boundaries, and fix the places of the stations B, n, and D. Now, if the measured length of Dn just fit between D and n, the work is right with respect to the triangles A Em, E D n. Lastly, prolong Dn to the O C, and, if the distance from thence to the B be the same as shewn by the field book, the whole of the work is right. But, if the distance D n do not agree, the work must be examined from the beginning; if only the distance BC fail, then only that distance and the portions m B, C n need be examined.

NOTE. For a variety of other methods of surveying irregular fields, small estates, &c., &c., see Baker's Land and Engineering Surveying, Chap. III.

PROBLEM IV.

SURVEYING LARGE ESTATES OR PARISHES BY THE CHAIN ONLY.

Having perambulated the boundary of the estate, parish, or lordship to be surveyed, if you find that its boundary approaches somewhat near to that of a four-sided figure, or trapezium, the system of fundamental lines, adopted by order of the Tithe Commissioners of England and Wales, is to be preferred. These fundamental lines are six in number, of which four must run close by, or as nearly as possible to, the boundary in question, thus forming a trapezium, four lofty station poles being placed at each angle, as objects for running the lines; the other two lines must form the diagonals of this trapezium, and therefore pass through the central parts of the survey, intersecting each other, the points of intersection being noted on measuring each line, so that when the system of lines are laid down on the plan, the proof of the accuracy of the work may be fully established, before the minor operations, or filling up, as it is called, is commenced. It will be necessary, moreover, in almost every case, to range the lines between every two of the main stations with long slender ranging poles, as the intervention of hills, fences, trees, buildings, &c., will frequently interrupt the view of even the loftiest station poles that can be obtained; and more especially so, when the main stations are at a great distance, which depends on the magnitude of the survey, and is sometimes as much as ten miles. In measuring these main lines, every fence, road, stream, building, &c., which is passed or crossed must be noted in the field book, the several crossings, and bends being sketched therein, to the latter of which offsetts must be taken. Stations must also be left on these main lines, at convenient situations for taking the interior fences, &c., of the survey, and their distances carefully noted in the field book. From and to the stations, thus

left, or from and to points near them, secondary lines must be run, as near the interior parts of the survey as possible, the crossings, offsets, and other remarks being made in the field book, as already directed for the measurement of the main lines. These secondary lines will accurately fit between the points from and to which they have been measured, when laid down on the plan; thus forming a net work of small triangles within the four large triangles, into which the survey is divided by the six fundamental lines. This principle of proof is founded on the obvious property of triangles having a common angle always fitting one within another, the common angle of both being coincident. The lines marked with the figures 1 to 6, represent the system in question, those without figures are the secondary lines.

The main lines are numbered with the figures 1, 2, 3, &c., in small circles, as the most convenient method of reference to the field book: the secondary lines must have these numbers continued on them, for the same purpose, but this is not done in the diagram, to avoid confusing it.

It will be seen that the secondary lines mn, rs are prolonged beyond the system of main lines, to give stability to the parts of the survey that protrude beyond line 2.

NOTE. For the method of keeping the field book in extensive surveys, the description and use of the theodolite and other surveying instruments, see Bakers Land and Engineering Surveying.

ENGINEERING SURVEYING.

LEVELLING.-DEFINITION OF LEVELLING.

By the art of levelling the inequalities of the upper boundary of any section of the earth's surface may be shewn, and thence may be determined the several heights of any number of points in that boundary, above or below an assumed line, called a level line; though, in reality, this line is a great circle of the earth, and is such as would be derived from a section of the surface of still water.

:

LEVELLING INSTRUMENTS.

(1.) Levelling instruments all depend on the action of gravity of these the plumb-line, on which the mason's level depends, is the most simple; but it cannot be used in extensive operations, on account of its practical inconvenience.

The fluid, or water level, in all its modifications, is slso found inconvenient for extensive practice.

(2.) Spirit levels are now commonly used, as the most accurate instruments for finding the differences of level, or vertical distances between two stations: of these there are several, we shall only here describe the Y level.

