brass plate these screws are worked against a second horizontal plate, for the purpose of levelling the table; the table having a ball and socket motion, similar to the limb of the theodolite.

For the purpose of levelling the table, a small detached spirit-level is used. This level being placed over the centre, and also over two of the levelling screws, the screws are turned contrary ways until the level is horizontal; after which, it is placed over the other two screws, and made horizontal in the same manner.

Between the upper horizontal plate and the table, there is a clamp-screw, similar to the clamp-screw of the theodolite, which being loosened, the table can be turned freely about its axis. There is, also, a small tangent-screw, by which the smaller motions of the table are regulated, after the clamp-screw is made fast. Neither of these screws can be seen in the figure.

The upper side of the table is bordered by four brass plates, about one inch in width, and the centre of the table is marked by a small pin, F. About this centre, and tangent to the sides of the table, conceive a circle to be described. Suppose the circumference of the circle to be divided into degrees and parts of a degree, and radii to be drawn through the centre and the points of division. The points in which these radii intersect the outer edge of the brass border, are marked by lines on the brass plates, and the degrees are numbered in the direction from left to right, from the point L to the point I, 180°, and from the point I to the point L, 180°. In some plane-tables, however, they are numbered from 0 to 360°.

There are, generally, diagonal scales of equal parts cut on the plates DLC and AIB, the use of which will be explained hereafter.

Near the two other edges of the table, two small grooves are made, into which the plates of brass DB and CA are fitted, and these plates are drawn to their places by means of milled screws, which pass through the table from the

of two of the screws, Q and S, are seen in the figure, as also one of the plates and its two screws in Fig. 3. The object of these plates is to confine a sheet of paper on the table. By loosening the screws, and pressing them upwards, the plates are raised above the surface of the table; the edges of the paper can then be placed under them: then, by turning the screws back again, the plates are drawn down and the paper held tightly. Fig. 1 represents the table with the paper partly put upon it: one edge of the paper has been placed under the plate DB, and the screws S and Q, tightened. The paper, before being put on, should be moistened, in order to expand it; and then, after it has been dried, it will fit closely to the table.

A ruler, AB (Fig. 2); with open vertical sights, is used with the plane-table. This ruler has a fiducial edge, which is in the same vertical plane with the hairs of the sights. A ruler with a telescope, and a vertical limb, similar to the vertical limb of the theodolite, is sometimes used with the plane-table. A compass, also, is often attached to the table, to show the bearings of the lines.

The plane-table is used for two distinct objects.

1st. For the measurement of horizontal angles.

2dly. For the determination of the shorter lines of a survey, both in extent and position.

TO MEASURE A HORIZONTAL ANGLE.

25. Place, by means of a plumb, the centre of the table directly over the angular point: then level the table; after which, place the fiducial edge of the ruler against the small pin at the centre: direct the sights to one of the objects, and note the degrees on the brass plate; then turn the ruler and sights to the other object, and note the degrees as before. If the ruler has not passed over the 0 point, the difference of the readings the angle sought; but, if it has, the larger taken from 180°, and the remainder added to the smaller, gives the required angle.

TO DETERMINE LINES IN EXTENT AND POSITION.

objects and lines which are to be determined, and select for a base a convenient portion of such a line of those already formed in the triangulation, that most of the objects can be seen from its extremities. Then place the plane-table with its centre, nearly, though not accurately, over one extremity of the base; make it truly horizontal, and turn it until the larger part of the paper lies on the same side of the base with the objects.

Then, tighten the clamp-screw, and mark with a pin the point of the paper directly over the station, which point is determined most accurately by suspending a plumb from the lower side of the table. Press the pin firmly on this point, bring the fiducial edge of the ruler against it, and sight to the other extremity of the base line, and mark with the pin or pencil, the direction of the line on the paper. Sight in like manner to every other object, and draw on the paper the corresponding lines, numbering them from the base line, 1, 2, 3, 4, &c.

Then, with a pair of dividers, take from the scale a certain number of equal parts to represent the base, and lay off the distance on the base line from the place of the pin. Take up the table, carry it to the other extremity of the base, and place the point of the paper corresponding to that extremity, directly over it. Place the fiducial edge of the ruler on the base line, and turn the table, by means of the tangent-screw, until the sights are directed to the first station. If, however, in bringing the table to this position, the corresponding point of the paper has been moved from over the extremity of the base line, move the legs of the tripod until it is brought back to its place. Let the table be then levelled, after which, place the ruler again on the base line, and bring the table to its proper position by the tangent-screw, and continue the adjustment until the extremity of the base line on the paper is directly over the station, and in the same vertical plane with the base line on the ground. Then direct the sights to all the objects sighted to from the other station, and mark the lines 1, 2, 3, 4, &c., from the base line, as before. The

&c., determine, on the paper, the positions of the several objects; and a reference of these lines to the scale of equal parts, determines the true distances.

27. Let it be required, for example, to determine, by

means of the plane-table, the relative positions of several houses.

From station A, and on one of the lines of the tri

angulation, as AB, measure

A

N

the base line AN, which we will suppose equal to 300 yards. Place the plain-table at A, and sight to the corners of the houses, and mark the lines 1, 2, 3, 4, &c. Then remove the table to N, and sight to the same corners as before, and draw the lines as in the figure. The points at which they intersect the corresponding lines determine the corners of the houses. the houses may then be drawn on the paper. Draw lines at right angles to the front lines, and on them lay off the depths of the houses, with the same scale as that used for the base line.

The

before drawn,

front lines of

To find the length of any line drawn on the paper, as the line 1, drawn through A, for example, place the dividers at A and extend them to the other extremity of the line, and then apply the line to the scale. The length of the line 1 is equal to 198 yards.

28. In this example, we determine from the base line CD, the positions of the points F, E, and H.

H

3

2

OF CHANGING THE PAPER.

29. When one paper is filled, and there is yet more work to be done, let the paper be removed, and a second paper put on the table; after which, the table may be

Now, in order that the two papers may be put toge ther and form one entire plan, it is necessary that two points determined on the first paper, be also determined on the second; and then, by placing the lines joining these points, one on the other, all the lines on the two papers will have the same relative position as the corres ponding lines on the ground; and the same for as many papers as it may be necessary to use. If different scales are used, the corresponding points will not join, and then the work must be reduced to the same scale, before the papers can be put together.

In the first example, the position of the point F was determined, in order to unite the first paper with the second.

In the second example, we sighted from C and D, the extremities of the base line, to the points N and F; we thus determined the line NF on the second paper. Placing the line NF of the one paper on NF of the other, we have the following plan.

In this plan, all the points and lines are accurately laid down. Any number of papers may be joined in the same

manner.

30. The principal use of the plane-table is for the interior filling up of trigonometrical surveys; it is also used with advantage, when only a plot of a field is wanted.

It ought not be used for the determination of long lines, nor can it be relied on for determining extended areas.

Having finished the field-work, some corrections are necessary, before plotting the survey. The principal coirec tions are, the reduction to the centre of the station, and