Mr. Shepard's reply to Prof. Del Rio. 321 



as with Breithaupt, who derives them all from the octahedron,* and 

 the reason I have followed the former in preference to the latter, or 

 others who have admitted different intermediate numbers, is because, 

 such a view of the subject is the most simple, and the least encum- 

 bered by geometrical constructions and mathematical calculations. 

 Repeated observation moreover has convinced me, that the refer- 

 ence of crystals to their primary forms, according to the system of 

 Brooke, is anything but a difficult problem. 



And respecting the case of the sulphuret of manganese, the forms 

 are indeed incompatible on every view except that of Breithaupt, 

 with whom also they would be irreconcilable as existing in one and 

 the same mineral species. For myself, though I have never seen 

 the Mexican mineral, I should have very little doubt that it con- 

 stitutes a distinct species; a supposition which is favored somewhat 

 by the fact, that while neither Klaproth nor Vait^uelin could find 

 above 17 per cent of sulphur in the European mineral, Del Rio de- 

 tected 36*77 in tliat from Mexico. 



The statement concerning IMitscherlich's observations, I sup- 

 pose alludes to his law of Isomorphism, as I know of no other dis- 

 covery of this philosopher at all affecting the subject. But as it 

 happens, this law instead of affirming that the same species ever as- 

 sumes two forms, (incompatible orles) declares that although one in- 

 gredient in the composition is replaced by an equivalent portion of 

 some similar ingredient, the form remains the same. For example 

 crystals of Pyroxene, from different localities, present the same an- 

 gles, when besides the silica essential to them all, they contain either 

 49-04 of protoxide of manganese, and 3-12of lime; or 2219of lime 

 17-38 of protoxide of iron, and 4-99 of magnesia ; or 23-57 of lime, 

 16-49 of magnesia, and 4-44 of protoxide of iron ; or 20-87 of lime, 

 and 26-08 of protoxide of iron; or finally, 24-76 of lime, and 18-55 

 of magnesia. 



Or if the angle is not the same among isomorphous compounds, 

 (though the name of the law signifies that it is.) as in the instances 

 of the carbonates of lime, magnesia, protoxide of manganese and of 

 iron, where the primary form is the same in figure, but differing by a 

 degree or two in the dimensions, (homoiomorphous bodies,) in these, 

 the discrepancy in the angle is invariably attended with a difference 



• The axis being in the regular octahedron 7*20, and in other cases greater or 

 less. 



Vol. XXVII.— No. 2. 41 



