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After we have generated our curve by rough grinding and smoothed it by fine grinding, we are ready to finish smoothing by polishing. During grinding, the grains of abrasive are rolled between the glass surfaces and chip out pits from the surfaces of the glass. Smoothing by fine grinding consists simply of continuing the process with smaller and smaller grains to reduce the pit size. Polishing smoothes the glass by a different process. In polishing, the abrasive is embedded in a softer surface and scrapes the surface of the glass. This softer surface is called the polishing lap or pitch lap.

We have several choices of abrasive for polishing and several choices of material to form the lap. The lap material should easily be conformable to our mirror curve, it should yield slowly under sustained pressure, and it should hold the abrasive firmly against the mirror face in polishing. Bee's wax or tar may be used, but we usually use pitch for the lap and cerium oxide for the abrasive.

What we shall actually start with is some lumps of rosin and a little turpentine, since they are easily available at hardware or paint stores, and reconstitute our pitch by mixing them together. (Editor's Note: If you do not wish to prepare your own pitch from rosin and turpentine, commercially prepared pitch may be purchases from a telescope supply company. Heat it the same way.) Slowly, we heat the rosin in a coffee can or the like over a low fire. We heat it and stir it until it reaches the consistency of cold honey. When the last lumps are gone we stir in a little turpentine, about two tablespoons per pound of rosin, and adjust the heat so that it stays about as pourable as cold honey.

Meanwhile, we have thoroughly cleaned our mirror glass and heated the tool in warm tap water. We have spread some old newspapers over the top of the worktable and moistened a wooden stick, such as the crossbar of a wooden clothes hanger, for grooving our pitch lap while it is still warm. We should also keep handy some cerium oxide, a container of water for wetting the mirror face, and a small cloth or paper for smearing turpentine on the face of the warm, dry tool.

When everything is ready we wet the mirror face and smear it with a little cerium oxide. We dry the tool face and smear it with a little turpentine. Then slowly we pour the warm pitch on the center of the tool face and watch it spread toward the edges of the tool. It shouldn't quite reach the edge. If it seems to be spreading too rapidly in one direction we shift our pouring position a little off center in the opposite direction. When it appears that without further pouring the pitch will spread almost to the edge of the disc we cease pouring and for a moment, we watch. If now the pitch appears to be approaching the edge too closely we may raise that edge slightly or restrain the flow with our wet fingers.

Almost immediately, when the flow has nearly ceased, we very lightly press the wet mirror face down on the pitch till the pitch flows almost to the edge. Then quickly we whirl the mirror a bit to be sure that it is loose and drag it quickly off the pitch. Then quickly we press grooves into the pitch face with the wet stick.

The first groove should cross the disc about half an inch from the center. We then press a series of grooves parallel to it a little more than an inch apart right out to the edges. We then press a groove almost across the center of the disc and perpendicular to the fist groove. Then again, parallel grooves a little more than an inch apart, right out to the edges, so that the final pitch lap resembles a plate of butterscotch candy all cut into squares. We then repress the first set of grooves, then the second set, and if necessary pull up the pitch around the edges of the disc with our wet hands. Then we repress the whole face of the lap with the wet face of our mirror blank and we are ready to polish.

When the pitch lap is repressed with the mirror face after grooving or "waffling", the pitch should still be sufficiently soft to allow the faces of the squares to conform to the face of the mirror. If the pitch appears too soft so that there is danger of squeezing out the grooves, the mirror should be removed and the pressing delayed a little. If necessary, repress the grooves. If the pitch gets too cook, heat it in the oven or in hot water.

While the lap is firming up by cooling, the mirror should be moved occasionally to avoid building up a waffled heat pattern in the mirror face, and any excess pitch which overflowed should be cut away.

If possible, the polishing should proceed immediately when the pitch lap is firm.

In connection with their telescope making classes, the San Francisco Sidewalk Astronomers have poured pitch laps in this manner at the rate of nearly twenty per hour. It is a hasty job and can be messy but it should not be thought of as difficult.

The purpose of grooving the lap is to allow the pitch, under pressure from the mirror face, to yield with equal facility over the entire curve. It allows the pitch to yield at the center of the lap as well as at the edge and thus allows the lap to keep its conformity with the mirror face.

If gradually, under use, the grooves squeeze shut, the lap should be heated and re-grooved. The lap may be heated in a hot water bath or in the oven, or weather permitting, in the sun. On a warm, windless, summer day the re-shaping of the lap in the sun is very easy, as there is then no anxiety that the pitch may get too cool.

The pitch lap need not be poured on one's own tool. The San Francisco Sidewalk Astronomers save the pitch laps from one class to be used by another. They require simply to be heated and reshaped to the new curves. One advantage of having a lap on another surface is that it leaves one's own tool available to repair any mistakes made in fine grinding without re-pouring the lap. The lap may be poured on another tool or even on a flat blank but the lap must be no large than the face of the mirror or pressing becomes virtually impossible.