse of the two beams reappear, and 

 become by so much the more distinct as these planes are brought 

 nearer to coincidence. 



This experiment teaches us, that two rays polarized in per- 

 pendicular planes always give by their reunion the same in- 

 tensity of light, whatever be the difference of the paths w hich 

 they have run over, starting from their common source. Now, 

 from this fact, it necessarily results that, in the two beams, the 

 vibrations of the aetherial molecules are performed perpendicu- 

 larly to the rays and in rectangular directions. To demonstrate 

 this, I shall first call to mind, that in the rectilinear oscillations 

 produced by a small derangement of equilibrium, the absolute 

 velocity of the vibrating particle is proportional to the sine of 

 the time reckoned from the origin of the motion, the duration of 

 a complete oscillation answering to a whole circumference. If 

 the oscillation is curvilinear, it may always be decomposed into 

 two rectilinear oscillations perpendicular to each other; to which 

 the same theorem will apply. 



In the luminous wave produced by the oscillation of the illu- 

 minating particle, the absolute velocities anhuating the molecules 

 of aether are proportional to the corresponding velocities of the 

 illuminating particle, and therefore also to the sine of the time. 

 Moreover, the space described by each of the elementary dis- 

 turbances of which the wave is composed is proportional to the 

 time ; and as many times as this space contains the length of an 

 undulation, so many entire oscillations have been performed 

 since the disturbance set out. If therefore (tt) represent the 

 ratio of the circumference to the diameter, (/) the time elapsed 

 since the origin of the motion ; if also (A) denote the length of 

 an undulation, and {x) the space described by the disturbance 

 in order to reach the point of aether which we are considering ; 

 the absolute velocity with vihich this point is animated at the 



