Chap. VIII.

GEOMETRY.

805

To measure the Distance between two Objectsinaccessible from one to the other, hut accessiblefrom a station, as the distance from the towerA to the tree B, supposing it to be possible toplace a piquet at C, whence we can proceedto the two objects A and B. Measure in aright line from A to the piquet C how manyfeet it is, as 70: then measure in a right lineon A C prolonged to D 70 feet, so that A C Dmay be 140 feet. Then from the point Bmeasure B C, in a right line, and call it 100feet; measure the same distance on B C pro-longed ; then measure the distance ED, 150feet, and which is that of the inaccessiblelength or distance A B.

By means of a Piquet to measure the Dis-tance from one Object to another, when it isonly possible to approach one of them, as tomeasure the opening or bar of a river. —Plantat the point A a perpendicular piquet, 4 or 5feet high, as at A C ; place on the summit (\the blade of a knife with its back turned tothe piquet; elevate or depress this blade untilyou see, looking along the back of it, thepoint B: then keeping the knife at the sameopening, turn round to the land side, oppositea level piece of ground ; replace the knife inthe piquet C, and its back against this piquet,in order to look along the back of the bladeuntil the visual ray cuts the ground, as at D;the distance A D will be that of the bar orentrance of the river A B.

An observation similarly made at E G, andtried along the ground from II to I, wherethe base may be measured, gives the width ofthe river.

By means of piquets, the length of the ridgeof a roof may be found, as that of the church atN O. Piquets placed at P It on the line a b , drawnon the ground parallel to the ridge having on theirtops two laths arranged like a cross : these mustbe moved along the line till they are perceived to beopposite the points N, O, and then the distanceP P being measured, the length of the ridge willbe similar.

To enable the observer to be more accurate, thepiquets placed at P and It on the base line a maybe mounted with cross staves, the arms ST andY X being in a line, and Y Z and Z 2 at rightangles with it: should the distance of the objectsbe considerable, the observations so made wouldbe far from accurate ; when within a few feet oryards, the dimension measured on the groundbetween the feet of the piquets might be suffi-ciently near the truth for ordinary purposes.This practice somewhat corresponds to the com-mon method of boning, or booming as it is some-times termed, which often leads to very erroneouscalculations. In Holland, wherever difficultiesare offered to the navigation of a channel bythe overflowing of the coast, and the coursenot distinctly known, poles are set up to enablethe sailors to steer in a straight direction, fromwhence probably we have the term; and in thismanner lines are set out with booms or sparswhen a canal is to be cut; but without great careit is scarcely practicable to make a very longline straight bv such means.

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Fig. 945.

Fig. 946.

Fig. 947.

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1 ig. 948