88 Mathematical Principles of Chemical Philosophy/. [Feb. 



of solid crystals, which are evidently formed by the application 

 of the above bases upon each other ; and in this, the particles 

 follow the same order of arrangement as in the bases themselves. 

 Thus in fig. 3, by the application of a number of equal and 

 similar bases upon each other, is formed a rhomb : if the bases 

 decrease continually in magnitude, the resulting figure is a qua- 

 drilateral pyramid. From fig. 5, results the cube, quadrilateral 

 Erism havmg equal sides, or the octohedron : from fig. 5, the 

 exagonal prisms and pyramids. The reason is nou^ evident 

 why the bases of different ciystals are so variously inclined to 

 their sides, for the base, which is obtained by splitting a crystal 

 entirely through its thickness, is evidently formed by the union 

 of regular rows of particles, prop. 13 ; so that having given the 

 angles of the nucleus, its position in, and the number ofsides of, 

 the crystal, it is easy to determine its entire structure. It is 

 obvious that what has been said applies only to crystals of 

 simple matter, or such compounds as consist of particles which 

 have the same magnitude. When the nature of combination has 

 been examined, a still more numerous class of external forms 

 will be exhibited, which, together with the former, will compre- 

 hend almost every variety found in nature, by the arrangement 

 of spherical particles only. It may be objected, that the angles 

 of crystals should undergo a change by the application of heat : 

 we must, however, recollect that in the elementary parallelogram 

 the smaller angle is just 60° at the absolute zero of temperature, 

 in a simple substance, and 90° at most, when, on the point of 

 fusing ; therefore, only a very small change can be expected by 

 e>en a very considerable variation of temperature ; yet from 

 certain experiments that I have made on this subject with some 

 highly infusible matters, it is evident that this change does 

 really take place ; but from the great differences which exist in 

 the cohesive force in the several parts of the same crystal, the 

 effect is considerably irregular. The results of these experi- 

 ments will appear at a future opportunity. 



We may now see the reason why alum, most of the metals, 

 and some other substances, which are formed in masses desti- 

 tute of any symmetric appearance, by slow solution, &c. present 

 an internal crystallization, as has been fully proved by the 

 researches of Mr. Daniel. 



{To be continued.) 



