CIRCLES AND VERNIERS.— The
horizontal and vertical circles
and their verniers are the parts of
the engineer’s transit by which the values
of horizontal and vertical angles are determined.
A stadia arc is also included with the vertical
circle on some transits. The horizontal circle and verniers of the transit that
are issued to SEABEE units are graduated to
give least readings of either 1 min or 20 sec of arc.
The horizontal circle is mounted on the lower plate.
It is graduated to 15 min for the 20sec transit
(fig. 118) and 30 min for the 1min transit (fig.
119). The plates are numbered from 0° to 360°,
starting with a common point and running both
ways around the circle. Two double verniers, known
as the A and B verniers, are mounted on the
upper plate with their indexes at circle readings 180°
apart. A double vernier is one that can be read
in both directions from the index line. The verniers
reduce the circle graduations to the final reading
of either 20 sec or 1 min.
Figure 119.Horizontal scales,
1minute transit.
The A vernier is used when the telescope is in its normal
position, and the B vernier is used when the telescope
is plunged.
The VERTICAL CIRCLE of the transit (fig. 1110) is
fixed to the horizontal axis so it will rotate with the
telescope. The vertical circle normally is graduated
to 30´ with 10° numbering. Each quadrant is
numbered from 0° to 90°; the 00 graduations define a
horizontal plane, and the 90° graduations lie in the vertical
plane of the instrument. The double vernier used
with the circle is attached to the left standard of the
transit, and its least reading is 1´. The left half of the
double vernier is used for reading angles of depression,
and the right half of this vernier is used for
reading angles of elevation. Care must be taken to read
the vernier in the direction that applies to the angle
observed.
In addition to the vernier, the vertical circle may have
an H and V (or HOR and VERT) series of graduations,
called the STADIA ARC (fig. 1110). The H
scale is adjusted to read 100 when the line of sight is
level, and the graduations decrease in both directions
from the level line. The other scale, V, is graduated
with 50 at level, to 10 as the telescope is depressed,
and to 90 as it is elevated.
Figure 1110.Vertical circle with verniers, scales,
and stadia arc.
The VERNIER, or vernier scale, is an auxiliary device
by which a uniformly graduated main scale can
be accurately read to a fractional part of a division.
Both scales may be straight as on a leveling rod
or curved as on the circles of a transit. The vernier
is uniformly divided, but each division is either
slightly smaller (direct vernier) or slightly larger
(retrograde vernier) than a division of the main
scale (fig. 1111). The amount a vernier division differs
from a division of the main scale determines the
smallest reading of the scale that can be made with
the particular vernier. This smallest reading is called
the LEAST COUNT of the vernier. It is determined
by dividing the value of the smallest division
on the scale by the number of divisions on the
vernier.
Direct Vernier.— A scale graduated in hundredths
of a unit is shown in figure 1111, view A, and
a direct vernier for reading it to thousandths of a unit.
The length of 10 divisions on the vernier is equal
to the length of 9 divisions on the main scale. The
index, or zero of the vernier, is set at 0.340 unit. If
the vernier were moved 0.001 unit toward the 0.400
reading, the Number 1 graduation of the vernier
shown in figure 1111, view A, would coincide with
0.35 on the scale, and the index would be at 0.341
unit. The vernier, moved to where graduation Number
7 coincides with 0.41 on the scale, is shown in
figure 1111, view B. In this position, the correct scale
reading is 0.347 unit (0.340 + 0.007). The index with
the zero can be seen to point to this reading. Retrograde
Vernier.— A retrograde vernier on which
each division is 0.001 unit longer than the 0.01 unit
divisions on the main scale is shown in figure 1111, view
C. The length of the 10 divisions on the vernier
equals the length of the 11 divisions of the scale.
The retrograde vernier extends from the index, backward
along the scale. Figure 1111, view D, shows
a scale reading of 0.347 unit, as read with the retrograde
vernier.
Vernier for Circles. — Views E and F of figure 1111
represent part of the horizontal circle of a transit
and the direct vernier for reading the circle. The
main circle graduations are numbered both clockwise
and counterclockwise. A double vernier that
extends to the right and to the left of the index makes
it possible to read the main circle in either direction.
The vernier to the left of the index is used for
reading clockwise angles, and the vernier to the right
of the index is used for reading
Figure 1111.Types of verniers.
counterclockwise angles. The slope of the numerals
in the vernier to be used corresponds to
the slope of the numerals in the circle being read.
Care must be taken to use the correct vernier.
In figure 1111, view E, the circle is graduated
to half degrees, or 30 min. On this vernier,
30 divisions are equal in length to 29 divisions
on the circle. The least reading of this vernier
is 30 min divided by 30 divisions, or 1 min. The
index (fig. 1111, view E) is seen to lie between 342°30´
and 343°. In the left vernier, graduation Number
5 is seen to coincide with a circle graduation.
Then, the clockwise reading of this circle
is 342°30´ plus 05´, or 342°35´. When the right
vernier is used in the same way, the counterclockwise
reading of the circle is 17°00´ plus
25´, or 17°25´. In figure 1111, view F, the circle
is graduated in 15min divisions and each half
of the double vernier contains 45 divisions. The
least reading on this vernier is 20 sec. The clockwise
reading of the circle and vernier is 351°30´plus
05´40" or 351°35´40". The counterclockwise
reading is 8°15´ plus 9´20", or 8°24´20".

