A Better Lap
By placing the punch carefully over a circle there, an arc of any size can be cut, and the segment of rubber cut out with a knife or razor blade. Trim the mat to within 3,4" of the holes. Remnants of the paper pattern can be removed by soaking the mat in
water. The operation of making the lap is best done on top of a scrap piece of windowpane or other sheet glass. So that the facets will not squeeze down quickly, the pitch for this lap should be on the hard side.
When melted, the pitch should be removed from the stove and allowed to cool briefly, and be thoroughly stirred before pouring. Have the mirror and tool in a pail of hot water while the pitch is melting. Lay the mat on the clean sheet of glass, and paint it all over with a light creamy mixture of rouge1 and water. While the pitch is cooling, remove the mirror from the hot water and dry it, then place it on the sheet of glass, face up, and paint
its surface and sides with rouge. Lay the rouge-coated rubber mat on it, carefully centered.
Take the tool from the hot water, dry it and place it nearby, convex side down. Quickly pour the hot pitch over the mat, starting at the center and spiraling outward nearly to the edge. Then, carefully centering the warm tool convex side down over the mirror, set it onto the pitch and press it firmly down to the rubber mat, squeezing the excess pitch out over the sides. After about a minute, invert the disks, and after a similar wait, slide the mirror off.
Allowing sufficient time for the pitch to harden, lift the mat from the lap. with a gentle stretching and pulling, carefully, so as not to break any edges off the facets. Trim around the edge of the lap with a sharp knife, flush it clean of rouge and pitch fragments, dry it and coat the surfaces of the facets with smoking hot beeswax. All of this takes about 15 minutes, less than half the time and fuss needed for the conventional lap. By working on a sheet of glass, messiness is avoided, and the surplus pitch can be recovered
and returned to the pot.
The theory of the graduated spacing (see diagram) is that an oblate spheroid can be brought spherical by concentrating the strokes on the diameter of greatest facet density, and that a spherical mirror can be similarly parabolized. There would be no walking around the barrel, but necessity for rotating the mirror and pressing frequently to maintain a surface of revolution on the lap.
But therein lies the rub: a similar surface must be present on the mirror. And so, because of the ever-present danger of an astigmatic surface resulting from this method, the above theoretical practice is not recommended. Used in the normal way, the graduated spacing permits a wider range of stroke than is possible on the channeled lap; thus "zones" are almost entirely eliminated, and the spherical and paraboloidal figures are more easily obtained.
Looking ahead, we find that this mat cannot be used for the lap. In this and succeeding discussions, "rouge" refers to any polishing agent.
for the diagonal mirror; the reader may therefore want to consider deviating from the above instructions.
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