The _apparent magnitude_ of objects denotes their magnitude as they appear to us, in contradistinction from their real or true magnitude, and it is measured by the visual angle; for whatever objects are seen under the same or equal angles _appear_ equal, however different their real magnitudes. If a half-crown or half-dollar be placed at about 120 yards from the eye, it is just perceptible as a visible point, and its apparent magnitude, or the angle under which it is seen, is very small. At the distance of thirty or forty yards, its bulk appears sensibly increased, and we perceive it to be a round body; at the distance of six or eight yards, we can see the king or queen’s head engraved upon it; and at the distance of eight or ten inches from the eye it will appear so large, that it will seem to cover a large building placed within the distance of a quarter of a mile, in other words, the apparent magnitude of the half-crown held at such a distance, will more than equal that of such a building, in the picture on the retina, owing to the increase of the optical angle. If we suppose A (fig. 41.) to represent the apparent size of the half-crown at nine yards distance, then we say it is seen under the small angle FED. B will represent its apparent magnitude at 4-1/2 yards distant under the angle HEG, and the circle C, its apparent magnitude at 3 yards distant, under the large angle KEI. [Illustration: _figure 42._] This may be otherwise illustrated by the following figure. Let AB (fig. 42.) be an object viewed directly by the eye QR. From each extremity A and B draw the lines AN,BM, intersecting each other in the crystalline humour in I: then is AIB the optical angle which is the measure of the apparent magnitude or length of the object AB. From an inspection of this figure, it will evidently appear that the apparent magnitudes of objects will vary according to their distances. Thus AB, CD, EF, the real magnitudes of which are unequal, may be situated at such distances from the eye, as to have their _apparent_ magnitudes all equal, and occupying the same space on the retina MN, as here represented. In like manner, objects of equal magnitude, placed at unequal distances, will appear unequal. The objects AB and GH which are equal, being situated at different distances from the eye, GH will appear under the large angle TIV, or as large as an object TV, situated at the same place as the object AB, while AB appears under the smaller angle AIB. Therefore the object GH is _apparently_ greater than the object AB, though it is only equal to it. Hence it appears that we have no certain standard of the _true magnitude_ of objects, by our visual perception abstractly considered, but only of the _proportions_ of magnitude.