206 REPORT—1885. 
the incident waves set up vibrations over the surface parallel to a fixed 
direction, and that these vibrations lie in the same plane as the incident 
vibrations, while these vibrations set up others in the diffracted waves 
which lie in the same plane as those over the surface, and are everywhere 
normal to the diffracted rays. Then, if ey be the angle between the 
incident wave normal and the disturbance over the surface, gy and @ the 
azimuths of the planes of polarisation on Fresnel’s hypothesis measured 
from the plane of incidence in the incident and diffracted waves, and 6 
the angle of diffraction, it can be shown that : 
cos ¢) tan =sin d cote) ++ cosdsingy . as. (39) 
This expression is given by Réthy, and agrees closely with the results 
.of Fréhlich’s experiments which were made with two gratings—the one 
of 19°76 lines to a millimetre, the other of 162 lines to a millimetre. 
The value of ey depends on the angle of incidence when this vanishes, 
so that the vibrations in the incident wave are parallel to the surface 
ey = 90°, and the above formula becomes identical with Stokes’s. 
In comparing the two it must be remembered that the azimuths of 
the planes of polarisation are measured, in Stokes’s expression, from the 
normal to the plane of incidence, while in Réthy’s they are measured 
from the plane of incidence. 
A eareful series of experiments by Cornu? also lead to the conclusion 
that the vibrations are normal to the plane of polarisation. This con- 
-clusion coincides with that arrived at by Lord Rayleigh and Lorenz from 
considerations based on the phenomena of reflexion and refraction, and 
is further strengthened by the phenomena of polarisation produced when 
light is scattered by a series of small particles. 
§ 5. Before considering this, reference must be made to a paper by 
Professor Rowland,’ of Baltimore, on the subject. This paper will be 
more completely discussed when we come to the electro-magnetic theory, 
to which it more properly belongs. Professor Rowland, however, con- 
-giders that he has discovered an error in Stokes’s work, in that according 
to it ‘ when a wave is broken up at an orifice the rotation is left discon- 
tinuous by Stokes’s solution.’ It is not quite clear, however, how this 
criticism is intended to apply; for the rotation in the main wave is 
completely determined when the displacement is known. Now, Professor 
Stokes has shown that when the orifice is of finite size the aggregate 
disturbance at any point due to all the elements of the orifice, as found by 
his formula, is the same as if the wave had not been broken up. The 
rotation, therefore, as given by this formula is also the same. 
Again, the rotation is propagated according to the same laws as the 
transverse disturbance, and hence the elementary rotation due to a given 
element of a wave propagated in a given direction is related to the 
direction and to the total rotation of the element in the same way as the 
elementary displacement propagated in that direction is related to the 
actual displacement. 
Thus, if the displacements over the wave be 
E=0,.« p=, f= esin* (bt—2), 
1 See Glazebrook, Proc. Camb. Phil. Soc. vol. v. p. 254. ? Cornu, C. R. 
3 Rowland, ‘On Spherical Waves of Light,’ Phil. Mag. June, 1884. 
