GEOMETRICAL INSTRUMENTS AND MODELS. 53 



they possess a great theoretical interest of their own, since it has 

 been ascertained that the geometry of figures traced upon' these 

 surfaces, is precisely that which the geometry of Euclid would 

 become, if we were to erase from it the assumption known as the 

 eleventh axiom. Models of both these classes of surfaces are 

 contributed by Professor Henrici. 



(5.) Crystallographic Models. 



These are either models of those geometric polyhedra (solids 

 bounded by plane faces) which actually occur in nature ; or they 

 are intended to serve as illustrations of the theory of crystallo- 

 graphy, and to exhibit the relations of the plane faces of a crystal 

 to its crystallographic axes. 







D. REPRESENTATIONS OF FIGURES IN SPACE BY MEANS 

 OF DRAWINGS ON A PLANE. 



We have lastly to refer to modes of representation by drawings 

 on a plane of figures in space. We have here at our disposal the 

 ordinary methods of perspective ; but the practical use of these is 

 too dependent on the hand and eye of the artist to satisfy the 

 requirements of geometrical rigour. The method known as 

 " Descriptive Geometry " is therefore preferred for the purposes of 

 geometrical drawing. This method consists in representing an 

 object in space, by means of its orthogonal projections on two 

 planes at right angles to one another. It therefore can hardly be 

 said to be of recent date, as, in principle, it comes to representing 

 a figure in space by a plan and elevation. But to Monge is per- 

 haps due the idea of placing the plan and elevation on one sheet, 

 and treating them (for the purpose of geometrical construction) as 

 one plane figure ; and to him is certainly due the development of 

 the principles of the method into a complete and scientific system. 

 The volumes of plates which accompany works on descriptive 

 geometry (of which, since the time of Monge, there have been a 

 considerable number) offer copious and varied illustrations of the' 

 method. But models have also been constructed, which serve to 



