horizontally and vertically (°). Unscrew the key D which is attached to the instrument as shown in Fig. 144 and fit it to the square head on the top of the box and bring the object and its image level with one another, thus °°. Now to make the object

and image coincide apply the key to the square head at side of the box. The instrument has then been adjusted. It is important that the object should be fully half a mile away when making this adjustment. The sun may be observed for the purpose.

Its use. The box sextant is very useful for the approximate measurement of angles, both horizontally and vertically. It is best employed as an aid to a chain survey and instead of checking each triangle by measuring a tie line. Surveys made with it, when triangles are not used, are only approximately accurate.

Disadvantages of the Box Sextant.-1. As the arc of 70° is divided into 140° any error of observation is doubled.

2. In measuring angles when the two objects are not on a level with the eye, the oblique angle is obtained which must be reduced to its horizontal projection by the proper formula before it is made use of.

3. Angles greater than 110° cannot be observed with it, as the angle of incidence is too great to allow proper reflection. This difficulty may be overcome, however, by interposing an intermediate object and dividing the angle into two smaller ones.

4. Parallax. The more distant the object sighted to the less is the error due to parallax. It will minimise the error if the more distant object is sighted to by reflection. If both objects are near, it is better to take some point which is in line with one of them at a distance away, and to observe this point by reflection and the near object by direct vision.

Method of plotting a small survey made with the aid of the box sextant.-A small area will suffice to show the best way of plotting angles with the protractor. Fig. 146 is the survey of a small enclosure wherein it was found impossible to run diagonal lines to form a base for triangulation. The sides were measured with the chain and the included angles with the box sextant. The sum of the angles taken should be equal to twice as many right angles as the figure has sides minus four right angles: this fact enables us to check the result of our observations.

AB is the base line. We must first obtain the bearings of the rest of the lines from the base line. To do this add together all the interior angles.

The interior angle at A= 86° 30' the bearing of AD

Add

D

94° 30'

Now place the protractor (shown in Fig. 65, Chapter IV) on the paper so that the point A is its centre, and by means of the arm prick off the bearings as shown. The protractor can now be taken off. By adopting this method the protracting of each angle separately is avoided and consequently the error in any one angle is not carried through the rest of the work: also the marking of the paper through placing the pointed feet of the protractor upon it in several places is similarly prevented.

Now draw the line AB with the scale selected for the plot to its measured length. Next draw AD similarly and bearing 86° 30'. Now draw DC with the parallel rule parallel to AE and mark off the point C with the scale according to its length, and lastly CB parallel to AF. The work is checked by CB closing on the point B if the measurements have all been correctly made.

If when adding the interior angles together they sum to more than 360°, then subtract 360°.

CHAPTER X

THE PLANE TABLE

THE Plane Table is a simple instrument, which is chiefly useful for filling in the detail of a survey, but also for making original surveys. It consists of a drawing board which is generally 23" × 16′′, though larger sizes are obtainable, mounted on a tripod in such a way that it may be turned horizontally, levelled, set in any direction and clamped. In addition a trough compass, a spirit level, a sight rule or alidade, a sheet of drawing paper, pins, pencil, indiarubber, and plotting scale are required for its use.

Fig. 147 shows a plane table with sliding adjustable tripod, revolving motion, fitted with clamped board size 23" x 16"; brass alidade 18", A, with divided edge and removable sights; telescope with level and graduated arc; trough compass B; and spirit level C.

It is not necessary that the alidade should be fitted with a telescope as shown in Fig. 147, but it is very useful for plotting in detail by single rays observed to a staff with stadia points, as explained in the chapter on Tacheometry. In the following notes the use of the telescope is dispensed with, an ordinary sight vane only being used.

The use of the Plane Table.-When starting a survey with the Plane Table and no fixed points have already been determined it is first necessary to measure a base line. This base line should be about the centre of the survey, and the longer the better within reason. It should be as nearly horizontal as possible. Set up the table over one end of this base line firmly upon its tripod; cut a sheet of drawing paper so as to have an overlap of about 2 inches all round the table; damp the paper, turn down the edges and fasten them underneath the board with pins. Now carefully level the table by means of the spirit level. Draw a line on the paper to scale to represent the base line on the ground. Place the sight rule against this line and turn the table until the sights come on to the other end of the base. Now clamp the table. Thus the line drawn between the two stations on the table is parallel to the line

between the stations on the ground. This is called orienting the table and is the most important point to be observed in Plane Table surveying, so as to secure accuracy. When the table has been oriented, the compass should be placed in one corner of the table and turned until the needle is pointing north. It is convenient to draw a pencil line round the box to mark the position of the compass for future reference. It should be noted that the point on the table which represents the station and not the centre of the table should be over the station on the ground. The table may be placed in the

required position near enough by dropping a stone from the corresponding point beneath the table, or by using a plummet.

We are now ready for fixing points by intersection. (See Fig. 148.) AB is the base line and ab the base line on paper. Place a pin in the table at A, hold the sight rule against the pin and pivot it until it is directed on to the station C. Now draw a ray along the edge of the sight rule as shown. Do the same for the rest of the stations D, E, F. These rays give the direction of the stations C, D, E, F from A. Now move the table and set it up at the other end of the base B. Carefully orient it and draw rays from b to all the stations as before. The intersections of these rays give the exact position to scale of the stations C, D, E, F. No important station should be intersected from the base if it is at a much greater

distance from either end than the length of the base; nor if it lies much outside of a perpendicular to the base at either end of it. As in ordinary chain surveying, the triangles should be as well conditioned as possible. The table may now be shifted to another well-fixed station and the same process gone through until the survey is completed.

Checking the work. The work should be frequently checked by sighting on to preceding stations from say every third station. Further checks may be made by measuring the distance between two stations on the ground and comparing it with the plotted

distance on the plan; and by setting up the table at any station and sighting on to other stations.

To continue the survey on a fresh sheet. The following_note has been taken from Hints to Travellers' published by the Royal Geographical Society. Draw a line through the farthest point fixed from the last station. Take the sheet off the table and fix another on, drawing a line upon it in a part most convenient for the work; then cut the sheet just taken off, by the line drawn on it. Apply this edge to the line on the new sheet, and as they lie in that position continue the lines from the other sheet on the new paper, and prick through the positions of as many stations that have been fixed on the old sheet as you conveniently can. If the positions of three fixed points are transferred to the new sheet,