1882. Malic Trans. IN. VY. Ac. Sez. 
(1873), it is attributed to unconscious comparison with térrestrial objects 
at the horizon. If such be sufficient, there should be no apparent 
enlargement when the rising moon is seen uponacalm 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, 
VITELLION (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 subiect 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 (1759), 
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 e¢ seg. 
