DISTANCE GIVEN BY BINOCULAR VISION. 



No knowledge derived from touch no measurement of real distances no actual 

 demonstration from previous or subsequent vision, that there is a real solid body 

 at M N, and nothing at all at m n, will remove or shake the infallible conviction 

 of the sense of sight that the object is at m n, and that d L or d R is its real dis- 

 tance from the observer. If the binocular centre be now drawn back to M N, the 

 image seen will disappear, and the real object be seen at M N. If it be brought 

 still farther back to/, the object M N will again .disappear, and will be seen at 

 M , as described in a former part of this paper. 



In making these experiments, the observer cannot fail to be struck with the 

 remarkable fact, that though the openings at M N, m n, and /* v, have all the same 

 angular magnitude, that is, subtend the same angle at the eye, viz., d L e, d R g, 

 yet those at m n appear larger than those at M N, and those at p v smaller. If 

 we cause the image m n to recede, and ^ > to approach, the figures in m n will 

 invariably increase as they recede, and those in P will diminish as they approach 

 the eye, and their visual magnitudes, as we shall call them, will depend on the re- 

 spective distances at which the observer, whether right or wrong in his estimate, 

 conceives them to be placed. 



Now, this is an universal fact, which the preceding experiments demonstrate ; 

 and though the estimate of magnitude thus formed is an erroneous one, yet it is 

 one which neither reason nor experience is able to correct. 



When Ave look at two equal lines, whose difference of distance is distinctly 

 appreciable by the eye, either directly, or by inference, but whose difference of 

 angular magnitude is not appreciable, the most remote must necessarily appear 

 the smallest. For the same reason, if the remoter of two lines is really smaller 

 than the nearer, and, therefore, its angular magnitude also smaller from both 

 these causes, yet, even in this case, if the eye does not perceive distinctly the dif- 

 ference, the smaller and more remote line will appear the larger.* 



The law of visual magnitude, which regulates this class of phenomena, may 

 be thus expressed. 



If we call A the angular magnitude of the nearest of two lines or magnitudes 



* MALEBRANCHE seems to have been the first who introduced the apparent distance of objects as 

 an element in our estimate of apparent magnitude. De la Recherche de la Verite, torn. i. liv. i. ; torn, 

 iii. p. 354. See also Bouguer, Mem. Acad. Par. 1755, p. 99. These views, however, have been 

 abandoned by several subsequent writers, and the real distance of objects has been substituted for their 

 apparent distance. VARIGNON, Mem. Acad. Par. 1717, p. 88. M. LEHOT, for example, says, 

 " L' expression de la grandeur visuelle d'un corps est egale a la grandeur reelle, multiplied par le lo- 

 garithme de la distance reelle divisee par cette distance." Nouvelle Theorie de la Vision, \" Mem. 

 Suppl. p. 7, 8. Paris, 1823. This estimate of distance is incompatible with experiment and observa- 

 tion. 



