Il6 LECTURE Xr. 



other, in tlie same proportion as the distance of the given point, and of tl)e 

 eye, from the plarie of projection. This may be readily done, when a ground 

 plan has been first made, by drawing a line from any point in the plan, to 

 the point of distance, which will cut the whole image of the line in the poitit 

 required. (Plate VII. Fig. 102.) 



When it is required to determine a point in a line parallel to the picture, 

 we may suppose a line to be drawn through it perpendicular to the picture, 

 and, by finding the image of this line, we may intersect the former image in 

 the point required. It is thus that the height of any number of columns, or 

 'figures, at different distances, may be readily determined. (Plate VIIL 

 rig. 103.) 



The projection of curvilinear figures is most conveniently effected, by draw- 

 ing across them parallel lines, which form small squares or rectangles, throwing 

 these divisions into perspective, and tracing a curve through the correspond- 

 ing points. There are also methods of determining mathematically, or of 

 drawing mechanically the ellipsis, which results from the projection of a circle, 

 in a given position, but they are considerably intricate, and a steady hand is 

 seldom in want of them. (Plate VIII. Fig. 104.) 



This system of perspective must necessarily be employed when we wish to 

 represent objects, which appear to us under angles of considerable magnitude, 

 and to give them as much as possible the appearance of an imitation of nature. 

 But for almost all purposes of science, and of mechanical practice, the most 

 convenient representation is the orthographical projection, where the distance 

 of the eye, from the plane, is supposed to be increased without limit, and the 

 rays of light passing to the eye to be parallel to each other. In order to re- 

 present any object in this manner, we must assume one line for the direction 

 of the centre of the picture, to which the images of all lines perpendicular to 

 the plane of projection must be parallel, and another for that of the point of 

 tlistance, by means of which we may measure the first lines, as if that point 

 were actually within reach; and in this manner we may determine the place 

 of any number of points of the object to be delineated. (Plate VIII. 

 Fig. 105.) 



