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DE equal to 1190 links, and at E erect the perpendicular EC equal to 625 links. Join DA, AB, BC, and DC, and the field is constructed.
Calculation. This field being a trapezium, its content must be found as directed in Prob. 7.
680 half the diagonal DB
6.57560 area in acres=6 acres, 2 roods, 12.096 perches.' 2. Required the plan and content of a field fron the following fieldbook.
Ans. The content is 1 acre, 2 roods, 4.3776 perches.
Note.-In either of the two figures, 4 aud 5, if the sides DC, CB, BA, AD, and the diagonal DB, had been measured with the chain, the figures might have been planned, and their contents found, by Prob. 5, without using a crossstaff, or measuring the perpendiculars AF and CE.
Unskilful measurers fregnently measure round a four-sided field, and find the content by adding each two opposite sides together, and taking half their sum; then they inultiply these half sums together for the area. It may be necessary to inform the learner, that this method is, generally, very erroneous, and ought never to be practised.
Prob. 3. To measure a four-sided field with crooked hedges.
Set up staves, or poles, at the corners D, C, B, fig. 6, as before directed. Then begin at A, and measure from A to B, noting all the necessary off-sets, and in this manner go round the field, tben measuro the diagonal AC.
Acres. The sides of the triangle ABC are 750, 1500, and 1294 links, and its content
485239 The sides of the triangle ACD are 1000, 800, and 1294 links, and its content.....
3.99907 Content of the off-sets along AB= 0.50250 Ditto
along BC= 1.67500 :
along CD= 107500
Sum= 12:10396 Content of the off-sets along DA, deduct 1.00000
Remains the content of the field=11•10396
Prob. 4. To measure an irregular field.
Set up station-staves at every angle, and divide the field into trapeziums and triangles ;
Thus, begin at A, fig. 7, and measure in a stralya't line towards C; at a take the perpendicular al, and at m the perpendicular mB. Then measure from C iowards H ; at n take the perpendicular nD, and at o the perpendicular ol.
Next measure from H towards E ; at w take the perpendicular wG, and at v the perpendicular vD.
Lastly, measure from E towards G ; and at s take the perpendicular sF.*
To cast up the content, draw a rough figure of the field, and place the dimensions upon the lines as you proceed.
Or, the dimensions being given in the following fuld-book, required the figure and the content.
The area of the whole.. 1040400
If any of the hedges AB, BC, &c. be crooked, these lines must be me sured and off-sets taken as iv Prob. 3.
Cut off five figures from the right hand, and the result will be 10:40400 acres = 10 acres, I ruod, 24:64 perches.
2. Required the plan and content of an irregular field, from the following
Off-sets Station, O, or OH-sets
Left. Base Line. Right.
Cut off five figures, and the result will be 10:40390 acres = 10 A, I R. 24.624 P.
Prob. 5. To survey a large estate. *
If the estate be very large and contain a great number of fields, it cannot be accurately surveyed and planned, by measuring each field separately, and then putting them together; nor hy taking all the angles, and measuring the boundaries which enclose it. For, in these cases, the several small errors will be so multiplied, that the different fields cannot be correctly laid down in the plan, and the whole figure of the estate will be distorted. Proceed in the following manner.
1. Walk over the estate two or three times in order to get a perfect idea of it, or till you can retain the figure of it in your mind. And to assist your memory make a rough draft of it on paper, putting the names of the different fields within them, and noting down the principal objects.
2. Choose two or more elevated places in the estate, for statione, from which all the principal parts of it can be seen, and let these stations be as far distant from each other as possible. In selecting the stations, be careful that the lines which connect them may run along
• Emerson's Surveying, page 47, et seq.
the boundaries of the estate, or some of the hedges to wbich off-sets may be taken when necessary. The smaller the number of stations you have to command the whole, the more exact your work will be, and especially if two or more lines proceed from one station.
3. Take such angles, between the stations, as you think necessary, and measure the distances froni station to station, always in a straight line : these things must be done, till you get as many angles and lines as are sufficient for determining all the points of the stations. In measuring the several station-distances, mark, accurately, where you cross any hedges, ditches, roads, lanes, paths, rivulets, &c. and where any remarkable object is placed, by measuring its perpendicular distance from the station-line; and be particularly careful always to measure in a straight line, which you may determine by taking back. sights and foresights along the station-line with a cross-staff or a theodolite. Also, take off-sets to all the ends of hedges, and to the different bends thereof which may fall near the station-line, and to any pond, house, mill, bridge, &c. noting every thing down that is remarkable ; for these are the data by which the places of such objects are to be determined on your plan.
Be careful to set marks up at the intersections of all hedges with the station-line, that you may know where to measure from when you come to survey the particular fields which are crossed by this line. These fields nust be measured as soon as you have completed your station-line, whilst they are fresh in your memory. In this manner all the station-lines must be measured, and the situations of all tha adjacent objects determined. It will be proper to lay down the work on paper every night, when you go home, that you may see how you go on.
4. With respect to the internal part of the estate, they must be deternsined 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 hy new station-lines ; taking the 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, ditches, roads, &c. also take off-sets to the bends of hedges, and to such objects as appear near these lines. Then proceed to survey the adjoining fields, by taking the angles which the sides make with the station-line at the intersections, and measuring the distances to each corner from these intersections : for every station line will be a basis to all future operations; the situation of every object being entirely dependent on 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 make 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 the outer ones, till the whole is finished. The oftener you close your work, and the fewer lines you make use of, the less you will be liable to error.