The vernier scale is a clever way of improving the precision of a reading on an instrument scale. It has been used on quite a number of instruments, many of which have nothing to do with surveying. Machinists’ calipers come to mind, for example. The scale has been especially useful for the so very fine angle scales of a theodolite. Although it has been largely replaced by optical and electronic micrometers, it is still in use.
In theory only, it should be possible to add another decimal place of precision to a scale by making the graduation intervals one-tenth as wide and ten times as dense. The problem soon becomes clear as the graduation marks are anything but clear. Even if it is possible to etch such a scale accurately, who could read it? The scale would become an indiscernible blur.
Below is an image of a simplified linear scale. Never mind what the units are. The bottom section is graduated in units and tenths. It can be read directly to one decimal place of precision. The vernier scale fits above it and has ten graduation intervals. These intervals are actually 0.09 units. The zero mark of the vernier scale is the pointer for the main scale. Use this to read units and tenths. Here the reading is somewhat more than 1.4 units. Now, from that pointer, count the intervals on the vernier scale until a mark aligns with one of the marks on the lower scale. In this image that happens on the third mark. The reading is 1.43 units.
So how does it work? Each interval on the vernier scale has a width of 0.09, so three intervals cover a distance of 0.27. Add that to the 1.43 of the lower scale. The sum is 1.70, which falls dead on one of the tenth marks of the lower scale.
The same concept can be applied to a circular scale like that used on a theodolite. In the image below, the main outer scale is graduated in intervals of 30 minutes. Each interval on the vernier scale has an arc measure of 29 minutes. Again, count graduations up to the point at which a mark aligns with one on the lower scale. This will show the number of minutes to add to the direct reading.
This scale is a bit more complex because the older-style instruments could read angles either right or left. There are two sets of numbers on the outside, stationary scale. The top numbers give the angle right, which is actually read to the left. This may be counterintuitive, but from this perspective the vernier moves to the left as the instrument turns to the right. There was a time (never to return) when I could read a one-minute scale without a magnifying glass. Verniers have also been used for a least-count precision of 30, 20, or 15 seconds. The scale is read with a magnifying glass, often attached to the instrument itself.
For Java-compatible browsers, animated vernier scales appear below. Drag the red points to move the scales.
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