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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". 

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