C6 MINERALOGICAL SYSTEMS. 



Explanation of in the proportions of lime, carbonic acid, and water, Thefe 



fonnal"oTo? '^^ pdrticles which are ftill rhomboids, are what the Abb6 



cryftais by the Hauy calls the integrant particles of tlie carbonate of lime. Irt 



n>ethodof Hauy. ^j^^ fuppofition therefore that a rhomboid of this fubftance can 



only be divided in three diredions, by fe6^ions parallel to the 



fides, it is evident that the integrant particles muft be fimilar 



rhomboids. 



If a cryftal can be divided by feftions in more diredions 

 than three, what will be the form of the integrant particles ? 

 For example^ in the phofphate of lime (the chryfolite of De 

 L'Ifle) where the fedlions are parallel to four planes, three of 

 which have a common interfedion. According to what has 

 been faid above, thefe fe6lions can produce either one hexahe- 

 dral prifm, or three parallelipipedons, or one triangular prifm. 

 It is evident that by carrying the divifion, according to thofe 

 fedlions, to its greateft length, either the laft hexahedral prifm, 

 or the laft three parallelipipedons, or the laft triangular prifm, 

 will be produced. Are thefe laft folids the integrant parti- 

 cles; are each of them fo; or is there only one of I hem en- 

 tilled to that denomination ; and if only one, which of them ? 

 My anfwer is, only one of them ; and that one, the triangular 

 prifm, which may be proved thus. 



It cannot be denied that the integrant particle is that little 

 folid which contains the leaft poffible quantity of the body, 

 without affeding the chemical compolition of the fubftance. 

 This granted, let us fuppofe the hexahedral prifm to be the in-* 

 tegrant particle. In that fuppofition the laft triangular prifm 

 muft contain the laft hexahedral prifm, and is equal to the 

 latter more three little triangular prifms, or in other words to 

 nine fimilar triangular prifms, while the hexahedral prifm only 

 contains fix. But the laft triangular prifm and the laft hexa- 

 hedral prifm each contain an exa<5l proportion, and therefore 

 a fimilar proportion of chemical component parts; therefore 

 their difference alfo contain an exa6t proportion ; but it is im- 

 poflible to conceive how their differences can contain the ex- 

 a6t proportion, unlefs each of the three little triangular prifms 

 alfo contain it, they muft therefore contain it, and each of 

 them muft be an integrant particle; therefore the hexahedral 

 prifm cannot be one ; neither can the parallelipipedons be in- 

 tegrant particles, as the fame arguments will ftand good againft 

 them which have been applied to the hexahedral prifm ; there- 

 fore 



