^56 SDLPHUUET OF LEAD, COPPER, A&D ANTtMO*!*. 



same ratio of 3 to 5 accords better with the customary di- 

 mensions of* the crystals of this substance, almost all these 

 Crystals exhibiting this proportion between their height and 

 breadth, while I have not yet found one in the proportion 

 of 2 to 5 : in determining the ratio of the height, or side of 

 the primitive prism to the side of its terminal faces, 1 fix 

 ou the proportion of 3 to 5, to which I was before guided 

 by the observation of the retro-gradations that take plate 

 along the edges of the terminal faces. In consequence I 

 Conclude, that the primitive crystal of endellion is a rectan- 

 gular tetraedral prism, the height of which is to the edges 

 of the terminal faces in the ratio of 3 to 5. 



I have not hesitated to give with considerable minuteness 



the method I pursued in determining the primitive crystal 



of this substance:; in the first place because it renders the 



Royal Society better acquainted with the grounds on whichr 



it is established, and shows, that this determination is by 



no means the result of an opinion adopted at first sight, or 



Theiktermi- of a slight observation of a single crystal merely: and se- 



jnUive crystal " ron&ry, because these details show how simple and easy 



■with sufficient such determinations are, when nature supplies us with suf- 



a, a sinip e ficient data, and at the same time how far the calculations 

 process. ' 



they require are from being complicated*. The same may be 

 said of the calculations foi determining the planes produced 

 in crystals by retiogradations of the crystalline laminae: they 

 never require any thing more than the resolution of a trian-* 

 gle, for which there are always sufficient data. I think I may 

 affirm, that, by means of the method given in my Treatise 

 on Mineralogy ; and the use of the protractor with a mova- 

 ble radius, which I have likewise made known, and which 

 greatly abridges the trials we are sometimes obliged to 

 make, for determining from the angles of incidence of 

 the secondary planes of the crystals the nature of the retro- 

 gradations calculated to give rise to them; there exists no 



* Additional note. This method having never yet been given in any 

 ■work on mineralogy in so simple and easy a manner, and besides the 

 Philosophical Transactions hitherto containing little on the subject of 

 crystallography were farther inducements for me to enter into these 

 particulars. To me it appears, that they cannot but render this paper 

 more interesting. 



science, 



