CHAPTER II.

Optics or Vision-At what Distance Objects appear largest-Axis of Vision -Quantity or Field of Vision-Ground apparently altered by the situation of the Spectator-Reflections from the Surface of Water explained and applied-Different Effects of Light on different ObjectsExample.

LANDSCAPE GARDENING being connected with optics or vision, or rather with the application of their rules to practical improvement, it may not be improper to devote a chapter to the following observations.

There is a certain point of distance from whence every object appears at its greatest magnitude. This subject was originally discussed, in consequence of observing that a particular rock at PORT ELIOT appeared higher or lower, at different distances. The inquiry into the cause of this difference led me to propose a question to several ingenious friends.

Query, At what distance does any object appear at its greatest height?

'The general optical distinction of the magnitude of objects is into real and apparent; the real being what its name imports, and the apparent, not that which may ultimately result to the mind, but that which is immediately impressed on the eye. This is measured by a plain and certain rule, namely, the angle which is formed at the eye, by lines drawn from the extremities of the object. The apparent height of a man, therefore, at a quarter of a mile distance, is not the conception which we form of his height, but the opening or angle of the two lines above-mentioned, viz. of the two drawn from the extremities of the object to our eye. This apparent height, therefore, of any object, will be measured always upon the simplest principles; and will vary according to, first, the distance of the object; secondly, the inclination it makes with the horizon; and, thirdly, our relative elevation or depression. Any two of the above three things continuing the same, the apparent magnitude will decrease with the third, though not in exact proportion to it.

Thus the object being perpendicular to the horizon, and our elevation remaining the same, its apparent height will decrease with the distance. Our elevation and the distance remaining the same, the apparent height of the object will decrease with its inclination to the horizon. The inclination and distance being the same, the angle, or apparent height, will decrease with our elevation or depression, supposing our height was, at first, the middle point of the object. This last being liable to some exceptions, the general rule is, that the distance from the object, measured by a perpendicular to it, being the same, the point at which its apparent height will be greatest, is, where the perpendicular from the eye falls upon

the centre.

The apparent height of a body, as upon the same principles any other of its dimensions, is a matter of easy consideration; its inclination, its distance, and the relative position of the observer being known. The difficulty is to know what the conception is that we shall form of the height and magnitude of an object; according to different circumstances, its apparent height, as well as its real height, remaining the same. This, you will see, belongs to wholly different principles, and such as cannot be reduced to certain rules; it appears, too, from hence, that the question has little or nothing to do with mathematical principles, at least beyond those simple ones which I have just stated. Of other principles, the consideration is more diversified: much may be ascribed to the habit, which we probably have, of estimating the height of objects, not by the angle, formed by lines to the summit and the base, when the base is below us, but by that formed between a line from the summit and a line parallel to the horizon; in this way our conception of the magnitude may be less, while the apparent magnitude may be greater. A thousand other causes may likewise operate, amongst which will be some that belong to what is called aerial perspective, or those rules by which we judge of the distance or dimensions of objects, not by their outline on the retina, but by their colour and distinctness. The existence and operation of these can hardly be found, but by a careful examination and comparison of particular instances.'

The concluding paragraph in this letter, from one of the

most able men of the age, encouraged me to examine and compare particular instances, as they fell under my own observation, and from a variety of these I am led to conclude, that, among those numerous causes here said to operate, independent of mathematical principles, one may proceed from the position of the eye itself; which is so placed as to view a certain portion of the hemisphere without any motion of the head. This portion has been differently stated by different authors, varying from sixty to ninety degrees.

The question before us relates to the height, and not to the general magnitude of the object, these being separate considerations; because the eye is capable of surveying more in breadth than in height; but it is also capable of seeing much farther below its axis than above it, as shewn by the following profile [fig. 44]. From hence it appears, that the projection of the forehead and eyebrow causes great difference betwixt the angle A B and the angle A c, and that the line parallel to the horizon A, which I shall call the axis of vision, does not fall in the centre of the opening betwixt the extreme rays B and c.

[Fig. 44.]

Doubtless these angles may vary in different individuals, from various causes, such as the prominency of the eye, the habit or usual position of the head, &c. yet the upper angle ▲ B will seldom be greater than one half of the lower angle A c; and I have ascertained, with some precision, that I could not distinguish objects more than twenty-eight degrees above my axis of vision, although I can distinctly see them fifty-seven degrees below it. From hence I conclude, that the distance at which an object appears at its greatest height, is, when the axis of vision and the summit of the object form an angle of

about thirty degrees; because, under this angle, the eye perceives its full extent without moving the head, yet not without some effort of the eye itself to comprehend the whole of the object.

To this theory it may, perhaps, be objected, that, in the act of seeing, the motion of the head is too rapid to effect any material difference; but it will be found, on examining this subject attentively, that the object is seen in a new point of view, from the instant the head is moved, because the rays no longer meet at the same centre; and, therefore, the effect of such vision on the mind, is rather a renewal in succession of similar ideas, than the same single idea simultaneously excited and this difference may be compared to that between seeing a landscape reflected in a mirror at rest, and the same landscape when the mirror has been removed from its original position.*

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From frequent observation of the difference between seeing an object with and without moving the head, I am inclined to believe, that, by the latter, the mind grasps the whole idea at once; but, by the former, it is rather led to observe the parts separately: hence are derived many of those ideas of apparent magnitude or proportion which induce us to pronounce, at the first glance, whether objects are great or small. I should, therefore, answer the question, "At what distance does any object appear at its greatest height?" by saying, when the spectator is at such a distance, that the line drawn from his eye to the top of the object, forms an angle of not less than twenty-eight degrees with the axis of vision; and thus, supposing the eye to be five feet six inches from the ground, the distance will be according to the following diagram [fig. 45].

The scientific observer will always rejoice at discovering any law of Nature by which the judgment is unconsciously directed. At a certain distance from the front of any building, we admire the general proportions of the whole but if the

* Perhaps this difference may be more familiarly explained by observing, that, when a lark ascends in the air, we have no difficulty in keeping the bird in sight so long as we continue our head in the first position; but from the moment the head is moved, we have to search for the object again, and often in vain, through the vast expanse of sky.

building can only be viewed within those angles of vision already described, it is the several parts which first attract our

(Fig. 45. Scale of feet, shewing the distance of the spectator from the several objects.]

notice, and we generally pronounce that object large, the whole of which the eye cannot at once comprehend.

Hence it is commonly observed by those who have seen both St. Peter's, at Rome, and St. Paul's, at London, that the latter appeared the largest at the first glance, till they became aware of the relative proportion of the surrounding space; and I doubt whether the dignity of St. Paul's would not suffer if the area round the building were increased, since the great west portico is in exact proportion to the distance from whence it can now be viewed, according to the preceding table of heights and distances: but if the whole church could be viewed at once, like St. Peter's, the dome would overpower the portico, as it does in a geometrical view of the west front.*

The field of vision, or the portion of landscape which the eye will comprehend, is a circumstance frequently mistaken in fixing the situation for a house; since a view seen from the windows of an apartment will materially differ from the same view seen in the open air. In one case, without moving the head, we see from sixty to ninety degrees; or, by a single

I have sometimes thought that this same rule of optics may account for the pleasure felt at first entering a room of just proportions, such as twenty by thirty, and fifteen feet high; or, twenty-four by thirty-six, and eighteen feet high; or, the double cube, when it exceeds twenty-four feet.