Dr. W. von Bezold on Binocular Vision. 



329 



Taking into consideration the result obtained, that this devia- 

 tion must always be within tolerably narrow limits, it will 

 be seen that these phenomena accord with the principle of 

 identity, if we only consider "identical points'" replaced by 

 u corresponding places." 



The latter construction of the principle is moreover more 

 natural and probable than the older one referring to mathe- 

 matical points. For even in monocular vision points are only 

 seen separate when the distance of their images on the retina 

 exceeds certain limits ; how much more must this be the case 

 for images on separate retinas. Hence the principle in its new 



Fig. 1. 



modification by no means loses in precision ; 

 but when brought into unison with the spe- 

 cial fact just mentioned, it acquires a form 

 which corresponds far better to all physio- 

 logical representations and analogies than 

 the original one. 



The rarity with which double images in 

 general are seen is at the same time ex- 

 plained. For if, taking as a basis limits of 

 distance as determined by experiment*, the 

 geometrical locus of all points seen singly 

 be sought, the so-called " empirical horop- 

 ter," a space of considerable extent, is found, 

 while only those points can appear as a 

 double image which lie within two spaces 

 that tolerably closely enclose the lines of 

 sight. This, as is well known, agrees closely 

 with considerations which some years ago 

 were published by Viethf. 



I have treated the question mathemati- 

 cally for horizontal lines of view KF, K'F, 

 and for a fixed point in the medial plane F, 

 and have utilized in my formula the mea- 

 surements made by Volkmann, Solger, and 

 myself, for the construction of the curves 

 in fig. 1. In this drawing HH is a portion 

 of the mathematical horopter; B, V, and 

 S are the bisections of the external, and 

 B', V, and S' those of the internal ho- 



* If to each eye be presented a vertical pair of lines, of which, however, 

 only one pair consists of two moveable lines, after they have been made to 

 coincide stereoscopically one pair can be altered until coincidence is no 

 longer possible. _ The difference of the distance of the two marks which 

 form each pair is then called the horizontal limiting* distance for a deter- 

 minate fundamental distance (that is, the distance of the two fixed lines). 



t Gilbert's Annalen, vol. lviii. 



