1 68 Paratlel oj Rome de I 1 Isle's mid 



intersection of the planes is two and two. Then wc obtain 

 cither 1 dodecaedron, with pentagonal, quadrilateral or tri- 

 angular faces, according to the sections made; or 15 oc- 

 taedrons, or 20 parallelopipedons, or 15 tetraedroms. It 

 tnay be proper to observe here that, though the sections pa- 

 rallel to the 6 planes may be clearly indicated, nevertheless,, 

 it rarely happens they can all be executed ; but it will suffice 

 for the purposes of geometry, that they be clearly indicated 

 to render the consequences drawn from them mathemati- 

 cally correct. 



Having laid down these premises, let us proceed to the 

 dissection of a crystal of carbonate of lime (the spath cal- 

 caire of De PIsle), whose primitive form is a rhomboid, or 

 a parallclopipedon bounded by rhombs. Hitherto sections 

 have only been obtained in the three directions parallel to its 

 faces. If these sections be directed so as to always pass 

 through the centre of two opposite faces, they will produce 

 8 rhomboids equal to each other, and- similar to the ori- 

 ginal one. The same operation may be repeated on each*of 

 these 8 rhomboids, and continued so long as the substance , 

 remains carbonate of lime, that is to say, to be a combination 

 of 55 parts of lime, 34 of carbonic ackl, and 11 parts of 

 water of crystallization (see Bergman), But this division of 

 the crystal into similar solids has a term r beyond which we 

 should come to the smallest particles of the body, which 

 could not be divided without chemical decomposition, that 

 is to say, without an alteration in the proportions of lime, 

 carbonic acid, and water. These last particles, which are still 

 rhomboids, are what the Abbe Unity calls integrant parti- 

 cles of the carbonate of lime. In the supposition, there- 

 fore, that a rhomboid of this substance can only be divided 

 in three directions, by sections parallel to the faces, it is 

 evident the inttgrant particles must be rhomboids. 



If a crystal can be divided by sections in more directions 

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

 For example, in the phosphate of lime (the chrysolite of 

 De Tlsle), where the section- are parallel to 4 planes, 3 of 

 which have a common intersection. According to what 

 has been said above, these sections can produce either 1 

 hexaedral prism, or 3 parallelopipedons, or 1- triangular 

 prism. It is evident that, by carrying the division accord- 

 ing to those sections to its greatest length, either the last 

 hexaedral prism, or the last 3 parallelopipedons y or the last 

 triangular prism, will be produced. Are these last solids the 

 integrant particles ; are each of them so > or is there only 

 5 - eue 



