The figuring is done in a fashion very similar to the polishing. The first step is to find out by optical tests such as are described in Chapter IX the location of the errors existing after the polishing, and once found, they must be eliminated by patient and cautious work on the surface.
Every optical expert has his own favorite methods of working out the figure. If there is a hollow zone the whole surface must be worked down to its level by repolishing; if, on the other hand, there is an annular hump, one may repolish with stroke and tool-face adapted to cut it down, or one may cautiously polish it out until it merges with the general level.
Polishing is commonly done with tools of approximately the size of the work, but in figuring there is great difference of practice, some expert workers depending entirely on manipulation of a full sized tool, others working locally with small polishers, even with the ball of the thumb, in removing slight aberrations. In small work where the glass can be depended on for homogeneity and the tools are easily kept true the former method is the usual one, but in big objectives the latter is often easier and may successfully reach faults otherwise very difficult to eliminate.
Among well known makers of telescopes the Clarks and their equally skilled successors the Lundins, father and son, developed the art of local retouching to a point little short of wizardry; the late Dr. Brashear depended almost entirely on the adroitly used polishing machine; Sir Howard Grubb uses local correction in certain cases, and in general the cautiously modified polisher; while some of the Continental experts are reported to have developed the local method very thoroughly.
The truth probably is that the particular error in hand should determine the method of attack and that its success depends entirely on the skill of the operator. As to the perfection of the objectives figured in either way, no systematic difference due to the method of figuring can be detected by the most delicate tests.
In any case the figuring operation is long and tedious, especially in large work where problems of supporting to avoid flexure arise, where temperature effects on tool and glass involve long delays between tests and correction, and where in the last resort non-spherical surfaces must often be resorted to in bringing the image to its final perfection.
The final test of goodness is performance, a clean round image without a trace of spherical or zonal aberration and the color correction the best the glasses will allow. Constant and rigorous testing must be applied all through the process of figuring, and the result seems to depend on a combination of experience, intuition and tactual expertness rarely united in any one person.
Sir Howard Grubb, in a paper to be commended to anyone interested in objectives, once forcibly said: “I may safely say that I have never finished any objective over 10 inches diameter, in the working of which I did not meet with some new experience, some new set of conditions which I had not met before, and which had then to be met by special and newly devised arrangements.”
The making of reflecting telescopes is not much easier since although only one surface has to be worked, that one has to be figured with extraordinary care, flexure has to be guarded against at every stage of the working, and afterwards, temperature change is a busy foe, while testing for correct figure, the surface being non-spherical, is considerably more troublesome.
An expert can make a good mirror with far less actual labor than an objective of similar aperture, but when one reads Dr. Henry Draper’s statement that in spite of knowing at first hand the methods and grinding machines of Lord Rosse and Mr. Lassell, he ground over a hundred mirrors, and spent three years of time, before he could get a correct figure with reasonable facility, one certainly gains a high respect for the skill acquired.