Although the foregoing is conclusive evidence of the illusory character of the enlargement there are other ways of making measurements. On viewing the sun at the horizon a bright after-image is obtained. This may now be projected upon the sky as a background at any desired altitude. It will appear much smaller at the zenith than the sun appears at the horizon. Certainly this is a simple and conclusive demonstration of the illusion. In this case the after-image of the sun or the sun itself will usually appear at least twice as large as the after-image at the zenith. If the variation in the position of the eyes is held to account for the illusion, this explanation may be supported by using a horizontal telescope with adjustable cross-hairs, and a mirror. By varying the position of the latter the disk of the sun may be measured at any altitude without varying the position of the eye. When everything is eliminated from the field but the moon's disk, it is found to be constant in size. However, this is not conclusive evidence that the variation in the position of the line of sight accounts for the illusion. As a demonstration of the absence of enlargement of the size of the moon near the horizon some have brought forward measurements of the lunar circles and similar phenomena. These are said to be unaffected by the altitude of the moon except for refraction. But even this does not change the horizontal diameter and actually diminishes the vertical one. The moon is further away when near the horizon than when at the zenith, the maximum increase in distance being one-half the diameter of the earth. This would make the moon appear about one-sixtieth, or one-half minute of arc smaller at the horizon than at the zenith. This is not only in the wrong direction to aid in accounting for the apparent enlargement, but it is so slight as to be imperceptible to the unaided eye. Nearly two centuries ago Robert Smith and his colleagues concluded that the sky appears about three times as far away at the horizon as at the zenith. They found that the relative apparent diameters of the sun and of the moon varied with altitude as follows: Altitude Relative apparent diameter 0 deg. (horizon) 100 15 " 68 30 " 50 45 " 40 60 " 34 75 " 31 90 " (zenith) 30 [Illustration: Fig. 80.--Explanation offered by Smith of the apparent enlargement of heavenly bodies near the horizon.]