Cll At*. VIII.

GEOMETRY.

835

Fig. 1051.

A and B, and in the third term 30, the length of the cursor; the quotient gives 225, thenumber of feet from A to B.

To -measure Heights by Jacob's Staff and Arithmetic _In tins case its rod is placed parallel,

and its cursor perpendicular to the horizon ; then boning from the end of the rod by theelevated end of the cursor, the summit of the height to be found, which is done by movingthe cursor nearer to or farther from the eye, and remarking the number of small divisionson the rod, comprised between the end boned and the place where the cursor stops;then measure the distance from the station to the foot of the required height; put for afirst term the number of small divisionsat which the cursor stands; for the secondthe distance in feet from the station; and forthe third term half the length of the cursor,the quotient will be the height sought.

The height A B is required. The staffM N is to be first placed parallel with thehorizon, and CD perpendicular to it; inorder that by honing from the end M, bythe elevated arm I) of the cursor, the point Bmay be seen. Count how many divisionsthere are on the rod between M and the cursor I), as 45 ; then measure the distance onthe ground to A, which here is 600 feet; then 45 : 600 : : 15: 200, to which quotient mustbe added the height of the stand, to obtain the height of the tower A B, 15 being half thelength of the cursor CD.

The Plane Table , and the metliod used formeasuring heights and distances, &c. with it.

This instrument is of great antiquity, andwas clearly in use when Vitruvius compiledhis book ; it is usually made of a plate ofbrass, either of a round or square form, onwhich is placed a sheet of paper to draw thelines necessary to form plans or maps, aswell as to obtain the distance between ob-jects. The plane table A for mapping is ofbrass, 10 or 12 inches in diameter, and onits edge is a circle B, capable of containingsix sheets of paper, and having a diametersufficient for measuring the 360 degrees. Inthe centre at C a point is placed, the upperpart of which is sunk to receive a screw.

On the centre is placed a brass alhidade,

EG, w’hieh fits into the hole C, and whichis furnished with a telescope.

The plane table is often used for forminga sketch map, and for filling up the detailsof a survey, where the principal points havealready been fixed'by the theodolite, butobservations made with it cannot be reliedupon where great accuracy is demanded: inmany plane tables the divisions into 360degrees is dispensed with, and the reverseface of the frame is divided into equal parts,as inches and tenths, which are very con-venient for ruling parallel lines, setting outsquares and other purposes. On one side isscrewed a compass-box, with a magneticneedle to indicate the bearings, and to enablethe engineer to place the instrument at anynew station parallel to its former position.

The brass rule or index with a sloping edgeand perpendicular sight vanes at each ex-tremity is all that is required to completethe apparatus.

Tlie modern plane table is commonly made of wood in order that pins may be readilyfixed in it: its size for taking distances is about 2 feet in length, and 18 inches in width,and about 1 inch in thickness; its station line being only 6 inches. When used a ruleLM is placed on its edge to serve for the sights, and we require a stand to place the tableon, some piquets, pins, and a chain to measure distances with: a sheet of paper is then

3 ii 2

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Fig. 1052.