It is to the refraction of light that we are indebted for the use of lenses or artificial glasses to aid the powers of vision. It lays the foundation of telescopes, microscopes, camera obscuras, phantasmagorias, and other optical instruments, by which so many beautiful, useful, and wonderful effects have been produced. In order therefore to illustrate the principles on which such instruments are constructed, it is necessary to explain the manner in which the rays of light are refracted and modified, when passing through spherical mediums of different forms. I do not intend however to enter into the minutiæ of this subject, nor into any abstract mathematical demonstrations, but shall simply offer a few explanations of general principles, and several experimental illustrations, which may enable the general reader to understand the construction of the optical instruments to be afterwards described. A lens is a transparent substance of a different density from the surrounding medium, and terminating in two surfaces, either both spherical, or one spherical and the other plain. It is usually made of _glass_, but may also be formed of any other transparent substance, as ice, crystal, diamond, pebbles, or by fluids of different densities and refractive powers, enclosed between concave glasses. Lenses are ground into various forms, according to the purpose they are intended to serve. They may be generally distinguished as being either _convex_ or _concave_. A convex glass is thickest in the middle, and thinner towards the edges. A concave glass is thin in the middle, and thicker towards the extremities. Of these there are various forms, which are represented in fig. 5. A, is a _plano-convex_ lens, which has one side plane, and the other spherical or convex. B, is a _plano-concave_, which is plane on the one side and concave on the other. C, is a _double-convex_, or one which is spherical on both sides. D, a _double-concave_, or concave on both sides. E, is called a _meniscus_, which is convex on one side and concave on the other. F, is a _concavo-convex_, the convex side of which is of a smaller sphere than the concave. In regard to the _degree_ of convexity or concavity in lenses, it is evident that there may be almost an infinite variety. For every convex surface is to be considered as the segment of a circle, the diameter and radius of which may vary to almost any extent. Hence, lenses have been formed by opticians, varying from one-fiftieth of an inch in radius, to two hundred feet. When we speak of the length of the radius of a lens,--as for instance, when we say that a lens is two inches or forty inches radius, we mean, that the convex surface of the glass is the part of a circle the radius of which, or half the diameter is two inches or forty inches; or in other words, were the portion of the sphere on which it is ground formed into a globe of corresponding convexity, it would be four inches or eighty inches in diameter.