80 LECTURES TO SCIENCE TE AGREES. 



No doubt you are familiar with its principle, which is 

 described in every book treating of drawing. 



There is one pantograph down stairs to which I would 

 call your attention. It is fixed upon a vertical pillar, and 

 under it is a table upon which it moves. It is intended for 

 etching and engraving. 



I had intended explaining another instrument, the 

 planimeter, which is used in surveying, but as there will 

 be a special lecture on that subject, I have no doubt it will 

 be fully explained to you then. 



Before commencing to describe the geometrical models I 

 shall say a word about geometrical drawing and descriptive 

 geometry, in order to impress upon you their use, and 

 almost their necessity, for engineering purposes. I need 

 not tell those who are present, that draughtsmen are daily 

 becoming more and more wanted, and that it is, besides, 

 daily easier to obtain the services of foreigners ; and thus 

 it becomes the more essential that, we, in these countries, 

 should learn earlier the subjects that boys abroad, especi- 

 ally in Germany, are perfectly familiar with. Descriptive 

 geometry, which may be called the theoretical part of 

 drawing, enables us to draw plane figures, surfaces, and 

 solids with their intersections, many of which would be 

 very difficult to represent without its aid. Besides there 

 are its various applications, of which I may enumerate, 

 first, what is called by the French plans cotes, or in English 

 " figured heights," which is the representation of solids on 

 one plane only, the figured heights which are marked on the 

 plan showing the elevation of the various parts. The most 

 important part of this subject is what we call Contouring, 

 which you are no doubt familiar with. By this means, using 

 what are called " figured heights " on the plan, you can 

 delineate with accuracy any particular section of a country. 

 The next application I should mention is that of shadows, 

 or shading, and next comes perspective. 



Besides there is a subject which we rarely treat of here 

 what is called gnomonics, or the construction of sun-dials. 

 It was long considered of great importance, and is 

 still largely used on the Continent. 



Then comes stone-cutting, by which the true surfaces to 

 which the stones are to be worked for architectural 

 purposes are determined, and templates constructed for 



