CHAPTER VI.

SURVEYING BY TRAVERSE.

A TRAVERSE is a polygonal or many-sided figure assumed by a number of straight lines lying in various directions, and which, by going North, South, East, or West, we follow from a given point, until we return to it; in tracing this circuitous route, it is necessary to measure the lengths of the sides, and also the angles, before we can make a plan of it. We shall best explain this method of surveying by referring to the lines in Fig. 67. Let a survey be required of the area contained between the stream and the road; set out the lines A B, BC, CD.... NA; measure the lengths of the sides and the angles, and it will be evident that the figure may be laid down on paper. The method of procedure in the field is as follows:

Starting from a point at which you can make observations on surrounding objects, as at A, set out the lines Aa, A O, A B, and plant the theodolite at A, in the manner above described; clamp the limb and vernier plates at 360°, or zero, and turn the whole instrument round until the magnetic needle points steadily on the North and South line N S, and clamp it firm in that position by means of the clamping screw which tightens the collar round the axis. Having perfected this, release the vernier plate, and bring the telescope to bear consecutively on A a, A ́O, AH, AP, A E, and lastly on AB, clamping the vernier plate each time, and perfecting the bisection of the cross wires with the object observed by means of the tangent screw T; having carefully entered at station A all the angles made by the above lines with the magnetic meridian, and leaving both clamps firmly fixed, the last reading being with the telescope bearing on A B, remove the instrument to B; plant it at this station, and carefully level it. Release only the clamp screw of the limb, that is the clamp connected with the collar round the axis of the instrument; the vernier plate must not be in the least disturbed, or you will have to begin over again; turn the theodolite bodily round, so that the telescope reversed may bear on A, where a man must be left to hold a flag pole, clamp the limb and perfect the contact by means of the slow motion screw S, and examine the readings of the verniers to see that no disturbance has taken

place. A few words are now required with regard to the telescope being reversed; this operation places the horizontal limb and the verniers in precisely the same position with regard to the magnetic meridian as that which is occupied at A; if, for instance, at A, the bearing of AB was 31° East of North, by doing as directed you have similarly placed the theodolite at B, with the same vernier still pointing 31° East of North, and it is the second vernier lying diametrically opposite, which now points towards A, and reading on the limb 31° + 180° = 211°. The new position of the theodolite being now understood relative to the limb and the verniers, we may proceed with our work. Release the upper or vernier plate, and turn the telescope round to bear on C; clamp and perfect the contact with the tangent screw T; read both verniers to get the mean of the bearing BC, which is here 96° 5′; now move the theodolite to C, release the horizontal limb, turn the instrument bodily round to B, clamp and perfect the contact, release the vernier plate, turn the telescope round to D, clamp and perfect the contact with the screw S; by reading off your instrument you get the bearing_of_CD, which here is 30° 5′; proceed in the same manner at D, E ... M, O, at which station, when you have fixed the back sight on M, and turned the telescope round towards A, the verniers should give exactly the same angle as was read off at A, with the telescope bearing on O; and this because OA makes the same angles with the meridian N' S' that A O does with the magnetic meridian N S.* If it be so, then the angles have been correctly taken; if otherwise, then the difference is the error committed. Besides taking at A the bearings of A O and A B, we have taken those of A a, A H, A P, and A E; the bearing of A a was taken in order to lay down the bit of road beyond the bridge, and to show the position of such road in connexion with the lands surveyed; and also in case the survey has to be extended in that direction, as in such a case the instrument would be planted at station a, and the back sight fixed on A, in the same manner as directions have just been given for doing at B, C, D, &c., until we had made another circuit; with regard to the bearings of A H and A E, they are here only as checks on the work as it proceeds, for it will be observed that E A makes with the meridian N" S" at E the same angle West, that A E, at A, makes East with NS; these observations have equal weight with regard to the bearings A H and HA; we have here taken H and E as points at the other end of the survey, and of which full view could be had from A; otherwise

*For all purposes of engineering field work we may consider the meridians as parallel lines.

