#### 1. Direct Vernier:

Principle:

If it is required to read 1/nth part of the smallest division on the main scale, (n-1) main divisions are taken and divided into n equal divisions on the vernier scale as shown in Fig. 9.2. Here 9 divisions on the main scale have been divided into 10 divisions on the vernier scale. In this case, the vernier scale divisions are shorter than the main scale divisions.

Let d= the value of the smallest division on the main scale.

v = the value of the smallest division on the vernier scale.

n = the number of divisions on the vernier.

Then, nv=(n-1)d

The difference between the value of a division on the main scale and that on the vernier scale =d-v.

This difference is known as the least count of the vernier.

The least count of the vernier shown in fig. 9.2. is equal to 1/10th of the smallest division on main scale.

The value of the least count of a vernier may, therefore, be obtained by dividing the value of the smallest division on the main scale by the number of vernier divisions.

In this type of vernier, both scales are graduated in the same direction, i.e. both, either from right to left or from left to right.

(i) Determine the least count of the vernier.

(ii) Note the main scale graduation beyond which the index lies. This is the approximate reading.

(iii) Observe which division of the vernier coincides exactly with any division on the main scale.

(iv) Multiply the number of the coinciding vernier division by the least count. This is the value of the fractional part. Add this to the approximate reading taken in (ii) to get the exact reading on the main scale.

In figure 9.3, the main scale in graduated to half a degree i.e. the smallest division on the main scale, d = 30 minutes, and the number of the vernier divisions, n = 60.

Therefore the least count of the vernier:

The approximate reading is 335° and the vernier reading 10′ 30″, giving a total of 335° 14′ 30″. It may be noted that the longer graduations and figures on the vernier scale represent whole minutes.

#### 2. Retrograde Vernier (Fig. 9.4.):

In this type of the vernier, (n+1) divisions of the main scale are taken and divided into n divisions on the vernier scale.

In this case:

(i) Vernier divisions are longer than the main scale divisions,

(ii) The graduations of main scale are marked in the direction opposite to that of the vernier scale-one from right to left and the other from left to right.

The only advantage of a retrograde vernier is that the graduations are bigger than those of a direct vernier. But as it has to be read in opposite direction, which is rather difficult, it is not commonly used.

Double Vernier (Fig. 9.5):

With a simple vernier, readings can be taken in one direction only, but a double vernier is required when the graduations on main scale are marked in both discussions from the common zero, such as in Abney’s level. In a double vernier, two simple verniers are placed end to end forming one scale with the zero in the centre. One is used for readings in the clockwise direction and the other for the readings in the anticlockwise direction (Fig. 9.5).

In the case of a vernier attached to the vertical circle of a transit theodolite which is divided into the quadrants, two sets of graduations are marked on a single vernier instead of providing a double vernier. In reading this vernier, only that set is used which increases in the same direction as the graduations on the quadrant which is being read.

There are some other special forms of vernier such as an extended vernier used on the astronomical sextant, and the double folded vernier used in compasses etc.