MICROSCOPE 259 although an ordinary eye does not form a distinct picture of an object at less than from 10 to 6 inches distance, a " myopic " or " short-sighted " eye (whose greater refractive power enables it to bring rays of wider divergence to a focus on the retina) may form an equally distinct picture of an object at from 5 to 3 inches distance ; and, as the linear dimensions of that picture will be double that of the preceding, the object will be " magnified " in that propor tion, and its details more clearly seen. The effect of the interposition of a convex lens between the eye and an object nearly approximated to it primarily consists in its reduction in the divergence of the rays of the pencils which issue from its several points, so that they enter the eye at the moderate divergence which they would have if the object were at the ordinary nearest limit of distinct vision. And, since the shorter the focus of the lens the more closely may the object be approximated to the eye, the retinal picture is enlarged, causing the object to appear magnified in the same proportion. Not only, however, are the component rays of each pencil brought from divergence into convergence, but the course of the pencils themselves is changed, so that they enter the eye under an angle corresponding to that under which they would have arrived from a larger object situated at a greater distance ; and thus, as the picture formed upon the retina by the small object ab, fig. 1, corresponds in all FIG. 1. Action of Simple Microscope. respects with that which would have been made by the same object AB of several times its linear dimension viewed at the nearest ordinary limit of distinct vision, the object is seen (by the formation of a " virtual image ") on a magnified scale. It is obvious that the " magnifying power " of any convex lens so used is measured by the ratio between the dimensions of the retinal picture formed with its assistance and those of the picture formed by the unaided eye. Thus, if by the use of a convex lens having 1 inch focal length we can form a distinct retinal image of an object at only an inch distance, this image will have ten times the linear dimensions of that formed by the same object at a distance of 10 inches, but will be only eight times as large as the picture formed when the object can be seen by ordinary vision at 8 inches distance, and only four times as large as the picture of the same object formed by a myopic eye at a distance of 4 inches. It is usual to estimate the magnifying power of single lenses (or of com binations that are used as such) by the number of times that their focal length is contained in 10 inches, that of 1 inch focus being thus taken as ten times, that of -Jg- inch as one hundred times, and so on. But the rule is obviously arbitrary, as the actual magnifying power varies in each individual with the nearest limit of distinct vision. Thus for the myopic who can see an object clearly at 4 inches distance, the magnifying powers of a 1 inch and y 1 ^ inch lens will be only 4 and 40 respectively. The amplifying power of every single convex lens, however, is impaired (1) by that inability to bring to the same focus the rays which fall upon the central and the marginal parts of its surface which is called "spherical aberration," and (2) by that dispersion of the rays of different wave-lengths, in virtue of their different refrangibilities, which produces coloured fringes around the points and lines of the visual picture, and is therefore called " chromatic aberration " (see LIGHT). These aberrations increase with the " angle of aperture " given to the lens, that is, with the proportion between the diameter of its actual " opening " and the focal distance of the object ; and thus, when a single lens of very short focus is used in order to gain a high magnifying power, such a reduction of its aperture by a perforated diaphragm or " stop " becomes necessary (in order, by excluding the peripheral rays, to obtain tolerable " definition " with freedom from false colour) that the amount of light admitted to the eye is so small as only to allow the most transparent objects to be thus viewed, and these only very imperfectly. In order to remedy this draw back, it was proposed by Sir D. Brewster to use instead of glass, in the construction of simple microscopes, such transparent minerals as have high refractive with low dispersive power ; in which case the same optical effect could be obtained with lenses of much lower curvature, and the aperture might be proportionately enlarged. This combination of qualities is found in the diamond, whose index of refraction bears such a proportion to that of glass that a diamond lens having a radius of curvature of 8 would give the same magnifying power as a glass lens whose radius of curvature is 3, while the " longitudinal aberration " (or distance between the foci of central and of marginal rays) would be in a diamond lens only one-ninth of that of a glass lens having the same power and aperture. Put ting aside, however, the costliness of the material and the difficulty of working it, a source of imperfection arises from a frequent want of homogeneousness in the diamond crystal, which has proved sufficient to make a lens worked from it give a double or even a triple image. Similar attempts made by Mr Pritchard with sapphire proved more successful ; and, as a sapphire lens having a radius of curvature of 5 has the same focus and gives the same magnifying power as a crown-glass lens having a radius of 3, it was found to bear a much larger aperture without serious impairment by either spherical or chromatic aberration. As the sapphire, however, possesses the property of double refrac tion, the duplication of the markings of the object in their retinal image constitutes a very serious drawback to the utility of lenses constructed of this mineral; for, though the double refraction may be reduced almost to nothing by turning the convex side of the lens towards the object, yet, as this is the worst position in regard to spherical aberration, more is lost than is gained. Fortunately, however, for biological investigators working with simple microscopes, the introduction of the Wollaston doublet superseded the necessity of any further attempts at turning costly jewels to account as high-power magnifiers. Wollaston Doublet. This consists of a combination of two plano-convex lenses, whose focal lengths (as directed by Dr Wollaston) should be as 3 to 1, with their plane sides turned towards the object, the smaller lens being placed lowest, and the upper lens at a distance of one and a half times its focal length above it. This construction, how ever, has been subsequently improved (1) by the introduc tion of a perforated diaphragm between the lenses ; (2) by a more effective adjustment of the distance between the two lenses, which seems to be most satisfactory when it equals the difference of their respective focal lengths, allowance being made for their thickness ; and (3) by the division of the power of the lower lens (when a shorter focus than J^ inch is required) into two, so as to form
a "triplet." When combinations of this kind are well