202 
Dr. Brewster on the laws of polarisation, &c. 
powerful double refraction, had, in place of calcareous spar, 
been put into the hands of Huygens, Dr. Wollaston, or 
Malus, or of any other philosopher, however skilful, it is 
demonstrable that their measurements would have accorded 
with the theory of spheroidal undulations. Laplace would 
have connected this theory with the principles of mechanics, 
and it would have been universally received as a rigorously 
physical law. Yet after all this display of experimental and 
mathematical genius, the whole investigation would have 
turned out a delusion; for it can be shown, by decisive expe- 
riments, that both nitre and arragonite have two axes of 
double refraction ; and that the aberration of the extraordi- 
nary ray cannot be explained by a single ellipsoid. 
From these observations, therefore, we conceive it to be 
proved, not only that the Huygenian law remains undemon- 
strated as the general law of double refraction ; but that it 
remains undemonstrated as a correct expression of the indi- 
vidual phenomena of calcareous spar. 
How then, it will be asked, are we to determine the law of 
extraordinary refraction, if the best experiments of our most 
eminent philosophers are set aside as insufficient ? This can 
only be done in two ways, either by the discovery of new 
methods of magnifying and measuring with great exactness 
the deviation of the extraordinary ray, when the light passes 
near the axis of a crystal ; or what is more practicable and 
correct, by examining the appearances which are exhibited 
by transmitting polarised light along the real or apparent 
axes of double refraction. 
In the year 1811, M. Arago discovered, that when pola- 
rised light was transmitted through thin plates of sulphate 
