166 Royal Irish Academy. 



directed; but, in addition, his Papers on Meteorology contributed 

 largely to the advance of that science, more particularly to the 

 development of the Law of Storms. 



It was by his remarkable investigations in physical optics that 

 he first fixed the attention of the scientific world. In the Third 

 Eeport of the British Association (1833) Professor Lloyd furnished 

 an account of the experiments by which he had established the 

 existence of conical refraction in biaxial crystals, in conformity 

 with the theoretical anticipations of Hamilton. It had been known 

 since the beginning of the last century, that when a pencil of light 

 is allowed to fall on certain crystals, it is in general divided into 

 two rays. In Iceland spar — a uniaxial crystal — in which the phe- 

 nomenon of double refraction is conspicuous, it was found that one of 

 these rays obeys the ordinary law of refraction, and by a sagacious 

 conjecture, based upon this fact, Huyghens obtained the law of the 

 other, or " extraordinary" ray. Huyghens' law was for a long time 

 supposed to apply to all doubly refracting substances, till Brewster 

 made known the existence of biaxial crystals, on which light may be 

 incident in either of two directions Avithout being bifurcated — a phe= 

 nomenon which showed that Huyghens' law does not prevail in these 

 crystals. Presnel thereupon investigated the most general laws of 

 double refraction from the legitimate and perfectly general hypothesis 

 that the ether within a crystal acts under the same laws as a body 

 whose elasticity varies in different directions. From this hypothesis 

 he deduced the equation of the wave-surface, and showed that all the 

 laws of biaxial crystals, known up to this time from the experiments 

 of Brewster and Biot — both those laws which regard the direction of 

 the rays, and those which determine their polarization — were conse- 

 quences of this theory. He also showed that Huyghens' law and 

 the other known phenomena of crystals with one optic axis followed 

 as consequences of the particular case of his hypothesis where the 

 elasticities are the same in directions parallel to one plane. 



The geometrical form of Fresnel's wave-surface — a surface of two 

 sheets intersecting at four points — was investigated in minute detail 

 by M'Cullagh and Hamilton. In the course of this inquiry, Hamilton 

 discovered that at each point of intersection a cone is tangent to the 

 surface, and that where the outer sheet, after passing the point of 

 intersection, bends back, it has a tangent plane which touches it 



