&c. In the same way the position of any other thing, as the house K, may be determined by drawing GK towards it when the table is at G, and HK towards it when the table is at H.

Secondly, with the Theodolite. Place the instrument at the first station G, and turn it till the needle points to the fleur-de-lis, and take the bearing of the station H, and measure GH. Then take the angle HGC, then CGD, DGE, &c., and lastly BGH. Remove the instrument to the second station H, and bring the needle to the fleur-de-lis; then the station Gought to bear upon the point opposite to that upo which H bore from G. If it does, then take first the angle GHF, then FHA, AHB, &c., and lastly EHG. The sum of the angles taken at each station ought to be exactly 360°.

Every thing else which is to be put in the plan must be surveyed in the same way, by taking at G the angle between GH and the line from G to it, and the same at H. All these observations must be placed in a field-book.

When the whole cannot be seen at two stations, more stations must be taken. The lines between the stations must be measured, and the angles taken as before. But care must be taken to determine the position of each of the lines joining the

stations.

1. Required the plan and the area of a field from the following

In this field-book, the angles at G are marked as taken with the theodolite when placed at that station. The sights, when at the beginning of the degrees, were directed to the station H, and the instrument fixed there. Then the move. able index was turned to C, and cut off 22° for the angle HGC, which, in the field-book, is marked C, the other two letters being found at the top; then it was turned to D, and cut off 86° 30' for the angle HGD; and the difference of these two is the angle CGD. It was then turned to E, and cut off 146° 30' for the angle HGE; and so on all the way

round. In the same way the angles were taken at H, both for determining the corners of the field and for finding the corner of the house at K.

In calculating the areas of fields surveyed from more than one station, it is necessary to calculate, by trigonometry, the length of all the lines drawn from one of the stations to the angles; and for this purpose we have, in every triangle of which GH is a side, all the angles and this side to find the ɔther side; after which the area is found as in the preceding problem. Here the distances from G are GA 1123.3, GB 1493-1, GC 1409.73, GD 917-43, GE 951-47, and GF 660-743 links; from which the areas of the triangles AGB, BGC, CGD, DGE, EGF, and FGA, are to be calculated.

Ans. 27 acres 5 perches 25 yards 3.47 feet. 2. Required the plan and the area of a field from the following

Ans. Area 100 acres 1 rood 19 perches 21 yards 1-4 foot.

· PROB. XXVI. To draw the plan of the field upon paper from the field-book.

Draw a faint line up and down the paper to represent the meridian, the upper end the north, and the under end the south. Using the data given in Ex. 1, Prob. XXV., in this line take a convenient point G for the first station. On the south side of G make an angle of 67° 30' towards the left hand, which will give the position of GH; and take 1038 from any convenient scale, and lay that extent from G to H,

B

to get the station H. The best protractor for laying down the angles is a circular one, divided into 360°. Place the centre at G, and the beginning of the degrees on GH. Make a mark at 22°, and at it write a faint C; make another mark at 86° 30′, and there write a faint D, and so on all the way round; and draw faint lines from G to the marks. Next place the centre of the protractor at H, and the beginning of the degrees on GH; and at 20° make a mark, and write F; at 72° make a mark, and write A, and so on; and draw lines from H through the marks. The lines from G and H, through the points where the same letter is written, must be drawn out till they meet, and their intersection is at the angle to which that letter belongs. Thus GA and HA will meet in the angle A, GB and HB will meet in the angle B, &c. After this join AB, BC, &c. for the boundaries of the field.

If the protractor be a semicircle, then, after laying down the angles less than 180°, the protractor must be laid on the other side of GH, and 180° taken from each of the remaining angles before they are laid down.

PROB. XXVII. To survey fields with crooked

boundaries.

The boundaries of fields are seldom straight lines, and therefore surveyors generally erect poles near the corners of the ground to be surveyed, and conceive these poles joined by straight lines. This constitutes the body of the field; and the parts between these lines and the boundaries are considered as offsets, and their areas found separately.

The points, therefore, which, in the preceding problems, were called angles or corners, are to be considered only as the places of these poles, and the fields surveyed as contained by the lines joining them; and to complete the survey, the situ ation and distance of the boundaries from these lines must be found.

Ea

XA

R

1. Let EIMP be a field to be surveyed. Poles are erected at A, B, C, D, near corners of the field, and the space ABCD is surveyed as before. The rest of the field is obtained by taking offsets from the lines AB, BC, CD, DA, and adding the spaces which are without these lines, and taking away the spaces within them.

N

SM

The field-book for such a survey must consist of three columns: the middle one contains the distance measured along

Left off

sets.

FIELD-BOOK.

Main lines

Right off

sets.

AC, S. 60° 25′ E. 1896.

844

Including

offset to cor.

86

746

Close to A.

152

688

594

462

200

Ꭰ

e main lines AB, BC, c.; and the other two re for the offsets, accord-i ig as they are on the right • left of the main line. or this purpose it is best begin at the bottom of e field-book, and to write pwards, that the offsets i the right side of the ain line may be placed the right-hand column, id the offsets on the left de in the left-hand coimn. Thus, in measuring om A to B, the offset a, which measures 106 nks, is on the left hand f AB, at the beginning f the line; therefore write in the middle column, t the bottom, and opposite ɔ it, in the left-hand coamn, write 106. Then easuring along AB, the oint f is to be found, upon which the perpendicular alls from F: this is 284 inks from A, and ƒF is 200 links; therefore write 284 in the middle column, and 200 opposite to it in the left-hand column. Again, at 442 links from A, the line AB crosses the boundary-line FG; therefore write 442 in the middle column, and in the adjacent columns draw straight lines in the direction of the straight line FG nearly, for the exact position of it is not required at this stage of the survey. At 530 the perpendicular from G meets AB, and Gg is 108; place therefore 530 in the middle column, and 108 opposite to it in the right-hand column.

To left.

Proceed in this way to B, where, besides the offset, BI is measured, and placed in the left-hand column, with the mark > to show that it is not perpendicular. At the same place in the right-hand column is placed the mark I, to show that now the surveyor turns to the right hand. This finishes the survey along the line AB, and a line is drawn across the book

to separate it from the next line. Proceed in the same way from B to C, from C to D, and from D to A.

The position of any one of the lines, as AC, being found with the compass, it will determine the position of the whole. But in using the compass, the variation should be allowed; and great care ought to be taken lest the needle be attracted by some metallic substance in its neighbourhood.

Ans. Area 14 acres 2 roods 19 perches 22 yards

Lay down the plans of the following properties from the field-book for the three examples, and calculate their contents.