of the Vibrations of Polarized Light by Diffraction. 329 
The mean index of refraction n was determined by experiment 
as to the angle of polarization, and I found 
log n= 0°18886. 
For 8=65° we should therefore have 5=2° 11’, which agrees 
pretty well with experiment, which gave 6=1° 52’, That 6 
should decrease as 3 increased, as appeared from experiment, 
follows also from this calculation. 
If, on the contrary, the smoked side of the glass is turned 
towards the incident ray, the light is diffracted before it reaches 
the surface of the glass, and is afterwards twice refracted. We 
have therefore 
tan (45°—8) = eee ; 
from which it follows that if B=65°, 5=16° 2! 30", 
In this case experiment gave a decidedly less value for 6, which 
shows that the actual circumstances are only approximately those 
assumed, and that the diffraction of the light only takes place 
partially within the substance of the glass. This is still more 
evident when the grating is placed obliquely to the incident rays, 
so as to make equal angles with them and the axis of the tele- 
scope; since in that case for 8=90° I found 6=20° instead of 
45°, which is given by calculation. 
It is obvious, therefore, that the circumstances, though very 
complicated, are naturally accounted for in all essential particu- 
lars, on the supposition that the vibration of polarized light is 
perpendicular to the plane of polarization, whereas the other hy- 
pothesis is altogether irreconcileable with experiment. 
In order to render these results less complicated and more 
susceptible of calculation, I contrived a different arrangement ot 
the smoke-gratings. Canada balsam was melted over the sur- 
face of the glass, and a smooth glass plate was pressed down on 
it, which it was found could easily be done without injuring the 
grating. As Canada balsam has almost the same index of refrac- 
tion as glass, all the circumstances could then easily be calculated. 
The grating was so placed that it made equal angles with the 
incident rays and the axis of the telescope. In this position of 
the apparatus the vertically polarized portion of the incident 
light was found to be weakened more than that polarized hori- 
zontally ; and therefore the change of the plane of polarization 
was positive, although reflexion at the two glass surfaces tended 
to turn the plane of polarization in the opposite direction. As 
the mean of many experiments with several gratings (2, 5, 10 
bars to the millim.), I found— 
