the vernier slides in the direction A B, and the degrees are indicated by the upper figures (60, 70, 80, etc.) on the graduated circle. The vernier MN' is used when angles are turned to the right, and the degrees are indicated by the lower figures (90, 100, 110, etc.) on the graduated circle. Nearly all transits have two combinations of verniers similar to N N', the zeros of which are 180° apart. Each of these combinations, although it really consists of two verniers, is referred to as one vernier, one of them being called vernier A and the other vernier B. For very accurate work, both verniers are read, and if they do not agree, the mean of the two readings is taken as the true reading.

Again referring to Fig. 12, suppose that, the center of the graduated circle being over the vertex of an angle to be

measured, and its zero on one of the sides, the vernier has been slid to the right along the graduated circle until the other side of the angle passes through the zero mark of the vernier, and that the vernier has then the position shown in the figure. Since the vernier has moved to the right, the side MN is to be read. The twenty-third mark of the vernier coincides with a division mark of the scale, and, as the least reading of the vernier is 1', its reading, in this case, is 23'. The reading of the scale, up to the division mark immediately preceding the zero of the vernier, is 74°. The reading of the instrument, or the measure of the angle, is, therefore, 74°23′ = 74° 23'.

20. The vertical circle or arc V, Fig. 1, is often graduated to degrees and halves, and the vernier v', Fig. 1, which is double, like the vernier of the horizontal circle, reads

either to single minutes or to 5 minutes. If the vernier is attached to the standards, it is stationary, and instead of it sliding along the vertical arc, the vertical arc slides on it. Care should be taken always to read that side of the vernier whose numbers increase in the same direction as those by which degrees are measured on the graduated circle.

EXAMPLES FOR PRACTICE

1. Each division of the scale of a barometer is .05 inch. (a) If the vernier is divided into twenty-five equal parts, what is its least reading? (b) If the reading of the scale is 29.10 inches, and the thirteenth division mark of the vernier coincides with a division mark of the scale, what is the reading of the barometer?

2. The graduated circle of a transit is divided into degrees and thirds, and the vernier, into forty equal parts; what is the least reading of the vernier?

Ans. 30 3. The graduated circle of a transit is divided into 10-minute spaces; how many of these spaces must the vernier cover, that its least reading may be 10"?

Ans. 59

4. What is the reading of the instrument in Fig. 12, the angles being measured from B toward A; that is, assuming that the vernier has slid along the circle in the direction N N'?

Ans. 105° 37'

MOTIONS OF THE TRANSIT

21. The Plate Levels.-Before an angle can be measured with the transit, the plates carrying the graduated circle and verniers must be made horizontal. This is effected by means of the four leveling screws S, Figs. 1 and 2, the horizontal position of the plates being indicated by the two plate levels I, l', which are placed at right angles to each other. Each of these levels is substantially the same as the large level attached to the telescope, Art. 3, but smaller. When they are adjusted properly and each air bubble is exactly in the center of its tube, the plate to which they are attached is perfectly level, and will revolve in a horizontal plane.

22. The Leveling Screws.-The leveling screws S, Fig. 3, have milled heads by which they are turned, and are arranged 90° apart about the axis of the instrument; they are thus in pairs, the two screws in each pair being on opposite sides of the center, and the vertical plane through one pair being at right angles to that through the other pair. Their upper ends screw into arms, or into a solid circular plate projecting from the centers, and their lower ends rest on the lower leveling plate. By turning the two screws in either pair, one in and the other out, the level plate can be tipped in the necessary direction to make it horizontal. A more complete description of this operation will be given later.

