Gauge means different things in different context.
Shotgun gauges – and less commonly rifle bores – are simple, as they tell you what weight of lead ball you could theoretically load it with. 1/x lb ball, where x is the gauge/bore number. E.g. a 12 gauge shotgun has a barrel wide enough to fit a 1/12 lb lead ball, and a 4 bore rifle can be loaded with a 1/4 lead ball. Such measurements are useful if the projectile being fired is a lead ball, but are less useful nowadays as few people use muskets.
Needle gauges are based off of wire gauges, which were determined by convenience. Needle gauges, like shotghn gauges, tell you how wide the opening is, and all three mentioned this far, decrease over diameter as gauge number increases.
Railway gauge measures distance between tracks. Unlike the three other gauges mentionedthis far, larger numbers do not mean greater track seperation. Rather, railway gauge is simply expressed as the distance between tracks, whether that be metric or imperial. Standard gauge is commonly held to be 1435mm or 4ft 8.5inches.
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