Changing the Paper.

272. 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 used as before.

Now, in order that the two papers may be put together 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 corresponding 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, determined on the first paper; 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 a similar manner.

273. For further description of the plane-table and its use, see "A Treatise on the Plane-Table and its use in Topographical Surveying," by E. Hergesheimer, U. S. Coast and Geodetic Survey, Report for 1880, Appendix No. 13.

SECTION III.

PLOTTING THE TRIANGULATION.

The sides of the triangles having been completed, the work may then be plotted, as already explained, either by means of the circular protractor, or by the method of chords.

The Circular Protractor.

274. This instrument consists of a brass circular limb, Fig. 131, of about six inches in diameter, with a movable index AB, having a vernier at one extremity A, and a milled screw at the other extremity B, with a concealed cog-wheel that works with the cogs of the limb, and thus moves the index AB about the centre of the protractor. At the centre of the protractor is a small circular glass plate, on which two lines are cut; the point of their intersection is the exact centre of the instrument. The limb is generally divided to half-degrees; the degrees are numbered from 0 to 360.

At the 0 point, and at the opposite extremities of the diameter passing through that point, are small lines on the inner edge of the limb; the two extremities of the diameter, perpendicular to this latter, are designated in the same way.

Two angular pieces of brass, each having a small and sharp steel pin at its extremity, are fastened to the index, and revolve freely around the lines ab and cd. The small screws,

a, b, c, and d, move them in the directions of the lines ab, cd, for the purpose of bringing the steel pins exactly into the line which passes through the 0 of the index and the centre of the protractor.

To adjust them to their places, place the centre of the protractor over a marked point, and the 0 of the index to the O of the limb. Then mark the place of the index by the pins; after which, turn the index 180°, and see if the pins will mark

the same points as before. If they do, the index is adjusted; if they do not, correct the error with the screws a, b, c, and d.

275. To lay off an Angle with the Protractor.-Let its centre be placed over the angular point, and the diameter passing through 0 and 180°, on the given line. Turn the screw that works the index, until the 0 of the vernier coincides with the division corresponding to the given angle; then let the angular brass pieces be turned down; the points dotted by the steel pins will show the direction of the required line.

If this line does not pass through the angular point, the pins are out of place, and must be re-adjusted.

276. First Method of Plotting.-Suppose it were required to make the plot of the harbor, Fig. 122, on a scale of 450 yards to an inch.

Divide the length of the base-line AB, which is equal to 1140 yards, by 450, and the quotient 2.53 will express the length which is to represent the base-line on the paper.

Draw an indefinite line AB, to represent the base; and having chosen any point, as A, for the first station, lay off 2.53 inches to B. The other extremity of the base-line will thus be determined.

Then, place the circular protractor at A, and lay off the angle BAE, and then the angle EAG. Next, place the protractor at B, and lay off the angles ABE and EBC. The intersection of the lines AE and BE will determine the station E. Let the protractor be then placed at this point, and all the angles of station E laid down.

The point G, where EG intersects AG, and the point C, where EC intersects BC, will then be found.

By placing the protractor at C and G, we can determine the points D and F, when the place, on the paper, of all the stations will be known.

To unite the work done with the compass, spread the compass-notes before you, and draw through A a line to represent the meridian. The course AE lies to the west of this meridian, and makes an angle of 12° with it.

Then, lay off from the scale the distances Aa, Ab, Aq, Ac, Ad, Ae, and at the several points erect perpendiculars to AE. Lay off, on these perpendiculars, the lengths of the offsets, and the curve traced through the points so determined, will be the margin of the lake.

At E, draw a parallel to the meridian through A, and lay down the course EH, which is easterly, and makes an angle of 50° with the meridian. Then, lay down the several distances to the offsets, and draw the offsets and lay off their lengths. Do the same for the course HI, and all the compass-work will be plotted.

The work done with the plane-table is united to the work done with the transit, by simply reducing it to the same scale, and then placing the line AN on the paper of the plane-table, upon the line AN, drawn on the plot of the triangulation.

277. Second Method of Plotting.-Place the centre of the protractor near the centre of the paper, and draw a line through the points 0 and 180°. This line will have the same position with the circular protractor that the base-line AB had with the limb of the transit.

Then lay off, from the 0 point, an arc equal to the direction from A to E, also an arc equal to the direction AG, and through the centre point, and the points so determined, draw lines. Lay off in succession, in a similar manner, the directions taken at all the stations; and through the centre point, and the points so determined, draw lines, and designate each by the letters of the direction to which it corresponds.