54 SCIENTIFIC APPARATUS. 



exhibit to the student the relations of the object represented to its 

 two projections, and of these to one another. We may refer, 

 among others, to the diagrams and models exhibited by Professor 

 Franz Tilser, of Prague, by Professor O. Reynolds, of the Owens 

 College, Manchester, by the Committee of the Russian Peda- 

 gogical Museum, and by Professor Pigot, of the Royal College of 

 Science for Ireland. 



The epures of descriptive geometry, however accurate, and how- 

 ever useful for constructive purposes, do not offer much assist- 

 ance to the imagination in conceiving complicated geometrical 

 figures. Such assistance, however, is abundantly afforded by 

 stereoscopic representations ; and it is earnestly to be hoped that 

 the applications of stereoscopy to geometry may hereafter receive 

 a much greater development than has been the case as yet. Any 

 polyhedron can (as is well known) be represented with extraordinary 

 beauty by stereoscopy ; the edges only of the polyhedron being 

 drawn on the two faces of the stereoscopic slide. It ought in the 

 same way to be possible to represent any twisted curve ; and 

 further, any developable surface, by representing first the twisted 

 curve which forms its cuspidal line, and then a sufficient number 

 of the straight lines tangent to that curve. Similarly to represent 

 a skew rectilineal surface, it would be sufficient to exhibit stereo- 

 scopically a certain number of its generating lines. Surfaces 

 which are not rectilinear could, theoretically at least, be repre- 

 sented by a sufficient number of their lines of curvature, or by 

 means of their curves of principal tangents, when those curves 

 exist. It must be admitted, however, that the accurate tracing of 

 the plane diagrams which would be required for such representa- 

 tions would be subject to very serious practical difficulties, which 

 it would be desirable to avoid by using special methods adapted 

 to each particular surface ; for example, in the case of the ellipsoid 

 and the other umbilical surfaces of the second order, by employ- 

 ing the two systems of circular sections. 



HENRY J. S. SMITH. 



