8 1G

TIIEOIIY AXI) PRACTICE OF ENGINEERING.

Cook I T.

Fig. 996.

To measure the depth of a shaft, ;s M X. thewidth or diameter at top M () being 9 feet : placethe demieircle at () in such a manner that thedegrees may he downwards, and its diameterparallel with the horizon, as is the line O M.Then turn the alhidade until the bottom of theshaft at N is seen ; measure the angles 31 () Nand O M N ; draw the scale P, and the rightline ItS, and set olF the 9 feet from It to T,then draw the angle TRY; and the height It Yon the perpendicular ItV, as measured by thescale, will be the depth required of 31 N.

The breadth of a ditch mayalso be found, as that of A B.

Being stationed at C abovethe point A, take the depthC A, and measure the angleA C B. Then with a scaleset out on the line E F, andfrom E draw the angle G E H,and at the point G the angleE G I, which answer to thosepreviously measured. Fromthe point L, where the twoangles cut, measure the lengthG L by the scale, which will hethe breadth required.

The width of the ditch at N may also be foundin like manner : from the point N, measure theangle K N 31 and the angle N K M, and draw thescale O. Draw the line P R, and set oft’ theheight taken from N to K, as PS. At the pointP, draw the angle SPT, and from the point Sthe angle FSV; then from the point X, wherethey cross, measure S X by the scale, and thebreadth of the ditch will be ascertained.

The various methods of measuring heights byangles are supposed to have had their origin inEgypt , from whence they were introduced intoGreece by Thales : there can be no doubt that afterPythagoras had discovered that celebrated pro-position concerning the square of the hypotenuse,trigonometry made rapid advances: we have mentionmade by Vitruvius of many philosophers who ad-vanced the science of computation by clearer de-finitions in geometry.

The Geometric Square is an instrument for mea-suring distances and heights, &c., and is valuablefor its portability as well as for the facility, by thecommon rule of three, of solving most of theproblems arising from its use: it is made ofbrass about 12 inches square, or of wood 15 or 18inches square : it is graduated from top to bottom,and from bottom to top, and may be called a quad-rant of 90 degrees. The two sides of the squarewhich are opposite to the angle of the centre D, ason the sides A B and B C, are each divided into100 equal parts, which commence at the two extre-mities of the quadrant, so that in both divisions thehundred-point finishes at the angle B, which isopposite to the centre D, and to facilitate the count-ing these degrees they are divided into tenths byshort lines tending to the centre.

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M s _ T_11

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Fig, 994.

Fig. 995.

Fig. 997.

Fig. 993.

Fig. 999.

The side D C represents the horizon : at the centre D is fixed an alhidade by meansof a screw, which equals the diagonal of the square A B C D, on which the same divisionsare marked as on the side of the square, and as the alhidade is longer than the side of thesquare, it will contain more than 100 equal parts : two sights are attached to it, and a socketjoint to one side for the purpose of turning or elevating it when required.