the j4lle Hmhfs Theories of Crystallography . 169 



one of them entitled to that denomination : and if only one, 

 which of them ? My answer is, Only one of then), and 

 that one the triangular prism ; which may be proved thus : 



It cannot be denied that the integrant particle is that lit- 

 tle solid which contains the least possible quantity of the 

 body, without affecting the chemical composition of the 

 substance. This granted, let us suppose the hexaedral 

 prism to be the integrant particle. In that supposition the 

 last triangular prism must contain the last hexaedral prism, 

 and is equal to the latter more three triangular prisms ; or, 

 in other words, to nine similar triangular prisms, while the 

 hexaedral prism only contains six. But the last triangular 

 prism, and the last hexaedral prism, each contain an exact 

 proportion, and therefore a similar proportion, of chemical 

 component parts ; therefore their differences also contain an 

 exact proportion. But it is impossible to conceive how their 

 differences can contain the exact proportion, unless each of 

 the three little triangular prisms also contain it; they must 

 therefore contain it, and each of them must be an integrant 

 particle ; therefore the hexaedral prism cannot be one t 

 neither can the parallelopipedons bfc integrant particles, as 

 the same arguments will stand good against them, which 

 have been applied to the hexaedral prism ; therefore the tri- 

 angular prism must be the integrant particle; therefore the 

 sections producing the hexaedral prism cannot lead to the 

 integrant particle ; therefore all sections, though perfectly 

 practicable in crystals, will not lead to the integrant particle, 



" The forms of the integrant particles," says the Abbe 

 (vol. i. p. 30.), "may be reduced to three : the tetraedron, 

 or the most simple of pyramids; the triangular prism, or the 

 most simple of prisms ; and the parallelopiptdon, or the 

 most simple of solids having parallel faces two and two; and 

 as four faces are necessary to circumscribe a space, it is evi- 

 dent £hat the above three forms, in which the number of faces 

 are successively 4, 5, and 6, are again in this point of view 

 the most simple posible." 



The phosphate of lime or chrysolite is a substance that has 

 given rise to much curious anecdote. Tt shows in what a state 

 the Abbe Haiiy found the mineralogical nomenclature, and 

 points out the accuracy of his analytical method, Achard, 

 a chemist at Berlin, had analysed the chrysolite, and pub- 

 lished that it contained of silex 15 parts, alumine 6*4>, 

 lime 17, and of iron 1. This startled the celebrated Vau- 

 quclin, who had seen Klaproth's analysis of the chrysolite 

 (the apatite of Werner), containing of lime 55 parts, and of 

 phosphoric acid 45 (probably the water of crystallization is 

 added to the dcid) . A Frenchman of the name of Launoy 



K 3 • sent 



