BINOCULAR VISION. 345 



which give us an idea of solidity far more real than can be obtained 

 with one eye alone. This difference is shown especially in the 

 combination of stereoscopic pictures, and in ordinary vision when 

 the light is dim, as in twilight, or in exact judgments of perspective 

 in the case of objects close at hand. If, for example, we close one 

 eye and attempt to thread a needle, light a pipe, or make any similar 

 co-ordinated movement that depends upon an exact judgment of 

 the distance of the object away from us, it will be found that the 

 resulting movement is far less perfectly performed than when two 

 eyes are used. The sensation elements upon which our judgments 

 of depth or perspective are founded may be classified as follows :* 



The Monocular Elements. That is, those that are experienced 

 in vision with one eye. (a) Aerial perspective. The air is not en- 

 tirely transparent, and, therefore, in viewing landscapes the more 

 distant objects are less distinctly seen, as is illustrated, for instance, 

 by the haze covering distant mountains. This experience leads us 

 sometimes to make erroneous judgments when the conditions are 

 unusual. An object seen suddenly in a fog looms large, as the 

 expression goes, since the feeling that hazy objects are at a great 

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

 tively large visual image made by the near object. 



(6) 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, 



* See Le Conte, "Sight," vol. 31 of "The International Scientific Series," 1881. 



