Royal Irish Academy. ] 35 



tersection, the reflected ray will be polarized parallel to the second 

 intersection, and there will be only a single refracted ray ot. A 

 right line drawn through the point o, perpendicular to the plane otp, 

 will lie in the plane a, and will be the transversal of the refracted 

 ray ot ; and if, measuring from the point o, the lengths of the three 

 transversals represent the amplitudes of the respective vibrations, the 

 transversal of the refracted ray ot will be the diagonal of the parallel- 

 ogram, whose sides are the transversals of the incident and reflected 

 rays. The problem is, therefore, completely solved in this case, and 

 it is obvious, that a construction precisely similar will apply to the 

 other case, in which or' is the only refracted ray. The plane b, which, 

 in this second case, answers to the plane a in the tirst case, is per- 

 pendicular to the plane ot'm, and parallel to the right line t'm. 



If the incident ray be polarized in a direction intermediate between 

 the two transversal directions which give only a single refracted ray, 

 the incident vibration may be resolved into two vibrations ?>arallel to 

 those two transversals. The reflected vibrations arising from each 

 of the component incident vibrations are to be found by the fore- 

 going rules, and then to be compounded. 



When the intersection of the planes a and b is perpendicular to 

 the direction of the reflected ray, this ray is polarized parallel to that 

 intersection, whatever be the plane of polarization of the incident 

 ray. The angle of incidence at which this takes place is the 

 polarizing angle. 



When the refracted ray ot or ot' is a normal to the wave-surface, 

 the plane a or b is the plane of polarization of the ray. For example, 

 if ot be the ordinary ray in a uniaxal crystal, the plane a contains 

 the ray ot and the axis of the crystal. 



The hypotheses from which Mr. MacCullagh has obtained the fore- 

 going laws, are these : 



1. The density of the aether is the same in all media. 



2. The vibrations are parallel to the plane of polarization. 



3. The vis viva is preserved. 



4. The vibrations are preserved : that is, the resultant of the in- 

 cident and reflected vibrations is the same as the resultant of the 

 refracted vibrations. 



The author finds that his theory represents very accurately the ex- 

 periments of Sir David Brewster and M. Seebeck, on the light re- 

 flected in air from a surface of Iceland spar. 



January 23. — Captain Portlock read a notice of the occur- 

 rence of Anatifa vitrea*, of Lamarck, in several localities on the 

 Irish coast. He commenced by enforcing the great importance of 

 recording as quickly as possible the first discovery in a new locality 

 of any species of the animal or vegetable kingdom, as tending to 

 perfect the Fauna or Flora of the district in which it is found; and 

 pointed out the value of such local Faunae and Florae in estimating 

 the relations and mutual dependencies of coexisting animals and 

 plants, and affording a basis of comparison by which future observers 

 may be enabled to test the probability of new organic beings occa- 



• Lcpas fascicularis of Ellis, Montagu, and other authors; Lepas dilata 

 of Donovan. 



