Crystals. 127 



matter furnished this, and, instead of "bricks", we reason about 

 " atomic groups," whose centres of mass are arranged in straight lines 

 and parallel planes, as were the centres of the "bricks" in Haiiy's 

 original theory. 



Weiss was the first, in 180S to point out the importance of the axes 

 of crystals, although Haiiy had referred to them. 



He says : "The axis is truly the line governing every figure round 

 which the whole is uniformally disposed. All the parts look to it, and 

 by it they are bound together as by a common chain and mutual 

 contact." These axes, it must be borne in mind, are not mere geo- 

 metrical lines; but it is in reference to them that the forces work which 

 have formed the crystals. 



Weiss proceeded to arrange Haiiy's primitive forms into four classes, 

 each distinguished by a purely geometrical character; and then from 

 these four classes of sets of lines, he deduced all the primitive forms by 

 the construction of planes passing: 



i. Through ends of three lines. 



2. Through ends of two of the lines and parallel to the third. 



3. Through an end of one of the lines and parallel to two of them 

 That is, these pianes passed through the end of a line, or else did 



not meet it at all. These axes were, in fact, the coordinates of the 

 crystal faces of the primitive forms of Haiiy. By taking points along 

 .each of these lines at distances equal to twice, three times, four times, 

 etc., the original length, he found, constructing planes as before, that he 

 obtained a set including all the secondary planes described by Haiiy as 

 occurring in actual crystals. 



Thus he was enabled to devise a very simple system of designating 

 the various faces of crystals, which also greatly facilitated the calcula- 

 tion of their angles. 



Haiiy had attempted this in conformity with his theory, but his 

 symbols were complex and unwieldy. 



It is a curious coincidence that at the same time as Weiss was 

 developing his system, Mohs, Werner's successor at Freiberg, working 

 quite independently, arrived at the same division of crystals into four 

 classes, but by a very differem process of reasoning. These four 

 classes he termed " Systems of Crystallization." 



