1 882. Jl^ Trans. N. V. Ac. Set. 



(1873), it is attributed to unconscious comparison with terrestrial objects 

 at the horizon. If such be sufficient, there should be no apparent 

 enlargement when the rising moon is seen upon a calm ocean ; but this 

 is the condition under which the phenomenon is really most striking. 

 For the following brief sketch of the views that have been held, I am 

 indebted mainly to Helmholtz.' 



The first opinions put forth on the perception of the third dimension 

 in space were in connection with these differences of apparent size of 

 the moon. 



Ptolemy (A.D. 150) said that the mind judges of the size of objects 

 in accordance with the previous appreciation of their distance ; this 

 would appear greater when there are many intervening objects, since 

 this occurs when the heavenly bodies are near the horizon. Neverthe- 

 less, he elsewhere attributes the enlargement to the refraction of rays 

 by vapors. 



Alhazen (1038) refutes the latter opinion and returns to the first. 

 He is followed by Roger Bacon, and opposed by Baptista Porta. 



VlTELLlON (1271) accords with Alhazen. and observes addition- 

 ally that the whole celestial vault appears more elongated horizontally 

 than toward the zenith. 



Keppler (1604), whose opinion was adopted by Descartes, said 

 that the distance between the two eyes is the base which we employ in 

 measuring the distance of objects. We have here the first enunciation 

 of the binocular theory afterward so emphasized by Brewster. 

 Keppler adds that since, in making measurements with the two eyes, 

 we learn to make them with the single eye, the magnitude of the 

 heavenly body, as perceived in the eye, would serve as a base for dis- 

 tances relatively slight. We furthermore appreciate different degrees 

 of light, and practically compare the size of an object with its dis- 

 tance, since we know by experience how much to extend the hands or 

 to advance toward an object to touch it. Keppler thus knew the 

 most important elements of the appreciation of distance, aside from 

 that of dissimilarity of images. 



The subject has been further considered by Gassendi (1658), 



HOBBES (d. 1679), MOLYNEUX (1687), DE La HIRE (1694), PERE 



GouYE (1700). Berkeley (1709), R. Smith (1728), Logan (1736), 



DESAGULIERS (1736), BOUGUER (1755), PORTERFIELD (l7S9)r 



Samuel Dunn (1762), Malebranche (1764), Lambert (1765) and 

 EuLER (1768). 



The opinions expressed by these writers need not be repeated, ex- 

 cept to say that Berkeley insisted upon the dim and pale aspect of 



5. Optique Physiologique, p. 870 et seq. 



