On Reflexion from Crystallized Surfaces. 103 
and whether there is any limit to the numbers of the orders of 
the combining atoms.” 
Under these circumstances, it would have been better not 
to construct any mineralogical formule, except the simple 
ones; and in future the composition of such minerals as 
involve the uncertain orders of atoms should be expressed 
simply by the proportion of each ingredient in 1000th parts, 
or by the nearest equivalent numbers of each, taking the 
element which occurs in the smallest quantity as an atomic 
unit. We should then express by our formule what we know, 
instead of contriving to represent an imaginary atomic consti- 
tution, which, if the atomic theory be true, is probably in all 
cases false. 
I am, dear Sir, yours truly, 
January 7th, 1836. H. J. Brooke. 
XIX. On the Laws of Reflexion from crystallized Surfaces. 
By J. MacCuraen, Fellow of Trinity College, Dublin. 
To Sir David Brewster. 
Dear Sir, 
I HAVE great pleasure in sending you an account of the 
laws by which I conceive that the vibrations of light are 
regulated when a ray is reflected and refracted at the sepa- 
rating surface of two media; especially as the only guide 
which I had, in my inquiry after these laws, was your paper 
on the action of crystallized surfaces upon light, published in 
the Philosophical Transactions for the year 1819.} The observa- 
tion which I found there, that the polarizing angle was the 
same for a given plane of incidence, ‘‘ whether the obtuse 
angle of the rhomb [of Iceland spar] was nearest or furthest 
from the eye, or whether it was to the right or left hand of 
the observer,” disappointed me at first, being contrary to 
what I had anticipated from principles analogous to those 
which had been employed by Fresnel in the problem of re- 
flexion from ordinary media. I then sought other principles, 
and the observation is now a result of theory. 
Assuming, as a basis for calculation, that Fresnel’s law of 
double refraction is rigorously true, I have been obliged to 
make an essential change in his physical ideas, Conceive an 
ellipsoid whose semiaxes are parallel to the three principal di- 
rections of the crystal, and equal respectively to its three 
principal indices of refraction, and let a central section of the 
ellipsoid be made by a plane parallel to the plane of a wave 
passing through the crystal. The section will be an ellipse, 
and the wave will be polarized by the crystal in a plane pa- 
