132 HISTORY OF OPTICS. 



function of the optical system to which the problem 

 belongs. From tliis function is deduced tlie surface of wave-sloumess 

 of tlie medium ; and by means of tins surface, the direction of the 

 rays refracted into the medium. From this construction also Sir "\Y. 

 Hamilton was led to the anticipation of conical refraction, mentioned 

 above. 



The investigations of MM. Cauchy and Lame refer to tlie laws by 

 which the particles of the ether act upon each other and upon the 

 particles of other bodies ; a field of speculation which appears to me 

 not yet ripe for the final operations of the analyst. 



Among the mathematicians who have supplied defects in Fresnel's 

 reasoning on this subject, I may mention Mr. Tovey, who treated it in 

 several papers in the Philosophical Magazine (1837-40). Mr. Tovey's 

 early death must be deemed a loss to mathematical science. 



Besides investigating the motion of symmetrical systems of particles 

 whicli may be supposed to correspond to biaxal crystals, Mr. Tovey 

 considered the case of unsvmnietrical systems, and found that the 



/ / 



undulations propagated would, in tlie general case, be elliptical ; and 

 that in a particular case, circular undulations would take place, sucli as 

 are propagated along the axis of quartz. It appears to me, however, 

 that he has jnot given a definite meaning to those limitations of his 



o o 



general hypothesis which conduct him to this result. Perhaps if the 

 hypothetical conditions of this result were traced into detail, they 

 would be found to reside in a screw-like arrangement of the elementary 

 particles, in some degree such as crystals of quartz themselves exhibit 

 in their forms, when they have plagihedral faces at both ends. 



Such crystals of quartz are, some like a right-handed and some like 

 a left-handed screw ; and, as Sir John Herschel discovered, the circular 

 polarization is right-handed or left-handed according as the plagihedral 

 form is so. In Mr. Tovey's hypothetical investigation it does not 

 ::|>[>ear upon what part of the hypothesis this difference of right and 

 left-handed depends. The definition of this part of the hypothesis is a 

 v< TV desirable step. 



"\Yhen crystals of Quartz are right-handed at one end, they are right- 

 handed at the other end : but there is a different kind of plagihedral 

 form, which occurs in some other crystals, for instance, in Apatite : in 

 these the plagihedral faces are right-handed at the one extremity and 

 left-handed at the other. For the sake of distinction, we may call the 

 former homologous plagihedral laces, since, at both ends, they have the 

 same name ; and the latter / 1 ti n logons plagihedral faces. 



