On the Phenomena presented by Light in its passage along the Axes of Biaxal 
Crystals. By the Rev. HUMPHREY LLOYD, A.M., M.R.I. A., Fellow of 
Trinity College, and Professor of Natural and Experimental Philosophy in the 
University of Dublin. 
Read January 28, 1833. 
Ir is well known that when a ray of light is incident upon certain crystals, such as 
Iceland spar and quartz, it is in general divided into two pencils, of which one is 
refracted according to the known law of the sines, while the direction of the other is 
determined by a new and extraordinary law, first assigned by Huycuens. 
These laws were long supposed to apply to all doubly refracting substances ; and it 
was not until the subject was examined by the ablest advocate of the undulatory _ 
theory, that the problem of double refraction was solved in all its generality. Setting 
out from the hypothesis, that the elasticity of the vibrating medium within the crystal 
is unequal in three rectangular directions, FRresNEL has shown that the surface of the 
wave is not, in general, either a sphere or spheroid, as in the Huyghenian law, but a 
surface of the fourth order, consisting of two sheets; and that the directions of the 
two refracted rays are determined by tangent planes drawn to these surfaces under 
known conditions. Such crystals have, in general, two optic axes, and are thence 
denominated biaral. When the elasticity of the medium is the same in two of the 
three directions, the equation of the waye-surface is resolvable into two, which repre- 
sent the sphere and spheroid of the Huyghenian law. ‘The two optic axes in this case 
coincide ; and the law of Huycuens is thus proved to be a case of a more general 
law, and shown to belong to wniawal crystals only. Finally, when the elasticity is the 
same in all the three directions, the wave-surface becomes a sphere; and the refraction 
is single, and takes place according to the ordinary law of the sines. This case com- 
prises a few of the crystallized, and most uncrystallized substances. 
There are two remarkable cases, however, in this elegant and profound theory, 
which its author seems to have overlooked, if not to have misapprehended. In a com- 
munication made to the Academy at its last meeting, Professor Hamiiron has 
supplied these omissions in the theory of Fresnex, and has been thus led to results in 
the highest degree novel and remarkable. 
VOL. XVII. 2P 