any other points as F, G, or I, would have been taken if convenient; as regards the various bearings on P, let it be observed that these also are checks, for if there is any error, these bearings will not all intersect at P, when the work is plotted and the bearings A P, EP, GP, &c., are laid off with the protractor. It is of course necessary that they be taken on some object in a commanding situation, such as we may depend on seeing, if not all round the traverse, at least at several points. Judgment is required in selecting such points, as they may often be very useful to chain upon in order to fill in interior work, as fences, buildings, &c. On an extensive traverse this should particularly be kept in sight, as it prevents the necessity of having again recourse to the instrument when we come to fill in. It will now be observed that not only care, but judgment also is required, not only in setting out the traverse itself, planting the instrument properly, and taking the angles or bearings, but also in laying out the interior work to the best advantage at the same time, and so as not to be obliged to bring out the instrument again; which not only saves time, but also chances of error, for it must be remembered that the greater the number of observations we can take from one station, the fewer stations for angular observations will be required, at least as a general rule. All these matters considered, a day will often be occupied in taking all the bearings that may be required on a traverse of any extent. As a general rule, lay out your lines as long as possible, as thereby you avoid an excess in the number of your stations. It is also to be observed that in our diagram the stations in the road are all shown as in the centre of it; but this has merely been done to avoid confusion, and not to be followed as a rule; on the contrary, it is to be avoided, inasmuch as all these stations require to be carefully marked, either by driving a picket, or making some other mark, which is often very awkward to do in the centre of a road; place your stations, therefore, as conveniently as you can somewhere near the roadside, but so that you can there plant your theodolite. This is merely mentioned that the subject may not be altogether lost sight of, as many ways of settling these minor matters will suggest themselves to any intelligent mind as circumstances arise, it being merely requisite that the stations be marked so that they may be found to a certainty when wanted, and so that the instrument may be planted over them, and observations conveniently taken. The traverse being thus set out, the sides are chained and the offsets taken in the usual manner, which has already been explained under the head of chain surveying. With regard to the magnetic needle care is required lest it be

affected by any local attraction; by pursuing the above method there will be opportunity to observe this at each succeeding station, as the back angles with the meridian are equal to the forward angles.

There is a considerable advantage in taking from the startingpoint A such bearings as A H and A E, for it subdivides the larger polygon into smaller ones, as in our example, where the figure A B, BC... OA, is subdivided by the above bearings into the smaller polygons A B, BC... EA, and AB, BC... HA; we are, therefore, enabled to check the work as we proceed, for in the same manner then the three angles of a triangle are equal to two right angles, and the four angles of a four-sided figure are equal to four right angles; so all the interior angles of a polygon are equal to twice as many right angles, less four, as the figure has sides. The proof of this may be seen in figures 68 and 69; in the first, let the polygon a b, bc... ko, be divided into triangles, by drawing lines from each angle of the polygon to any point o, in the interior of the figure; then because the three angles of a triangle are equal to two right angles, we shall have twice as many right angles as the figure has sides, for there is a triangle for every side; and all the angles formed by the lines intersecting at o, are together equal to four right angles; subtracting these, we shall have for remainder twice as many right angles, less four, as the figure has sides. In Fig. 69, from any point a in the polygon draw lines to each of the remaining angles, as ac, a d, &c.; the polygon will thus be divided into as many triangles as the figure has sides, less two, for there is only one triangle for each of the two sides ab, bc, and a i, ik; and one triangle for each of the remaining sides. In any case, therefore, multiplying 180° by the number of sides of the polygon, minus two, will give the interior angles of the polygon.

Thus, in Fig. 67, where the polygon has thirteen sides, all the interior angles will be equal to 180° x 11; or to 90° × 26 = 360°. In the same manner, the angles of the polygon AB, BC... E A = 180° × 3, because the figure has five sides; and the angles of the polygon AB, BC ... HA = 180° × 6, the figure having eight sides.

The rules often given to find the interior angles of the polygon, lead rather to confusion than anything else; the simplest way is to carry a small semicircular protractor, about 3 inches in diameter, in the pocket, and plot the bearings in the field-work, merely writing in the degrees and minutes, &c., inside the several angles; or even to sketch in two lines, at right angles to each other, for the magnetic meridian and the East-West line; and sketch in your bearings as you go along. Many surveyors sketch

or roughly plot a traverse in a field-book, quarto size, instead of that which we have formerly mentioned under the head of "Field-book;" a very good way where the traverse is small, and the weather is such as to admit of the use of such a book in the field; but it is very inconvenient in wet, stormy weather, when time presses, and the work must go on.

After reading the observations that will now be made on the subject of "plotting," or laying down the field-work on paper, the student is advised to lay down any irregular polygon on a large sheet of paper with a protractor, setting off also parallel lines to represent the meridians; by this means he will find considerable assistance to the better understanding of this very important subject in the matter of surveying; for want of anything more perfect, he may construct a paper protractor in the manner shown at p. 39, which will answer his purpose perfectly well for a traverse of small extent. He will thus be able to study how the theodolite is worked, before going into the field, and study some of the features of a traverse.