The common perception that a rising or setting Moon is magnified by the atmosphere is an optical illusion:  Click link:  http://en.wikipedia.org/wiki/Moon_illusion

The apparent angular diameter of the Moon actually increases slightly as it rises higher, because the rotating Earth is bringing you closer to it.  When near the horizon the lower limb of the Moon is refracted higher than the upper limb, thus it appears squashed in the vertical dimension.  There is no distortion in the horizontal dimension.

When you see a rising Moon, extend your arm toward it and compare the Moon to the size of a dime.  If you do the same thing a few hours later, you will see that the size of the Moon has hardly changed at all.

Regarding an alleged horizontal magnification of the Moon when near the horizon, consider this thought experiment.  Imagine a giant torus (hula-hoop) with its larger diameter the same as the Moon’s orbit.  Picture the smaller diameter of the tube being the same as the diameter of the Moon.  Then paint 720 alternately colored striped rings around the tube of the torus, each would be the same width as the diameter of the tube/Moon.  To an observer at the center of the torus, the painted rings would appear to be squares.

Now imagine you are on a boat in the ocean and the torus is placed so that it is visible along your entire 360° horizon with you at its center.  It would be positioned so that the bottom of the torus nearly meets the horizon with the rest of it extending upward.  If the atmosphere actually magnified objects horizontally, how would that change the appearance of the rings that are supposed to look like squares from your perspective?  Differing refraction levels for the top and bottom of the torus would make it appear squeezed vertically, but there is no room for the alternately colored rings (squares) to push into each others’ space.  The result is that the squares would be seen as rectangles with the same width as the squares but with a lesser height.

The above thought experiment demonstrates how a rising or setting Moon may appear squashed vertically but with no distortion of its horizontal dimension.

It is true that one Full Moon can appear more than 10% larger than another one seen some months later.  The difference is due to whether the Moon is near apogee or perigee.  The recent Full Moon occurred near apogee making it appear smaller than usual.  During the coming months the Full Moons will appear increasingly larger until the December Full Moon happening near perigee.  The occasion of Full Moon at perigee (or apogee) recurs over a cycle of 14 lunar months (1.13 years).  See my illustration by clicking:  http://www.curtrenz.com/astronomical.html

Below is a photo I took from Arlington Heights, Illinois of the Full Moon rising on 2007 JUL 29 at 20:33 CDT.  That was 18 minutes after sunset and 8 minutes after moonrise.  The altitude of the center of the Moon would have been 0.9°.  The Moon’s horizontal diameter was 0.5°.  The apparent compression in the vertical dimension is obvious in the photo.  Beneath it is a diagram I created with self-written software to show the scene as it would have theoretically appeared, taking into account the differing refraction factors for the upper and lower limbs but allowing no change in the horizontal dimension.

 Centaur - I always thought the Moon at the horizon looks bigger than when up higher in the sky because when alone in the sky, there are no "Earthly" objects nearby to compare in size (horizon, mountains, trees, etc.). Even as an optical illusion, I love watching the Moon rise/set at the horizon; it looks so much more impressive to me. Some say the thicker atmosphere (looking through more of it at the horizon) does amplify its visual size but only at a small amount. Doing the "dime" comparison, I can't see any obvious difference between it being at the horizon or high overhead.

  I have to watch out. Talking too much about the Moon may turn me into a lunatic (I'm pretty much on the way as it is). Mr Q
 

There is some thought that the physical position of looking up overhead can contribute to the effect also.  Terence Dickinson covers the subject well in Nightwatch.  He suggests using an asprin tablet held at arm's length for the comparison.

I have heard as well that it is an optical illusion caused by one's brain fitting in the celestial visitor to well known and pre-examined foreground objects.  The way to test this was explaned to me by having one spread one's legs while standing upright, bending over and viewing the moon through the legs.  This would change the brains accepted and familiar orientation and the Moon would look its actual size.  Since this is a most difficult and undignified position I have never tried this but if someone with a bit more flexibility does let me know how it works out. 

Interesting thread Curt,

L

mr Q:

Some say the thicker atmosphere (looking through more of it at the horizon) does amplify its visual size but only at a small amount.  

A rising Moon appears squashed in the vertical dimension due to the rapid rate of change in atmospheric density between the directions of  the Moon’s upper and lower limbs.  In the horizontal dimension there is virtually no change in the atmospheric density.  Imagine 720 Moons side-by-side filling the entire 360° horizon.  If any of the Moons appeared stretched horizontally, others would have to appear squeezed.