Steve Willner <swillner@cfa.harvard.edu>

The effect is an optical illusion.  You can verify this for yourself
by comparing the size of the Moon when it's on the horizon to that of
a coin held at arm's length.  Repeat the measurement when the Moon is
overhead.  You will find the angular size unchanged within the
accuracy of the measurement.

In fact two effects contribute to making the Moon slightly *smaller*
on the horizon than overhead.  Atmospheric refraction compresses the
apparent vertical diameter of the Moon slightly.  A really precise
measurement will reveal that the horizontal diameter is about 1.7%
smaller when the Moon is on the horizon because you are farther from
it by approximately one Earth radius.

The Sun, incidentally, shows the much same effects as the Moon, though
it's a *really* BAD idea to look directly at the Sun without proper
eye protection (NOT ordinary sunglasses).  The change in apparent
angular diameter is, of course, less than 0.01% instead of 1.7%
because the Sun is farther away.  (See the next entry.)

The probable explanation for this illusion is that the "background"
influences our perception of "foreground" objects.  If you've seen the
"Railroad Track Illusion"---in which two blocks of the same size
placed between parallel lines will appear to be different
sizes---you're familiar with the effect.  The Moon illusion is simply
the railroad track illusion upside-down. For some reason, the sky
nearer the horizon appears much more distant than the point directly
overhead.  The explanation for this apparent difference in distance is
not known, but an informal survey by one of the authors (CJW)
indicates that all people see this distance difference.  The
explanation for the Moon illusion is then that when we see the moon
"against" a more "distant" horizon it appears larger than when we see
it "against" a much "closer" one.

Additional evidence in support of this idea is the behavior of
"afterimages."  An afterimage of a constant size can be impressed upon
the human eye by staring at a light bulb for a few minutes.  By
projecting the afterimage on a sheet of white paper, the size of the
afterimage can be varied by changing the eye-to-paper distance.  A
similar effect is seen with the night sky---an afterimage projected
toward the horizon appears larger than one projected toward the
zenith.

 Much more extensive discussions are available in 

 * The Planetarian, Vol. 14, #4, December 1985, also available
   at <URL:http://www.griffithobs.org/IPSMoonIllus.html>; and
 * Quarterly Journal of the Royal Astronomical Society, vol. 27,
   p. 205, 1986.