Brewster's Theory of Binocular Perspective. 437 



which shall appear at a given distance in the stereoscope in 

 their true relief." This table is constructed from the following 

 formula* (" a denoting the distance between the two eyes, 

 and 6 the inclination of the optic axes "): — 



D = J a cot \ 6. 



From this formula it is obvious that if the axes become 

 parallel, D becomes infinite; if divergent, D becomes negative. 

 Wheatstone makes no reference to the attainment of optic 

 divergence; but his stereoscope was constructed in such man- 

 ner that the visual lines might be made parallel. Of the 

 images thus produced he notes as a peculiarity"!"; " although 

 the optic axes are parallel, or nearly so, the image does not 

 appear to be referred to the distance we should, from this cir- 

 cumstance, suppose it to be, but it is perceived to be much 

 nearer." 



These apparently contradictory statements of Wheatstone 

 show how difficult it is to interpret our sensations when the 

 conditions attendant upon normal vision are disturbed. Wheat- 

 stone notices the distortion of perspective produced by making 

 the angle between the camera axes different from that between 

 the visual lines when the stereograph is viewed %\ but in this 

 connexion he does not mention any apparent change in dis- 

 tance of the picture as a whole. 



In 1844, Sir David Brewster published a paper § " On the 

 Knowledge of Distance given by Binocular Vision," in which 

 he elaborated the idea that apparent distance is determined by 

 intersection of visual lines, giving an interesting geometric 

 discussion of the subject, and describing many experiments 

 performed without the aid of the stereoscope. The intersec- 

 tion of the visual lines he calls the binocular centre; and for 

 its distance from the card on which the conjugate pictures are 

 drawn he deduces a formula, the discussion of which leads to 

 results identical with those deduced from Wheatstone's for- 

 mula. In his paper relating to the lenticular stereoscope ||, 

 and other forms of the instrument devised by him, he fre- 

 quently refers to the external intersection of axes coincident 

 in direction with the rays after refraction or reflection, but 

 makes, no reference to divergence of visual lines. 



The theory of apparent distance of objects perceived in the 

 stereoscope, to which Wheatstone, and especially Brewster, 

 gave prominence, has been abundantly reproduced in our 

 text-books on Physics ; indeed it is expressed either directly 



* Phil. Mag. p. 512 (1852). f Ibidem, p. 514. \ Ibidem, p. 512. 

 § Edinburgh Transactions, yoI. xv. p. 663 (April 1844). 

 H Phil. Mag. Jan. 1852, p. 16. 



