Sclirauf on the Optical Constants of Crystallized Substances. 479 



Being persuaded that crystallo-physics, more than any -other 

 branch of physical science, is founded on quantitative calculation of 

 absolute exactitude, I contrived to obtain first incontestable facts 

 connected with the hitherto somewhat neglected phenomena of dis- 

 persion and refraction. Nearly 1000 substances have been crystallo- 

 graphically investigated, and about 200 have been made the object of 

 optical researches ; many of them, however, have remained unknown 

 as to their dispersive and reflective powers, which, representing the 

 quantitative and qualitative action of any substance on the pro- 

 pagation of light, are of absolute necessity for the construction of 

 any sound theory. 



It becomes every day a greater necessity to obtain, within these 

 extensive dominions of human knowledge, a certain number of 

 general views, subservient to the explanation and systematic arrange- 

 ment of a great number of isolated facts, as only a small portion of 

 the present investigation has led to the establishment of general laws. 

 The great problem of crystallo-physics proposed for solution may be 

 expressed by the question, What is the causal connexion between che- 

 mical constitution and morphological and optical properties ? The 

 phenomena of isomorphism, discovered by Prof. Mitscherlich, have 

 indeed thrown considerable light on the mutual relation of chemical 

 constitution and morphological properties ; yet little, if anything, has 

 been done to arrive at the solution of the problem in its general form. 



As latterly several doubts have been expressed as to the possible 

 existence of such a connexion, the purpose of my investigations shall 

 be not only (as expressed in their title) to fill up deficiencies in the 

 knowledge of facts, but also to propose several explanations indicating 

 the real existence of such a connexion, and the necessity of making 

 it an object of earnest research. 



In the following paragraphs I intend only to mention some 

 theorems whose solution is already achieved. Another series of my 

 investigations, to be published subsequently, is to afford general 

 demonstrations and applications of consequences in strict connexion 

 with duly stated facts. 



The most important of the theorems, as far as they may be simply 

 enunciated, are — 



§ 1 . The calculation, graphic representation, and derivation of all 

 the crystallographical and physical properties of the rhombohedral 

 system are possible if three rectangular axes are assumed ; the axis c 

 coinciding with the principal rhombohedral axis, and the axes a and 

 b with the diagonals of the prism of 60°. 



§ 2. The following indices represent consequently the character- 

 istic equations for the symmetrical crystallographic systems : — 



Rectangular Axes. 



Tesseral a : b : c = 1:1:1 

 Pyramidal = 1:1:1 



Rhombohedral = ^3 : 1 : 1 



Prismatic = h : 1 : /. 



