302 Tlie American Geologist. May, isoo 
blindness which prevails even among adejDts in reference to 
some of its features — features which have a direct bearing on 
the profoundest cosmical problems, and which in scope and 
grandeur are without a parallel in other dej)artments of science. 
One of the most significant discoveries of modern physics — 
a discovery in which the sciences of mineralogy, optics and 
molecular dynamics are, perhaps, equally involved — is that of 
the singular relations which exist betAveen the external shape 
and the optical properties of crystals. It is not a discovery; 
which, like the announcement of Kirchhoff's lucky interpreta- 
tion of the mysterious Fraunhofer lines, has startled us by its 
suddenness, or indeed one for which we are indebted to the 
genius of an individual. It was foreshadowed by Newton's 
great contemporary Huyghens^ and, in a measure, outlined by 
Fresnel, Arago and Brewster, though its evolution proper may 
be said to date from the moment when, in 1814, Wollaston dis- 
covered the rings of Iceland spar, and mineralogists, after end- 
less comparisons and angle-measurements, had come to the 
conclusion that all crystals could be arranged in six groups or 
systems. 
A review of the fundamental facts of crystallography, or 
mere repetition of what may be found in every elementary 
text-book, is not here intended. It is taken for granted that 
the reader is aware of the difference between a tetrahedron 
and a hexagonal prism, especially in reference to axial rela- 
tions, still a detailed knowledge of the intricacies presented by 
the world of crystals is by no means essential to a full compre- 
hension of the points which I am about to present. 
We have six crystallographic systems, and it has been math- 
ematically demonstrated by Quenstedt that a seventh is im- 
possible. All mineral bodies, whether compound or elemen- 
tary, whose form and structure is determined by a symmetri- 
cal accumulation of particles in three directions and which 
present polyhedral boundaries can be arranged in six groups, 
and no matter what the mineralogy of the future may have in 
store for us in the way of surprises, the number of fundamen- 
tal systems will never be increased. An accumulation of par- 
ticles, development or '"growth" in less than three directions is 
inconceivable, and the discovery of a fourth would be equiva- 
lent to that of the mysterious "fourth dimension of space" so 
-Tractatus de Lumine. (1690.) 
