298 Analysis of Scientific Books, 



the crystalline forms of zircon, sulphur, and other minerals. He 

 next treats of the order in which the faces lie in a perfect crystal, 

 and the determination of such faces as are adjacent or otherwise. 

 To this end he conceives an ellipsoid inscribed within the crystal, 

 having for its three axes the three most remarkable lines in the 

 primitive form, and by means of the well-known equation of the 

 second degree representing such an ellipsoid, combined with the 

 equation of any proposed face, he deduces the longitude and lati- 

 tude (on the surface of the ellipsoid) of the point at which it would 

 be touched by a plane parallel to such face. The results are in- 

 cluded in general and explicit formulae, by whose application in 

 any proposed case the sequence and arrangement of the faces in 

 the perfect crystal is readily discovered. 



The angles made by edges of the secondary form are next in- 

 vestigated, after which the author, having recapitulated his results, 

 takes occasion to refer to a paper by Mr. Levy, who had previ- 

 ously, but unknown to Mr. Whewell, employed the representation 

 of a secondary plane by its equation referred to the three princi- 

 pal edges of the primitive form, but only in a particular case, 

 whereas the investigations and notation in the present paper are 

 absolutely general. 



In the course of this paper Mr. Whewell instances the applica- 

 tion of his analysis in the solution of the following problems :— 



Knowing the dihedral angles of the secondary rhomboid, to find 

 the symbol of its faces, or their laws of decrement. 



To find what laws of decrement give a secondary rhomboid 

 similar to the primary one. 



Knowing the lateral angles made by the planes of any bi-pyra- 

 midal dodecahedron, to find the symbols. 



Knowing the angles made by any plane with two primary 

 planes, to find its symbol. 



To find what laws give prisms parallel to the axis of the rhom- 

 boid. 



To find the symbol of a plane which truncates the edge of any 

 secondary rhomboid. 



V. Explanation of an Optical Deception in the Appearance of the 

 Spokes of a Wheel seen through Vertical Apertures. By P. M. 

 Roget, M.D., F.R.S. 



The optical deception here described is that which people see 

 when they chance to look at a revolving carriage-wheel through 

 the upright bars of a window-blind, or railings, or any similar 

 series of fixed vertical obstacles ; in such a case, all the spokes, 

 except such as happen to be perpendicular, appear curved, the 

 convexity being always turned downwards. 



A certain degree of velocity in the wheel is necessary to pro- 

 duce ^his deception, and if this be gradually communicated, the 



