By the first method, mark two convenient points one or two chains apart in the survey line just before arrival at the obstacle, lay off two equal rectangular offsets, thus obtaining through their extremities a line parallel to the original survey line that will clear the obstacle; continue the chaining on this new line, and revert to the original direction by setting off two rectangular offsets equal to the former; their extremities will be in the original direction. (See figure 11.)

Thus the operations consist in setting out AB, ab, using the new direction BbC for chaining, then setting out CD and cd to obtain the original direction, Dd, which will be in line with Aa. The length of the unmeasured distance ad then = bc. Further precision may

be obtained by using three or four offsets on each side of the obstacle instead of two.

FIGURE 12. DETOUR IN CHAINING.

By the second method (see figure 12), having chosen similarly two convenient points, A, a, in the original line, set out half right angles at those points with the

cross-head, measure AB, ab, of equal length, check Bb, which should be equal to Aa, set out two rectangular offsets, BC, bc, equal in length to AB, ab; then Cc will be in the original direction, and the unmeasured distance. AC ac AB × 1'4142.

=

Whichever of these methods be used, if the obstacle to continuous chaining admits of being seen over, as a pond or marsh, the resulting direction admits of verification by simple ranging.

4. To continue a survey line beyond an impassable obstacle when chaining round is impracticable.

First. When the obstacle can be seen over, as a stream or river, the direction of the survey line may be ranged in beyond it with ranging rods; and the length of unmeasured interval alone is required. (See figure 13.)

A

K

N

B

FIGURE 13. INTERVAL IN CHAINING.

Choose two convenient points A and C, one chain or two chains apart, in the original line; set out a rectangular offset AB to double the length of AC; at the point B set out the right angle CBD, having ) fixed in the survey line beyond the obstacle.

Then the unmeasured interval AD=4 AC.

Or if AB is not fixed at exactly double AC, then ADAB÷AC.

A check on the accuracy of the point D may be obtained by setting out AB' to the left of the given direction CAD, making AB'=AB, and setting out the right angle CBD to obtain the identical point D given by the former operation; or if the ground does not admit of using equal triangles on each side of the line, unequal triangles may be used, and a second point K may be obtained.

Secondly. When the obstacle cannot be seen over in the original direction, as if a house or clump of trees should intervene on the bank of the stream.

Range a parallel line clear of the house by means of a pair of rectangular offsets, so that its continuation may be ranged in beyond the river; a second pair of offsets

will then give the original direction, and the mode just explained will give the unmeasured interval.

Thus in the figure 14. Let CA be the original direction, use two equal rectangular offsets, so that the parallel line EBHF may be visibly fixed beyond the river; the original direction DG can then be regained by equal offsets HD, FG. Then let K be any point in DG visible from P; set out the right angle KPL, obtaining a point L, and measure AL; then the unmeasured interval AKAD2÷AL.

A similar operation may be conducted to the left of the given direction so as to afford a check.

There are several other modes of carrying out such minor operations, based on the principle of similar triangles, but these described are the most simple, rapid, and convenient. Whenever more complicated measurements and operations become necessary in ordinary chain surveys the original survey line must have been badly selected, and is best abandoned.

5. To test by calculation the length of a tie line (x) of any triangle ABC, measured from the angle C to the side c, so as to divide c into two parts m and n, of which m is adjacent to the side b, and ʼn adjacent to a.

And if the tie line r is at right angles to the side c,

x = √ a2 — n2= √ b2 m2.

6. Chaining on an inclination.

Sometimes, when there is a long piece of sloping ground of unvarying inclination to be chained and few offsets are required, the chaining is for the sake of rapidity measured on the declivity, instead of horizontally. In this case the difference between an inclined chain and a projected horizontal chain plumbed down must be measured with the offset staff and added to every chain thus measured.

For example, let AB be the chain lying on the declivity, mark A and B; then have the chain held truly horizontal as AC, and plumb down CD and mark the point D; measure BD with the offset staff or tape; BD is the correction to be added for each inclined chain

measured in order to obtain the correct chainage; and this correction should be measured with such exactitude that the final total may not be materially affected by

7. Traversing with the chain.

On the offset system.-Short pieces of traverse may sometimes be done with the chain and cross staff only; as for instance along a boundary, a footpath, or on one bank of a stream in comparatively open country, lying between two determined survey points.

Thus in Plate I., A and H are two fixed points, a stream lying to the left of AH, whose course must be surveyed. The right angle OAB is set out with the cross staff, and checked by measuring Aa, Aa', and aa'; the line AB is then used as a survey line, from which offsets to the stream can be taken. At B a half right angle bBC is set out with the cross staff, and checked by three measurements Bb, bb' and Bb'; the line BC then becomes a new survey line from which offsets to the stream can be taken. In the same way by setting out a succession of checked right angles and half right angles as required, the traverse is completed up to near the final point H, which is determined both by one rectangular offset GH and two oblique offsets, gH,g'H.