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    The Moon Illusion, as explained by Mackay in 1809
    From: Frank Reed
    Date: 2011 Mar 22, 07:16 -0700

    From Andrew Mackay's wonderful treatise on longitude, which you can find in the list of resources on the main NavList page: http://www.fer3.com/arc/navbooks2.html. He's describing what we call the "Moon illusion" today. Note that the general explanation given by Mackay 200 years ago is essentially the same as what you'll find today in many accounts of this phenomenon. For some reason, it has become popular again to claim that the phenomenon cannot be explained.

    Note that Mackay calls it the "Horizontal Moon" meaning the Moon "at the horizon". This is the same sense of "horizontal" in the expression "horizontal parallax" which we still use in navigation today.

    Mackay writes:
    "Of the Horizontal Moon.

    That the moon is imagined to appear much larger when in or near the horizon, than when at any considerable degree of elevation, is an observation familiar to every person : whereas, the semidiameter of the the moon really subtends a less angle in the first case, than in the second, by the quantity of the augmentation. To account for this seeming paradox, has exercised the skill of many eminent astronomers and philosophers, who have given various solutions for that purpose. These, however, we may probably have occasion to mention in another work—and, therefore, we shall confine ourselves to that solution which is now generally received. For this purpose, it will be necessary to premise the following lemmata.

    I. The nearer that any object is to the eye of an observer, it will appear under a greater angle.
    II. Let there be two objects of the same magnitude, and placed at equal distances from an observer; but from some illusion, one of them is imagined to be more distant than the other ; then, that object which is judged to be at the greatest distance, will be considered as the largest of the two.
    III. The expanse, or firmament, from whatever cause, whether from the appearance of clouds in the atmosphere, these towards the zenith being nigher than those near the horizon ; from the appearance of a number of interposed objects between the observer and the most distant, parts of the horizon; the greater quantity of vapours near the horizon, which render objects fainter than when elevated, or otherwise ; is imagined to be a small portion of a spherical surface, the nearest point being the zenith, and the most distant the horizon.

    Now, since the heavenly bodies are, to imagination, disposed on the surface of this circular or vaulted arch; and since, therefore, an object is judged to be more distant when in or near the horizon, than it is when at any considerable degree of elevation; it hence follows, that of two objects of the same magnitude, and at equal distances from an observer, that which is apparently farthest distant will, to imagination, be the largest of the two. Now, let one of these objects be near the horizon, and the other near the zenith ; then, in consequence of the vaulted appearance of the sky, the former will be imagined to be more distant than the latter. Hence, when the moon is in the horizon, being then supposed to be more distant from the observer than when in any any other position, that object will, therefore; be judged to be larger; and, to imagination, will continually decrease in magnitude until it has attained the meridian, when it will be supposed to be least. However, that the moon is not larger when in the horizon, than when in the meridian, may be inferred from the following simple experiment: Roll up a sheet of paper in form of,a tube, of such a size, that the moon when in the horizon may appear to fill it exactly; then observe the moon when in the meridian, or at any considerable degree of elevation,iand, in place of appearing less, will, when viewed through the same tube, appear a little greater, in consequence of being nearer to the observer.

    It is upon account of this vaulted appearance of the sky, that reckoning, by estimation, any small number of degrees from the zenith towards the horizon, and the same number from the horizon towards the zenith, the former will actually be a greater arch than the latter. Also, the distance between any two stars, when observed near the horizon, is imagined to be much greater than the same distance when the stars are near the zenith. This will appear evident by observing the stars Castor and Pollux, when in or near these two situations."

    -FER

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