Then turn the index about the point C, till the mark E be seen through the sights, by which draw a line, and measure the distance to E, laying it on the line from C to E. In like manner determine the positions of CA and CB, by turning the sights successively to A and B; and lay the lengths of those lines down. Then connect the points with the boundaries of the field, by drawing

the black lines CD, DE, EA, AB, BC.

2. FROM A STATION WITHIN THE FIEld.

When all the other parts cannot be seen from one angle, choose some place O within; or even without, if more convenient, from whence the other parts can be seen. Plant the table at O, then fix it with the needle north, and mark the point O on it. Apply the index successively to O, turning it round with the sights to each angle A, B, C, D, E, drawing dry lines to them by the edge of the index; then measuring the distances OA, OB, &c., and laying them down upon those lines.

E

Lastly, draw the boundaries AB, BC, CD, DE, EA.

3.-BY GOING ROUND THE FIGURE.

When the figure is a wood, or water, or from some other obstruction you cannot measure lines across it; begin at any point A, and measure round it, either within or without the figure, and draw the directions of all the sides thus: Plant the table at A, and turn it with the needle to the north or flower-de-luce; fix it, and mark the point A. Apply the index to A, turning it till you can see the point E, there draw a line; then the point B, and there draw a line: then measure these lines, and lay them down from A to E and B. Next, move the table to B, lay the index along the line AB, and turn the table about till you can see the mark A, and screw fast the table; in which position also the needle will again point to the flower-de-luce, as it will do indeed at every station when the table is in the right position. Here turn the index about B till through the sights you see the mark C; there draw a line, measure BC, and lay the distance upon that line after you have set down the table at C. Turn it then again into its proper position, and in like manner find the next line CD. And so on quite round by E to A again. Then the proof of the work will be the joining at A: for if the work is all right, the last direction EA on the ground, will pass exactly through the point A on the paper; and the measured distance will also reach exactly to A. If these do not coincide, or nearly so, some error has been committed, and the work must be examined over again.

PROBLEM VIII.

To survey a field with the theodolite, &c.

1.-FROM ONE POINT OR STATION.

When all the angles can be seen from one point, as the angle C (first fig. to last problem), place the instrument at C, and turn it about till, through the fixed sights, you see the mark B, and there fix it. Then turn the moveable index about till the mark A is seen through the sights, and note the degrees cut on the instrument. Next turn the index successively to E and D, noting the degrees cut off at each; which gives all the angles BCA, BCE, BCD,

Lastly, measure the lines CB, CA, CE, CD; and enter the measures in a fieldbook, or rather against the corresponding parts of a rough figure, drawn by guess to resemble the field.

2.-FROM A POINT WITHIN OR WITHOUT.

Plant the instrument at O (last fig.), and turn it about till the fixed sights point to any object, as A; and there screw it fast. Then turn the moveable index round till the sights point successively to the other points E, D, C, B, noting the degrees cut off at each of them; which gives all the angles round the point 0. Lastly, measure the distances OA, OB, OC, OD, OE, noting them down as before, and the work is done.

3. BY GOING ROUND THE FIELD.

By measuring round, either within or without the field, proceed thus: Having set up marks at B, C, &c. near the corners as usual, plant the instrument at any point A, and turn it till the fixed index be in the direction AB, and there screw it fast: then turn the moveable index to the direction AF; and the degrees cut off will be the angle A. Measure the line AB, and plant the instrument at B, and there in the same manner observe the angle B. Then measure BC, and

observe the angle C. Then measure the distance CD,

B

and take the angle D. Then measure DE, and take the angle E. Then measure EF, and take the angle F. And, lastly, measure the distance FA.

To prove the work: add all the inward angles A, B, C, &c., together; for when the work is right, their sum will be equal to twice as many right angles as the figure has sides, wanting four right angles. But when there is an angle, as F, that bends inwards, and you measure the external angle, which is less than two right angles, subtract it from four right angles, or 360 degrees, to give the internal angle greater than a semicircle, or 180 degrees.

OTHERWISE.

Instead of observing the internal angles, you may take the external angles, formed without the figure by producing the sides further out. And in this case when the work is right, their sum altogether will be equal to 360 degrees. But when one of them, as F, runs inwards, subtract it from the sum of the rest, to leave 360 degrees.

