VERNIER
Sometimes the marking on the thimble of the micrometer
does not fall directly on the index line of
the sleeve. To make possible readings even
smaller than thousandths, an ingenious device
is introduced in the form of an additional scale.
This scale, called a VERNIER, was named after
its inventor, Pierre Vernier. The vernier
makes possible accurate readings to the
tenthousandth of an inch.
Principle of the Vernier
Suppose a ruler has markings every tenth of an
inch but it is desired to read accurately to hundredths.
A separate scale (fig. 63) is
added to the ruler. It has 10 markings on it
that take up the same distance as 9 markings
on the ruler scale. Thus, each space on the
vernier is 1/10 of 9/10
inch, or 9/100 inch. How much smaller is a
space on the vernier than a space on the
ruler? The ruler space is 1/10 inch, or
10/100 and the vernier space is 9/100 inch. The vernier space is smaller by the
difference between these two numbers, as follows:
Figure 63.Vernier scale.
Each vernier space is 1/100 inch smaller than a ruler
space. As an example of the use of the
vernier scale, suppose that we are measuring
the steel bar shown in figure 64. The end of
the bar almost reaches the 3inch mark on the
ruler, and we estimate that it is about
halfway between 2.9 inches and 3.0 inches.
The vernier marks help us to decide whether
the exact measurement is 2.94 inches, 2.95 inches, or 2.96inches.
Figure 64.Measuring with
a vernier,
The 0 on the vernier scale is spaced the distance
of exactly one ruler mark (in this case, one
tenth of an inch) from the left
hand end of the vernier. Therefore the
0 is at a position between ruler marks which
is comparable to the position of the end of
the bar. In other words, the 0 on the vernier
is about halfway between two adjacent marks
on the ruler, just as the end
of the bar is about halfway between two
adjacent marks. The 1 on the vernier scale is
a little closer to alignment with an adjacent ruler
mark; in fact, it is one hundredth of an inch
closer to alignment than the 0. This is because
each space on the vernier is one hundredth of an inch shorter than each space on
the ruler.
Each successive mark on the vernier scale is
one hundredth of an inch closer to 0 on the vernier must be five hundredths of an
inch from the nearest ruler mark, since five increments,
each one hundredth of an inch in size, were
used before a mark was found in alignment.
We conclude that the end of the bar is five hundredths
of an inch from the 2.9 mark on the ruler,
since its position between marks is exactly comparable to that of the 0 on the
vernier scale. Thus the value of our
measurement is 2.95 inches.
The foregoing example could be followed through
for any distance between markings. Suppose
the 0 mark fell seven tenths of the distance between
ruler markings. It would take seven
vernier markings, a loss of onehundredth of
an inch each time, to bring the marks in line at
7 on the vernier.
The vernier principle may be used to get fine
linear readings, angular readings, etc. The
principle is always the same. The vernier has
one more marking than the number of markings on
an equal space of the conventional scale of
the measuring instrument. For example, the vernier
caliper (fig. 65) has 25 markings on the
vernier for 24 on the caliper scale. The caliper
is marked off to read to fortieths (0.025) of
an inch, and the vernier extends the accuracy to
a thousandth of an inch.
Figure 65.–A vernier caliper.
Vernier Micrometer
By adding a vernier to the micrometer, it is possible
to read accurately to one tenthousandth of
an inch. The vernier markings are on the sleeve
of the micrometer and are parallel to the
thimble markings. There are 10 divisions on
the vernier that occupy the same space as 9 divisions
on the thimble. Since a thimble space is
one thousandth of an inch, a vernier space is 1/10
of 9/1000 inch, or 9/10000 inch. It is 1/10000 inch less
than a thimble space. Thus, as in the preceding explanation
of verniers, it is possible to read
the nearest tenthousandth of an inch by reading
the vernier digit whose marking coincides with
a thimble marking.
In figure 66 (A), the last major division showing
fully on the sleeve index is 3. The third
minor division is the last mark clearly showing
(0.075). The thimble division nearest and
below the index is the 8 (0.008). The vernier marking
that matches a thimble marking is
the fourth (0.0004). Adding them all together, we
have,
The reading is 0.3834 inch. With practice these readings
can be made directly from the micrometer, without
writing the partial readings.
Figure 66.–Vernier micrometer settings.
Practice problems:
1. Read the micrometer settings in figure 66.
Answers:
1. (A) See the foregoing example.
(B) 0.1539
(C) 0.2507
(D) 0.2500
(E) 0.4690
(F) 0.0552
