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How does a vernier scale work?

Splitting the Difference : The Vernier Scale
It is difficult to describe in words how a vernier scale “works? but here we have a try. Typically , the main scale of an inch-reading vernier caliper is divided into 1/40-inch (0.025) intervals. Twenty-four such divisions, then , span 24×0.025=0.600inch.
The vernier scale, which is attached to the movable jaw, also spans 0.600inch, but that distance is marked off into 25 equally spaced intervals, not 24-each is0.024 inch in which. The difference between the width of a single space on the main scale and one on the vernier scale is thus 0.025-0.024=0.001 inch , or 1 “thou?
In use, the first part of the reading is made on the main scale. Note how many inches, tenths, and fortieths lie to the left of the zero mark on the vernier scale.
The trick is to find two marks, one on the main scale and one on the vernier scale, that exactly coincide.
There is more than one way to arrange a vernier scale . At least two manufacturers of precision instruments now offer a “long-scale?vernier , using 50 graduations on the main scale and 49 on the vernier scale, rather than the more usual 25 and 24. this spreads the marking out further , allowing easier reading. The verner principle is used on a great many measuring tools other than slide calipers , including micrometers, height and depth gauges of various sorts, protractors, etc.
Although seldom encountered , some verniers are calibrated in simple fractions, rather than decimal fractions , these invariably read to the nearest 1/128 inch. Naturally , there are also metric verniers, plus instrument that offer both metric and either fractional or decimal inch units. Usually, a metric vernier scale has 20 divisions, and so reads to 0.05 millimeter. Just as in inch-measuring instruments, however, there are “long scale?metric units that have 50 divisions, reading to 0.02millimeter.