10,

PROBLEM IX.

To survey a field with crooked hedges, &c.

With any of the instruments, measure the lengths and positions of imaginary lines running as near the sides of the field as you can ; and, in going along them, measure the offsets in the manner before taught; then you will have the plan on the paper in using the plain table, drawing the crooked hedges through the ends of the offsets; but in sur

veying with the theodolite, or other instrument, set down the measures properly in a field-book, or memorandum-book, and plan them after returning from the field, by laying down all the lines and angles.

So in surveying the piece ABCDE, set up marks a, b, c, d, dividing it into as few sides as may be. Then begin at any station u, and measure the lines ab, bc, cd, da, taking their positions, or the angles a, b, c, d; and, in going

along the lines, measure all the offsets, as at m, n, o, p, &c., along every station line.

When

And this is done either within the field, or without, as may be most convenient. there are obstructions within, as wood, water, hills, &c., then measure without, as in the figure here given.

PROBLEM X,

To survey a field, or any other thing, by two stations.

This is performed by choosing two stations, from whence all the marks and objects can be seen; then measuring the distance between the stations, and at each station taking the angles formed by every object, from the station line or distance.

The two stations may be taken either within the bounds, or in one of the sides, or in the direction of two of the objects, or quite at a distance and without the bounds of the objects or part to be surveyed.

In this manner, not only grounds may be surveyed, without even entering them, but a map may be taken of the principal parts of a

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county, or the chief places of a town, or any part of a river or coast surveyed, or any other inaccessible objects; by taking two stations, on two towers, or two hills, or such like.

PROBLEM XI

To survey a large estate.

If the estate be very large, and contain a great number of fields, it cannot well be done by surveying all the fields singly, and then putting them together; nor can it be done by taking all the angles and boundaries that inclose it. For in these cases, any small errors will be so multiplied, as to render it very much distorted.

1. Walk over the estate two or three times, in order to get a perfect idea of it, and till you can carry the map of it tolerably well in your head. And to help your memory, draw an eye draught of it on paper or at least of the principal parts of it, to guide you; setting the names within the fields in that draught.

2. Choose two or more eminent places in the estate, for stations, from whence all the principal parts of it can be seen; and let these stations be as far distant from one another as possible.

3. Take such angles, between the stations, as you think necessary, and measure the distances from station to station always in a right line: these things must be done till you get as many angles and lines as are sufficient for determining all the points of station. And in measuring any of these station distances, mark accurately where these lines meet with any hedges, ditches, roads, lanes, paths, rivulets, &c.; and where any remarkable object is placed, by measuring its distance from the station line; and where a perpendicular from it cuts that line. And thus as you go along any main station line, take offsets to the ends of all hedges, and to any pond, house, mill, bridge, &c., omitting nothing that is remarkable, and noting every thing down.

4. As to the inner parts of the estate, they must be determined in like manner, by new station lines: for after the main stations are determined, and every

thing adjoining to them, then the estate must be subdivided into two or three parts by new station lines; taking inner stations at proper places, where you can have the best view. Measure these station lines as you did the first, and all their intersections with hedges, and offsets to such objects as appear. Then proceed to survey the adjoining fields, by taking the angles that the sides make with the station line, at the intersections, and measuring the distances to each corner, from the intersections. For the station lines will be the bases to all the future operations; the situation of all parts being entirely dependent upon them; and therefore they should be taken of as great length as possible; and it is best for them to run along some of the hedges or boundaries of one or more fields, or to pass through some of their angles. All things being determined for these stations, you must take more inner stations, and continue to divide and subdivide till at last you come to single fields; repeating the same work for the inner stations, as for the outer ones, till all is done; and close the work as often as you can, and in as few lines as possible.

5. An estate may be so situated, that the whole cannot be surveyed together; because one part of the estate cannot be seen from another. In this case, you may divide it into three or four parts, and survey the parts separately, as it they were lands belonging to different persons; and at last join them together.

6. As it is necessary to protract or lay down the work as you proceed in it, you must have a scale of a due length to do it by. To get such a scale, measure the whole length of the estate in chains; then consider how many inches long the map is to be; and from these will be known how many chains you must have in an inch; then make the scale accordingly, or choose one already made.

