SYSTEMS OF CRYSTALLIZATION. 329 



derive it from the rhombic prism, why should the acute angles always 

 suffer decrements corresponding in a certain way to those of the obtuse 

 angles, as they must do in order to give rise to a square pyramid ? 



The introduction of the method of reference to Systems of Crystal- 

 lization has been a subject of controversy, some ascribing this valuable 

 step to Weiss, and some to Mohs. 3 It appears, I think, on the whole, 

 that Weiss first published works in which the method is employed; 

 but that Mohs, by applying it to all the known species of minerals, has 

 had the merit of making it the basis of real crystallography. Weiss, 

 in 1809, published a Dissertation On the mode of investigating the 

 principal geometrical character of crystalline forms, in which he say?, 4 

 "No part, line, or quantity, is. so important as the axis ; no considera- 

 tion is more essential or of a higher order than the relation of a crystal- 

 line plane to the axis ;" and again, " An axis is any line governing the 

 figure, about which all parts are similarly disposed, and with reference 

 to which they correspond mutually." This he soon followed out by 

 examination of some difficult cases, as Felspar and Epidote. In the 

 Memoirs of the Berlin Academy, 6 for 1814-15, he published An Ex- 

 hibition of the natural Decisions of Systems of Crystallization. In 

 this Memoir, his divisions are as follows : The regular system, the/owr- 

 membered, the two-and-tiuo-membered, the three-and-three-membered, 

 and some others of inferior degrees of symmetry. These divisions are 

 by Mohs (Outlines of Mineralogy, 1822), termed the tessular, pyrami- 

 dal, prismatic, and rhombohedral systems respectively. Hausmann, in 

 his Investigations concerning the Forms of Inanimate Nature, 6 makes 

 a nearly corresponding arrangement ; the isometric, monodimetric, 

 trimetric, and monotrimctic ; and one or other of- these sets of terms 

 have been adopted by most succeeding writers. 



In order to make the distinctions more apparent, I have purposely 

 omitted to speak of the systems which arise when the prismatic system 

 loses some part of its symmetry ; when it has only half or a quarter its 

 complete number of faces ; or, according to Mohs's phraseology, when 

 it is hemihedral or tetartohedral. Such systems are represented by the 

 singly-oblique or doubly-oblique prism ; they are termed by Weiss 

 td'o-and-onc-membered, and one-and-one-membered ; by other writers, 

 Monoklinometric, and Triklinometric Systems. There are also other 



* Edi". Phil. Trans. 1823, vols. xv. and xvi. * pp. 16, 42. 



Ibid. 6 Gottingen, 1821. 



