768

THEORY AND PRACTICE OF ENGINEERING.

Book II.

When angles are to be set out upon the ground, linesor cords are made use of; and if an angle of 144 degreesis to be set out from the line OP, the centre of the pro-tractor must be placed at the point N, or where the angleis required, and then the number of degrees counted fromIt to S, and then a string or cord attached to the pointN is stretched over the division at S towards M, andO M is the angle required. Or, what would be the samething, the smaller angle of 36° may be counted off from thebase line towards S.

By the same means, on the line M N, from the point O,an angle equal to CDE may be drawn, and so of otherangles ; but sometimes it may be required to make on thecord ST, at its extremity S, an angle equal to P R Q ; wemust then fix a stump or piquet at the point R, andanother at each of the points P and Q, V and X . Then,with a cord, we must measure the distance from R to X ,and set it off from S towards Y, and place a piquet there ;from X we must take the distance to V, and set it off fromY to Z, describing an arc at Z. Then the length R Y is setoff from the piquet S, and an arc described cutting the otherat Z : through this point of intersection a line is to bestretched, and then the angle Z S Y will equal that of V R X.

An Equilateral Triangle upon the base line A B is formedby striking arcs of a circle, having the same radius fromthe points A and B: where these intersect at E, B C andA D are drawn, and the figure is complete.

Before any of these figures can be set out, it is neces-sary that a straight line should be first established, andthe engineer commences by marking the two ends of therequired line, by fixing at each point a piquet staff. Thentaking up a position at a short distance behind one ofthem, and closing one eye, he looks along the edge of onestaff, and directs his attendant to place between the twopiquets first set up other intermediate ones at regular dis-tances, taking care that they are all so placed that theyare in the line between the two first. This kind of ad-justment, which is termed boning a line through, requiresconsiderable practice before it can be relied upon ; and theassistant who follows the direction of the engineer mustwell understand the signals that are made to him by themotion of the hand to the right or the left, or the difficultywill be increased. The same practice is adopted in settingout a base or any other straight line when an instrumentis used; and all lines which are to be measured should bepreviously set out in this manner, for then those whocarry the chain will be guided in the right direction, andnot be subject to a deviation, which, whether to the rightor left, would increase the dimensions beyond the truth.

All diagonals and angles require the same precautions tobe taken, where accuracy is desired. After a base line isestablished, perpendiculars and angles may be raised uponany point of it in the manner already described.

In an Isosceles Triangle the angles at the base are equalto one another, and if the equal sides are produced, theangles upon the other side of the base are likewise equal:to set out such an angle from the point F, with any radiusgreater than the base F G, describe the arc H, and fromthe point G describe with the same radius the arc I, cut-ting each other at K : draw F K and G K : K G F is theisosceles required. The isosceles triangle, which has thetwo equal sides less than the base, may be set out in asimilar manner, using, however, from the points M and Na radius less than its length, which will intersect eachother at L: LMN will then be the isosceles required.

A Scalene Triangle maybe formed on the line O P of Fig. 818.any required dimension ; from the point O strike the arc which will intersect another struckwith a different radius from P: and then by drawing through S the lines OS. PS, theangle is formed.

Fig. 815.

Fig. 816.

Fig. 817.