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If logic and economics were tossed into the mix, it favors stamp/rollmark. Engraving would take longer than all the other combined labor in a Sterlingworth.
The reality is that it takes about 5 minutes to engrave each side with the 'Fox Sterlingworth' as you see it having a pattern to lay it down with. If you have to lay it out on one side first add a couple of minutes for that. Make a card pull of the first cut and use it as a transfer for the opposite side. It's a simple lettering style, quick & easy to cut w/one chisel and it's nicely done in this case.
It's hand cut, simple as that. All you have to do is look at it to see that, and do the work I guess. The tool marks are there,,the variations, all of it.
That wriggle pattern and few chisel marks they call the rest of the Sterlingworth engraving,,add 20 minutes for the entire gun if you take your time. That's on new work.
About 30 minutes,,probably less in a factory repetative situation,, to cut a Sterlingworth complete (new work). I don't have any idea of how much combined hand labor went into one of these, but I'd guess 30 minutes or less on the apprentice level engravers bench wasn't more than the sum of the rest of the operations.
Takes longer to re-cut one for restoration if part of the old engraving is still visable after prep. Doing a good job you pick up the remnants of the old work walking the graver into and out of the old cuts instead of just running a new pattern right over it trying to hide it,,,which is done quite often.
VH Parkers are the same. Plus you match your tool shape and width to the one used to cut it originally. Something you don't have to be so precise about on an entirely new cut as there's nothing to match up.