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For a start, Geoffrey, the frames of sextants were not brass, a copper-zinc alloy of dubious corrosion resistance, but bronze, whose main constituents were copper and tin. The composition of bronze varies widely, but "bell metal", with a high tin content was preferred. This is a tough and tenacious metal and one has to remember that the instrument maker in the late eighteenth and early nineteenth centuries used man-powered lathes, so turning a large radius was difficult. The metal had hard spots that could deviate the stylus of the dividing engine, so a dovetail was cut into the limb and a sliver of silver whose section was a segment of a circle was hammered into the dovetail and filed or turned flush. Silver of the time was available as almost pure silver, soft and without hard spots. I have an early sextant, probably from the late eighteenth century (see https://sextantbook.com/2010/06/10/a-sextant-210-years-on/), in which a brass limb was screwed on to the bronze of the frame and the heads filed off flush, perhaps because the turning power of the lathe was not up to turning the bronze. The silver was let into the brass limb in the usual way. I have another in which a limb of silver was attached to the bronze frame and an arc of gold let in. This has the advantage that it never tarnishes like silver does, but I suspect that using a silver limb was just showing off. 

For a brief period, a platinum alloy was used for the arc of some sextants, probably because like gold it does not tarnish and perhaps because no other use could be found for it at the time.

To minimise centring errors, the whole frame would be mounted on the dividing engine and the arc would certainly not be divided prior to attaching it to the limb, as Paul Dolkas suggests.

Bill Morris

Pukenui

New Zealand