NOTES TO BOOK IX. 513 



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 de- 

 fects in FresneFs reasoning on this subject, I may mention 

 Mr. Tovey, who treated it in several papers in the Phi- 

 losophical 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 which may be supposed to correspond to biaxal 

 crystals, Mr. Tovey considered the case of unsymmetrical 

 systems, and found that the undulations propagated would, 

 in the general case, be elliptical ; and that in a parti- 

 cular case, circular undulations would take place, such as 

 are propagated along the axis of quartz. It appears to 

 me, however, that he has not given a definite meaning 

 to those limitations of his general hypothesis which con- 

 duct 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 Her- 

 schel 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 

 appear upon what part of the hypothesis this difference of 

 right and left-handed depends. The definition of this 

 part of the hypothesis is a very desirable step. 



When crystals of Quartz are right-handed at one 

 VOL.11. LL 