23. The Axes of Rotation.-The design and construction of the transit is such as to provide two axes of rotation. The more important of these is the axis of the instrument. (Art. 6), which must be truly vertical when the level plate is horizontal; this axis is also called the vertical axis of the telescope. The other is the transverse or horizontal axis of the telescope (Art. 2). This axis, when adjusted properly, is at right angles to the vertical axis, and is therefore horizontal when the instrument is level. The point where these two axes intersect is the center of the instrument; that is, the point from which all measurements are taken, and is the point that is always understood when the center (not centers) of the instrument is referred to. In a properly constructed transit, the line of collimation should pass exactly through this point.

24. Rotation in Two Planes.-The line of sight has two distinct turning motions, namely:

1. Horizontal Rotation About the Vertical Axis of the Instrument.-As has been explained, the centers of the transit are so made that this motion can be effected in two ways either by revolving the upper plate only, or by revolving both plates together. Since measurements of azimuth are made by means of the rotation of the instrument about its vertical axis, this motion is commonly spoken of as rotation in azimuth, and the convenient phrases to revolve in

azimuth, to reverse in azimuth, etc. are often used with reference to it. The operation of revolving the telescope on its vertical axis through one-half of one revolution, or 180°, so that it will point in the opposite direction, is sometimes called reversing in azimuth.

2. Vertical Rotation About the Transverse Axis of the Telescope. The operation of revolving the telescope in a vertical plane, that is, turning it on its transverse axis, so that it will point in the opposite direction, is called plunging the telescope. In general, to reverse the telescope is to turn it through 180° about either axis so that it will point in the opposite direction. The term is sometimes used in the sense of revolving the telescope 180° in azimuth, but oftener in that of plunging the telescope. In order to avoid ambiguity, it is preferable to employ the terms reverse in azimuth and plunge, or else the self-explaining expressions reverse the telescope on its vertical axis, reverse the telescope on its horizontal axis.

TRANSIT FIELD WORK

PLACING THE INSTRUMENT IN POSITION

25. Setting Up the Instrument.-Since much of the work of an engineering party is suspended while the instrument is being set up, it is highly important that facility in performing this operation be acquired. In setting up a transit over a point from which measurements are to be taken, three preliminary conditions should be satisfied as nearly as possible, viz.:

1. The tripod feet should be planted firmly.

2. The plate on which the leveling screws rest should be approximately level.

3. The plumb-bob should be directly over the mark (as a tack) by which the point is defined or indicated.

The first condition is very essential in order that the instrument may maintain its position unchanged. It is desirable that the second condition be obtained approximately, so as to avoid turning the leveling screws to their

extreme positions. The third condition must be obtained perfectly, and this is rendered comparatively easy by the shifting center with which most modern transits are provided. (See Art. 8.) The string by which the plumb-bob is suspended from the centers should be so adjusted that the point of the bob almost touches the mark over which it is desired to set it.

If the instrument has no shifting center, the plumb-bob must be brought directly over the point by moving the legs of the tripod. The direction in which they must be moved will be clearly indicated by the position of the plumb-bob. In soft soil, the transitman, after laying down the instrument, goes around it, pressing the legs into the ground, so as to insure steadiness. The plumb-bob can usually be brought over the point by exerting a little extra pressure on one or two of the legs.

26.

Leveling the Instrument. -The next operation is to make the level plate horizontal. This is called leveling the instrument, and is accomplished as follows: Loosen the lower clamp and turn the instrument on its vertical axis so that one of the plate levels is parallel to the line passing through a pair of opposite leveling screws. As the plate levels are at right angles to each other, when one level is parallel to the line passing through one pair of leveling screws, the other level is also parallel to the line passing through the other pair of leveling screws, so that one is leveled with one pair of screws and the other is leveled with the other pair. By grasping the milled heads of the two leveling screws in either pair, one between the thumb and forefinger of each hand, turn one screw in and the other out until the bubble of the corresponding level is centered approximately, then manipulate the other pair of leveling screws in the same manner and repeat with each pair of leveling screws alternately until each bubble is centered exactly. The leveling screws being all right-handed, if the thumbs of both hands move toward the center of the instrument in turning either pair of screws, the right-hand