Bazyle –
I remember that fim scene. The character (played by Albert Finney?) was operating a capstan-lathe and looking beyond the notion of dramatic licence, it's quite possible his real-life version would have had the lathe set up for him, and taken the setter sufficiently on trust not to need measure the piece-parts himself.
The inspector would have measured the first two or three off and maybe odd ones at intervals, and once happy, let the turner carry on until the long-awaited clocking-off time broke the monotony.
Automatic or semi-automatic lathes, controlled by cams profiled for the work, had been around though, and for decades before 1960. One photo I have seen appears to show the cams as strips screwed to a perforated drum on the outer end of the headstock, but I don't know how their motion was transmitted to the saddle, etc.
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As for losing sight of the inches as Howard warns, I manage to lose sight of whole inches, not just mere one-hundredths of them!