The smoothing with the bed of hones is continued until the face of the speculum is brought to a very true and fine surface, uniformly bright, it is then put into the tube of the telescope, and tried as to sphericity and reflection, and any errors of figure that may be thus detected are removed by returning to the use of the bed of hones as often as may be requisite. The surface is made as perfect as possible with the hones, in order to leave but very little to be effected with the polisher, as should the polishing be long continued it is liable to depreciate the figure of the speculum.

Specula are polished on metal blocks coated with pitch, or a combination of pitch and resin, materials that are employed on account of their inelasticity.

The degree of hardness of the pitch, and its perfect freedom from all impurities, are matters of primary importance. For removing the impurities, the pitch is carefully washed with water and when melted, strained through linen. It is then thickened by boiling it slowly, until it is of such a consistence that when cold it will just admit of being slightly indented with the finger nail. Sometimes the pitch is hardened by the addition of about an equal quantity of resin, and this compound has the advantage of being less brittle than when pitch of equal hardness is used, and is therefore less liable to chip in the polishing. Should the pitch be made too hard, it may be softened with a little tallow.

The Earl of Rosse employed resin, melted and mixed with about one-fifth its weight of spirits of turpentine to soften it, this was adopted on account of the difficulty of obtaining the pitch free from gritty particles. But whether pitch or resin be employed, the hardness requires to be adjusted with great care.

If the pitch is too hard it will not readily take the figure of the speculum, and if too soft it will not sufficiently retain the figure.

In consequence of the different qualities of various samples of pitch and resin, no regular proportions can be adopted, and the degree of hardness must be decided experimentally in every case.

The form of the polisher is also a matter of considerable importance, the face of the speculum should be polished, not strictly spherical, but slightly parabolical. Mr. Mudge obtained an approximation to the parabolical form by first polishing the speculum as truly spherical as possible, and at the last finish giving the speculum a few large circular strokes upon the round polisher, so as to increase the radius of curvature near the margin. See Trans. Royal Soc, Vol. LXVII.

The elliptical polisher introduced by the Rev. John Edwards, and first described in the "Nautical Almanack" for 1787, will however give a much nearer approach to the parabolical form, without any other than straight or elliptical strokes in all directions. Mr. Edwards speaking of the proportions of the ellipse says, "for common foci and apertures, viz. from two-and-a-half to nine-and-a-half focus or 3.8 inches in diameter to eighteen inches focus the diameters should be as ten to nine. The shortest diameter of the ellipse being accurately the same as the diameter of the metal, and the longest diameter of the ellipse to the shortest diameter as ten to nine." Mr. Edwards also recommends that for speculums having a hole through the center, the polisher should also have a hole through it, of the same size or somewhat less than the hole in the speculum, and he adds, "I have always found that small mirrors without any hole in the middle, will polish much better and the figure will be more correct, if the polisher has a hole in the middle of it."

The Earl of Rosse, among his numerous experiments on the grinding and polishing of specula, tried this form of polisher, and expresses himself as follows: - "The experiments to which I have alluded were made with the elliptic polisher of Mr. Edwards, a contrivance in my opinion possessing more merit than has usually been ascribed to it. I found that a speculum of four inches aperture and eighteen inches radius, after having been polished by hand as truly spherical as I could make it, was invariably improved by working it on the elliptic polisher."

The polisher, generally made of pewter or lead, is turned on the face to the true curve of the speculum, but left rough in order to hold the cement. It is then warmed, and the melted pitch or resin is very uniformly spread over its surface about one-eighth of an inch in thickness, and when the pitch is sufficiently cooled to retain the impression of the finger, the speculum is dipped in water and pressed firmly upon the pitch as in taking the impression of a seal. Owing to the slow conducting power of the pitch, there will be no danger of the speculum being cracked by the heat, if the temperature of the pitch dees not exceed about 80 degrees, although a slight difference in the temperature of any quickly conducting substance, if placed directly upon the speculum, would be almost certain to cause a crack.

When the polisher has been moulded to the form of the speculum, the rough edges are pared away from the margin, and also around the central hole, if the polisher have one. The surface of the pitch is then divided into small squares by making grooves quite through its thickness with a heated knife, to allow of the polisher more readily adapting itself to the surface of the speculum.

The thickness of the coat of pitch is partly dependent on the size of the speculum, and partly on the hardness of the pitch: the hardness and thickness of the pitch requiring to be so adjusted, that the polisher will always yield to the surface of the speculum, so as exactly to fit it during the whole process. If the layer of pitch is too thin, it cannot expand laterally to enable it to ply to the surface of the speculum; and if too thick, it will expand so readily as not to retain the figure.

Oxide of iron, prepared as explained on page 1082, is in general employed for the polishing of specula. Sometimes the oxide of tin is used; but it is considered to give a whiter polish, that is less reflecting. The powder is kept mixed with water in a vial, and applied in the same manner as the polishing powder for lenses; but it is better to employ at the commencement as much of the polishing powder as is necessary for the completion of the polish, and if a further quantity is required, it should be applied as sparingly as possible.