198 



nicety of Mr. 

 Haiiy's mea- 

 surements. 



Dodecaedral 

 sulphuret of 



Not the regu- 

 lar dodecae- 

 dron, as sup- 

 posed b> Wer 

 ner and I'lsle. 



ON THE MEtONlTf., 



cuvac}' of tlie measures given ia the work of Mr. Haiu'. It is 

 in p. 39 of the first volume of his Trade de Mineralogic. 

 Among the number of forms exhibited by sulphuret of iron 

 may be observed the dodecaedron with pentagonal faces. 

 This crystal is divisible parallel to the sides of a cube; which 

 is the form of its nucleus, and at the same time that of its 

 integrant molecules, which perform the functions of sub- 

 tractive molecules. On each face of the primitive cube two 

 simultaneous decrements are supposed to take place in the 

 additional laminae; one of two rows in breadth, setting 

 out from two opposite edges; and one of two rows in 

 height, setting out from the other two edges of the sam« 

 face. The decrements that take place on the faces contigu- 

 ous to the nucleus follow the same laws, and in directions 

 crossing each other, so that the slower decrement on one face 

 answers to the move rapid decrement on that contiguous to 

 it. The nature of the decrements, added to the direction 

 of the laminse, gives rise to a new polyedron ; the faces of 

 which, becoming level with each other in pairs, are reduced 

 to twelve, instead of twenty-four. The sulphuret of iron has 

 assumed the form of a dodecaedron with pentagonal faces. 

 But it is possible to conceive an infinite number of these 

 dodecaedra, by varying the respective angles of incidence of 

 the contiguous pentagons. What then is the dodecaedron of 

 the sulphuret of iron } is it the regular pentagonal dodecae- 

 dron of geometricians? So two learned natural philosophers, 

 . Werner and Rome de I'Jsle thought : but it is strictly de- 

 monstrated by algebra, that such a polyedron cannot result 

 from any law of decrement. The angle of incidence be- 

 tween two contiguous pentagons at a given edge common to 

 both alone determines all the other angles; and it is demon- 

 strated algebraically, that, in the case of decrement of whicli 

 we are speaking, this angle must be 126° 51' 8". Now, on 

 measuring with the goniometer the angle that occurs in the 

 sulphuret of iron, it is found to be nearly l^?^; and from 

 this agrement of the calcvilation with what is actually ob- 

 served I infer, that the existence of the law of decrement is 

 confirmed. Such is the rigorous method, in which Mr. 

 Haiiy constantly proceeds, when he applies his theory to the 

 structure of crystals, to determine species in mineralogy. 



11. Meionitf, 



