1.
Vernier scales
Most common measuring instruments have a
simple scale. For example in using a ruler, the
ruler is placed next to the item being measured
and the mark closest to the end of the item is
recorded. If we want increased precision, we use
a ruler with finer divisions on the scale, that is a
smaller instrument least count. This is
suggested in Figure 1.
Any instrument that uses a vernier will have two
scales, a main scale and a vernier scale as is
seen in Figure 2. A measurement is made by
combining the readings from the two scales.
The main scale works just like a ruler: the 0-
mark on the vernier is compared to a main scale
and the result is written down. Use the mark
next to the zero, not the mark next to the edge of
the vernier. Be sure to record the value of the
main scale mark that is just to the left of the
vernier zero mark as is shown in the above
diagram. That is, record the value of 3.3 cm
rather than 3.4 cm, even though the answer is
closer to 3.4 cm.
Now look closely at the vernier scale in Figure
2. Notice that 10 divisions on the vernier match
9 divisions on the main scale. This guarantees
that one of the vernier markings will line up
exactly with a mark on the main scale. Decide
which vernier mark comes closest to matching a
main scale mark, in our example this is vernier
mark 8. Combine the two readings to give the
final length of 3.38 cm.
Guide to Reading a Bevel
Protractor
In this bevel protractor guide, we talk you
through how you read a bevel protractor to
get accurate measurements of your angles.
Step 1 - Count Number of Full
Degrees
Count the number of full degrees between
the 0-degree mark on the degrees scale
and the 0-minute mark on the vernier scale.
This forms the first part of the angle.
The reading is between 28 degrees and 29
degrees.
Therefore, the first part of the angle is 28
degrees
Step 2 - Count Number of Minutes
Count the number of minutes on the vernier
scale from the 0-minute mark until you
reach a minute mark which matches up
exactly to a degree mark on the degree
scale. This forms the second part of the
angle. This will give you the angle, which
will read in the form of “x degrees, x
minutes”.
The reading is 28 degrees and 15 minutes.
It is important that the vernier scale is read
in the same direction that the primary scale
is being read. The correct direction will
depend on which way the angle you are
measuring faces.
Reading clockwise (cw):
The first part of the angle is 178 degrees.
The line of the vernier scale that aligned
with the main scale is 12 minutes.
The zero mark of the vernier scale is at the
second half of the degree mark of the main
scale.
Therefore, the minute reading is 42 minutes
(30 minutes plus 12 minutes)
Final angle reading is 178 degrees and 42
minutes (178o 42’)
Reading counter clockwise (ccw):
The first part of the angle is 181 degrees.
The line of the vernier scale that aligned
with the main scale is 18 minutes.
The zero mark of the vernier scale is at the
first half of the degree mark of the main
scale.
Therefore, the minute reading is 18 minutes
Final angle reading is 181 degrees and 18
minutes (181o 18’)
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.
he 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.
Reading a Vernier:
(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.
