806

THEORY AND PRACTICE OF ENGINEERING.

Cook II.

Fig. 049.

Fig. 960.

By means of Piquets to measure the Distance between inaccessible Places , as that fromthe tower A to the windmill D. Trace on the ground, where you are to perform theoperation, a line parallel to the given length B

to be measured, as the line S V; then attachtwo rules at right angles, placed in the formof a cross, on the heads of the two piquets,each 4 or 5 feet in height. Place thesetwo piquets at any points on the line SV,and look along them in such a manner as todiscover the objects as well as the piquets, asat C ; by the rule IK you may see the towerA, and by the rule E F the piquet D. Thenfrom the piquet D, observe by the rule L1\Ithe mill 13, and by the rule H G the piquetC, which may be done by bringing these two piquets nearer together or further apart,always keeping them in the line S V, until you can discover the objects before named, whichhappens when at the points C and D : then the length C D will be equal to the inaccessiblelength, A13, between the tower A and mill B.

To find the Height of an Object , AB, when it can be approached .— Place a mirror at Chorizontally at any place on the ground, with itsback downwards, so that the glass may be upper-most; retire from the mirror at a distance pre-cisely equal to the height of the eye from theground, as at D, and standing perfectly upright,observe if the top of the proposed height can beseen in the middle of the mirror ; if not, see if themirror be too near or too far from the object,and place it either nearer or. farther from it.

When the view of the object in the mirror hasbeen obtained, measure on the ground the dis-tance from the centre of the mirror to the footof the proposed height, as from C to A, and itwill be the height required.

To measure by means of two Piquets Heights towhich the Foot is accessible. — Take two piquets, asE, C, one of which is half the length of the other ;elevate them perpendicularly in the ground, on alevel with the foot or base of the height whichis required to be ascertained, and so that the shorterpiquet may be its own length distant from thelonger one ; look along their tops, and walk citherbackwards or forwards, keeping them the samedistance apart, until by the same visual ray thesummit of the object to be measured can be seen.

The distance from the foot of the object to the footof the short piquet, viz. from C to A, added toits length, gives the height of the object.

To measure a Height, when the Base is accessible

by means of a Piquet -Retire from the foot of

the height to be measured as much as the heightis supposed to be ; plant a piquet upright on theground, as at D E, on the same level as the foot ofheight, and as high as the eye: lie down on theground with the feet against the piquet, and lookalong its top until in the same visual ray the sum-mit of the height to be ascertained is seen. Thedistance from the foot of the height, A to C, tothe place where the eye was when lying on theground, will be the required height.

Examples might be multiplied of measuringheights by means of the piquet, and it is men-tioned in several ancient writers. We may imagine that Archimedes and Apollonius , whoenriched geometry with so many new theorems, made use of the staff or piquet for severalpurposes, particularly where the properties of similar angles were to be exhibited : seventeencenturies have passed since these great men taught in the academies: the principlesthey have left us have been but little added to, although they have been varied in theirapplication. Wherever the piquet is employed, its perpendicular position should be

Fig. 951.

Fig. 952