Crystals. 



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8. The four-sided prism, with edges inclined obliquely to the base, 

 me base being either a rectangle, a rhomb, or merely a parallelogram. 



9. The regular six-sided prism, 



10. The double six-sided pyramid. 

 He also grouped all these forms in a general way thus: 



1. Figures bounded by parallelograms. 



2. Figures bounded by eight triangles. 



3. The regular tetrahedron. 



4. The regular six-sided prism. 



5. The double six-sided pyramid. 

 Hauy was let by his study of cleavage to frame a theory regarding 



the structure of crystals and to discover a second great law governing 

 their formation, namely the one which connects the secondary faces 

 with those of the primitive form. 



He found that the kernels which he obtained by cleavage could be 

 split up,apparently indefinitely, into smaller fragments of the same shape, 

 and, not believing that this process could go on to infinity, came to the 

 conclusion that every crystal of the same substance could, theoretically 

 at least, be cleaved into minute bricks of a definite size and shape though 

 two small to be separately visible, and therefore that with these bricks 

 a crystal possessing any of the forms in which the particular mineral 

 occurs, might be built up. 



As the simplest illustration take the case where the bricks are 

 little cubes The conditions to be produced are that the built-up 

 crystal must possess cleavage, and at all its parts the faces obtainable by 

 cleavage are to have the same directions, also that its outer surface must 

 consist of a series of plane faces. 



A cube composed of these little bricks could be increased in- 

 definitely in size by adding layers of these bricks to each of its faces. 

 Conversely, it might be decreased in size by taking away the layers. 



But suppose that the decrease takes place by the regular subtraction 

 of one or several ranges of bricks in each successive layer ; theory, by 

 calculating the number of these ranges required for a particular form, 

 can represent all known forms of crystals and also indicate possible forms 

 for a particular mineral which may not yet have been observed in th 



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