If the rope which passes round the sheave of the block be small, it will be more flexible; a less force will be necessary to nip" it round the pin, and there will be less resistance by friction against the inside of the shell of the block. Perhaps we shall not be far wrong in ordinary cases if we estimate one sixth of the original force to be consumed by friction each time that the rope passes round a sheave. Thus, supposing the tension or strain on the hauling part to be 6, that on the next will be 5, the next 4, the next 3, and so on. So that if the strain on the fall of a two-fold tackle be 6, the tensions or strains on the parts of the rope will be represented by the figures 6, 5, 4, 3, and their sum 18 will nearly represent the power of the tackle instead of 24, which it would have been had there been no friction; or about one fourth of the force would have been consumed by it. in which the moving pressures upon the capstan are reducible to a couple manifestly occurs when they are arranged round it in any number of pairs, the two pressures of each pair being equal to one another, acting on opposite sides of the centre, and perpendicular to the same line passing through it. This symmetrical distribution of the pressures about the axis of the capstan is therefore the most favourable to the working of it, as well as to the stability of the shaft which sustains the pressure upon it." -Moseley's Mechanics. Suppose a weight of 24 to be suspended by the above tackle. If the fall would just bear a weight of 6, the four parts would be sufficient to suspend the weight; but if it were required to raise it, we must have a rope at least one third stronger; or equal to sustain a weight of 8. The tensions would be, according to the above rule-8, 62, 51 and 4, and their sum will be 24, which is what we require to lift. From these considerations we gather, that work is lightened by using large blocks and small ropes; that the Boatswain's rule, that the hauling part of a fall bears double the strain of the standing part, is not far wrong; that as the pin of a block is more worn on one of its sides, it should be frequently turned; and that as sheaves nearest the standing part do least duty, they should be shifted occasionally with the others.* CHAP. VIII. THE TELESCOPE. To comprehend the general principles on which the Achromatic Telescope is constructed, it will be necessary to understand certain facts respecting the composition and effects of Light. 66 "Vision or Sight is produced by the rays of light, which fall from the sun (or other source of light) on an object; being reflected from thence, so as to fall upon the retina or back part of the eye; thus, the moon is seen by the rays of light which fall on it from the sun, being reflected back to the eye; and a tree or house, or any other object, is seen by the daylight which falls on the tree or house, being in like manner reflected on the eye."† Transparent bodies of various forms are called Lenses, and rays of light passing through any lens undergo certain changes in their direction, according to its form and density. Thus, the tendency of a convex lens is to concentrate parallel rays * See page 158. Bell's Bridgewater Treatise. passing through it, and bring them all to one point or focus; whereas that of a concave lens is to disperse them, by throwing them more apart from each other. The density of the lens, or transparent medium, effects similar changes; a ray passing from a rarer to a denser medium, as from air into water, or glass, is said to be refracted or bent from its straight direction - an effect, which may be observed in the bent appearance of an oar when dipped in the water. A set of rays diverging from any point is called a Pencil of rays; the central ones being called its Axis. The distance of the focus of a double lens equally convex on both sides is equal to the radius of the curve. From the nature of a convex lens the axis of each pencil will pass straight through the lens, but its other rays will be collected on the axis in a focal line, at a distance beyond the lens equal to its radius. If all light be excluded except that which passes through the lens, and a screen be placed at the focal distance, the rays from the object will present an inverted image of it on the screen. It may be said, in passing, that this is what takes place in the human eye. Its principal apparatus is a double convex lens, called the crystalline humour, which is protected by a transparent coat called the cornea. Between these, and surrounding the crystalline humour, is a membrane, the iris, having a circular hole called the pupil, furnished with a muscular provision, by which its openings may be enlarged or diminished. In the back part of the eye, is an expanded network of nerves (the retina), which is connected with the brain by means of the optic nerve. The visual rays from the object pass through the pupil to the convex lens, which produces their inverted image on the retina, whence the optic nerve communicates their impression to the brain. An inverted image being formed in the tube of the telescope by the object glass A B, at n m (fig. 55), is presented in the natural position of the object by means of the different refractive powers of other lenses at m n, where it is viewed by the eye-glass, G H. The use of the eye-glass is to cause the rays emerging from E F to converge sufficiently to focalise on the retina; and thus the image is not only as minutely examined as though the object were close, but, being magnified in proportion to the focal length of the lens, is distinctly visible in all its details. For it is a law in cptics that we see everything in the direction of that line in which the rays approach us last. Thus, for instance, in fig. 56, a pencil of rays is shown diverging from the extremities of the smaller arrow; which rays, being refracted by the lens, are re Fig. 56. ceived in the eye precisely as if they emanated from the larger one. Such, in general language, is the Refracting Telescope; but the term "achromatic" involves a few words on the composition of light as well as the substance of lenses. By darkening a room, and placing a glass prism in an aperture in the closed shutter, so that a ray of solar light will pass through it, it has been shown that such light is a compound of other lights, all of which have different colours, and different degrees of refrangibility: and that in passing through transparent media, or lenses of unequal thickness, it becomes decomposed. In this mode of analysing light, the different rays are dispersed, and appear on the wall as in the order represented in fig. 57. Now, such being the composition of light, and as lenses act more or less like prisms, dispersing colour, it follows that the image of an object formed by single lenses must, from this interference of colour, be indistinct. This, opticians tried in vain to overcome, until it was discovered that, by composing and combining two or more Fig. 57. VIOLET INDICO BLUE GREEN YELLOW ORANGE RED lenses of different kinds of glass, each having different degrees of dispersive power, and so forming them as to refract the rays in counteracting directions, this chromatic aberration could be removed. Thus The object glass of an achromatic (free colour) telescope is P B ひ Fig. 58. FY composed of a double convex lens of crown glass outside, and another of flint glass, double concave, inside. "By the refractive power of the convex crown glass lens (fig. 58), the red rays in the pencil of light P Q would, if not interfered with, proceed in the direction a b. But the refractive power of the concave flint glass lens, c D, acts from its form in a direction contrary to that of a B, causing the rays either to diverge from the axis, x y, or to meet it in points beyond v and r, towards Y. Suppose the curvature of this lens to be such that the red rays in the pencil P Q would, after refraction in both lenses, meet the axis in F (the ray q b, r taking the direction b F), then the dis |