13* Jioj/al Irish Academy. 



is polarized in the plane of incidence, or in the perpendicular plane. 

 Consequently, if the incident ray be polarized in any intermediate 

 plane, the refracted ray should be ellipticallv polarized ; and on ex-. 

 amining the light transmitted by gold leaf, this was found to be the 

 case. Of course the same thing is true of the light which enters the 

 other metals, and which is subsequently absorbed. The same remark 

 explains the appearance of double infraction in specimens of the 

 diamond which give only a single image j and it is likely that other 

 precious stones will be found to possess similar properties. Mr. 

 MacCullagh has obtained a general formula for ihe difference of phase 

 between the two component portions of the refracted light, one po- 

 larized in the p'ane of incidence, and the other perpendicular to it. 

 He finds from this formula, that the difference of phase, which is no- 

 thing at a perpendicular incidence, increases until it becomes equal 

 to the characteristic at an incidence of 90°; and when the light emer- 

 ges into air, the difference of phase is doubled. The formula has not 

 yet been submitted to the test of experiment. 



Mr. MacCullagh then read a paper " On the Laws of Crystalline 

 Reflexion and Refraction.*" 



In this paper the solution of the following problem is given for the 

 first time : — Supposing a ray of light, polarized in a given plane, to 

 fall on a doubly refracting crystal, it is required to find the plane of 

 polarization of the reflected ray, and the proportion between the am- 

 plitudes of vibration in the incident, the reflected, and the two re- 

 fracted rays. 



The constructions to which the author has been led by his theory 

 are extremely simple, and may be explained most easily by referring 

 to a paper which he has already published in the Transactions of the 

 Academy, vol. xvii. pp. 23 1, 252. To avoid circumlocution, he uses 

 the term transversal, to denote a right line parallel to the plane of 

 polarization of a ray, and perpendicular to the direction of the ray 

 itself. When ihe transversal is spoken of as a finite magnitude, its 

 length is understood to be proportional to the amplitude of the vibra- 

 tions in the polarized ray. Let o (as in the place just referred to) 

 be the point of incidence on the crystal, and ot, ot' the directions 

 of the two refracted rays, the points t, t' being on the wave-surface. 

 Corresponding to the points r and t' on the wave-surface, there are 

 two other points, p and m, on a second surface, which is reciprocal to 

 the wave-surface. The points p and m are derived from the points 

 t and t' by an easy rule, which is given in the place before cited. 

 Now if we wish to find in what direction the incident ray must be 

 polarized in order that the ray o t' may disappear, let us draw, thiough 

 the point o, a plane a perpendicular to the plane otp, and parallel 

 to the right line tp, which joins the corresponding points t, p. This 

 plane a will intersect the planes of the incident and reflected waves 

 in two right lines, which will be the transversals of those waves ; so 

 that if the incident ray or wave be polarized parallel to the first in- 



• Papers on this subject by Prof. MacCullagh will be found in Lond. 

 and Ediub. Phil. Mag., vol. viii. p. 103, vol. x. p. 42.— Edit. 



