90 LECTURE XL 



other. In order to represent 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 he parallel, and 

 another for that of the point of distance, hy means of which we may 

 measure the first lines, #s 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.) 



If we wish to apply the mechanical method of drawing by the assistance 

 of a frame to this mode of representation, instead of a fixed aperture for a 

 sight, or a second frame of smaller dimensions, we must employ a second 

 frame of the same magnitude with the first, in the manner which has 

 already been described. Professor Camper* has censured Albinus for not 

 adopting this method in his figures : but subjects so large as those which 

 he has represented would have had less of the appearance of nature, if they 

 had been projected orthographically, nor would such projections have been 

 materially more instructive. 



It frequently happens, that in geographical and astronomical drawings 

 we have occasion to represent, on a plane, the whole or a part of a spherical 

 surface. Here, if we employ the orthographical projection, the distortion 

 will be such that the parts near the apparent circumference will be so much 

 contracted as to render it impossible to exhibit them with distinctness. It 

 is, therefore, more convenient, in this case, to employ the stereographical 

 projection, where the eye is supposed to be at a moderate distance from the 

 object. The place of the eye may be assumed either within or without the 

 sphere at pleasure ; and according to the magnitude of the portion which 

 we wish to represent, the point, from which the sphere may be viewed with 

 the least distortion, may be determined by calculation. But in these cases 

 all circles obliquely situated on the sphere must be represented by ellipses : 

 there is, however, one point in which the eye may be placed, which has the 

 peculiar and important advantage, that the image of every circle, greater or 

 lesser, still remains a circle. This point is in the surface itself, at the 

 extremity of the diameter perpendicular to the plane of projection ; and 

 this is the point usually employed in the stereographical projection of the 

 sphere, which serves for the geometrical construction of problems in spheri- 

 cal trigonometry. The projection of the whole surface of the sphere would 

 occupy an infinite space, but within the limits of the hemisphere, the 

 utmost distortion of the linear measure is only in the proportion of 2 to 1, 

 each degree at the circumference of the figure occupying a space twice as 

 great as at the centre. The angles, which the circles form in crossing each 

 other, are also correctly represented. (Plate VIII. Fig. 106.) 



For projecting figures on curved or irregular surfaces, the readiest method 

 is to trace cross lines on them, with the assistance of such a frame as has 

 been described for drawing in perspective, representing the appearance of 

 uniform squares or rectangles, and to delineate in each of these the corre- 

 sponding parts of the object, or of the drawing which serves as a copy. . 



The arts of writing and drawing, in all their varieties, are extended in 



* Cogan's Translation of Camper, on the connection between Anatomy and the 

 Arts of Painting, Sculpture, &c. 4to, Lend. 1794. 



