Vernier, an instrument attached to a scale for the purpose of measuring spaces smaller than those into which the scale is actually divided. The principle of the vernier will be best understood from the figure. The lower scale, marked 8-9, is part of a scale of inches divided into tenths. The upper scale, marked 0.... 10, is the vernier, and is movable upon the scale of inches. The ten divisions of the vernier are exactly equal to nine subdivisions of the scale of inches, consequently each division of the vernier equals 9/10 of 1/10 of an inch, or 0.09 inch. When the 0 of the vernier coincides with one of the marks of the principal scale, the 1 of the vernier will fall 0.01 inch short of the next division of the principal scale, the 2 of the vernier will fall 0.02 inch short of the next division of the principal scale, and so on. If we shove the vernier forward 0.01 inch, its 1 will exactly coincide with one of the subdivisions of the principal scale; if we shove it forward 0.02 inch, its 2 will exactly coincide, and so on. In the figure the vernier has been pushed forward until its 0 falls between 8.6 and 8.7 inch, and is supposed to be at the point to which we wished to measure.
Looking along the vernier, we see that its division marked 7 exactly coincides with one of the divisions of the principal scale. The correct reading of the whole apparatus then is 8 inches, 6 tenths, and 7 hundredths, or 8.67. In what are sometimes called "retrograde verniers " 10 divisions of the vernier correspond to 11 of the principal scale, and are numbered and read in the opposite direction to the principal scale, but the principle involved is the same. Other ratios besides 9: 10 or 10: 11 between the vernier and the principal scale are employed in different instruments, according to the purposes for which' they are intended. When great delicacy is required, the measuring instrument is furnished with a microscope, in order to perceive more accurately what lines exactly coincide, and also with two or three verniers, and all are read and the mean is taken. The vernier derives its name from Peter Vernier of Brussels, an engineer, who invented the instrument in 1631.