Port Eliot Red Book: The Question of Perspective

Qu: At what distance does any object appear in 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 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 his figure to our eye. This apparent height, therefore, of any object will be measured always upon the simplest principles and will vary according to 1st) the distance of the object, 2nd) the inclination it makes with the horizon, and 3rd) our relative elevation or depression. Any two of the above three things continuing the same, the apparent magnitude will decrease with the third, tho' 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 Rule in general is

That the distance from the object measured by a perpendicular to it being the same, the point at which its apparent length will be greatest is when the perpendicular from the eye falls upon the centre."

For ease of reading, punctuation and capitalization have been modernized.