36 Theory of CryJIallization. 



menfe number of facts, formerly unconnected, now become 



arranged, as if of themfelves, around a fingle one on which 



they depend, and which ferves to conned them all by mutual 



relations. 



I confefs, however, that this theory can be well underftood 

 only by the help of analytical calculations *. Befides the 

 advantage which analyfis has of involving in the fame for- 

 mula the folutions of an infinite number of different pro- 

 blems, it alone can give to the theory the character of abfo- 

 lute certainty, by producing refults perfectly agreeable to 

 thofe we receive from obfervation. 



Notwithstanding thefe confiderations, I thought it would 

 be better for thofe unacquainted with the fcience of calcu- 

 lation, if I adhered to fimple reafoning, accompanied by 

 geometrical figures, which are fo ufeful in aflifting the ima- 

 gination to conceive the arrangement of thofe fmafl folids 

 that concur to form a cryftal, but which were wanting to 

 the firll paper* • 



This arrangement I call Jlruclure, as oppofed to the term 

 trganizatiotty which expr-effes the far more compound me- 

 chanifm of animals and plants. 



If this procedure be lefs direct, Iefs expeditious, and left 

 precife ; and if it requires us to attend to thofe details 

 which algebra pafles over in order to conduct; os fpeedily 

 to its object, it is at leaft attended with this advantage, 

 that the mind by its means perceives better the connexion of 

 the different parts of the whole under its confideration. 



I. Mechanical Divifwn of Cryjlals. 



It is known that the fame mineral fubftance is fufceptiblc 

 of many different forms well denned, fome of which do not 

 prefent, on the firfl view, any common point of refemblancc 

 that feems to indicate their relation. If we compare, for 

 example, calcareous fpar in a regular hexaedral prifm with 



f S# Mcmoues de l'Acad. d«s Sciences, An 1790, 



the 



