A microscope, as we have before explained, may be either a single, or simple, or a compound instrument. The simple microscope may consist of one or of two or three lenses; but these latter are so arranged as to have the effect only of a single lens. In the compound microscope, not less than two lenses must be employed: one to form an inverted image of the object, which, being the nearest to the object is called the object-glass; and the other to magnify this image, and from being next the eye of the observer, called the eye-glass. Both these may be formed out of a combination of lenses, as will be hereafter seen.

We have hitherto considered a lens only in reference to its enlargement of the object, or the increase of the angle under which the object is seen. A further and equally important consideration is that of the number of rays or quantity of light by which every point of the object is rendered visible; and much may be accomplished, as we have before pointed out, by the combination of two or more lenses instead of one, thus reducing the angles of incidence and refraction. The first satisfactory arrangement for this purpose was the invention of the celebrated Dr. Wollaston. His doublet consisted of two plano-convex lenses having their focal lengths in the proportion of one to three, or nearly so, and placed at a distance which can be ascertained best by actual experiment. Their plane sides are placed towards the object and the lens of shortest focal length next the object.

It appears that Dr. Wollaston was led to this invention by considering that the achromatic Huyghenian eye-piece, which will be presently described, would, if reversed, possess similar good properties as a simple microscope. But it will be evident, when the eye-piece is understood, that the circumstances which render it achromatic are very imperfectly applicable to the simple microscope, and that the doublet, without a nice adjustment of the stop, would be valueless. Dr. Wallaston makes no allusion to a stop, nor is it certain that he contemplated its introduction: although his illness, which terminated fatally soon after the presentation of his paper to the Royal Society, may account for the omission. The nature of the corrections which take place in the doublet is explained in the annexed diagram, a portion of the cornea of the eye, and the stop, or limiting aperture.

Now it will be observed that each of the pencils of light from the extremities of the object is rendered eccentrically by the stop; consequently, each passes through the two lenses on opposite sides of their common axis; thus each become affected by opposite errors, which to some extent balance and correct each other. To take the pencil; for instance, which enters the eye: it is bent to the right at the first lens, and to the left at the second : and as each bending alters the direction of the blue rays more than the red and moreover as the rays fall nearer the margin of the second lens, where the refraction being more powerful than near the centre , compensates in some degree for the greater focal length of the second lens, the blue rays will emerge very nearly parallel, and of consequence colorless to the eye. At the same time, the spherical aberration has been diminished by the circumstances that the side of the pencil which passes one lens nearest the axis passes the other nearest the margin.

This explanation applies only to the pencils near the extremities of the object. The central pencils, it is obvious, would pass both lens symmetrically, the same portions of light occupying nearly the same relative places on both lenses. The blue light would enter the second lens nearer to its axis than the red ; and being thus less refracted than the red by the second lens, a small amount of compensation would take place, quite different in principle, and inferior in degree, to that which is produced in the eccentrically pencils. In the intermediate spaces the corrections are still more imperfect and uncertain; and this explains the cause of aberration which must necessity exist even in the best-made doublet. It is, however, infinitely superior to a single lens, and will transmit a pencil of an angle of from 35 to 50 without any very sensible errors. It exhibits, therefore, many of the usual test-objects in a very beautiful manner.

The next step in the improvement of the simple microscope bears more relation to the eye-piece; this was effective by Mr. Holland: it consists in substituting two lenses for the first in the doublet, and retaining the stop between them and the third. The first bending being thus effected by two lenses instead of one, is accompanied by smaller aberrations, which are, therefore, more completely balanced or corrected at the second bending, in the opposite direction, by the third lens.