To produce a true and uniform curve is, however, the acme of troubles, whether it is desired to obtain the spherical, or parabola, or any other curve. It is generally supposed that the spherical curve is a very easy matter, so easy indeed that it is difficult to avoid. This is a very great mistake—a spherical curve of undeviating truth is as difficult a problem as a true parabola. The spherical curve is the _only uniform_ curve, it has but _one_ focus, and the polisher must coincide with, and be of the same radius as the glass, at every instant. This is why the optician strives to obtain a semi-polish with the grinder to lessen the risk of losing his curve on the polisher, for the curves of an object glass are spherical. The curve most liable to be obtained by the amateur is the spheroidal, a curve with its marginal rays _shorter_ than the central, or half the radius of curvature.
There are no means with the _telescope_ of telling the spheroidal, approximating to the sphere, _from_ the sphere. There are _no_ means of analyzing the exact character of a curve _equal_ to certain methods at the centre of the curvature, but to accomplish this requires much practice and observation, with “surroundings” perfectly free from vibration. If the amateur can overcome this, and lives in or very near a town, he should only work at the polishing and figuring during the late hours of the night, when traffic, &c. have subsided. Then, by carefully preventing any draughts in the apartment, and with the mirror of the same temperature as the air in the room, he will then be able to see how varied and numerous are the chances of error in working a mirror, and the great care necessary to avoid or cure them. He will find the surface exceedingly prone to receive zones and irregularities during work, and much more so than to “work true.”
The necessity for avoiding incautious handling or heating may be realized by the following little experiment when one can manage and understand it:—Place the tip of one finger on the surface, as it hangs in the dark room ready for testing, and with very gentle pressure let it remain long enough to spell one’s name; it will then be seen that the feeble heat of the finger has, by expansion, raised a mound on the surface of the glass, and though this amount of swelling must be _very_ small, yet it is enough to cast a shadow across the surface, as if something were laid on it, and quite ten minutes will elapse before the heat will leave this spot and the surface again become level. Now if the polisher were placed on the glass while this hillock was there, a permanent hollow would be the result. For a full account of these methods (of which Foucault was the discoverer) the reader is referred to Sir John Herschel’s and Dr. Draper’s works on the telescope.