292 MR. R. T. GLAZEBROOK ON PLANE WAVES IN A BIAXAL CRYSTAL. 
But replacing a by y, this is exactly the form found above for v x in Fresnel’s 
second experiment. 
Now let us take a wave perpendicular to the plane yz inclined at an angle <£ to 0 y. 
Then l— 0, m= sin <£, n = cos <f>, and the equation for Y 3 becomes 
& 2 sin 2 <4 c 2 cos 3 <6 
-_r_L_- - = 0 
V 2 -6 3 ^ Y~—c~ 
Y 3 (6 2 sin 3 </>+c 3 cos 3 <£) = & 3 c 2 
or 
Y 3 (l —/3 sin 3 (f> — y cos 3 f) — (1 —/ 3)(1 — y) = 1 — (/3-py) 
to the same approximation 
Y={1— i(/3+y)}{l+^(y8 sin 3 <£+y cos 3 f)} 
= 1 —-|(/3 cos 3 ^>+y sin 3 <£) 
, and this agrees with the formula used in Fresnel’s third experiment. 
Thus Fresnel’s experiments afford as much a verification of Lord Rayleigh's 
theory as of his own, and are, therefore, an insufficient test of the truth of either. 
They are, however, the only attempts made to verify the theory. 
Section II.— Description of the Apparatus used and Method of making the Experiments. 
My own work was undertaken in the hope of obtaining results sufficiently accurate 
to decide between some of the various theories which have been propounded. 
I proceed to describe the apparatus used. 
The crystal itself was a piece of arragonite, very clear and of a light colour, obtained 
from Germany by the Demonstrator at the Cavendish Laboratory, Cambridge, through 
Hilger, of Tottenham Court Hoad, London, W.C. 
Originally it was in the form of an hexagonal prism. 
Four of the faces were those marked m in Professor Miller’s mineralogy, the other 
two were the faces marked a. 
The natural ends had been cut off, and the artificial ends were approximately per¬ 
pendicular to the m and a faces. 
The crystal consisted of several twins, the twin planes being parallel to two of the 
m faces. 
At this stage Professor Stokes kindly undertook to examine the crystal, to deter¬ 
mine in which direction to cut it with the greatest advantage for the purposes of the 
experiment. He found that fair reflexions were obtained from three of the m faces, 
and decided that they should be left untouched to determine the position of any other 
cut faces. 
Again, the mean axis of elasticity bisects the angle between the contiguous m faces; 
