378 Theory of Ciyjlallifafum. ■ 



There is no cryftal from which a nucleus in the form of a 

 parallelopipedon may not be extracted, if we confine our- 

 felves to fix fections parallel two and two. " In a multitude 

 of fubftances this parallelopipedon is the laft term of the 

 mechanical divifion, and confequently the, real nucleus. 

 But there are certain minerals where this parallelopipedon is 

 divifible, as well as the reft of the cryftal, by farther feclions 

 made in the different directions of the faces ; and there 

 thence neceffarily remits a new folid, which will be the 

 nucleus, if all the parts of the fecondary cryftal, fuper- 

 added to this nucleus, are fimilarly fituated. When the 

 mechanical divifion conduces to a parallelopipedon, divifible 

 only by feclions parallel to its fix faces, the moleculae are 

 parallelopipedons fimilar to the nucleus; but, in all other 

 cafes, their form differs from that of the nucleus. This I 

 fhall illuflrate by an example. 



Let achsno {fg- Co.) be a cube, having two of its folid 

 angles a, s, fituated on the fame vertical line. This line will 

 be the axis of the cube ; and the points a and $■ will be its 

 fummits. Suppofc this cube to be divifible by feclions, each 

 of which, fuch as a hn, panes through one of the fummits 

 a, and by two oblique diagonals ah, an, contiguous to this 

 fumniit. This feelion will detach the folid angle i; and as 

 there are fix folid angles, fituated laterally, viz. i, h, c, r, o,n t 

 the fix feclions will produce an acute rhomboid, the fummits 

 of which will be confounded with thofc of the cube. Figure 

 61 reprefents this rhomboid cxifting in the cube, in fuch a 

 manner that its fix lateral folid angles h, d,f, p, g, e, cor-r 

 refpocd to the middle of the faces a c hi, cr s h, hin s, &c. 

 of the cube. But geometry {hews that each of the angles, 

 *t the fummits hag, d'sf, p sj] &c. of the acute rhom- 

 boid, are equal to 6o°, from which it follows that the lateral 

 fugles a bj] agf, kc. are equal to 1 20 degrees, 



Befides, it is proye<J by theory, that the cube refults from 

 d decrement whkh takes place by a fingle range of fmall 



rhomboids, 



