82 



Laws of th« 

 ftrufture of 

 cryflals, and 

 theory thence 

 rcfulting. 



THEORIES OF CRYSTALLOGRAPHY. 



Thefc are the decrements parallel to the edges, or, as the 

 Abb^ calls them, decrements on the edges. But they may 

 take place in a parallel with the diagonal of the faces of th6 

 primitive ; they are then called decrements on the angles, be- 

 caufe the diagonals are drawn from one angle to the oppofite 

 angle. This fecond fpecies of decrement follows the fame 

 laws as the firft. 



There is a third, fpecies, called by our author intetmediatc 

 decrements. In this cafe they are neither parallel to the edges 

 nor to the diagonals of the faces, but to intermediate lines, 

 which if prolonged would interfe6l both the edges and dia- 

 gonals, but otherwife they follow the fame laws as the two 

 firft. It is a general law, therefore, that in all cafes the lamince 

 decreafe in arithmetical progrejfion, and its ratio or the number 

 of ranges fubtraBed is alivays commeiif arable. 



The particles of which the laminae are compofed are to be 

 conlidered as parallelopipedons ; not that the integrant par- 

 ticles always have this figure ; but if they have it not, they 

 niuft leave vacuities between them, and each vacuity being 

 added to its correfponding particle, will complete the paral- 

 Iclopipedon. If this was not the cafe, the faces of the fecond- 

 ary cryllals would not be planes, nor could they be fpiit 

 fmoothly in any diredion. Thefe little parallelopipedons 

 which compole the fubtra6led ranges are what I called above, 

 alter our author, fubtra^ive particles, 



I fuppofed the conftrud^ion of the fecondary form only to 

 take place on one of the faces of the rhomboid ; but what was 

 faid relative to that face is applicable to all the others. It is 

 alfo to be remarked that different laws of decrement may affe6t 

 the different faces ; even further, different laws may fuccef- 

 lively affeft the fame face. Hence a diverfity of forms arife 

 fcarcely credible to a perfon unacquainted with the do^^rine of 

 combinations. The Abbe Haiiy has calculated, " that con- 

 . fining one's-felf to decrements by 1, 2, 3, or 4- ranges, and 

 not taking intermediate or mixt decrements into account, the 

 rhomboid is capable of 8,324,60 !• varieties of cryflalline forms. 

 It is an important remark, that whatever may be the variety 

 of form, the forms (in complete cryftals) will always be fym- 

 metrical. There are two forts of fyrametry, the perfect alid 

 imperfefl. In the pcrfed, the right is fymmetrical with the 

 . left, and the top with the bottom ; but in the imperfed, the 



top 

 3 



