ON MODELLING, PERSPECTIVE, ENGRAVING, AND PRINTING. 117 



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 re- 

 presented would have had less of tlie appearance of nature, if they had been 

 projected orthographically, nor Avould 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 si- 

 tuated 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 im- 

 portant advantage, that the image of every circle, greater or lesser, still re- 

 mains a circle. This point is in the surface itself, at the extremity of the di- 

 ameter 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 spherical trigonometry. The pro- 

 jection 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 mea- 

 sure 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. rig. 106.) • • 



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



