From T Zeno   October 8th, 1862¹

LII. On the Changes in the Apparent Size of the Moon. | By T. Zeno. | To Professor Tyndall.

Guy’s Hospital, October 8th, 1862.

SIR,

MY attention having been called to a letter in the May Number of the Philosophical Magazine, “On the Changes in the Apparent Size of the Moon,”² where reference is made to my explanation of the phenomenon (Recreative Science, No. 24), I find it necessary to ask your indulgence while I make some allusion to that reference, as well as to the novel and ingenious experiment of your correspondent Mr. Lewis.³

First, with regard to the reference to my explanation, it is obvious that, to satisfy the “popular mind” as to the subjective character of the phenomenon, it would have been better to have quoted my second experiment, that of looking at the rising sun till an ocular spectrum was obtained, and then directing the eye to the zenith, where this spectrum immediately diminished, to enlarge again on looking to the opposite horizon. Secondly, with regard to the experiment of Mr. Lewis, it must be noticed that, while it necessarily involves the condition of binocular vision, the phenomenon it proposes to illustrate is equally exhibited to monocular vision; the experiment nevertheless, so far as I can judge, very well illustrates that law by which, when two bodies subtend equal angles, both bodies being of the same size, but one assumed to be nearer than the other, the (assumed) nearer appears to be smaller. And though, consequently, the moon in the zenith would appear smaller if the senses assumed it to be nearer, the experiment of your correspondent does not hint at the latter condition. Now as the gravamen of the evidence lies here, you will perhaps allow me to state briefly why it is that the luminary (seen with one eye or with both eyes) in the zenith is felt to be nearer than it is when seen in the horizon. I say felt, not reasoned, inasmuch as this is a sensory perception which no intellection can alter, seeing the setting or rising sun is no less enlarged to the eye of an astronomer (whose reason rejects the illusion) than it is to the eye of the most uninformed rustic.

I propose that the luminary appears nearer at zenith than horizon, because, first (A), the visible sky appears nearer at zenith than horizon, and, secondly (B), the apparent distance of the luminary accords with that of the sky.

A. Everything visible is seen by rays proceeding from it*.⁴ Whatever, then, constitutes the visible sky is thus seen. Now sky would appear black if atmospheric particles did not reflect rays; it would appear white if intervals of black space beyond did not leave points of the retina unexcited; and it appears blue by a law (experimentally deduced by Da Vinci) that retinal excitation (by white light) interspersed with retinal points of rest (derived from the blackness of space) is the sensory condition blue. But the (partial) blueness of sky at horizon shows that the blackness of space is not altogether shut out by intervening reflecting particles: whence it follows that the furthest reflecting particles of our atmosphere cannot have their light wholly intercepted by the nearer; and that the whole atmospheric area contributes, with the blackness of space beyond, to constitute the visible sky. The whole atmosphere, then, give the real locality of that we call visible sky—seen by rays proceeding from it (its varying shades, from blue to nearly black, in various latitudes, showing that colour is its visible accident and not its visible essence). Now, whether we draw a line from the spectator to the limit of the atmosphere or to any assumed point within it, the line in direction of horizon will be longer than in that of zenith; and in whatever form any part, or the whole, of this transpicuous extent of atmosphere is manifested to vision by the aforesaid rays, such manifestation in direction of horizon is more or less obscured, in consequence of the rays depicting it coming from the greater distance and under a smaller angle; in other words, every visible quality and attribute of the sky will appear more distinct at the nearer point (zenith) than at the further point (horizon)^†5.

But if this necessarily curtailed demonstration should not be fully conclusive, the facts, reasoned to, are obvious; the sky is more definite and more blue in appearance at the zenith: moreover we naturally express our sensation by naming it the “near sky,” and that at the horizon the “far sky.”

The synthetic argument, finally, seems irrefragable: engraver and painter succeed in presenting, the one the form, and the other the form and colour of the sky as we really perceive them by the sense, their success depending solely on an observed law of perspective, which mathematically demonstrates the sky they depict at the horizon to be further considerably than that they represent at the zenith. Now the senses, in recognizing the truth of this representation of the sense-perceived form of the sky, assert unequivocally what the sense-perception is.

It remains to show, B, that the apparent distance of the luminary coincides with that of the sky. It may be argued, since there is no sensory evidence of the actual distance of the luminary, 1st, that the sense can only refer it to the ground which surrounds it; 2nd, that, by the universal law determining visual distance with one or both eyes, no object is felt to be beyond or in advance of another surrounding it, unless, the size, parts, texture, or colour of both being known or assumed, the sight detects that one is more obscured than the other, in which case the less obscured is inferred to be less distant, and vice versa; 3rd, a strong light, placed at any distance behind a hole in a semi-illuminated screen, appears to fill the aperture and be there situate; or a sunbeam piercing an interstice appears to emanate from the object in which the interstice exists.

If, then, the positions A and B are established, it follows that the luminary in the zenith appears nearer than at horizon; and, subtending (practically) the same angle in both cases, it is hardly necessary to add (what my paper referred to sets forth) that when the luminary is supposed to be nearer it is necessarily perceived to be smaller.

Trusting you will excuse the unforeseen length of this explanation of my views, perhaps somewhat misunderstood by your correspondent,

Believe me to be, Sir | Yours very respectfully, | T. ZENO.

T. Zeno, ‘On the Changes in the Apparent Size of the Moon’, Phil. Mag., 24 (1862), pp. 390–92