86 Mr, Emmett on the [Feb. 



Let E G F H, fig. 3, be a parallelogram 

 formed of symmetrically arranged particles ; 

 if split in the directions A B, or C D, the 

 surtace will be smooth and plane, for the 

 resisting force of cohesion is constant in 

 every part of these lines, or their parallels, 

 and each particle has to be separated only ^o^^^^^iib^ 

 from one, as a, c, or e,/; but in any other 

 direction, E F, each particle has to be separated from two, 

 as a from b and c ; therefore, the fracture cannot proceed 

 according to that line, but must follow those directions in which 

 it meets with the least resistance. 



Cor. 1. — Hence, in an irregular fracture, all the irregularities 

 are parts of parallelograms, having the constant angles E G F, 

 orGFH. 



Cor. 2. — Hence, by continual mechanical division, a number 

 of nuclei may be obtained, which are all equiangular, and which 

 are similarly situated in the original crystal. 



Cor. 3. — Since all the fractures of crystals, or the directions 

 of their rows of particles, are parallel to, or form a constant 

 angle with, each other, every base of a crystal may be consi- 

 dered as a parallelogram which wants some of its parts. 



Cor. 4. — Since any number of such bases may be applied 

 upon each other, which, by prop. 10, must follow the same law 

 of arrangement as the bases, every solid crystal may be consi- 

 dered as formed from a parallelopipedon, similar to that which. 

 is obtained by the mechanical division of the crystal, by remov- 

 ing some of its parts. 



We may now proceed to examine some of the external forms 

 of crystals, and the first part to be investigated is the construc- 

 tion of the base, or that surface which results when a crystal is 

 split, quite through its thickness : these are of two sorts ; those 

 which have some of their sides parallel to the directions of spht- 

 ing, or to the sides of the original parallelogram, and those 

 which have none of their sides so posited. Of those which have 

 some of their sides parallel to those of their nucleus, the follow- 

 ing willbe some ofthe principal varieties: ABCD, 

 fig. 4, being a parallelogram, composed of 

 particles which are regularly arranged, E F and 

 G H, which are parallel to its sides, are the 

 directions of splitting, by prop. 13 : the paral- 

 lelogram is, therefore, one figure which the 

 base of the crystal may assume. If the part 

 A B C be removed, the external figure A D C is a triangle^ 

 whose angles are D = smaller angle of the figure ; and D A C, 

 D C A, each equal to half the greater angle : or if B C D be 

 removed, the resulting triangular base has the angles A B D, 

 A D B, each equal to'half the smaller angle of the nucleus, and 



