1. Seen from a distance, objects appear reduced and close together, however far apart they be: within easy range, their sizes and the distances that separate them are observed correctly.

Distant objects show in this reduction because they must be drawn together for vision and the light must be concentrated to suit the size of the pupil; besides, as we are placed farther and farther away from the material mass under observation, it is more and more the bare form that reaches us, stripped, so to speak, of magnitude as of all other quality.

Or it may be that we appreciate the magnitude of an object by observing the salience and recession of its several parts, so that to perceive its true size we must have it close at hand.

Or again, it may be that magnitude is known incidentally [as a deduction] from the observation of colour. With an object at hand we know how much space is covered by the colour; at a distance, only that something is coloured, for the parts, quantitatively distinct among themselves, do not give us the precise knowledge of that quantity, the colours themselves reaching us only in a blurred impression.

What wonder, then, if size be like sound -- reduced when the form reaches us but faintly -- for in sound the hearing is concerned only about the form; magnitude is not discerned except incidentally.

Well, in hearing magnitude is known incidentally; but how? Touch conveys a direct impression of a visible object; what gives us the same direct impression of an object of hearing?

The magnitude of a sound is known not by actual quantity but by degree of impact, by intensity -- and this in no indirect knowledge; the ear appreciates a certain degree of force, exactly as the palate perceives by no indirect knowledge, a certain degree of sweetness. But the true magnitude of a sound is its extension; this the hearing may define to itself incidentally by deduction from the degree of intensity but not to the point of precision. The intensity is merely the definite effect at a particular spot; the magnitude is a matter of totality, the sum of space occupied.

Still the colours seen from a distance are faint; but they are not small as the masses are.

True; but there is the common fact of diminution. There is colour with its diminution, faintness; there is magnitude with its diminution, smallness; and magnitude follows colour diminishing stage by stage with it.

But, the phenomenon is more easily explained by the example of things of wide variety. Take mountains dotted with houses, woods and other land-marks; the observation of each detail gives us the means of calculating, by the single objects noted, the total extent covered: but, where no such detail of form reaches us, our vision, which deals with detail, has not the means towards the knowledge of the whole by measurement of any one clearly discerned magnitude. This applies even to objects of vision close at hand: where there is variety and the eye sweeps over all at one glance so that the forms are not all caught, the total appears the less in proportion to the detail which has escaped the eye; observe each single point and then you can estimate the volume precisely. Again, magnitudes of one colour and unbroken form trick the sense of quantity: the vision can no longer estimate by the particular; it slips away, not finding the stand-by of the difference between part and part.

It was the detail that prevented a near object deceiving our sense of magnitude: in the case of the distant object, because the eye does not pass stage by stage through the stretch of intervening space so as to note its forms, therefore it cannot report the magnitude of that space.

2. The explanation by lesser angle of vision has been elsewhere dismissed; one point, however, we may urge here.

Those attributing the reduced appearance to the lesser angle occupied allow by their very theory that the unoccupied portion of the eye still sees something beyond or something quite apart from the object of vision, if only air-space.

Now consider some very large object of vision, that mountain for example. No part of the eye is unoccupied; the mountain adequately fills it so that it can take in nothing beyond, for the mountain as seen either corresponds exactly to the eye-space or stretches away out of range to right and to left. How does the explanation by lesser angle of vision hold good in this case, where the object still appears smaller, far, than it is and yet occupies the eye entire?

Or look up to the sky and no hesitation can remain. Of course we cannot take in the entire hemisphere at one glance; the eye directed to it could not cover so vast an expanse. But suppose the possibility: the entire eye, then, embraces the hemisphere entire; but the expanse of the heavens is far greater than it appears; how can its appearing far less than it is be explained by a lessening of the angle of vision?