AB is taken as the base line of the survey: it is 17.40 chains long. At B the first angle ABC is then taken, 123° 40':-This angle gives the direction of the next line BC. Now, in taking the angle ABC, it must be carefully remembered, that BC is a new line, and AB an old one; the latter already known, both on the ground and on the paper; the former depending for its direction upon the number of degrees contained in the angle, ABC.

In taking this angle, the theodolite being set at B,

the whole instrument, with the two zeros together, is turned round to A, and then clamped; the upper plate is then released and turned round to C. Standing at B, therefore, and looking towards it, the angle thus read, will, from the direction in which the lower limb of the theodolite is graduated, viz., from left to right, be always reckoned, if it be on the side where BC is now found to be, less than 180°; if it be on the other side, as Bc, greater than 180°. The angles ABC, ABc, are equal; but the line BC, being in the one case, in the second quadrant, makes the angle 123° 40′; whereas, the line Bc being in the third quadrant, makes the other angle, as read by the instrument, to be 236° 20'. Had the road run in the direction of Bc, instead of BC, and the angle ABC been put down in the book as 123° 40', it would have been necessary to have added "to the right." This is the plan adopted by some persons; but in the hurry of field work, this mark is oftentimes omitted whether to the left, or

and the direction of the new line, to the right, becomes a matter of doubt; the work cannot be plotted, and the angles have to be taken again. The method I have adopted guards against every chance of such

an error.

In taking any angle, set your instrument first to the end of the old known line; and when it is turned to the new, the angles, read off it, will always tell whether the new line is on the left, or on the right of the old line, looking in the direction towards which the latter was measured; if the angle is less than 180°, it will be on the left, if more than 180°, on the right.

In the present case the angle ABC is 123° 40'; it is less than 180°, and therefore the direction of the new station is

I

to the left of the old line. To plot this, therefore, draw any line, AB, upon paper, of the required length, 17·40 chs., place your protractor at B, having the bottom edge close against BA, and from the A end, count off 123° to the right; mark this off (C), and join BC, then measure BC, 7.35 chs.

At C, on reference to the Field Notes, you will find the next angle, BCD, is 231° 30'. The new line, CD, therefore, turns to the right, and is in the third quadrant. Place your protractor at C, having the right side of the under edge close against CB; and from B, lay off to the left, the angle (360°-231° 30'), or 128° 30'. (Should the protractor, however, be a circular, instead of an ivory oblong one, the instrumental angle 231° 31′ can be read off on its right direction at once.) This will give you the angle BCD, and the direction of the next line CD, which is 9.70 chs. long. At D the next angle is 91°, and therefore turns to the left; the protractor must be placed with its centre at D, and the lower edge close against CD; and the angle 91° marked off from the left to the right; this gives DE, which is 9.85 chs. long. The next angle is 296° 30′, and turns to the right; it must, therefore, be subtracted from 360°, and the remainder 63° 30′ must be laid off on the right of DE, giving the new line EF, 16.72 chs. The following angles are all greater than 180°, and therefore turn always to the right, looking in the direction the preceding line was measured, until you come to I, when the angle is 146° 55'; this must, therefore, be laid off to the left. At K it is 289°, and turns to the right. At A the angle is 291° 20'. This angle is a check angle, as it proves the accuracy of the whole previous work. It must be here observed, that these

angles are the exterior angles of an irregular polygon; and as the sum of all the interior angles are equal to twice as many right angles, as the figure has sides, wanting four; and as the sum of all the exterior, together with all the interior angles, are equal to four times as many right angles as the figure has sides; therefore, all the exterior, that is, all the observed angles added together should amount to four more than twice as many right angles as the figure has sides.

Now, there are in the given figure ten sides, and therefore the sum of the angles should amount to twice 10, plus 4, or 24 right angles, equal to 2160°. This, on adding them together, will be found to be the case.

fore, may be presumed to be correct.

The angles, there

The taking the sum of the angles is a check upon the field work. The proof of the plotting being correct, is that of the work closing. No offsets must be put in before the angles are laid off, and the work found to close.

I have annexed the field notes of another example of Road Traverse, for the learner's practice.