In reference to apparent magnitudes, we scarcely ever judge any object to be so great or so small as it appears to be, or that there is so great a disparity in the visible magnitude of two equal bodies at different distances from the eye. Thus, for example, suppose two men, each six feet 3 inches high, to stand directly before us, one at the distance of a pole, or 5-1/2 yards, and the other at the distance of 100 poles, or 550 yards--we should observe a considerable difference in their apparent size, but we should scarcely suppose, at first sight, that the one nearest the eye appeared a hundred times greater than the other, or that, while the nearest one appeared 6 feet 3 inches high, the remote one appeared only about _three fourths of an inch_. Yet such is in reality the case; and not only so, but the visible bulk or area of the one is to that of the other, as the square of these numbers, namely as 10,000 to 1; the man nearest us presenting to the eye a magnitude or surface ten thousand times greater than that of the other. Again, suppose two chairs standing in a large room, the one 21 feet distance from us, and the other 3 feet--the one nearest us will appear 7 times larger both in length and breadth, than the more distant one, and consequently, its visible area 49 times greater. If I hold up my finger at 9 inches distant from my eye, it seems to cover a large town a mile and a half in extent, situated at 3 miles distant; consequently, the apparent magnitude of my finger, at 9 inches distant from the organ of vision, is greater than that of the large town at 3 miles distance, and forms a larger picture on the retina of the eye. When I stand at the distance of a foot from my window, and look through one of the panes to a village less than a quarter of a mile distant, I see, through that pane, nearly the whole extent of the village, comprehending two or three hundred houses; consequently, the apparent magnitude of the pane is equal to nearly the extent of the village, and all the buildings it contains do not appear larger than the pane of glass in the window, otherwise, the houses and other objects which compose the village could not be seen through that single pane. For, if we suppose a line drawn from one end of the village, passing through the one side of the pane, and another line drawn from the other end, and passing through the other side of the pane to the eye, these lines would form the optical angle under which the pane of glass and the village appears. If the pane of glass be fourteen inches broad, and the length of the village 2640 yards, or half a mile--this last lineal extent is 6,788 times greater than the other, and yet they have the same _apparent_ magnitude in the case supposed.