that the vertical plane through B and its opposite sight may bisect O. Then the number of degrees and the arc GH will measure the angular distance of O from P. The moveable diametral band is next directed to Q, and in like manner is obtained the angle PEQ; subtracting the previously obtained angle OEP, we obtain the difference OEQ.

As a correction of GEH, or OEP, HEp may be taken, and subtracted from 180°, giving a remainder GEH. If this differs from the value before obtained, the mean value will be found by taking half the sum of the two results.

If the objects are in the same vertical plane, the instrument must be so placed by means of the joint at E, that the circular limb shall pass through them; and the sights will then have their wires horizontal.

In order that the diameter may be moved through a very small arc, so as to bring the wires exactly over the object, the end in contact with the semicircle is furnished with a clamp, whereby it is made to bite the limb; and its further motion, which was before produced solely by the hand, is then regulated by a screw with a milled head.

THE PLANE TABLE.

276. This instrument consists of a plane board of any convenient size, say 24 inches by 16, and on its upper face a piece of paper is affixed, upon which it is required to draw a plan of any plot of ground. The paper is securely fastened, either by broadheaded nails, or by pasting the edges. The board rests, as in the graphometer, on a tripod, in the upper part of which is a socket, wherein there drops a cylinder surmounted by a framework supporting the board. Between the cylinder and the framework is a universal joint, so that the board can be turned in any direction whatever. The horizontal position of the Plane Table is secured by the use of a spirit-level.

Suppose the proposed piece of ground to be of the form of the polygon ABCDEF: it may be correctly plotted by this instrument in one of the three following different ways.

(1) Place the instrument at one of the angles, A: and after having secured the table being horizontal, make a mark on the paper exactly above the point A. This is done by means of a spirit level and a plumb-line. Call the point so marked a.

At A, B, C, D, E, F, G, flag-staffs must be placed vertically.

Now at a place one extremity of one of the wires of the moveable sight, described in the graphometer, and with the eye at a make the staff at B to be just seen in the wire of the opposite sight; then draw through the wires in the direction AB an indefinite line upon the paper. Without moving the plane table, direct the eye in like manner to F, and draw an indefinite line in that direction: we now obtain the BAF, or, on the paper, baf. Next send an assistant to measure successively AB and AF with a chain: set off ab and af upon the indefinite lines before drawn, representing AB and AF, according to some convenient scale. Then transfer the instrument to B, placing the point b of the partially drawn plan vertically over B. Direct the sight to A, making ba coincide in direction with BA; turn the sight to C, and thus obtain the ABC. Draw the indefinite line bc, measure BC, and then lay down be according to the scale agreed upon, and mark c on the plan. Proceed in like manner to obtain the other angles at C, D, E, F, and the lengths CD, DE, EF, which give cd, de, ef, on the plan: the whole outline is then plotted on the paper. is not necessary to carry the instrument to F, as af was already traced, when the observer was at A.

It

(2) If the staves at B, C, D, E, F, can all be readily observed from A, the process will be very much shortened.

F

B

Plant the table at A, as before; and mark the point a exactly above A. Without moving the table, direct the sight successively to B, C, D, E, F, and draw indefinite lines ab, ac, ad, ae, af. Let one or more assistants measure the lines AB, AC, AD, AE, AF, and lay down upon the indefinite lines ab, ac, &c....distances representing AB, AC, &c. according to some convenient scale: we thus obtain the points b, c, d, e, f. Join these points, and a plan of the polygon is obtained, as before. This method has the great recommendation that the task of planting the table horizontally has to be performed but once.

(3) If all the angular points cannot be observed from any one of them as above, it often happens that they may be so observed from some central point, O, as in the next diagram. Then, as before, we direct successively the sight to the angular points of the polygon; trace the lines Oa, Ob, Oc,...upon the plan; measure OA, OB, OC...; and lay down upon the paper, Oa, Ob, Oc...according to scale; hence we determine the angular points, a, b, c...and by joining these points, we obtain abcdef, a plan of the proposed polygon, as in (1) and (2).

NOTE. If the surface to be planned be of greater length than can be conveniently mapped upon a single sheet of paper of the size of the instrument, the board may be furnished with rollers on two of its opposite sides,

B

E

upon which a sheet of the required length is wrapped; and as a portion is completed, and wound round one roller, fresh paper may be unrolled from the other.

277.

THE OPISOMETER*.

This simple instrument measures the length of any crooked lines, as roads, rivers, fences, walls, &c. on any map, or plan, which is drawn to a scale, without requiring any arithmetical calculation.

The principle of the Opisometer is, that, after having been applied to any line, it retraces or measures backwards precisely the same length on the scale with which the line is to be compared. It consists of a milled wheel with a steel screw for its axis, mounted on a convenient * Made and sold by Messrs Elliott, Brothers, 30, Strand, London.

handle. To measure the length of a line, as the distance between two towns by the road traced upon a map, turn the milled wheel up to one end of the screw until it stops; and then place the instrument on the map, in an upright position, as represented in the diagram, the wheel resting upon one extremity of the line to be measured; then run the wheel along the road, following every bend as closely as possible. Care must be taken to keep the wheel in contact with the paper, but the pressure need not be such as to injure the map. When the wheel has arrived at the other extremity of the line, lift the instrument carefully from the paper, and carry it to the zero end of the scale; run the wheel backwards along the scale, until it stops at the same end of the screw from which the measurement began; the division of the scale, at which the wheel stops, shews the length of the line measured on the map. Should the scale be shorter than the line measured, when the wheel arrives at the end, carry it to the zero mark again as often as may be necessary, counting the number of repetitions.

The accuracy of the result given by the Opisometer is unaffected by the dimensions of the instrument itself, and depends entirely on the care with which it is used. The chief point is to see that the handle of the instrument is perpendicular to the surface at the beginning and end of each step of the measurement.

AMSLER'S PLANIMETER*.

278. This singularly beautiful instrument was lately invented by Professor Amsler, of Schaffhausen, by means of which the area of any portion of a map, or plan, drawn to scale, is readily and accurately measured, however irregular the boundaries may be.

The PLANIMETER, when ready for use, as in the annexed diagram, rests upon three points D, E, F; these are respectively, 1st a point of the circumference of the divided wheel D; 2ndly, a point of the tracer F, at the end of the arm A; 3rdly, a point E, at the end of the' other arm B, which is kept fixed during the time of

*

This instrument is to be had only from Messrs Elliott, Brothers, 30, Strand, London, and the price is £3 13s. 6d.