TRANSACTIONS OF THE SECTIONS. 7 
the expressions are different, according as the light is polarized in the plane of inci- 
dence, or in the perpendicular plane. 
On pursuing the inquiry, however, the author found reason to conclude that there 
could be no sensible intensity in the reflected light without a sudden change in the 
elasticity of the medium; and he was accordingly driven to combine this hypothesis 
with that already referred to, the xther being supposed to vary continuously up to 
a certain plane, at which an abrupt change took place. On this principle he has 
obtained expressions for the magnitudes of the reflected vibrations corresponding with 
those of Fresnel, the two angles which enter the formule being connected with the 
original angle of incidence by the known law of the sines, by means of two constants. 
These expressions seem to explain, generally at least, the variations in the intensity 
of the light reflected from metals; but it remains to account for the difference of 
phase depending on the plane of polarization. The author hoped that he would be 
excused by the Section in laying before it an outline of a theory still incomplete. 
The problem, however, is one encompassed with difficulties; and any attempt, how- 
ever imperfect, to obtain its solution may serve to direct further investigation, 
Notice of an Experiment on the Ordinary Refraction of Iceland Spar. 
By Sir DAvip Brewster. 
Professor MacCullagh of Trinity College, Dublin, in following out an hypothesis re- 
specting light, has been led to a law of double refraction more general than that of 
Fresnel. One of the results of this law, though not a necessary consequence of Pro- 
fessor MacCullagh’s theoretical views, was, that in all crystals with one axisiof double 
refraction the ordinary ray was refracted according to a law different from that of 
Snellius. Instead of the two refractions being regulated by the sphere and spheroid 
of Huygens, they would be regulated by two ellipsoids touching each other at the ex- 
tremities of a common diameter coinciding with the axis of the crystal—one ellipsoid 
differing slightly from a sphere, and the other slightly from a spheroid. Professor 
MacCullagh requested me to ascertain whether or not the ordinary refraction of Iceland 
spar varied at different inclinations to the axis, in the hope of finding such a differ- 
ence as his theoretical views indicated. In place of doing this, by measuring the 
ordinary index with two separate prisms, I adopted the plan of cutting two prisms out 
of the same piece of Iceland spar—one having the refracted ray coincident with, and 
the other perpendicular to, the axis. These prisms were fastened by cement to a 
plate of glass, and their second surfaces ground and polished in that state, so that their 
refracting angles were necessarily equal. When this was done, I refracted the yellow 
homogeneous ray D of Fraunhofer, produced by a candle witha salted wick, and passing 
through a narrow aperture; and, looking through the refracting edges of both prisms 
with the same eye, I observed the most perfect coincidence between the two refracted 
images of the sharp line D, This placed it beyond a doubt that the ordinary ray had 
the same index of refraction in both prisms within the limits of the errors of observa- 
tion. Professor MacCullagh’s law, however, may still be true. The prisms used in this 
experiment were made with singular accuracy by Mr, George Sanderson, lapidary, 
Edinburgh. 

Remark relative to the preceding Notice. By Professor MacCuLuacn. 
The law referred to in the foregoing communication was merely conjectural, As 
Sir David Brewster has rightly remarked, it is not a necessary consequence of any 
principles that I have adopted. Its existence was barely permitted by those princi- 
ples, so long as they were not restricted by the usual hypothesis of symmetry. Per- 
haps it may be proper to mention that the law was proposed chiefly with the view of 
accounting for certain very singular phenomena observed by Sir D. Brewster in the 
reflexion of light from Iceland spar. These phenomena are unsymmetrical with re- 
spect to the axis of the crystal, and this circumstance induced me to suppose that there 
might possibly be a corresponding want of symmetry in the law of refraction. The 