THE NEW METHOD OF SURVEYING.

In the former method of measuring a large estate, the accuracy of it depends on the correctness of the instruments used in taking the angles. To avoid the errors incident to such a multitude of angles, other methods have of late years been used by some few skilful surveyors. The most practical, expeditious, and correct, seems to be the following:

Choose two or more eminences, as grand stations, and measure a principal base line from one station to the other, noting every hedge, brook, or other remarkable object as you pass by it; measuring also such short perpendicular lines to the bends of hedges as may be near at hand. From the extremities of this base line, or from any convenient parts of the same, go off with other lines to some remarkable object situated towards the sides of the estate, without regarding the angles they make with the base line or with one another; still remembering to note every hedge, brook, or other object that you pass by. These lines, when laid down by intersections, will, with the base line, form a grand triangle on the estate; several of which, if need be, being thus laid down, you may proceed to form other smaller triangles and trapezoids on the sides of the former: and so on, until you finish with the enclosures individually. This grand triangle being completed, and laid down on the rough plan-paper, the parts, exterior as well as interior, are to be completed by smaller triangles and trapezoids.

In countries where the lands are enclosed with high hedges, and where many lanes pass through an estate, a theodolite may be used to advantage, in measur ing the angles of such lands; by which means, a kind of skeleton of the estate may be obtained, and the lane lines serve as the bases of such triangles and trapezoids as are necessary to fill up the interior parts.

The field-book is ruled into three columns. In the middle one are set down the distances on the chain line at which any mark, offset, or other observation is made; and in the right and left hand columns are entered the offsets and observations made on the right and left hand respectively of the chain line.

It is of great advantage, both for brevity and perspicuity, to begin at the bottom of the leaf and write upwards; denoting the crossing of fences by lines drawn across the middle column, or only a part of such a line on the right and left opposite the figures, to avoid confusion; and the corners of fields, and other remarkable turns in the fences where offsets are taken to, by lines joining in the manner the fences do, as will be best seen by comparing the book with the plan annexed to the field-book following, page 462.

The letter in the left hand corner at the beginning of every line, is the mark or place measured from; and, that at the right hand corner at the end, is the mark measured to. But when it is not convenient to go exactly from a mark, the place measured from, is described such a distance from one mark towards another; and where a mark is not measured to, the exact place is ascertained by saying, turn to the right or left hand, such a distance to such a mark, it being always understood that those distances are taken in the chain line.

The characters used are, for turn to the right hand,

for turn to the left hand, and a placed over an offset, to show that it is not taken at right angles with the chain line, but in the line with some straight fence; being chiefly used when crossing their directions, and it is a better way of obtaining their true places than by offsets at right angles.

When a line is measured whose position is determined, either by former work, (as in the case of producing a given line, or measuring from one known place or mark to another,) or by itself (as in the third side of a triangle) it is called a fast line, and a double line across the book is drawn at the conclusion of it; but if its position is not determined (as in the second side of a triangle), it is called a loose line, and a single line is drawn across the book. When a line becomes determined in position, and is afterwards continued, a double line half through the book is drawn.

When a loose line is measured, it becomes absolutely necessary to measure some line that will determine its position. Thus, the first line ah, being the base of a triangle, is always determined; but the position of the second side hj, does not become determined, till the third side jb is measured; then the triangle may be constructed, and the position of both is determined.

At the beginning of a line, to fix a loose line to the mark or place measured from, the sign of turning to the right or left hand must be added (as at j in the third line); otherwise a stranger, when laying down the work, may as easily construct the triangle hjb on the wrong side of the line ah, as on the right one: but this error cannot be fallen into, if the sign above named be carefully observed. In choosing a line to fix a loose one, care must be taken that it does not make a very acute or obtuse angle; as in the triangle pBr, by the angle at B being very obtuse, a small deviation from truth, even the breadth of a point at p or r, would make the error at B, when constructed, very considerable; but by constructing the triangle pBq, such a deviation is of no consequence.

Where the words leave off are written in the field-book, it is to signify that the taking of offsets is from thence discontinued; and of course something is wanting between that and the next offset.

The field-book for this method, and the plan drawn from it, are contained in the four following pages.