in passi?ig through biaxal Crystals, 119 



Finally, when the apertures on the two surfaces were trans- 

 posed, 1 found that no change was made in the resulting phe- 

 nomena; and that they seemed, in fact, to be in all respects 

 similarly related to the surfaces of incidence and emergence. 



It is easy to render an account of these various appearances. 

 When the aperture on the second surface is considerable, 

 the rays proceeding to its circumference from a point on the 

 first surface will be sensibly inclined to the optic axis, which 

 we shall suppose to be in the line connecting the point with 

 the centre of the aperture. Consequently the interior, as well 

 as the exterior rays, into which each of them is divided, will 

 be inclined outwards; and it is obvious that there will be a cen- 

 tral bright space, every point of which is illuminated by one 

 interior and one exterior ray. This space therefore will have 

 double the brightness of the surrounding space, each point of 

 which is illuminated by one ray only; and as the rays which 

 combine to form it are polarized in planes at right angles to 

 one another, the resulting light will be unpolarized. 



When the aperture is diminished, the inclination of these 

 interior rays to one another decreases ; until finally they be- 

 come parallel, and the central bright space is reduced to a 

 point. When the aperture is still further diminished, the 

 interior rays become inclined inwards, and cross; and it is 

 obvious that beyond the point of junction there will be a dark 

 space illumined by no ray whatever. As there is no meet- 

 ing of rays oppositely polarized in this case, the whole of the 

 light will be polarized, and according to the law already ex- 

 plained. Finally, when the aperture is still further diminished, 

 the interior rays at one side approach to parallelism with the 

 exterior at the other ; and the central dark space enlarges, 

 and approaches to equality with the outer and limiting cone. 

 Thus the annulus of light is indefinitely diminished in breadth, 

 and the cone approaches to a mathematical surface. 



It will be easily seen that the angle of the true cone is, 

 nearly, half the sum of the angles of the exterior and interior 

 limits of the observed conical annulus; and that when a bright 

 space appears in the centre, as is the case when the aperture 

 is considerable, the true angle is half the difference of the an- 

 gles of the interior and exterior cones. When the whole cone 

 is of uniform brightness, and the central dark space reduced 

 to a point, the observed cone is just double of that sought. 



Now this last was very nearly the case in the experiments 

 from which the measures already mentioned were taken ; and 

 consequently the corrected angle, being in this case half the 

 observed, coincides very nearly with that deduced from theory. 



