in passing through biaxal Crystals. 117 



I discovered the remarkable law, — that " the angle between the 

 planes of polarization of any two rays of the cone is half the angle 

 contained by the planes passing through the rays themselves 

 and its axis." This law accounts for the disappearance of one 

 radius only of the section of the cone, the opposite radius be- 

 ing in fact polarized in a plane at right angles to the plane of 

 polarization of the first. The law itself can be easily shown 

 to be a necessary consequence of the general theory applied 

 to this particular case; it is, however, but approximately true, 

 and holds only on the assumption that the biaxal energy of 

 the crystal is small, — an assumption justified by the pheno- 

 mena of all crystals hitherto examined. 



The general phenomena being observed, it remained to 

 take measurements, and to compare them with the results of 

 theory. For this purpose I determined the magnitude of a 

 section of the cone, at a considerable distance from the crystal, 

 by observing, with the assistance of a small telescope, the 

 points at which the aperture ceased to be visible by means of 

 the transmitted light. The distance being then accurately 

 measured, the angle of the cone could be obtained from a 

 table of tangents. This angle was thus found to amount to 

 6° 14' in the plane of the optic axes, and to 5° 46' in the per- 

 pendicular plane, — the mean being exactly 6°. I then placed 

 the flame of a wax taper at the centre of this section, and 

 removing the plate from the second surface of the crystal, 

 placed a mark at a considerable distance on the line of the 

 reflected ray. Then placing a Hadley's sextant with its centre 

 in the place of the crystal, I measured the angular distance 

 between the flame and the mark. This angle was found to 

 be 31° 56', and consequently the angle of emergence corre- 

 sponding to the axis of the cone was 15° 58'. 



Now assuming the three indices for arragonite to be 1 *5326, 

 1*6863, 1*6908, which are the indices for the mean ray E, as 

 determined by Professor Rudberg # , Professor Hamilton has 

 shown that the direction of the emergent rays in the plane of 

 the optic axes will be given by the formulae 

 sin R = 1*6863 . sin I 

 sin R e = 1*68708 .sin (1-1° 44' 48") 

 in which I is the internal angle of incidence, or the angle 

 which the cusp ray makes with the normal to the surface of 

 emergence ; and R , R e are the corresponding angles of re- 

 fraction in air. But in the present instance the normal to 

 the surface of emergence bisects the angle of the optic axes, 

 and therefore 1 = 9° 56' 27". Consequently R = 16° 55 f 27", 



* See Lond. and Edinb. Phil. Mag. and Journ., vol. i. p. 140— 141.— Edit. 



