444- Prof. Chapman on the Identity of 



with all the rest, or (as pointed out to me by my eminent 

 friend Prof. W. Thomson) it becomes apparent as a particular 

 case of a more general proposition, or representing the mo- 

 tion about the successive axes as effected by two equal pyra- 

 mids having a commou vertex at the centre of motion, of 

 which the one is fixed in space, and the other is fixed in the 

 revolving body and rolls over the first, so that the correspond- 

 ing equal faces are successively brought into coincident appo- 

 sition. 



26 LincolnVInn-Fields, 

 November 5, 1850. 



P.S. To find the pole of rotation whereby PQ may be 

 brought into the position P'Q', we may use the following sim- 

 ple construction. 



Measure off from O the node of the great circles (or right 

 lines) containing PQ and P'Q', two distances in the proper 

 direction upon each (four distinct assumptions may be made), 

 say OR and OS equal to one another and to the difference 

 between OP and OF, then the pole of rotation required, 

 say E, is the centre of the circle described about ROS, and 

 the amount of rotation is the angle subtended by OR or OS 

 at E. The writer of this paper suggests that axis of dis- 

 placement would be a convenient term for designating the line 

 whereby any finite change in the position of a body moveable 

 about a fixed centre may be brought about ; a geometrical 

 theory of rotation leading to the investigation of a very curious 

 species of correlation, now opens upon the view, the general 

 object of which may be stated as follows : — 



" Given upon a sphere or plane any curve considered as the 

 locus of successive poles of instantaneous rotation, and the 

 ratio of the rotation about each pole to its distance from the 

 one that follows*, to construct the curve of the poles of dis- 

 placement, and to determine the amount of rotation corre- 

 sponding to each such pole." 



The discussion of this question offers a fine field for the 

 exercise of geometrical taste and skill. 



LIX. On the Identity of Breislakite and Augite. i?^ Edward 

 J. Chapman, Professor of Mineralogy in University College, 

 London j% 



THE Breislakite is well known to occur in minute capil- 

 lary crystals in certain lavas of Vesuvius, and at Capo 

 di Bove near Rome. Its crystalline form has not hitherto 

 * Which by analogy may be termed the "density of rotation." 

 f Communicated by the Author. 



