Perhaps the most important improvement effected in this form of the simple microscope was that ascribed to the celebrated Dr. Wollaston, who devised a doublet of two plano-convex lenses having their focal lengths, in the proportion of one to three, mounted with their convex side directed towards the eye of the observer, and the lens of shorter focal length next the object. The explanation given of the correction thus effected in Dr. Wollaston’s doublet will be best understood on reference to the annexed diagram, _l l′_, in Fig. 49, being the object for a segment of the cornea of the eye, and _d d′_ the stop or diaphragm. Now, it will be seen that each pencil of light proceeding from _l l′_, the object, is rendered excentrical by the limiting aperture or the diaphragm _d d_; consequently, they pass through the lenses on opposite sides of their common axis _o p_; thus each becomes affected by opposite errors, which to some extent balance and correct each other. To take the pencil _l_, for instance, as it enters the eye at _r b_; _r b_ 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 ray more than the red, and as the blue ray falls nearer the margin of the second lens, where the refraction is greater than that nearer the centre, and compensates to some extent for the greater focal length of the second lens, the blue rays will emerge very nearly parallel, and colourless to the eye. At the same time, its spherical aberration has been diminished, since the side of the pencil as it proceeds through one lens passes nearer the axis, and in the other nearer the margin. This must be taken to apply to pencils farthest from the centre of the object. Central rays, it is obvious, would pass both lenses symmetrically, the same portions of rays occupying nearly the same relative places in both lenses. The blue ray would enter the second lens nearer its axis than the red; and being thus less refracted than the red by the second lens, some amount of compensation would take place, differing in principle, and inferior in degree, to that which is found in the excentrical pencils. In the intermediate spaces the corrections are still more imperfect and uncertain; and this explains the cause of aberrations which must of 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°. The next step towards improving the simple microscope was in relation to the eye-piece, and was effected by Holland. It consisted in substituting two lenses for the first in the doublet, and placing a stop between them and the third. The first bending of the pencils of light being effected by two lenses instead of one, produces less spherical and chromatic aberration, which are more nearly balanced or corrected at the second bending, and in the opposite direction, by the third lens.