312 SCIENTIFIC APPARATUS. 



centres of mass distributed at equal distances along parallel and 

 along symmetrically similar directions, drew a priori conclusions 

 with regard to the symmetry which it is possible for such a system 

 to present, and even for the necessity of the crystallographic law. 

 Karsten further deduced the necessity of this fundamental law 

 from his geometrical treatment of cohesion. Victor von Lang 

 and Axel Gadolin, independently of each other, deduced results 

 similar to the former of those obtained by Bravais, from the 

 crystallographic law without any molecular hypothesis, though 

 their proofs lacked something of completeness, as well as sim- 

 plicity. So that now it may be seen that the rules of symmetry, 

 which observers have laid down as those which regulate the forms 

 of crystals, are really but deductions from a simple fundamental 

 law. 



But while geometrical crystallography has thus been moving 

 onwards to its goal, the fact that a crystal is not merely a geo- 

 metrically constructed polyhedron, but that its very form is only 

 one of the results of physical and chemical laws embodied in its 

 material, forced itself on the minds of crystallographers. How 

 largely the science of light already owed to crystal structure, from 

 the days of Huyghens to those of Fresnel, need not be recounted ; 

 but the extension of this knowledge from such minerals as Iceland 

 spar and quartz to. the whole range of crystallized substances 

 became now the duty of the crystallographer, and instruments and 

 modes of observation proportionately delicate had to be employed. 

 The splendid series of observations by Brewster and Biot early in 

 the century, had already correlated the optical and morphological 

 characters of crystals so far as to show that singly refracting uni- 

 axal and biaxal characters were conterminous with particular 

 crystallographic systems. The observations of Sir J. Herschel and 

 Neumann led to the knowledge that the dispersion of the optic 

 axes (for different wave-lengths) was not symmetrical to an axis 

 except where a mean-line of the optic axes coincided with an axis 

 of morphological symmetry. 



