APPRECIATION OF DISTANCES. 



285 



distance from the eye, shuts off the sun, although its diameter is eight 

 hundred and eighty-eight thousand miles. The sun and moon, again, 

 by subtending nearly the same visual angle, appear to us of nearly the 

 same size ; and the illusion persists in spite of our being aware of the 

 mathematical accuracy, with which it has been determined, that the 

 former is ninety-six millions of miles from us, and the latter only two 

 hundred and forty thousand. The visual angle, again, subtended by 

 an object, differs greatly according to the position of the object. A 

 sphere has the same appearance or bulk, when held at a certain dis- 

 tance from the eye, whatever may be the position in which it is viewed ; 

 and, accordingly, the visual angle, subtended by it, is always identical. 

 Not so, however, with an oval. If held, so that the rays from one of 

 its ends shall impress the eye, it will occasion a circular image, and 

 subtend a much smaller angle than if viewed sideways, when the image 

 will be elliptical, or oval. The same thing must occur with every 

 object, whose longitudinal and transverse diameters differ. It is 

 obvious, that if any such object be held in a sloping position towards 

 the eye, it will appear more or less shortened; in the same manner as 

 the slope of a mountain or inclined plane would appear much greater, 

 if placed perpendicularly before the eye. This appearance is what is 

 called foreshortening ; and it may be elucidated by the following figure. 

 Suppose a man to be standing on a level plain, with his eye at c (Fig. 

 128), looking down on the plain. The portion of the surface a d, which 

 is next to him, will be seen without any foreshortening ; but if we sup- 

 pose him to regard succes- 

 sively the portions df,fg, 

 and g b of the plain, the 

 angle, subtended by each 

 portion, will diminish; so that 

 if the angle a c d be 45, d 

 c/will be I8,fcff 8, and 

 so on; until, at length, the 

 obliquity will be so great, 

 that the angle becomes inappreciable. This is the cause why, if 

 we look obliquely upon a long avenue of trees, we are unable to 

 see the intervals between the 

 farthest in the series ; although 

 that between the nearest to us 

 may be readily distinguished. 

 In all paintings, of animals 

 especially, the principle of fore- 

 shortening has to be rigidly 

 attended to; and it is owing to a 

 neglect of this that we see such 

 numerous distorted representa- 

 tions of the human figure 

 especially. It has been already 

 stated, that objects appear 

 smaller according to their dis- 

 tance; hence, the houses of a Perspective. 



Fig. 128. 



Foreshortening. 



Fig. 129. 



