the Abbs' Haiti/* s Theories of Crystallography. 225 



genuity, inferior to few ; and the mathematical skill and 

 industry of its author are entitled to the greatest applause. 



" But what we consider as the most important part of 

 that philosopher's labours, is the method which they point 

 out of discovering the figure of the integrant particles of 

 crystals; because it may pave the way for calculating the 

 affinities of bodies, which is certainly by far the most im- 

 portant part of chemistry. This part of the subject, there- 

 fore, deserves to be investigated with the greatest care." 



But I return to the point whence this digression carried 

 me, — to the vacuities left between the integrant particles in 

 the construction of a primitive form. The Abbe considers 

 them as filled either by the water of crystallization or by 

 some other substance. Is it not an admissible supposition 

 that this other substance is composed of the same elements 

 as the integrant particles, but in different proportions ? At 

 least, such is the conclusion I should be tempted to draw 

 after reading Berthollet's excellent Researches on Affinities. 



1 shall now proceed to the laws of formation in secondary 

 srvstals. It is easy to deduce them from these two facts: 

 viz. 1st, That the sides of the secondary crystals are planes; 

 2dly, That they divide by smooth sections parallel to the 

 Slides of their primitive form. 



Let us take a rhomboid of carbonate of lime for example. 

 If on one of the sides of the rhomboid I wished to raise a 

 pyramid, I should lay lamina of rhomboidal particles upon 

 each other. These laminae would decrease in surface until 

 the last is reduced to a single rhomhoid. Thus the second 

 lamina contains fewer particles than the first, the third 

 fewer than the second, and so on. As the faces of these 

 pvramids are always to be planes, the successive decrements 

 of the lam: me must be equal ; that is to say, the second la- 

 mina is less by one range in every direction than the first, 

 and the third than the second, Sec. If the decrement is 

 more rapid ; that is to say, if two or three ranges are sub- 

 tracted in the second lamina, the same number will be sub- 

 tracted from the third, and so on successively till the pyramid 

 is completed. As the sections are to be smooth, the joints 

 must form one continued plane ; therefore the ranges and 

 even the particles at the joints must not encroach on each 

 other : hence, it follows that the number of ranges succes- 

 sively subtracted from each lamina can never be incommen- 

 surable ; that is to say, the decrement may be I, 2, 3, 4, 

 &c; but never \/2, s , 3, Sec. 



These are the decrements parallel to the edges, or, as th<$- 

 Abbe colls thexaj decrements on the edges. But they may 



take 



