72 Mr. Mac Cullagh on the Laws of 



same cause, whatever it is, which produces a change of phase in metallic 

 reflexion. 



It will be proper to conclude this Essay with a brief sketch of the researches 

 of Sir David Brewster and M. Seebeck, the only other writers who have treated 

 of the subject of crystalline reflexion. 



So early as the year 1819, Sir David Brewster published, in the Philoso- 

 phical Transactions, a paper " On the Action of Crystallized Surfaces upon 

 Light."* In this paper the author details a great variety of experiments on 

 the polarising effects of Iceland spar. He gives the measures of the polarising 

 angles in different azimuths, when the reflexion takes place in air ; but he 

 does not notice the accompanying deviations, which were probably too small 

 to attract his attention. In another instance, however, he obtained very large 

 deviations. He conceived the idea of pushing his experiments into an extreme 

 case, by masking, as it were, the ordinary reflecting action of the crystal, 

 and leaving the extraordinary energy at full liberty to display itself. This was 

 done by dropping on the reflecting surface a little oil of cassia, a fluid whose 

 refractive index is nearly equal to the ordinary index of Iceland spar. When 

 common light, incident at 45°, was reflected at the separating surface of the oil 

 and the spar, the reflected pencil was found to be partially, and sometimes com- 

 pletely, polarised in planes variously inclined to the plane of incidence, the 

 inclination going through all magnitudes from to 180°, as the crystal was turned 

 round in azimuth. This general result is no more than what theory would lead 

 us to expect, when the angle of incidence is nearly equal to one of the angles of 

 refraction ; but, to institute a minute comparison of theory with experiment, 

 wovdd require troublesome calculations, which I have not had time to make. 

 With the view, however, of showing clearly, from theory, that the range of the 

 deviation is unlimited, I have considered the simple case in which n = b, or in 



A'j — ^3^:90°, the conjugate incidences are equal, the ratio -2- is a minimum, and the axes of the 



''3 



elliptic vibration are parallel and perpendicular to the plane of incidence. When A'3 = 90°, or 

 M//.:=l, the value of t', is a minimum, and equal to tan |;^. 



The foregoing formulae differ slightly from those which I have given in No. I. of the Proceedings 

 of the Royal Irish Academy. The small quantity y^, which occurs in the latter, has been purposely 

 neglected, as its presence interferes with the simphcity of the expressions. 



* Phil. Trans. 1819, p. 145. 