A is an

The foregoing figure represents this instrument. achromatic telescope, resting on two supporters, which in shape resemble the letter Y; hence the name of the instrument. The lower ends of these supporters are let perpendicularly in a strong

₹

brass bar, which carries a compass box C. This compass is con-
venient for taking bearings, and has a contrivance for throwing
the needle off its centre, when not in use.
One of the Y sup-
porters is fitted into a socket, and can be raised or lowered by the
screw B.

Beneath the compass box, which is generally of one piece with the bar, is a conical axis passing through the upper of two parallel plates, and terminating in a ball supported by a socket. Immediately above the upper parallel plate is a collar, which can be made to embrace the conical axis tightly by turning the clamping screw E; and a slow horizontal motion can be given to the instrument by means of the tangent screw D. The two parallel plates are connected together by the ball and socket already mentioned, and are set firm by four mill-headed screws, which turn in sockets fixed to the lower plate, while their heads press against the under side of the upper plate, and thus serve the purpose of setting the instrument truly level.

Beneath the lower parallel plate is a female screw, adapted to the staff head, which is connected with brass joints to three mahogany legs, which support the instrument.

The spirit level is fixed to the telescope by a joint at one end, and a capstain headed screw at the other, to raise or depress it for adjustment.

(3.) Previous to using this instrument the following adjustments must be attended to.

1. The adjustments of the telescope for parallax and collima

tion.

2. The adjustment of the bubble tube.

3. The adjustment of the axis of the telescope perpendicularly

to the vertical axis.

1. The adjustment for parallax and collimation. Move the object-glass by the screw, and the eye-glass with the hand, till distant objects and the cross wires within the telescope, appear clearly defined; and the adjustment for parallax will be completed. Next, direct the telescope to some well-defined object at a great distance; and see that the intersection of the cross wires cuts it accurately; then loose the clips that confine the telescope in the Ys, and turn it round on its axis, observing whether the centre of the wires still continue to cut the object, during a whole revolution. If it does, it is in adjustment; if not, the line of collimation, or optical axis of the instrument, is. not in the line joining the centres of the eye and object-glasses. To correct this error, turn the telescope on its axis, and by

means of the four conjugate screw a, a, &c., that move the cross wires, correct for half the error, alternately loosing one screw and tightening its opposite one, till the cross wires cut the same point of the distant object, during an entire revolution of the telescope round its axis.

2. The adjustment of the bubble tube.-Move the telescope till it lies in the direction of two of the parallel plate screws, and by giving motion to these screws bring the air-bubble to the centre of its run. Now reverse the telescope carefully in the Ys, that is, change the places of its ends; and should the bubble not settle in the same point of the tube as before, it shows that the bubble tube is out of adjustment, and requires correcting. The end to which the bubble retires must then be noticed, and the bubble made to return one-half the distance by turning the parallel plate screws, and the other half by turning the capstain headed screws at the end of the bubble tube. telescope must now again be reversed, and the operation repeated, until the bubble settles at the same point of the tube, in the centre of its run, in both positions of the instrument. The adjustment is then perfect, and the clips, that confine the telescope in the Ys should be made fast.

The

3. The adjustment of the axis of the telescope perpendicularly to the vertical axis.-Place the telescope over two of the parallel plate screws, and move them, unscrewing one while screwing up the other, until the bubble of the level settles in the centre of its run; then turn the instrument half round on its vertical axis, so that the contrary ends of the telescope may be over the same two screws, and, if the bubble does not again settle in the same point as before, half the error must be corrected by turning the screw B, and the other half by turning the two parallel plate screws, over which the telescope is placed. Next turn the telescope a quarter round, that it may be over the other two screws, and repeat the same process with these two screws; and when, after a few trials, the bubble maintains the same position in the centre of its run, while the telescope is turned round on the vertical axis, this axis will be truly vertical; and the axis of the telescope being horizontal, by reason of the previous adjustment of the bubble tube, will be perpendicular to the vertical axis, and remain truly horizontal, while the telescope is turned completely round. The adjustment is therefore perfect.

There are several other highly approved levelling instruments, as Troughton's and Gravatt's levels, &c., for the descriptions of which, see Baker's Land and Engineering Surveying.