## Verniers

A Vernier, named after Pierre Vernier, is a very elegant way of determining the position of one line, on one scale between two other lines on another scale.

Suppose we have a scale that is for measuring in millimeters. This will consist of a series of lines spaced at 1mm. This scale can be as long as is needed. With a scale like this we can measure very easily to the nearest millimeter but the space between any two of the lines has to be estimated.

To read it more accurately we need another, special, scale. In the simplest case this scale might be just 10mm long but it has 11 rather than ten spaces. This means that each space on the vernier is very nearly just 0.9mm.

fig

In the above example the fiduciary line is at a position of 0.5 mm from the nearest millimeter mark on the scale. However it will be seen that given the spacing on the Vernier is 0.9mm it so happens that the next graduation on the Vernier that lines up with a graduation on the scale is 0.5 plus 5 * 0.9 which happens to be the fifth line so the reading is whatever we started from plus 0.5mm.

This idea can be extended in the following photo the primary scale is in millimeters. The Vernier is 50mm long but is split into 51 spaces. This enables the scale, which is in millimeters, to be read to 1/50 of a millimeter, that is, 0.02mm.

It might seem that this idea could be extended indefinitely but it cannot. The limit depends upon the fact that what has to be determined is whether two lines, one on either scale, line up. This is limited by the acuity of vision. In practice on a straight scale 0.02 is about the limit. It can be improved by means of a magnifying glass.

Another way it to “stretch” the scale. This cannot be done on a linear scale but it can be done on a circular scale. How this works can be seen on some micrometers. On a conventional hand held micrometer it is possible to read to 0.02mm.

fig a micrometer scale

A few micrometers like this do have verniers but this is unusual. If a micrometer is required to read smaller amounts the scale is “stretched” simply by making the scale longer by making the diameter of the mircometer barrel larger.

fig a “stretched” micrometer scale

fig detail of stretched scale

Verniers can also be used to measure angles. Here, again, the scale can be made longer by increasing the diameter of the scale.

fig vernier on protractor

fig vernier on a scale from a spectrometer