Let the quantity of incideut light be to that which arrives at the eye as 1 to as; then r being the radius of the pupil, and ti that of Wet the aperture of a telescope, will express the ratio between the quantity of light transmitted to the naked eye, and through a dioptrio telescope : therefore the space-penetrating power varying with the square root of the quantity of light, r f expresses the penetrating power. With respect to reflecting telescopes, if n' be the radius of the small speculum, the penetrating power will be expressed by r N/111*(0-0)1. It is necessary to observe that, in these expressions, it is supposed that the pencil of light transmitted by the telescope is not greater than the pupil of the eye.
It has been said above that, in reflecting telescopes, a speculum at one extremity of the tube serves the purpose of the object-glass in refracting telescopes by forming an image at its focus; and the manner in which, in the former instruments, the image is transmitted to the eye remains now to be explained.
The following diagram represents a longitudinal section through the the flexure of each sector it may be divided into three portions of equal weight, and the centre of gravity of each portion being found, it in turn is supported on a pin or knob on one angle of a smaller or secondary iron slab, which in its turn is supported on its centre of gravity by resting on one of the points of the primary triangle. In the case of a six-feet speculum each of these secondary areas may be subdivided into three equal tertiary areas similarly supported on tertiary triangular slabs each supported at its centre of gravity on one angle of a secondary one. In this way the mirror may be conceived as being subdivided into twenty-seven equal areas, each separately sup ported at its centre of gravity, and thus not liable to bend by its own weight. In practice, however, certain levers are introduced, the action of which does not interfere with the principle of the contrivance. This clever arrangement, however, was defeated by the adhesion or stickage, as it is called, of the metal to its cushion, and this stickage amounted to two tons when the speculum was resting on the bottom of the tube. Hence it has been found necessary to suspend the speculum from above, by means of bends of steel or some other support.
A reflecting telescope is liable to irregular action from currents of unequally heated air in the tube, which cause remarkable distortions and movements in the images of objects. Sir John Herschel (' Results of Cape Observations') describes a method of substituting for the tube an open frame-work of iron which gets rid of the objection from counter currents of air.
Under SPECULUM some details are given respecting the composition, the grinding, and the polishing of specula. As similar information respecting glass lenses is not given under the article LENS, the deficiency may to some extent be supplied in this place ; the reader desirous of more ample information is referred to the third volume of Holtzapffel's Mani. pulation,' 1850. The spherical surfaces of lenses are formed by grinding the glass in counterpart metal tools (jig. 10), prepared te • the proper curvatures with the assistance of grinding and polishing powders. The tools are in pairs, concave and convex, and these art first made to correct each other's errors, which they do on the principle which applies also tc the lenses themselves '• of the natural tendenc3 of two surfaces which grind each other bi equable rubbing over every part to work each other into a apherica concavity and convexity exactly fitting." (Herschel) Hence it ii
comparatively easy to form lenses into truly spherical surfaces. The concave and the convex tools grind each othem true with Oa assistance of emery and water,- although Mr. Ross thinks greater accuracy is attained by using the emery dry. The glass tcm the lens is brought to the circular form by means of thanks or flat pliers o soft iron, or to save the material (since good optical glass is mon precious than geld) selected fragments of glass blocss are softenei of heating to redness, moulded to nearly the required form, and them carefully annealed. Each lens is then coated on one side with a layer o cement, which is run into a hemispherical mass sufficiently thick to hi grasped, so as to form a handle : but if the lens is of large size it i cemented to a metal handle, as a wooden one would swell. Thi cement is made by mixing wood-ashes with melted pitch. The glass i first rough ground within the metal shell or basin (jig. 11), either witl river-sand and water, or coarse emery am water, until the surface is brought nearly ti the curve of the shell. The glass is rubbcs with large circular strokes, and when th grinding has been carried far enough, thy glass is warmed, the cement handle is shifted to the other aide, and the grinding is continued on the second surface of the lens. Th parallelism of the two sides is obtained by observing that the edge o the glass is of equal thickness all round. The grinding is then coo tinned with washed emery, six sizes being used, the last size beia the fine powder collected after one hour's subsidence, and which leave so smooth a surface that when tho lens is held between the eye and the light it shows a semi-polish. Grinding the lens to the true figur or (racing the lens, as it is called, is generally done upon a post witl the concave brass tool, much in the same manner as the concave any the convex brass tools are made to correct each other. The grinding i continued with each size of emery, until the marks made with th previous size are removed ; everything being carefully waahe between the changes of sizes; for should a speck of a larger size gc into the work it might make a scratch which would render it necessar to re-commence the grinding. The polishing is performed with th assistance of putty powder, sifted through lawn and enclosed in a bo with a lid perforated with small holes; or still better, mixed wit water in a corked bottle, which is shaken up every time the powder to be applied, and allowed to subside for a few seconds., A arna quantity of the water hi then taken out with a clean stick, and throw upon the polisher, so that only the suspended portions of the putt powder are used. The powder is put upon a piece of thick silk (put, string), cut to the width of about seven-eighths the diameter of tl. lens, and stretched across the middle of the braes tool. The lens rubbed backwards and forwards in straight lines along the silk, whi the same time it is twisted round in the hand, and also traversed •adually sideways, until the centre of the lens is brought to the edge the silk, when the direction of the traverse is reversed. For the lost carefully finished lenses, however, a pitch tool is prepared as escribed under SPECULUM.