MODELLING, PERSPECTIVE, ENGRAVING, PRINTING. .89 



our picture as a reduced copy of a projection formed on an imaginary plane, 

 which, as well as the picture, is generally supposed to he in a vertical situa- 

 tion, and which stands on the horizontal plane, at the point where the 

 ohjects to be represented hegin. In order to find the position of the image 

 of a given right line, we must determine the point in which a line parallel 

 to it passing through the place of the eye cuts the plane of the picture ; this 

 is called the vanishing point of the given line and of all other lines parallel 

 to it, since the image of any such line, continued without limit, will he a 

 right line directed to this point, hut never passing it. When the lines to he 

 represented are parallel to the picture, the distance of their vanishing point 

 becomes infinite, and their images are also parallel to the lines and to each 

 other. The centre of the picture, or that point which is nearest to the eye, 

 is the vanishing point of all lines perpendicular to the picture ; through 

 this point it is usual to draw a horizontal and a vertical line : we may then 

 lay off downwards on the vertical line the distance of the eye from the 

 picture, in order to find the point of distance, which serves to determine 

 the position of any oblique lines on a horizontal plane : for if we draw a 

 ground plan of any object, considering the picture as a horizontal surface, 

 we may find the vanishing point of each of its lines, by drawing a line 

 parallel to it through the point of distance until it meets the horizontal 

 vanishing line. (Plate VII. Fig. 100, 101.) 



In order to find the position of the image of a given point of a line, we 

 must divide the whole image in such a manner that its parts may be to each 

 other in the same proportion as the distance of the given point and of the 

 eye, from the plane 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 ia 

 the point 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 VIII. 

 Fig. 103.) 



The projection of curvilinear figures is most conveniently effected by 

 drawing across them parallel lines, which form small squares or rectangles, 

 throwing these divisions into perspective, and tracing a curve through the 

 corresponding points. There are also methods of determining mathemati- 

 cally, or of drawing mechanically the ellipsis, which results from the 

 projection of a circle, in a given position, but they are considerably intri- 

 cate, 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 mag- 

 nitude, and to give them as much as possible the appearance of an imitation 

 o 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 



