OF TRANSPARENT PLATES UPON LIGHT. 
147 
pencil AI that enters the plate, undergoes partial reflexions, and the part reflect- 
ed from the first surface carries along with it another portion of light polarized 
in the plane of reflexion, so that four portions of light polarized in the plane 
of reflexion reach the eye, while only two portions reach it polarized at right 
angles to the plane of reflexion, viz. those which are polarized by the refrac- 
tion of each of the surfaces of the plate. Now the part of the pencil A I which 
suffers a first reflexion from each of the surfaces of the plate, is, as we shall 
presently show, defective in polarized light compared with that which has ex- 
perienced two refractions, so that it requires the above additional quantities to 
produce a compensation with the transmitted pencil B O. If this is not the true 
cause of the apparent compensation, that is, if M. Arago took means to exclude 
the reflected pencils which seem to have produced the compensation, we must 
then ascribe the equality of the two images to inaccuracy of observation. 
But even if we admit that M. Arago’s experimental results are correct 
with regard to plates, it necessarily follows that they cannot be true with 
regard to surfaces : for it is obvious from the slightest consideration of the 
subject, that the phenomena of the one can never be interchangeable with 
those of the other. 
In order to demonstrate these views by an analysis of the changes which the 
intromitted light experiences from the two refractions and the intermediate 
reflexion of a transparent plate, I took a plate of glass of the shape M N (Fig. 3.) 
having an oblique face M d 
cut upon one of its ends. 
A ray of light R A, pola- 
rized + 45° and — 45°, was 
made to fall upon it at A, 
at an angle of incidence of 
nearly 83°, so that the incli- 
nation of the planes of pola- 
rization of the reflected ray 
A P was about 36^°. Now the ray A C after reflexion in the direction C S, 
without any refraction at B, where it emerges perpendicularly to M d , would 
also have had the inclination of its planes of polarization equal to 36|° if there 
had been no intermediate refraction at A ; but this refraction alone being 
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