Distance given hy Binocular Vision. 317 



recede, and those in ju-v v/ill diminish as ihey approach the eye, 

 and their visual inagnitiides, as we shall call them, will depend 

 on the respective distances at which the observer, whether 

 right or wrong in his estimate, conceives them to be placed. 



Now this is a universal fact, which the preceding experi- 

 ments 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 we look at two equal lines, whose difference of di- 

 stance 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 mag- 

 nitude also smaller from both these causes, yet, even in this 

 case, if the eye does not perceive distinctly the difference, the 

 smaller and more remote line will appear the larger*. 



The law of visual magnitude, which regulates this class of 

 pheenomena, may be thus expressed. 



If we call A the angular magnitude of the nearest of two 

 lines or magnitudes whose apparent distance is d, a the an- 

 gular magnitude of the remoter line, whose apparent distance 

 is D, and V, v the visual magnitudes of the two lines, then 



V:u=AxD:axD. 



Now let the two lines MO, NP be the two sides of a qua- 

 drilateral figure seen obliquely by an eye at E, then, if the 

 apparent distances of MO, NP are such, that 



A X ^ > « X D, then V > u, 



and the lines MN, OP will converge to a vanishing point 

 beyond NP. But if 



A xrf=flXD, then V=u, 



and the line MN, OP will appear to be parallel. And if 



A X ^ < a X D, then V < y, 



* Malebianche seems to have been tlie first who introduced t\\e ajijyarent 

 distance of objects as an element in our esiliniate of apjmrcnl nia<;nitude. 

 IJc la Recherche dc la Vcrilr, torn. i. liv. i. ; torn. iii. p. 354. See also 

 Bouguer, M<'m. Acad. Par. 1755, p. 91). These views however have been 

 abandoned i)y several siibsctjuent writers, and the real distance of objects 

 has been substituted for tiieir upparenl thstance. Varignon, Mim. Acad. 

 I'ar. 1717i p. ^H. M. Lehot, for example, says, " L'expression de la gran- 

 deur visuellc d'un corps est (''gale a la grandeur rcelic, inultipiiec par Ic 

 logarithnie de la distance rt'el/c diviscc par cettc distance." — Nouvcllc 

 Tlii'iirie de la Vision, ler Mem. Suppl. p. 7, H. Paris, 1823. This estimate 

 of distance is incompatible with experiment and observation. 



