Nonio or vernier scale
Before the discovery of the laws of electromagnetism and optics between the end of the 19th century and the beginning of the 20th, the vast majority of measuring instruments used a graduated scale to show the measurement.
Think of rulers, scales, thermometers, clocks, barometers… They all have a subdivided scale with little marks. The separation between these marks determines the minimum appreciation or resolution of the instrument and therefore, the possible maximum precision with which we can measure.
Image 1. Examples of graduated scales
The same scale, different sizes. Sometimes two measuring instruments
On occasion, two measuring instruments of the same magnitude may have markings of different lengths apart despite representing exactly the same thing.
For example, in a classic mercury thermometer we can calibrate it by measuring the height of the mercury column by putting the thermometer in ice and later in boiling water. If we divide the difference in height into 100 equal parts, each division will be what we know as a degree Celsius.
However, in each thermometer the separation of a degree can occupy very different lengths. That will depend on the diameter of the glass tube through which the mercury rises and, above all, on the amount of it. Yes, that’s what the little ball of the thermometer is for, which acts as a deposit.
Image 2. Same temperature, different length
The problem comes when we want to have a very small measurement resolution, for example if we want to measure tenths of a degree. The human eye has a limit in its appreciation, below a millimeter it is difficult for us to discern and it is almost impossible for us to appreciate separations of less than 0.1 mm.
That implies that in order to appreciate tenths of degrees in a temperature range of about 100 degrees we would have to make huge thermometers. If you have an old mercury thermometer, you will see that it normally indicates tenths of a degree, but only for an interval of about 6-7 degrees (35-42 ºC), if we needed to measure tenths in a range of 100 degrees we would need a mercury thermometer. more than 15 times that length.
This is the case of the thermometer, but for example, if we seek to measure length, no matter how long we make the ruler, its resolution will be the same. This is where one of the most important inventions in the history of science comes in, one that you have surely seen and used but did not even know its name, THE NNON.
What is a vernier?
A vernier is an auxiliary scale to the main scale that many measuring instruments have, which allows to measure with greater accuracy than the main scale.
The best known example of the use of the vernier is undoubtedly the caliber or caliper. As seen in the following image, there is an auxiliary ruler (vernier) that can be moved along the main scale. In this case, it is a vernier with 20 samples and it would allow measuring with 0.05 mm precision, 20 times better than if the vernier did not exist and we only had the main ruler.
Later on it will be explained how the vernier works, but let’s stop for a moment to analyze what this brilliant invention achieves. In the image we have two rulers, one with a resolution of 1mm and the other with a resolution of almost 2mm.
However, the resolution of both rulers combined is 0.05 mm. At a glance I can easily see that the instrument in the photo is marking 27.1 mm, thanks to the fact that the divisions of both rulers are easily distinguishable by our eye.
Origin of the vernier
The vernier receives its name from the Portuguese mathematician and astronomer Pedro Nunes (Petrus Nonius in Latin) who in 1514 invented this device to measure angle fractions with an astrolabe.
Depending on the country and scope of use, this invention is also known as a Vernier scale after the French mathematician Pierre Vernier (1580 -1637) who better documented the invention and used it to make highly accurate length measurements.
Its use became popular at the end of the 18th century and the beginning of the 19th century during the industrial revolution, allowing the production of mechanical components with very high precision. Without this degree of precision, the scientific revolution that would take place during the 19th century would not have been possible.
Image 3. Telescope with a Vernier scale (1887 – 1920)
National Museum of American History
How does it work?
The vernier has a very simple working principle, it is a second mobile rule that moves over the main rule with a different scale and a length equal to a multiple of divisions of the main rule.
Generally, a number of divisions of the main rule is chosen and the vernier is designed to have that length but with one division more or
one less for easier reading.
A very typical case in gauges where there is a rule with 1mm resolution, is to make a vernier of 19mm in length or 39mm (the one in the image) with 20 divisions. Therefore the combined resolution will be 1 / 20 = 0.05 mm.
To read the measurement of a gauge, it is enough to first see between which values the 0 of the vernier has remained, with that we will know between which values the final measurement will be. In the case of the following image, we know that the measurement will be between 27 and 28.
The second step is to observe which mark of the vernier coincides with a mark of the main rule. In this case, the second mark of the vernier coincides, so that by representing each mark 0.05 mm, the gauge measurement will be 27.1 mm.
Conclusions
Although the appearance of electronics and digital instruments has relegated this invention to the background. The vernier is still used in a multitude of analog and manual measuring instruments, which allow the user to visualize measurements with precision without the need for batteries or access to the electrical network.
In addition to the caliper, the combination of the vernier with a fine pitch screw, also known as a micrometer, are two measuring instruments in common use today, whose design has hardly changed since its origin, and which have been allowing us for more than 100 years measure with micron precision.
