804

THEORY AND PRACTICE OF ENGINEERING.

Book IT.

The demicircle is placed at E, and the anglethat the bottom of the well or surface of thewater makes with the perpendicular line EF isaccurately measured ; then by means of a scaleor trigonometrical calculation, when the diameteris ascertained, its depth can be readily found ;or, if the angle be taken, and the depth ascer-tained by measurement, the width at bottom maybe found. Whenever it is required to measurea distance or space that is not accessible, caremust be taken not to make the angle moreacute than absolutely necessary, and the samerule must be observed in planting over piquetsto measure angles between other objects: in allinstances we must endeavour to obtain them aslarge as possible.

By means of the triangle A C B we can as-certain the distance from A to B, and by thetriangle DFE that from the windmill to thechurch.

The exact situation of these points mayalways be determined by means of the triangle ;but we cannot by instruments measure themexactly : to resolve its value by construction, itis only necessary to establish the data of thethings given, and then measure the lines andangles that are unknown ; if the data be suf-ficient this representation on paper affords us

Fig. 942.

the means of finding the lines and angles that are not given, and when these unknown quan-tities are drawn out proportionate to a scale of the known, it is only requisite to measurethem by the same scale to ascertain their values. Suppose it is required that the distancebetween the inaccessible points A, B, should be known, as we can take up a station at C, andmeasure the distance from C to A and from C to B, the three terms of the triangle A B C,viz. the length of two sides and the angle comprised can be found. The distance from thewindmill, D, to the church, E, may be also calculated when the angle from F is known,together with the length, FI) and F E.

The knowledge of the three angles is notenough to enable us to obtain the length ofeach side, as there may be many triangles likeLMV and GHI equal to each other, andthe length of their sides different: we must,therefore, always be enabled to measure a baseline ; as when the distance from one place toanother is required, we must place our piquetsin such positions with regard to our instrumentsthat the angles made are not too acute or tooobtuse.

Trigonometry being based on the know-ledge of sides and angles, it is necessaryto be very exact in our observations, as wellas in the measurement of the line from whichwe calculate our angles, for if the ground-workbe insecure, the building up will be in jeo-pardy.

To find the distance between one place andanother without actually measuring it maybe done when it is allowed to approach them,as from the point F to that at G: a piquetplanted at I was found to be by measurement50 yards from F; the same distance was setout in a straight line towards K, whereanother piquet was planted. The distancefrom G to I was then measured, which wasfound to be GO yards, and this distance wasset out towards L, and a piquet planted : then Fig- 944 *

the distance from L to Kwas measured, which was found to be 102 yards, the exact dis-tance from F to G, afterwards measured with a cord.

Fig. 943.