illustrating the Relation of their Optic Axes. 21 



its two optic axes. This crystal is suitable for our purpose as 

 having scarcely any axial dispersion, so that one of its axes 

 gives sensible circles, which many other biaxials do not. 

 Placing it in the stage, we have a system of rings traversed 

 by a straight brush (fig. 4), which, on interposing the first 

 quarter-wave plate, becomes a grey line, on each side of which 

 the semicircles are dislocated (fig. 5) ; but now interposing 

 the second quarter-wave plate, we have perfect unbroken 

 circles as before (fig. 6). 



Now this might seem to imply that the optic axis of the 

 uniaxial calcite resembled in its character that of a single 

 axis of the sugar, or biaxial. It need hardly be said here, 

 that such was not the view taken of the matter by those intel- 

 lectual giants who chiefly shaped into definite form the theory 

 of double refraction in crystals. Gradually this theory was 

 simplified, until Fresnel finally framed the conception of three 

 elasticities within the crystal in the direction of three rectan- 

 gular axes. If all three elasticities were equal, there was no 

 double refraction ; if only two were equal, there was a single 

 axis of no double refraction in the direction of the third ; if 

 all were unequal, there were two such optic axes. In any 

 conceivable case the wave-surface could be calculated or geo- 

 metrically projected upon this hypothesis; and it is needless 

 to repeat how, after its author had passed away, Sir William 

 Hamilton worked out from his conceptions the remarkable and 

 unforeseen results of conical and cylindrical refraction which 

 were experimentally verified by Dr. Lloyd (also removed from 

 us during the past year). That extraordinary verification of 

 Fresnel's theory, which makes the optic axes mere resultants 

 of three rectangular elasticities, has always been considered to 

 have placed it upon an impregnable basis, and seems only to 

 have left for future experiment the possibility of perhaps some 

 further illustration, which is the sole object of this paper. 



For observe that, according to this theory, the optic axis of 

 our calcite would not correspond in character with a single 

 axis of the sugar or any other biaxial, but must be regarded 

 as simply a limiting case in which both such axes coincide. 

 This is well illustrated by the celebrated experiments of Pro- 

 fessor Mitscherlich in gradually applying heat to crystals, 

 especially to a crystal of selenite, and thereby altering by the 

 unequal expansion their respective elasticities. 



Of the two axes gradually approaching till they unite into 

 one as the elasticities are gradually equalized, there could be 

 no clearer proof than this old experiment. But it seemed 

 worth while to seek further illustration of one particular point, 

 viz. that the axis of the uniaxial crystal did actually retain or 



