UNCLOSED TRAVERSE.

157

protractor, but the greatest minuteness is necessary, for it is only what is called an "unclosed" traverse.

The most generally adopted system of traversing is by observations from magnetic north, as is illustrated in Fig. 200, which is an unclosed traverse; in other words, the survey has no means of being adjusted to its starting point, either from real cause or option. If we were to take such a figure as an octagon (Fig. 201), and work all round its eight sides at the points A, B, C, D, E, F, G, and H, then, if we had observed the necessary care in taking the angles, when we closed from H upon A we should find our work prove itself. But in the case of Fig. 200, which is the traverse survey of a meandering road on either side of which are dense

plantations, in terminating our work at F we have nothing to guarantee its accuracy, as it is impossible to command the starting point a, which, if we could do so, would enable us to test our work.

Now, in commencing a traverse, or any operations in which the compass is used, it is imperative to guard against any metallic attraction, as even with the most studious care traversing is a very delicate process. It is necessary to carefully select your stations, and by means of pegs or other means to mark the various points, such as A, B, C, D, E, and F; the measuring the lines between these points, together with the necessary offsets right and left, may be accomplished in the first case or subsequent to the instrumental observations, but the one operation should be distinct from the other. Possibly it would be more convenient to have made the survey first, so that the angles and other information may be neatly entered in the book in their proper order and place. should be here noted that after the instrument has been adjusted, the upper and lower plates being clamped at zero (and duly levelled, care having been taken to firmly plant it exactly over the point of intersection of the line *), and when the zero of the upper and lower plate have been made to coincide with magnetic north, that the lower plates should be firmly clamped, and on no account must

It

This is best accomplished by driving a brass-headed nail in the centre of the peg, and let the point of the plumb-bob be coincident with it. See Fig 202.

it be touched either by accident or intent, otherwise the work will be in error. Now having taken all these necessary precautions, the instrument being placed at A (Fig. 200), direct the telescope to a rod held on the peg at B, being careful that the wires intersect the spike of the rod. In the illustration before us the angle which B makes with magnetic north at a is 50 deg. on the A vernier and 210 deg. on that at B; now remove the instrument to в, with the upper plate still clamped at 50 deg., and, after having adjusted it, direct the telescope back to A, and by means of the tangent screw see that the wires exactly cut the bottom of the rod.

Plenty of Assistance required. Here let me say that plenty of assistance is required in traversing, as I am opposed to leaving a rod either stuck in the hole of the peg or behind the peg itself, either of which in the case of road or town surveying is impossible. Consequently I prefer that the spike of a rod should be held by an assistant on the point of the peg. Having intersected the point a, unclamp the upper plates and bring it to zero; the result should be that the needle will record magnetic north, if not, something wrong has occurred, which must be attended to at once, even to the commencement de novo. Having satisfied ourselves that the needle is in its normal position, unclamp the upper plate and turn the telescope to c, which will give 135 deg. or 85 deg. from magnetic north. Keeping 135 deg. in the instrument, remove it to c, observe back upon в, bring the top plate to zero, and the needle should again assume magnetic north. Next direct the telescope to D, when the reading will be 282 deg. or 147 deg. from magnetic north, and so proceed at the points D, E, and F; the various angles should be entered as follows:

Northings and Southings.-Now in plotting the foregoing it is necessary, to ensure accuracy, to draw a series of vertical and horizontal lines intersecting the various points, and really converting them into a series of right-angled triangles, whose base and perpendicular are the sines and cosines of the complements of the various angles; they are also designated "northings" and "southings" for the perpendiculars, and "eastings" and "westings" for the horizontal lines. In the first case draw the vertical line representing magnetic north at the point a. Now we have seen that

Most theodolites have their vernier marked A and B, the former being used to take the angle proper and the lath as a check.

=

the sine and cosine of the complement of an angle will give us the lengths of the base and perpendicular as a a, a в (Fig. 200), therefore 90° 50° 40°, and the natural sine of 40° is 64279, which, if multiplied by the length A B = 2100, will give 1,349 links as the length a B; and the cosine of 40° =76604 x 2100 = 1608 = A a. Again, в c makes an angle of 85° with magnetic north, consequently 90° 85° = 5°, then nat. sin. 5° = ·08716 x 2880 251 = bc, or nat. cos. 5° 99619 x 2880 2869 = Bb. Now if the angle be greater than a right angle it must be deducted from 180 deg., and if greater than two right angles then from 270 deg., and if greater than 270 deg. from 360 deg. Thus in the case of D the right angle being 147 deg., we must deduct it from 180 deg.; thus 180° 147° 33°, and nat. sin. 33° = •54464 × 1400 = 762 = d D, nat. cos. 33° = 83867 × 1400 = 1174 = dc; and in like manner all the various sides may be calculated which are tabulated as under :

143° 37° 2150 1293 1717 .

