In the construction of the microscope, either simple or compound, the curvature of the lenses employed is usually spherical. Convergent lenses, with spherical curvatures, have the defect of not bringing all the rays of light which pass through them to one and the same focus. Each circle of rays from the axis of the lens to its circumference has a different focus, as shown in Fig. 15. The rays _a a_, which pass through the lens near its circumference, are seen to be _more refracted_, or come to a focus at a shorter distance behind it than the rays _b b_, which pass through near its centre or axis, and are _less refracted_. The consequence of this defect of lenses with spherical curvatures, which is called _spherical aberration_, is that a well-defined image or picture is not formed by them, for when the object is focussed, for the circumferential rays, the picture projected to the eye is rendered indistinct by a halo or confusion produced by the central rays falling in a circle of dissipation, before they have come to a focus. On the other hand, when placed in the focus of the central rays, the picture formed by them is rendered indistinct by the halo produced by the circumferential rays, which have already come to a focus and crossed, and now fall in a state of divergence, forming a circle of dissipation. The grosser defects of spherical aberration are corrected by cutting off the passage of the rays _a a_, through the circumferences of the lens, by means of a stop diaphragm, so that the central rays, _b b_, only are concerned in the formation of the image. This defect is reduced to a minimum, by using the meniscus form of lens, which is the segment of an ellipsoid instead of a sphere. [Illustration: Fig. 15.--Spherical Aberration of Lens.] The ellipse and the hyperbola are forms of lenses in which the curvature diminishes from the central ray, or axis, to the circumference _b_; and mathematicians have shown that spherical aberration may be practically got rid of by employing lenses whose sections are ellipses or hyperbolas. The remarkable discovery of these forms of lenses is attributed to Descartes, who mathematically demonstrated the fact. If _a l_, _a l′_, for example (Fig. 16) be part of an ellipse whose greater axis is to the distance between its foci _f f_ as the index of refraction is to unity, then parallel rays _r l′_, _r′′ l_ incident upon the elliptical surface _l′ a l_, will be refracted by the single action of that surface into lines which would meet exactly in the farther focus _f_, if there were no second surface intervening between _l a l′_ and _f_. But as every useful lens must have two surfaces, we have only to describe a circle _l a′ l′_ round _f_ as a centre, for the second surface of the lens _l′ l_. [Illustration: Fig. 16.--Converging Meniscus.]