Let o be the upper part of an object, and let o N be the direction of the rays in a pencil of light diverging from o; the rays of this pencil will, after being reflected at n, converge to o, which will be the lower part of the imago or. From o the rays in the pencil diverge, and having fallen upon the small mirror at n, they are reflected from thence towards the eye-piece Er : having passed through the orifice Ink, they fall on the lens at r, by which they are made to unite at p, where an image, pq, of the object is formed. From p the rays in the same pencil again diverge, and, falling on the lens at F., they are made to emerge in parallel directions, so that the eye is enabled to obtain dis tinct vision of the object in the same position as if the latter were viewed by the naked eye. The rays, after being reflected at n, might with a due concavity of the smaller mirror have united, as at p', in front of the great mirror, and the second image might have been formed at A': in this case the rays in each pencil, after crossing one another, would have fallen in a divergent state on the lens at F, and then, by the refractive powers of both lenses, they would have entered the eye in parallel directions as before. The positions of the lenses at t: and r, and the curvature* of their surfaces, are determined according to the method of Iluyghens ; and the construction differs in no respect from that which has been described in speaking of the eye-pieces of dioptric telescopes.
The magnifying power of a reflecting telescope of this kind is ex pressed by the in which vs is the focal length of the xy.nz great speculum, oy is the distance of the small speculum from the image pq, x y is the focal length of the second eye-glass, and nz is the focal length of the small speculum for parallel rays.
In the Cassegrainian telescope the small mirror o is made convex, and it is placed so as to intercept the rays from the great speculum N before the image of is formed; the rays of each pencil consequently fall in a convergent state on the small mirror, and, after reflection from thence, unite to form the image either at III' or after refraction in the first eye-glass F. It is obvious that these telescopes, with equal !nag raying power, will be shorter than the Gregorian telescopes by inure than twice the focal length of the small speculum ; and it may be added that, in some degree, the spherical aberration is corrected by the con trary curvatures of the two mirrors.
The Newtonian reflecting telescopes have one concave speculum at the bottom of the tube ; and, in each pencil of light, the rays reflected from it fall in a convergent state upon a small plane mirror placed so as to make an angle of 45° with the axis x v of the telescope : after the second reflection the rays unite and form an imago which is viewed through a Huyglienirin eye-piece fixed in the side of the tube A n ,oppo site the plane mirror ; that is near the open cad of the tube.
The great telescope constructed by Herschel differs from the New tonian telescope only in having no small mirror. The surface of the great speculum, which is 4 feet in diameter, has a small obliquity to the axis x v, so that the imago formed by reflection from it falls near the lower side of the tube at its open end : at this place there is a sliding apparatus which carries a tube containing the eye-glasses. The observer in viewing, is situated at the open end of the tube, with his back to the object, and he looks directly towards the centre of the speculum, the magnitude of which is such that the rays intercepted by his head, in coining from the object, do not in any sensible degree diminish the brightness of the image.
Formerly the great speculum of a reflecting telescope was pressed into its cell by means of springs attached to the interior side of the brass plate at A ; but the vibrations of the springs were found to cause tremulous motions in the image at the focus of the mirror ; and this effect was so great as to render reflecting telescopes inferior to those of the dioptric kind. The Rev. Mr. Edwards, who detected the cause of the tremors, at once removed it by taking away the springs (' Naut. Alm,' 178i); and the same gentleman further improved the distinct ness of the image by enlarging the aperture to which the eye is.applied.
It has been observed also that when the great speculum is nearly in a vertical position, and consequently rests on its lower extremity, its weight bends it, and thus causes a change in the figure of its polished surface : on this account it is recommended that the speculum should be made to rest on two small wedges, placed one on each side, at about 45° from the lowest point.
Since specula have been enlarged in their proportions the difficulties in the way of attaining distinct vision have increased. Sir W. herschel's 4S-inch reflector weighed 25 cwt., but the 6-feet speculum of Lord Rosso weighs no less than 4 tons. This, as Sir John Herschel remarks, requires the use of very powerful and costly machinery in the construction of such specula and also in their management when con structed. Speculum metal, though highly elastic and rigid is, as above noticed, liable to bend, and thus lose its figure. Herschel notices the case of a speculum of 18 inches aperture, 20 feet focus, and 2 inches in thickness which was found to be totally spoilt, by being supported on three points at its circumference, and when reclined against a flat and strong wooden back, with a single thin packthread interposed down the middle, all trace of figure was destroyed, and the surface was divided into two lobes, each producing an imperfect image of a star, connected with an irregular burr of light. Lord Roam found that a strong pressure of the hand at the back of his 6-feet speculum, which is nearly 6 inches in thickness, produced sufficient flexure to distort the image of a star ; and in one of Foucault's silver-glass mirrors the excess of central pressure of a somewhat over-inflated air cushion destroyed distinct vision. The speculum, therefore, requires to be uniformly supported over every part of the back. Where the weight does not exceed 200 or 300 lbs. a bed of several layers of even textured woollen blanket is sufficient, provided, as Herschel remarks " the whole be supported on a back so strong as not to yield under the pressure in any part more than a small aliquot of the total compression of the cushion." For small mirrors or for light glass ones an air cushion is a good contrivance. For a very heavy one, such as Lord liosse's six-feet speculum, an ingenious plan was adopted on the idea of the common " splinter bar," by which the pull of two, four;or eight horses drawing at once is equalised so as to distribute the work equally among them. The back of the mirror, supposed to be of uniform thickness, is divided into three sectors of 120°. Let the centre of gravity of each of these sectors be sustained by a projecting knob, at one of the angular points of a sLah of iron in the forum of au equilateral triangle, which is itself sustained by a point under its centre of gravity. In this way each sector being separately supported would produce no strain on the others, and the whole weight would be equally distributed among the three points of support. But to prevent jametrating power, he observe" that the quantity of light received by the natural eye varies directly with the aperture of the pupil, or with the equate of its maim, and inversely with the square of the distance of the object : also that the quantity of light transmitted by a tele scope. suppoeing none to be lost in the reflections from the mirrors, or in refraction through the lenses, will vary directly with the square of the radius of the aperture and inversely with the square of the distance of the object. But, from experiments on the measure of light, it appears that the whole quantity incident upon a plate of glass is to the quantity transmitted through it as 1 in to '0381, or to the quantity .rat as 1 is to '0619; and from this, the whole quantity of incident light being unity, an estimate may be made of the quantity of light transmitted through all the lenses of a telescope : with renpect to the quantity lost in reflection from mirrors Sir W. Herschel found that out of 100,000 incident rays, only 45,242 reached the eye after two re tlections.