ON THE DIOPSIDE. ]7 



Tins fignre is analogous to that described in the Journal The angles of 

 i ™ . -i. *■ ** ii' i i a crystal must 



de Physique, May J806, p. 430, as belonging to the regular be accurate iy 



crystals of alalite. The author of the description was aware, ascertained, 

 that, to give an accurate idea of a crystal, the number and 

 position of the faces will not be sufficient, but that the quan- 

 tities of the angles they form with each other must be as- 

 signed; so that if he had contented himself with mentioning 

 the number of sides that form the prism; and the faces that 

 terminate it, he would have given but a very imperfect idea 

 of the crystalline form he wished to make known, as the de- 

 scription would apply to several different figures, on which 



account it would be of little use. However, having had re- ,. , 



. /. i • i which cannot 



course to the goniometer alone, the measures of which arebe done by 



merely approximations, without the assistance of calcula- measure ment 

 tion, he has not sufficiently guarded against the danger of 

 giving angles inconsistent with the principles of geometry, 

 to which the crystallographer exposes himself, who neglects 

 the resources of algebra. Thus the faces M M being ac- 

 knowledged to form a right angle with each other, and the 

 angles of incidence between / M, and / s, or the edge that 

 sometimes occupies'the place of the latter, being given, the 

 third, or inclination of the face adjacent to s, follows neces- 

 sarily. Now on calculating this from the other data in the • 

 Journal de Physique, we find, that the result of the mecha- 

 nical measurement is erroneous by several degrees. 



The descriptions of Rom e-de-F Isle, though in general Rom 4 de risle 



accurate, sometimes exhibit instances of these contradic- some, , ime ^ 



, ii /» l i /» t mistaken from 



tions between the values ot the angles of the same crystal, trusting to the 



This learned gentleman, for instance, after having given 105° g° niometer » 

 as the great angle of the rhombus of inverted carbonate of 

 lime, which he called muriatic calcareous spar, gives 115° 

 for the great angle of the principle section, or that which 

 passes through the oblique diagonals of two opposite faces, 

 and the intermediate edges*. Now if we take the first angle 

 as given, we shall be led by calculation to IQQ°4 for the se- 

 cond, which, makes a difference of more than 5° degrees 



cepted by it toward the point A will be V'ai : v'T; and this inter, 

 cepted part will be to either of the edges, G or H, as I to 5. 



* Ctistallographie, vol, I, p. 520. 



Vol. XXII.— Jan. 1808. C ^ f rom 



