A Te 
TRANSACTIONS OF THE SECTIONS. 5 
tional cases, are following that simple law, that while the intensity and the western 
declination increase, the inclination decreases. In respect to the variations of the 
luminous phenomenon itself, he had only been able to ascertain that during the first 
of the above periods the aurora borealis was in general exclusively seen in the north- 
- ern part of the heaven, while during the second period it extended itself more to the 
south, so that the magnetical variations before mentioned seem to be accompanied by 
a translation of the light from north to south. 
On a Difficulty in the Theory of Light. By G. G. Stoxxs, M.A. 
The distinction between’ common light and elliptically polarized light is fully 
accounted for, on the undulatory theory, by the very natural supposition that in 
common light the mode of vibration changes a great many times in the course of 
one second ; so that even in a very small fraction of a second there is, on the ave- 
rage, as much light polarized in one way as there is light polarized in the opposite 
way. So unlikely does it seem that this should not be the case, when we consider 
the enormous number of vibrations which take place in one second, that, as the 
author contended, it would be a most serious difficulty in the way of the undulatory 
theory if common light exhibited the rings in crystals, or any of the peculiar 
phznomena exhibited by elliptically polarized light. It had however been thought 
necessary, in order to account for the phenomena, to suppose that the mode of 
vibration passed abruptly from one thing to the other. This abruptness of transition 
was the ‘‘difficulty” alluded to in the title; and the author contended that there 
was no occasion to suppose any such abruptness to exist. In fact, the apparent ne- 
cessity for the supposition of an abrupt transition appears to have arisen from find- 
ing that common light could not be represented by supposing the particles to move 
in ellipses the major axes of which slowly revolve. But such a mode of vibration re~ 
sults from the superposition of two series of vibrations, of nearly equal length of wave 
but of unequal intensity, belonging respectively to right-handed and to left-handed 
circularly polarized light. Hence such a mode of vibration is not a fair representa- 
tion of common light, the very notion of which implies that it contains as much of 
any one kind of polarized light as of the opposite. . 
On the Refraction of Light beyond the Critical Angle. 
By G. G. Svoxes, M.A. 
The principal object of the author in this communication was to give an expres- 
sion, obtained from the undulatory theory of light, for the intensity of the central 
spot of Newton’s rings, when the angle of incidence exceeds the critical angle. It 
has been shown by those who have treated the subject of reflexion and refraction 
dynamically, that when the angle of incidence exceeds the critical angle, the expres- 
sion for the disturbance in the second medium contains an exponential, involving 
the co-ordinate perpendicular to the surface, so that the disturbance is insensible at 
a distance from the surface of a small multiple of A the length of a wave. The ex- 
pressions for this superficial disturbance have not, however, so far as the author is 
aware, been hitherto applied to the explanation of any phenomenon, although the 
existence of the central spot in Newton’s rings beyond the critical, angle has been 
unhesitatingly attributed tothis cause by Dr. Lloyd, in his Report on Physical Optics. 
The author has not entered into any particular dynamical theory, but has preferred 
deducing his results from Fresnel’s expressions for the intensity of reflected and 
refracted polarized light, which, except perhaps in the case of very highly refracting 
substances, are at least a very near approximation to the truth. The method 
employed does not even render it necessary to enter into the question, whether the 
vibrations of plane polarized light are in or perpendicular to the plane of polarization. 
When the angle of incidence exceeds the critical angle, Fresnel’s expressions become 
imaginary ; and by reasoning similar to that employed by Mr. O’Brien in interpreting 
those expressions in the case of reflected light, the author has arrived at the follow- 
ing simple rule, which embraces all cases. 
Let « be measured along the reflecting surface, y perpendicular to that sur- 
