§. 177. Measurements of magnitude by the eye.

What has been said naturally leads us to the consideration of MAGNITUDE. This is a general term for Extension when we conceive of it not only as limited or bounded, but as related to, and compared with other objects. Although we make use of the eye in judging of it, it is to be kept in mind, that the knowledge of magnitude is not an original intimation of the sight, but is at first acquired by the aid of touch. So well known is this, that it has been common to consider Magnitude under the two heads of tangible or real, and visible or apparent; the tangible magnitude being always the same, but the visible varying with the distance of the object. A man of six feet stature. is always that height, whether he be a mile distant, or half a mile, or near at hand; the change of place making no change in his real or tangible magnitude. But the visible or apparent magnitude of this man may be six feet or not one foot, as we view him present with us and immediately in our neighborhood, or at two miles' distance; for his magnitude appears to our eye greater or less, according as he is more or less removed.-Hence the general principle, that of two objects equally distant, that, which has the greatest visible magnitude, is supposed to have the greatest tangible magnitude.

Among the multitude of instances, which might be adduced in illustration of this principle, the following statement to be found in the seventh number of the Edinburgh Journal of Science, is a striking one. In examining a dioramic representation of the inside of Rochester cathedral, which produced the finest effect from the entire exclusion of all extraneous light and of all objects, excepting those on the picture itself, the writer of the statement referred to was struck with an appearance of distortion in the perspective, which he ascribed to the canvass not hanging vertically. Upon mentioning this to the gentleman, who exhibited the picture, he offered to walk in front of it, and strike its surface with the palm of his hand, to show that the canvass was freely suspended.

Upon doing this, a very remarkable deception, or illusion rather, took place. As his hand passed along, it gradually became larger and larger, till it reached the middle, when it became enormously large. It then diminished,

till it reached the other end of the canvass.

As the hand moved towards the middle of the picture, it touched the parts of the picture more and more remote from the eye of the observer; and consequently the mind referred the hand and the object in contact with it to the same remote distance; and consequently gave it a fictitious magnitude, corresponding with the visible figure it presented, combined with the supposition of its being placed at a distance. (See Edin. Journ. of Science, No. VII, p. 90, and Art. Science, Edin. Ency.)

§. 178. Of objects seen in the mist and of the sun and moon

in the horizon.

In accordance with the above mentioned principle it happens, that objects, seen by a person in a mist, seem larger than the life. Their faint appearance rapidly conveys to the mind the idea of being considerably removed although they are actually near to us. And the mind immediately draws the conclusion, (so rapidly as to seem a simple and original perception,) that the object, having the same visible or apparent magnitude, and yet supposed to be at a considerable distance, is greater than other objects of the same class. So that it is chiefly the view of the mind, a law or habit of the intellect, which in this particular case gives a fictitious expansion to bodies; although it is possible, that the result may in part be attributed to a difference in the refraction of the rays of light, caused by their passing through a denser and less uniform medium than usual.

These remarks naturally remind us of the well known fact, that the sun and moon seem larger in the horizon than in the meridian. Two reasons may be given for this appearance; and perhaps ordinarily they are combined together.-(1) The horizon may seem more distant than the zenith, in consequence of intervening objects.

We measure the distance of objects in part by means of those that are scattered along between, and any expanse of surface, where there are no such intervening objects, appears to us of less extent than it actually is. Now if the rays of light form precisely the same image in the eye, but the source of them is supposed to be further off in the horizon than in the zenith, such have been our mental habits that the object in the horizon will probably appear the largest.-(2) Another reason of the enlarged appearance of the sun and moon in the horizon is, that the rays from them fall on the body of the atmosphere obliquely, and of course are reflected downwards towards the beholder, and subtend a larger angle at his eye. Hence, as we always see objects in the direction of the ray just before it enters the eye, if we follow the rays back in the precise direction of their approach, they will present to the eye the outlines of a larger object as their source, than they would if they had not been refracted.-When the atmosphere is not clear, but unusual masses of vapour are accumulated in it, whether immediately around us or any where else in the direction of the rays, the refraction is increased, and the object proportionally enlarged. This circumstance helps to explain the fact of the enlargement not being uniform, but sometimes greater and at others less. It may be added, that, on a principle practically the same with that of refraction, there will be an increased enlargement, when the disc of the sun or moon is seen through distant woods; the rays being separated and turned out of their course by the trunks and branches.

§. 179. Of the estimation of distance by sight.

We are next led to the consideration of distances as made known and ascertained by the sight. By the distance of objects, when we use the term in reference to ourselves, we mean the space, which is interposed between those objects and our own position. It might be objected, that space interposed is only a synonymous expression for the thing to be defined. Nevertheless no one can be supposed to be ignorant of what is meant. Even blind men

have a notion of distance, and can measure it by the touch, or by walking forward until they meet the distant object.

The perception of distance by the sight is an acquired and not an original perception; although the latter was universally supposed to be the fact, until comparatively a recent period.

All objects in the first instance appear to touch the eye; but our experience has corrected so many of the representations of the senses before the period, which we are yet able to retrace by the memory, that we cannot prove this by a reference to our own childhood and infancy. It appears, however, from the statement of the cases of persons born blind on the sudden restoration of their sight.

"When he first saw, (says Cheselden, the anatomist, when giving an account of a young man, whom he had restored to sight, by couching for the cataract,) he was so far from making any judgment about distance, that he thought all objects touched his eye, as he expressed it, as what he felt did his skin; and thought no object so agreeable as those, which were smooth and regular, although he could form no judgment of their shape or guess what it was in any object, that was pleasing to him."

This anatomist has further informed us, that he has brought to sight several others, who had no remembrance of ever having seen; and that they all gave the same account of their learning to see, as they called it, as the young man already mentioned, although not in so many particulars; and that they all had this in common, that having never had occasion to move their eyes, they knew not how to do it, and, at first, could not at all direct them to a particular object; but in time they acquired that faculty though by slow degrees.

Blind persons when at first restored to sight, are unable to estimate the distance of objects by that sense, but soon observing, that certain changes in the visible appearance of bodies always accompany a change of distance,

they fall upon a method of estimating distance by the visible appearance. And it would no doubt be found, if it could be particularly examined into, that all mankind come to possess the power of estimating the distances of objects by sight in the same way. When a body is removed from us and placed at a considerable distance, it becomes smaller in its visible appearance, its colours are less lively, and its outlines less distinct; and we may expect to find various intermediate objects, more or fewer in number corresponding with the increase of the distance, showing themselves between the receding object and the spectator. And hence it is, that a certain visible appearance comes to be the sign of a certain distance.

Historical and landscape painters are enabled to turn these facts to great account in their delineations. By means of dimness of colour, indistinctness of outline, and the partial interposition of other objects, they are enabled apparently to throw back to a very considerable distance from the eye those objects, which they wish to appear remote. While other objects, that are intended to appear near, are painted vivid in colour, large in size, distinct in outline, and are separated from the eye of the spectator by few or no intermediate objects.

§. 180. Of the estimation of distance when unaided by intermediate objects.

As we depend in no small degree upon intermediate objects in forming our notions of distance, it results, that we are often much perplexed by the absence of such objects. Accordingly we find, that people frequently mistake, when they attempt to estimate by the eye the length or width of unoccupied plains and marshes, generally making the extent less than it really is. For the same reason they misjudge of the width of a river, estimating its width at half or three quarters of a mile at the most, when it is perhaps not less than double that distance. The same holds true of other bodies of water; and of all other things, which are seen by us in a horizontal position, and under similar circumstances.