MINERALOGICAL SYSTEMS. 55 



have a common inlerfedion or not; and it m lift be reraem- Explanation of 

 bered that if the four planes have a common interfeflion, i^o formation^of" 

 folid can be produced, as they can neither bound nor include cryftals by the 

 a fpace. If therefore three of the four planes have a common*"^^ ° "^^^ 

 interfedion, the fplittings will produce either one hexahedral 

 prifm, or three parallelipipedons, which will be fimilar or dif* 

 iimilar, according to the fimilarity or difiimilarity of inclinai' 

 lion of the planes, or one triangular prifm. On the contrary, 

 if the four planes only interfcdt each other two and two, there 

 will be produced either one OiSlahedron, or four parallelipipe- 

 dons, or one tetrahedron. 



Laflly, let us fuppofe the fmooth furfaces to be parallel to 

 fix planes; then there arife an immenfe number of cafes.—* 

 But we will for the prefent confine ourfelves to the only cafe 

 that has hitherto been obferved in nature : Where the inter- 

 re6tion of the planes is two and two, then we obtain either, 

 1. dodecahedron with pentagonal, quadrilateral or triangular 

 fides, according to the fedions made, or fifteen odahedrons, 

 or twenty parallelipipedons, or fifteen tetrahedrons. It may 

 be proper to obferve here that though the fedtions parallel to 

 the fix planes may be clearly indicated, neverthelefs it rarely 

 happens they can all be executed, but it will fuffice for the 

 purpofes of geometry that they be clearly indicated to render 

 the confequences drawn from them mathematically correal. 



Having laid down thefe premifes, let us proceed to the dif- 

 fedion of a cryfial of carbonate of lime (the fpath calcaire of 

 De L'Ifle) whofe primitive form is a rhomboid or a parallelipi- 

 pedon bounded by rhombs. Hitherto fedions have only been 

 obtained in the three directions parallel to its fides. If thefe 

 feflions be dired^ed fo as to always pafs through the center of 

 two oppofite fides, they will produce eight rhomboids equal 

 to each other, and fimilar to the original one. The fame 

 operation may be repeated on each of thefe eight rhomboids, and 

 continued fo long as the fubftance remains carbonate of lime, 

 that is to fay, to be a combination of 55 parts of lime, 34? 

 of carbonic acid, and 1 1 parts of water of cryftallization : — 

 (fee Bergman.) But this divifion of the cryftals into fimilar 

 folids has a term> beyond which we fliould come to the fmalleft 

 particles of the body, which could not be divided without 

 chemical decompofilion ; that is to fay, without an alteration 



Da in 



