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.
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 5½ 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.
Hence we may learn the absurdity and futility of attempting to describe the extent of spaces in the heavens, by saying, that a certain phenomenon was two or three feet or yards distant from another, or that the tail of a comet appeared several yards in length. Such representations can convey no definite ideas in relation to such magnitudes, unless it be specified at what distance from the eye, the foot or yard is supposed to be placed. If a rod, a yard in length, be held at nine inches from the eye, it will subtend an angle, or cover a space in the heavens, equal to more than one fourth of the circumference of the sky, or about one hundred degrees. If it be eighteen inches from the eye, it will cover a space equal to fifty degrees; if at three feet, twenty-five degrees, and so on in proportion to the distance from the eye; so that we can form no correct conceptions of apparent spaces or distances in the heavens, when we are merely told that two stars, for example, appear to be three yards distant from each other. The only definite measure we can use, in such cases, is that of degrees. The sun and moon are about half a degree in apparent diameter, and the distance between the extreme stars in Orion’s belt, three degrees, which measures being made familiar to the eye, may be applied to other spaces of the heavens, and an approximate idea conveyed of the relative distances of objects in the sky.
From what has been stated above, it is evident that the magnitude of objects may be considered in different points of view. The true dimensions of an object, considered in itself, give what is called its real or absolute magnitude; and the opening of the visual angle determines the apparent magnitude. The real magnitude, therefore, is a constant quantity; but the apparent magnitude varies continually with the distance, real or imaginary; and therefore, if we always judged of the dimensions of an object from its apparent magnitude, every thing around us would, in this respect, be undergoing very sensible variations, which might lead us into strange and serious mistakes. A fly, near enough to the eye, might appear under an angle as great as an elephant at the distance of twenty feet, and the one be mistaken for the other. A giant eight feet high, seen at the distance of twenty-four feet, would not appear taller than a child two feet in height, at the distance of six feet; for both would be seen nearly under the same angle. But our experience generally prevents us from being deceived by such illusions. By the help of touch, and by making allowance for the different distances at which we see particular objects, we learn to correct the ideas we might otherwise form from attending to the optical angle alone, especially in the case of objects that are near us. By the sense of touch we acquire an impression of the distance of an object; this impression combines itself with that of the apparent magnitude, so that the impression which represents to us the real magnitude is the product of these two elements. When the objects, however, are at a great distance, it is more difficult to form a correct estimate of their true magnitudes. The visual angles are so small, that they prevent comparison; and the estimated bulks of the objects depend in a great measure upon the apparent magnitudes; and thus an object situated at a great distance, appears to us much smaller than it is in reality. We also estimate objects to be nearer or farther distant according as they are more or less clear, and our perception of them more or less distinct and well defined; and likewise, when several objects intervene between us and the object we are particularly observing. We make a sort of addition of all the estimated distances of intermediate objects, in order to form a total distance of the remote object, which in this case appears to be farther off than if the intervening space were unoccupied. It is generally estimated that no terrestrial object can be distinctly perceived, if the visual angle it subtends be less than one minute of a degree; and that most objects become indistinct, when the angle they subtend at the pupil of the eye is less than six minutes.
We have deemed it expedient to introduce the above remarks on the apparent magnitude of objects, because the principal use of a telescope is to increase the angle of vision, or to represent objects under a larger angle than that under which they appear to the naked eye, so as to render the view of distant objects more distinct, and to exhibit to the organ of vision those objects which would otherwise be invisible. A telescope may be said to enlarge an object just as many times as the angle under which the instrument represents it, is greater than that under which it appears to the unassisted eye. Thus the moon appears to the naked eye under an angle of about half a degree; consequently a telescope magnifies 60 times if it represents that orb under an angle of 30 degrees; and if it magnified 180 times, it would exhibit the moon under an angle of 90 degrees, which would make her appear to fill half of the visible heavens, or the space which intervenes from the horizon to the zenith.
CHAPTER IV.
ON THE DIFFERENT KINDS OF REFRACTING TELESCOPES.
There are two kinds of telescopes, corresponding to two modes of vision, namely, those which perform their office by refraction through lenses, and those which magnify distant objects by reflection from mirrors. The telescope which is constructed with lenses, produces its effects solely by refracted light, and is called a Dioptric, or refracting telescope. The other kind of telescope produces its effects partly by reflection, and partly by refraction, and is composed both of mirrors and lenses; but the mirrors form the principal part of the telescope; and therefore such instruments are denominated reflecting telescopes. In this chapter I shall describe the various kinds of refracting telescopes.