There has been a lot of speculation about this term. It often shows up when describing British long-range rifles; for example, a sharpshooter is said to have killed Gen. Sedgwick in the Wilderness with a "globe-sighted Whitworth."
Some have thought this meant a telescope. I think, instead, the term referred to a hooded front sight (often a ball on a post) and perhaps an aperture rear sight ("peep sight").
Of course, the term could have meant different things to different people back then.
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Geoff Walden