•THSORIES OF CRYSTALLOGRAPHY'. 76 



•pedons, and their laws of formation very fimple; for there Laws of the ^^ 

 will be the fame number of integrant particles in each row, as ^ ^^j^^ ^^^ 

 there are rows in each lamina, as there are laminae in the pri- theory thence ' 

 mitive form. It is eafy to conceive that all the joints perfedl) ^efultrng. 

 coincide witH each other, and form continued planes ; neither 

 will there be any vacuity left between the particles. If the 

 primitive be not fimilar to the integrant particle, then the fim- 

 plicity of the former cafe difappears. I have already fiated 

 -that there are three forms of integrant particles; the telra- 

 edron, the triangular prifm, and the parallelopipedon. There 

 are alfo fix primitive forms ; the parallelopipedon, the odtae- 

 dron, the tetraeclron, the regular hexaedral prifm, the dode- 

 -caedron bounded by rhombs all equal and (imilar, and the 

 dodecaedron with triangular fides and formed by two right 

 -pyramids united bafe to bafe. Of Ihefe fix primitive forms 

 there are only the parallelopipedon and the regular hexaedral 

 prifm that can exadly fill up a fpace without leaving any va- 

 cuity. The integrant particles of the former are parallelopi- 

 pedons; of the latter, triangular prifms. As to the other four 

 primitive forms, their integrant particles are tetraedrons. The 

 dodecaedron bounded by rhombs is produced by twenty-four 

 fimilar tetrnedrons without any vacuity between them ; the 

 o£lae Iron and tetraedron are formed by tetraedrons leaving 

 octaedral vacuities ; and the dodecaedron bounded by tri- 

 angles, to be formed of tetracvlrons, mufl imply fedions pa- 

 rallel to more than fix planes; which perfectly coincides with 

 obfervation. 



Thefe vacuities, whofe exifience muft be admitted in the 

 integrant particles, as well as between thofe particles when 

 forming a primitive, give rife to the following reflexions : 



When the elements of a fubfl:ance are chemically combined, 

 that fubfiance is homogeneous. Let us fuppofe a cryfial of 

 fuch a fubftance to be fubdivided into fmall parallelopipedons 

 equal and fimilar ; as the fubftance is homogeneous, and thefe 

 little parallelopipedons having no vacuities between them, it 

 is evident the elements that compofe them are equal in number 

 and proportion. We will next fuppofe the cryftals of this fub- 

 ftance can be divided by fections parallel to fix planes. In 

 ihat fuppofition, nineteen or twenty diiFerent fpecies of pa*>- 

 rallelopipedons can be produced. Among thefe fpecies (bme 

 -will be fimilar, others not ; but none of the fpecies will be ex- 



aaiy 



