The Vernier

Usually, the marking on the thimble of the micrometer does not fall directly on the index line of the sleeve. To make possible readings even smaller than thousandths, an ingenious device is introduced in the form of an additional scale. This scale, called a VERNIER, was named after its inventor, Pierre Vernier. The vernier makes possible accurate readings to the ten-thousandth of an inch.
Principle of the Vernier
Suppose a ruler has markings every tenth of an inch but it is desired to read accurately to hundredths. A separate scale (fig. 6-3) is added to the ruler. It has 10 markings on it that take up the same distance as 9 markings on the ruler scale. Thus, each space on the vernier is 1/10 of 9/10 inch, or 9/100 inch. How much smaller is a space on the vernier than a space on the ruler? The ruler space is 1/10 inch, or 10/100 and the vernier space is 9/100 inch. The vernier space is smaller by the difference between these two numbers, as follows:
Vernier scale.
Each vernier space is 1/100 inch smaller than a ruler space. As an example of the use of the vernier scale, suppose that we are measuring the steel bar. The end of the bar almost reaches the 3-inch mark on the ruler, and we estimate that it is about halfway between 2.9 inches and 3.0 inches. The vernier marks help us to decide whether the exact measurement is 2.94 inches, 2.95 inches, or 2.96inches.