328 MM. L. Lorenz on the Determination of the Direction 
different gratings, and content myself therefore with giving the 
mean results for them all. 
When the grating was perpendicular to the incident ray, and 
on the side of the glass towards the telescope, as was the case in 
Holtzmann’s experiments, I found the angle 6, through which 
the plane of polarization was turned, extraordinarily small, and ~ 
therefore only determined it accurately for a single angle of dif- 
fraction (65°). The plane of polarization of the incident light 
was in all the following experiments inclined at an angle of 45° 
with the vertical. 
The mean result for 8=65° was 
Sead; O2's 
The plane of polarization therefore had become very slightly 
more horizontal. For greater values of 8 I found 6 still smaller, 
which at first greatly perplexed me. 
When the grating was turned round so as to be on the side 
towards the incident ray and perpendicular to it, the plane of 
polarization was turned through a greater angle in the same 
direction, and for 8=65° I found 
6=12° 30'. 
These results agree neither with Holtzmann’s experiments, nor 
with the conclusions that seem to follow from theory. I think, 
however, they can be explained as follows. | 
When the light first passes through the glass and then through 
the grating, the circumstances are almost the same as when it 
encounters the grating in the substance of the glass, as may be 
concluded from the fact that there is no reflexion at the boundary 
between the smoke and the glass. The diffraction therefore 
takes place within the substance of the glass, and the diffracted 
light 1s afterwards refracted in passing out of the plate. If , 
be the diffraction in the glass (8 being the observed diffraction), 
and n the index of refraction of glass, then sin@=nsinf,. In 
consequence of the refraction, the plane of polarization is again 
altered and becomes more veréical. Supposing now that the 
vibrations are perpendicular to the plane of polarization, the 
change of the plane of polarization 6,, caused by the diffraction 
§,, is determined by the equation 
tan (45°—6,)=cos@. 
If therefore 6 be the angular change of the plane of polarization 
after eflexion at the first surface of the glass, we have by Fres- 
nel’s formule, 
__ tan (45—6,) _—cos8 
tan (15° 8) = cos (B= Ai) ~ eos (B— A) 
