BINOCULAR VISION. 377 



distance leads us to give a proportional overvaluation to the rela- 

 tively large visual image made by the near object. 



(b) Mathematical perspective. The outlines of objects before 

 us are projected upon the surface of the eye in two dimensions only, 

 just as they are represented in a drawing. The lines that indicate 

 depth are therefore foreshortened, and lines really parallel tend to 

 converge more and more to a vanishing point in proportion to their 

 distance away from us. When one stands between the tracks of a 

 railway, for instance, this convergence of the parallel lines is dis- 

 tinctly apparent. We have learned to interpret this mathematical 

 perspective correctly and with great accuracy. The use of this 

 perspective in drawings is, in fact, one of the chief means employed 

 by the artist to produce an impression of depth or solidity. For 

 distant objects at least this factor is probably the most potent of 

 those that can be appreciated by monocular vision. 



The importance of the mathematical perspective for our visual judgments 

 may be illustrated very strikingly by a simple experiment. If one takes a 

 biconvex lens of short focus and standing at a window that looks out upon a 

 long street holds the lens in front of the eyes at arm's length he will be able 

 to see, by focusing on the inverted image formed by the lens, that not only 

 are objects inverted as regards their surface features, but, for most persons 

 at least, the perspective is also inverted. Objects actually in the foreground 

 will appear in the background, and one may have the curious sensations of 

 watching persons who. as they walk, seem to recede farther and farther into 

 the distance in spite of the fact that they continue to increase in size. The 

 inverted or pseudoscopic vision thus produced is due undoubtedly to the in- 

 version of the lines of perspective. Parallel lines which, without the lens, 

 would have on the retina a projection of this kind /\ are with the lens projected 

 inverted \/, and our visual judgments are controlled by this factor in spite 

 of the opposing evidence from the size of the retinal images. In order for 

 the experiment to succeed it is necessary that the objects viewed shall be far 

 enough away so that a flat picture may be given by the lens, that is, a pic- 

 ture in which the foci for the near points shall not differ practically from those 

 of more distant points, otherwise the muscular movements of accommodation 

 interfere with the delusion. The relative importance of this last factor 

 (see succeeding paragraph) is well illustrated by varying the experiment in 

 this way: Place two objects upon a well-lighted table, one at the near end 

 and one at the far end. Then standing close to the table view these objects 

 through the lens as before. They will be seen in their right relations to each 

 other. If, however, one backs away from the table while watching the images 

 there will come a distance at which the near object will be seen to shift around 

 to the rear of the far object. 



(c) The Miiscle Sense (Focal Adjustment). For objects near 

 enough to require accommodation it is obvious that the nearer 

 object will need a stronger contraction of the ciliary muscle, and 

 also of the internal rectus in order to bring the line of sight to bear 

 correctly. By means of the fibers of muscle sense we have a verv 

 exact conception of the degree of contraction of these muscles, and 

 this sensation is perhaps the most important factor used in making 

 our monocular judgments of depth for objects at a short distance 