But these calculations are not alone sufficient to ensure accuracy, as it is necessary to treat an enclosed traverse somewhat in a similar manner to plotting a section. Referring again to Fig. 200, it will be seen that ƒ E is 1717, and e E is 367, therefore eƒ is 1717 367 = 1350; now de are in the same plane, consequently a" d is 1350, and do is 1174, whilst d b is 1174 251 = 923, and b B is parallel to a a, therefore a" d + db = 1350 + 923 = 2273 = a' B; consequently if we mark on the line A' F the horizontal distances ▲ a', a' a", a" a"", a" ƒ, and ƒ F, which are 1608, 4477, 5239, 7991, and 9284, and then plot a' a = 924, a′ b = 2273, a" c = 2524, a′′" D = 1350 ƒ E = 1717, we shall have satisfactorily accomplished our traverse, and assured ourselves as to its accuracy. If it be possible, with the instrument at F, to command a station at A', then taking the last angle, viz. 143° from 180° 37°, consequently E FA 53°; if, therefore, from F 53° be set from E towards a' it should give a point 924 links below A, which is of course an important check equally as the length A' F could it be accurately chained, which would give 9,284 links.

As to closing a Traverse. Of course, if it is possible, it is always desirable to close a traverse, even to the extent of working back to your starting point by a circuitous route, as illustrated in

Α

Fig. 208, whereby, after having accomplished from A to F, which was work requiring to be done, it would be satisfactory to continue back to A by the zigzag route F G, G H, H J, J K, and K ▲; and

B

Fig. 203.

although it would be more satisfactory to have the lengths of these lines as well as their bearings, yet it is not absolutely necessary, as the sum of the angles will give, if the observations be carefully taken, the result of working back on to A as we commenced. By such a method the necessity of calculating the sines and cosines is obviated.

Care in Checking. In taking angles from magnetic north it is necessary to be very careful that the readings are correct; and as an additional check upon the work, especially in a close survey, it is desirable to take frequent objects, such as the chimney at м in Fig. 203, to which observations may be made at the points D, E, F, G, H, and K.

Relative Position of Bearings.-In booking the bearings, it is desirable to have them in their proper order. For instance, all angles less than 90 deg. will be N.E.; between 90 deg. and 180 deg. S.E.; between 180 deg. and 270 deg. S.W.; and between 270 deg. and 360 deg. N.W. When it is possible to take the included angle between points such as E F G, it is, of course, very desirable to do so.

Magnetic Variation.-It is necessary to make allowance for what is termed the magnetic declination or variation, which alters every year. At the present time, at the Royal Observatory, Greenwich, the variation is 17.40° west, and diminishes at the rate of seven minutes annually. It is needless to say that this varies with the geographical position of the point of observation.

CHAPTER VIII.

TOWN SURVEYING.

To make a survey of a town or even a village is by no means an easy task, added to which it is a very tedious proceeding, for it seldom happens that lines of any great length can be arranged. It is desirable, however, that when possible a base-line should be taken through the town from end to end, in order to tie all the other lines on to it. Triangulation is almost impossible, owing to the irregularity of the streets. It is equally out of the question to do town surveying without an instrument for taking the angles of the various lines.

The surveyor should provide himself with a skeleton plan of the principal thoroughfares, upon which he should lay out such lines as appear to him feasible and then proceed to examine them upon the ground. Having determined upon some of the chief lines, he should establish stations, where possible using hydrants or sewerventilators to mark the spot. In the absence of such, he will have to drive down iron spikes or "dogs" into the pavement, for which

purpose he should be provided with a small steel bar and a fairly heavy hammer. The spikes should be of -in. iron and from 2 in. to 4 in. long, pointed at one end. They should be driven well home and their position very carefully observed by means of a detail sketch, with several measurements from well-defined points, as in Fig. 204, taking distances from the four angles of Cross Street

M