The vertical circle and the vertical vernier of a transit were discussed in chapter 11 of this training manual. They are used for measuring vertical angles.

A vertical angle is the angle measured vertically from a horizontal plane of reference. (See fig. 13-14, view A.) When the telescope is pointed in the horizontal plane (level), the value of the vertical angle is zero. When the telescope is pointed up at a higher feature (elevated), the vertical angle increases from zero and is a PLUS VERTICAL ANGLE or ANGLE OF ELEVATION. These values increase from 0 to +90 when the telescope is pointed straight up. As the telescope is depressed (pointed down), the angle also increases in numerical value, A depressed telescope reading, showing that  it is below the horizontal plane, is a MINUSVERTICAL ANGLE or ANGLE OF DEPRES-SION. These numerical values increase from 00 to 90 when the telescope is pointed straight down.

To measure vertical angles, you must set the transit upon a definite point and level it. The plate bubbles must be centered carefully, especially for transits that have a fixed vertical vernier. The line of sight is turned approximately at the point; the horizontal axis is clamped. Then, the horizontal cross hair is brought exactly to the point by means of the telescope tangent screw. The angle is read

Figure 13-14.-Vertical angles and zenith distances.

on the vertical limb by means of the vertical vernier.

On a transit with a movable vertical vernier, the vernier is equipped with a control level. The telescope is centered on the point as described above, but the vernier bubble is centered before the angle is read.

The ZENITH is an imaginary point overhead where the extension of the plumb line will intersect an assumed sphere on which the stars appear projected. The equivalent point, directly below the zenith, is the NADIR. Use of the zenith permits reading angles in a vertical plane without using a plus or a minus. Theodolites have a vertical scale reading zero when the telescope is pointed at the zenith instead of in a horizontal plane. With the telescope in a direct position and pointed straight up, the reading is 0; on a horizontal line, the reading is 90; and straight down, 180. When measuring vertical angles with the theodolites (fig. 13-14, view B), you should read the angle of elevation with values less than 90and the angle of depression with values greater than 90. These angle measurements with the zenith as the zero value are called the ZENITH DISTANCES. DOUBLE ZENITH DISTANCES are observations made with the telescope direct and reversed to eliminate errors caused by the inclination of the vertical axis and the collimation of the vertical circle. Zenith distance is used in measuring vertical angles involving trigonometric leveling (discussed in the next chapter) and in astronomical observations. (See Engineering Aid 1 & C, NAVEDTRA 10635-C.)