The preceding rules for calculating the magnifying powers of microscopes, are founded on the principles which have been adopted by all optical authors ; but it will appear, we trust, from a very slight considera tion of the subject, that the magnifying power thus found is not the real measure of the assistance afforded by the microscope. Let us take the case of a compound microscope, with two lenses, and let us suppose that the distance of the object from the object-lens is one foot, the distance of the image behind it 20 feet, the focal length of the eye-glass 1 inch, and the dis tance at which the eye sees microscopic objects 6 inches. Hence the magnifying power of this microscope, corn 6 20 putcd on the old principle, is — x — = 120 times ; 1 that is, the object appears 120 times larger than if it had been placed at the distance of 6 inches from the eye. But the object is actually placed at the distance of 21 !..cet from the eye, and the image is not only magnified 20 times by the object-glass, but it is brought to such a distance that the eye can see this magnified image at the distance of 6 inches. Hence the real magnifying effect, 20 feet 21 feet by the object-glass alone, is 1 X _ 840 ; and when we look at this image with an inch eye-glass. it is again magnified 6 times, and the total magnifying power is 840 x 6= 5040 times, in place of 120, accord ing to the old principle.
Although this is obviously a correct measure of the benefit which the eye derives from the microscope, and of the effect of the instrument, yet it will be said that, though the object is placed at the distance of 21 feet from the eye, the eye can advance to it and examine it at the distance of 6 inches, so that 120 times is the measure of the assistance which the eye receives when it has placed itself in the best position for examining the object. This is undeniable ; but we might as well say that a. telescope directed to a table of logarithms, at the dis tance of 1000 feet, did not magnify 20 times (provided that was its magnifying power) because the observer could advance to the book, and see the figures under a larger angle with his naked eye.
If we suppose that the microscopic object is placed in a cavity, whose depth is 12 inches, then, if the ob server does advance to it, he cannot see it at a less dis tance than 12 inches ; so that even on the old principle the magnifying power is 240 times. If the object is placed in a position where the eye cannot advance to it at all, then, on every principle, the real power it 5040.
VIII. On the Method of viewing and illuminating Viii. On the Method of viewing and illuminating Microscopic Objects.
The art of illuminating microscopic objects is not of less importance than that of preparing them for obser vation. No general rules can be given for adjusting the intensity of the illumination to the nature and character of the object which is to be examined ; and it is only by a little practice that this art can be acquired. In
general, however, it will be found that very transparent objects require a less degree of light than those which are less so ; and that objects which reflect white light, or which throw it off from a number of lucid points, re quire a less degree of illumination than those whose surfaces have a feeble reflective force.
Most opticians have remarked, that microscopic ob jects are commonly seen better in candle light than in day light, a fact which is particularly apparent, when very high magnifying powers are employed ; and we have often found, that very minute objects, which could scarcely be seen at all in day light, appeared with toler able distinctness in candle light. So far as we know, the cause of this has not been investigated ; and as it leads to general views respecting the illumination of microscopic objects, we shall consider it with some at tention.
Let LL, Plate CCCLXXVII. Fig. 24, be a single mi croscope, placed before the eye at E, and let f be a mi croscopic object, placed in its anterior focus, and illu minated by two candles at A and B. As the rays Af a, and Bf b cross at f, the focus of parallel rays, and as the two shadows of the microscopic object will be formed at a and b, as it were by rays diverging from f, the im ages of these two shadows formed upon the retina will coincide, and make only one image, so that the object f will appear perfectly distinct. if the object, however, is placed either within or without the focus f, its sha dows being formed as it were by rays diverging from a point either within or without, the principal focus f, will not coincide on the Mafia, but appear to formstwo images, either overlapping each other, or completely separated.
instead of two candles A, B, we have 4, 5, or 6, we shall have 4, 5, or 6 overlapping or separated images. Now, as it is impossible to place the different parts of a mi croscopic object exactly in the focus f, and as every lens has different foci for the differently coloured rays, and even for homogeneous light, in consequence of its spherical aberration, it necessarily follows, that when microscopic objects arc illuminated by light proceed ing from several points, the image of it upon the retina must consist of a number of images not accurately co incident ; and hence it becomes of the greatest import ance that it be illuminated only from one point, and not from a large surface of light, such as the sky, which is equivalent to an infinite number of radiating points." The following rules may therefore be laid down re specting the illumination of microscopic objects, and the method of viewing them.