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XVI. On the Forms of Sulphur et of Nickel and other Substances. 

 By W. H. Miller, M.A., Fellow and Tutor of St, John's 

 College and Professor of Mineralogy in the University of 

 Cambridge,* 



T F a sphere be described round any point in a crystal as a 

 -■- centre, and if radii be drawn perpendicular to the faces of 

 the crystal, meeting the surface of the sphere in points, which 

 we shall call the poles of the corresponding faces, the supple- 

 ment of die angle between any two faces will be measured by 

 the arc joining their poles; and if any number of faces lie in the 

 same zone, their poles will lie in the same great circle : also, 

 the supplement of the angle between the intersections of any 

 face with each of two other faces will be equal to the angle 

 contained by the great circles drawn from the pole of the 

 former face through the poles of the two latter. Hence, a 

 sphere having the })oles of the faces of a crystal mapped upon 

 its surface in the manner above described, or its projection, 

 will serve to determine the form and relative positions of the 

 faces of a crystal. This method of representing crystalline 

 forms, the invention of which is due to Professor Neumann of 

 Konigsberg, will be used to illustrate the crystallographical 

 notices which follow. 



The degrees and minutes express the values of the arcs 

 joining the poles of the faces, or the supplements of the angles 

 between the faces themselves. 



The symbols of the faces are expressed in the notation pro- 

 posed by Mr.Whewell, in a memoir published in the Philo- 

 sophical Transactions for 1825, and of which an account is 

 given in the Encyclopaedia Metropolitana, Art. Crystallo- 

 graphy. The chemical notation and atomic weights are taken 

 from the fifth edition of Dr. Turner's Chemistry. 



Sulphuret of Nickel. Ni + Su. — The crystals of this mi- 

 neral belong to the rhombohedral system, and usually occur 

 in very slender hexagonal prisms, which, when broken across, 

 exhibit the feces O, Q, R, S, V : one crystal was terminated 

 by dull faces T, forming an acute rhombohedron. In order, if 

 possible, to determine the value of O T, the crystal was fixed 

 to a ruler so that the faces M T were perpendicular to the 

 plane of the ruler, and placed under a compound micro- 

 scope having a fine wire stretched in the focus of the eyepiece. 

 The ruler was then turned round in its own plane till the 

 images of M T seen edgeways coincided successively with the 

 wire, and the position of the ruler at each observation marked 

 by a line drawn along its edgQ on a table; the angle contained 



* Communicated by the Author. 



