Fine work!

I guessed before we reached there that the video demonstrates what I would call a “reciprocity” technicque.

This was used to make the first surface-plates, in fact; by hand-scraping and/or mutual lapping trios of them.

I wonder if too, this was used for the early astronomical telescopes and mirrors. That quote part-way though does talk of “speculae”, the fancy name for mirrors.

In one of his books Helmholtz describes grinding concave surfaces by abrading and polishing the surface of a circular blank.

It is clamped round its rim down to rings of very accurately (or precisely?) set screw-jacks. This raises the centre so when that convexity has been ground down flat, on release the glass springs back to leave the centre low. Obviously the underside will have been ground flat in the first place.

Note for anyone intending to experiment: use new glass. Glass becomes more brittle with age, I am informed by those in the windows trade.

I knew the basic principle from a very different field, or rather, lake – testing nominally-identical hydrophones.

If of sufficiently “reciprocal” characteristics they will act as “projectors” (underwater loudspeakers) as well as hydrophones (microphones).

The three we can call A, B and C are made to “ping” at each other in water, using the same set of amplifiers, signal-generators and analysers. The results come out of a load of maths described in the text-books, though a computer did that for us; but in essence the technique is still the same, A to B, A to C, B to C.

And reverse if wished as with mutually-lapping those stones, although the soggy analogue is not necessary if one of the transducer trio has been calibrated independently, by an external laboratory, to give the necessary confidence test of the whole system.

The amateur method of making a concave mirror is sneakingly cunning. A round blank is inverted over a round lap of the same size, both flat at the start,  and moved in a straight line across it, rotated a little and repeat for ages. A little thought will show that the middle of the blank spend more of its time over the lap while the edges are over air some of the time. Hence the middle gets more grinding than the edge and it ends up dished.

I use a 8″ diameter cbn wheel I think it was £40 when I bought it. It wears down pretty quickly doing stones but that’s compared to normal grinding and I’m still on my first one.

Mmm, torn between 3 stones and trying to grind flat.

Something to ponder over whilst stuffing too much turkey down my throat 😊