Supposing we wish to make a reflecting telescope of six feet focus, or a surface of an object-glass of twelve feet radius, all we have to do is to get a long rod, a little more than twelve feet long, and pin it to a wall at its upper end so that it can swing, pendulum fashion; then at a distance of twelve feet below the point of suspension a pin is stuck through the rod and its point made to scratch a line on a sheet of metal laid against the wall; then this line will be part of a circle struck with a radius of twelve feet. If then the plate be cut along this line we get a convex and a concave surface of the desired radius, and then we can take a block of iron or brass and turn its surface, convex or concave, to fit the sheet of metal or template. For a reflector we should make a convex tool, and for a refractor a concave one. Generally this grinding tool is divided into squares or furrows all over it, in order that the emery which is used in rough grinding may flow freely about with the water. A disc of glass is then laid on the tool, or the tool on the glass, the two being pressed together by a weight or spring; emery powder, with water, is strewn between them, and one is rubbed over the other by a machine similar to those used for polishing, which we shall explain presently. This operation is continued until the glass is ground all over, and in this process of rough grinding the rough emery is used between the tool and the glass, so that whatever irregularities the glass or tool may have they are got rid of, and it is easy to obtain a spherical surface, and indeed, it is the only surface that can be obtained. Then finer and finer emery is used, till it ceases to be a sufficiently fine substance to use, and a surface of iron or lead is also too hard a surface. Now the polishing begins, and the optician and amateur avail themselves of a suggestion due to Sir Isaac Newton, who always saw much further through things than other people. [Illustration: FIG. 65.—Showing in an exaggerated form how the edge of the speculum is worn down by polishing. ] Even when he first began to make the first reflector, he used pitch, a substance not too hard, nor yet too soft, and one that can be regulated by temperature; therefore for polishing, instead of having a tool made of metal, pitch laid on glass or wood and supplied with rouge and water is used. This polisher of pitch is divided into squares by channels to allow free flow of rouge and water, and is laid on the mirror or object-glass, or vice versâ, and moved about over it. When the maximum of polish is attained the work is done, and the object-glass finished, as here we have to do with a spherical surface. In the grinding of the two discs for Mr. Newall’s telescope 1,560 hours were consumed, the thickness of the crown disc having been reduced one inch in the process.