which occasionally impose upon us in estimating magnitudes. Thus a person of an ordinary height standing very near a very tall one, or coming in at a very high door, appears shorter than the truth; lean persons seem tall, fat persons short, &c.
The principal criterion of distance is the magnitude of the picture, which some known object makes on the retina. But the five following associated circumstances seem to have also some influence on our judgments concerning distance, in certain cases, and under certain limitations: the number of objects which intervene, the degree of distinctness in which the minute parts are seen, the degree of brightness, the inclination of the optic axes, and the conformation of the eye. It will appear from the sixty-second and sixty-third propositions that the two last are associates to each other in their proper degrees, since each depends on the distance of the object. The influence of the three first, as well as that of the magnitude of the picture on the retina, is evident from the methods of expressing distance in pictures.
From the principles laid down in the last paragraph, we may explain the following fallacies in vision. An object viewed through a perspective appears to be nearer than it is, because the picture on the retina is thereby rendered both larger, and more distinct; but if we invert the perspective, and so diminish the picture, the object will appear farther off. At sea, and on plains, where few or no objects intervene, we judge the distances to be less than the truth; and the contrary happens in scenes diversified with a proper variety of objects. A large object, when apprehended to be one of a common size, appears nearer than the truth; and the same happens, when we view objects in rural scenes, such as houses, towns, hills, &c. in a bright light, or through a very clear atmosphere. In trying to judge of small distances by one eye, it is usual to be mistaken for want of the criterion from the inclination of the optic axes.
Since our judgment concerning the magnitude of an unknown object depends upon the distance, and our judgment concerning the distance of every object chiefly upon that concerning its magnitude, the conjectures of different persons, concerning the magnitudes and distances of unknown remote objects, both as seen through telescopes, and with the naked eye, may vary considerably from each other, according to their respective associated prejudices. If the distance be fixed previously by a known object, we may afterwards judge of the magnitude of an unknown object thereby. The number of intervening objects, and the inclination of the optic axes, seem to afford considerable assistance in determining distances, where known objects are wanting; the first in large distances, the last in small ones: but the other three inferior criterions above-mentioned, viz. the degree of distinctness, the degree of brightness, and the conformation of the eye, when singly taken, are of small signification.
We judge of motion by the motion of the pictures on the
