Chap. VIII.

GEOMETRY.

80 1

If it !>e required to ascertain whether thereis any fall from the point A to the littlehillock at G, piquets may he placed first atA and K, and the level F, having made thenecessary observations at the station E, mayhe removed to I, where the piquets II and Dcan he observed; then by a simple calculationthe difference in the levels may he found.

Tiie difference between the levels of two houses E and O may also be found by plantingpiquets at G and L, and the level at D, II, and C : so may the inequalities of a country,

Fig. 933.

as from A to C, be marked, and a canal set out upon a dead level, K, O, P, being piquets, andLIIT the position of the level used for making the observations : M and Q show the depthof cutting.

In this latter example D, F, H, and T show the position of the level for taking the ob-servations, and K A, O N, P It the station of the piquet.

c f h

Fig. 932.

Fig. 934,

The ordinary method of levelling the foundations of abuilding, or an area of moderate extent, for the pur-pose of forming a drain or watercourse, is by a level10 or 12 feet in length, formed of wood, and having attachedat A a string which holds a plummet that falls into ahole below; this simple instrument is blocked up untilit is brought perfectly level; then the difference in theheights of the blocks is taken, which added togetherconstitutes the variety in the level.

The level shown at B has an upright straight edge,which when placed against a wall or building at onceindicates, by the play of the plummet, how much in thatlength it is out of the perpendicular.

These implements all depend upon the circumstances ofa level line being a tangent to the earth’s curvature and ofa plumb line disposing itself into the direction of a radiusof the earth, of course perpendicular to the middle of thattangent, and that the level direction is a right line. Toprove the correctness of such an instrument it should beplaced upon a surface known or ascertained to be perfectlylevel, and such may always be formed by wedging up aplank at one end or the other: after finding that theplummet hangs in its proper vertical direction, it shouldbe reversed by turning the two ends of the level in an op-posite direction or position, when, if the plummet retainsthe same place over the line, the instrument may bedepended upon.

C and E are other varieties of levels which are in usefor ascertaining how much a stone or other body maybe out of a level; the plummet in the one falls overa mark on the cross piece towards D, when it is perfectlylevel at the feet, and in the other over a graduated arcof a circle.

Q

i'

i

/ _

Ftg. 936.

B

/i\

l/$\J

Fig. 936.

C R

fig. 937.

3 F