TO PLOT THE Traverse.-Assume a point on the drawing paper for O1. Through this draw a line to represent the meridian or direction line. Place the protractor with its 0-180° diameter on this line, its center at 1. Mark on the paper by a fine dot or pin-point the azimuth of O2, 38°. From 1 through this point draw a straight line and on it lay off from Ol the distance to 2. Through 2 draw a line parallel to the direction line through 1 and lay off the azimuth to 3, and so on to the end of the traverse (Fig. 111). If the traverse closes upon itself, the last line plotted should pass through 1 if the work has been accurate.

If the traverse has been run from one to another A, the end of the last course should be at the second . Since a higher degree of accuracy is possible in the field-work than in the plotting, extreme care should be taken in the latter, so that any failure to check within limits may not be in the plotting. If the discrepancy is too large, the traverse must be replotted. If from one A to another A, recompute and replot the line joining them also. Compare the plot and notes and see if any probable error can be discovered, and if so, where and of what kind. If found, with the instrument in the field, obtain the correct information. If it does not appear that any error can be located further than the kind, as in azimuths, or in distances, then the traverse must be rerun for this alone. In traversing, check azimuths should be taken at each station. to some one object which can be seen from all, and then, if the plotting does not close within limits, these check readings. should be plotted. If some pass through one point and the remainder through another point, it is probable that the azimuth or distance of the course joining the two sets is in error. TO DETERMINE THE TRUE MERIDIAN.-Polaris, popularly called the North Star, is not situated exactly in the North Pole of the heavens, but revolves around it at a distance of about 1° 16' therefrom (Fig. 115). A complete revolution is made once in 23 hrs. 56 min. 4.09 sec. Hence it will appear on the

true meridian once above the Pole (at 3) and once below (at 1), and also once at its extreme eastern position (at 2), and once at its extreme western position (at) 4) every day. Any one of these four positions that is most convenient may therefore be used. Let it be when east or west of the Pole. The angular distance of Polaris from the North Pole when at its extreme eastern or western position is called the Azimuth of Polaris at elongation. When at elongation, the star apparently remains stationary for a short time, then begins to move backward, which is of advantage in using that position, since it is then not moving in azimuth.

FIG. 115.

Great Bear

Motion

North Pole

Polaris

Apparent

Cassiopera

If, when facing north, the above diagram be held up with the Great Bear on the left, it will represent the configuration of the constellations, with Polaris near eastern elongation at midnight about July 10th; with the Great Bear below, it will show Zeta (Mizar) of the Great Bear, Delta of Cassiopeia and Polaris on the meridian, Polaris at upper culmination, at midnight about October 10th; with the Great Bear on the right, it will show Polaris near western elongation at midnight about January 10th; with the Great Bear above, it will show Polaris near lower culmination at midnight about April 10th.

Upper culmination occurs 5 h. 54.8 m. after eastern or

before western elongation, and 11 h. 58 m. before or after lower culmination.

Lower culmination occurs 6 h. 3.25 m. after western or before eastern elongation.

Eastern elongation occurs 11 h. 49.6 m. before or 12 h. 6.5 m. after western elongation.

DETERMINING the True MERIDIAN WITH THE TRANSIT.-From Table III., Appendix, find the watch time of the most convenient elongation. From April to September, inclusive, eastern elongations occur at night and western elongations in the day time, and from October to March, inclusive, visa versa. Also from the Table of Azimuths of Polaris, when at elongation, Appendix, find his azimuth for the year and latitude of place of observation.

Having selected a piece of ground as level as possible, several hundred feet long, in the direction of the meridian, drive a stake at the south end, in the top of which drive a tack. About 15 or 20 minutes before the Pole-star is to reach its greatest eastern (or western) elongation, as found from the table, set the transit up exactly over the tack in the stake, and level carefully. Some arrangement must have been made for lighting the cross-wires during the observation by having an assistant hold a dark lantern so as to shine down the telescope withont obstructing the view, or some kind of a reflector of light must be used as in Fig. 112, or a bright piece of tin,

FIGURE 112.

or board covered with white paper, having in the center a hole smaller than the end of the telescope, but so large that the star can be seen through it when placed several inches in front of the telescope and illuminated.

Then bring the vertical wire upon the star and follow it by the tangent motion until it ceases to move laterally. Keeping the wire at this position, the star will soon appear to depart from it in the direction from which it came. Without disturbing any horizontal motion of the instrument, carefully lower the object end of the telescope and have an assistant drive a stake some 200 or 300 feet forward, "lining him in" with the telescope, sighting on a plumb-line. The assistant has a board with a hole in it, across which he holds the plumbline and behind a lamp or lantern.

Being aligned, he drives a stake, in the top of which he drives a tack. Or a narrow slit, in a board covered with tissue paper, behind which a light is held, may be used by the assistant. The line passing through the tack a under the instrument and the tack b set in the forward stake makes with the true meridian an angle equal to the azimuth of the North Star at elongation.

Now multiply the natural tangent of the azimuth by the distance between the two stakes and lay off this result from b to c, on a perpendicular to ab on the side of the true meridian.

Or, turn off the azimuth on the horizontal limb to the west if an eastern elongation, or to the east if a western elongation, and the telescope will be in the true meridian. Have the assistant put a stake c in this line, and ac will mark the true meridian. The two may be used for a check.

CHAPTER VIII.

THE COMPASS.

DESCRIPTION.-Figure 113 shows the ordinary compass, like the one on the transit, mounted on a graduated horizontal limb, with the vernier reading to minutes, and accompanying clamp and tangent movement; it is also provided with a line. of sight, which consists of two vertical slits in flat brass bars, with large circular apertures at intervals for more readily finding objects sighted.

One of these bars is attached to each end of the plate, the slit in it being in the vertical plane containing the needle pivot and the zero line. At the bottom and top of the "S" end sight are small eye-pieces for reading vertical angles on tangent scales on the edges of the "N" end sight. On the plate are two bubbles placed at right angles for leveling. A small round disk figured from 1 to 16, with an index turned by a milled head, is used for keeping tally in chaining, etc.

The whole is suitably mounted by being fitted to a slightly conical spindle and having on its outer end a ball confined in a socket so that it can be moved in any direction in leveling. The compass may be supported on a single pole, called a Jacob-staff, with proper mountings on top and a pointed iron shoe on the bottom for setting it firmly in the ground; or it may be supported on a tripod, with or without the usual leveling screws.

The compass in some form is one of the most valuable instruments used in military topography. It is simple in construction, convenient, and easy to use. It measures angles fairly reliably, although never exactly. Its needle always points in a known direction, to which the bearing of any line may be referred. This direction is, in a few places, true north and