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the length and breadth of the parchment or paper you are confined to ; if the former be three, four, or five times greater (that is, longer and broader) than the latter, reduce each copied map severally to a scale that is three, or four, or five times less, as before; and the same parts of the boundaries you cut by in the large maps, by the same you must also cut in small ones, and unite the small as the large ones were united; cementing them together with white wafer: thus your map will be reduced to the assigned size, which copy over fair on the parchment or paper you were confined to.
But it is not always that a person is confined to a given area of parchment, or paper; in such cases, if there are many large maps to be united into one, reduce each of them severally to a scale of 160 perches to an inch, and unite those by the contiguity or boundaries, as before: or if you have a few, it will be sufficient to reduce them to a scale of 120, &c." But having the maps given, and the scale by which they are laid down, your reason will be sufficient to direct you to know what scale they should be reduced to.
Directions concerning surveys in general.
If you have a large quantity of ground to survey, which consists of many fields or holdings, and that it be required to map and give the respective contents of the same, it is best to make a survey of the whole first, and to be satisfied that it is truly taken, as well as to find its contents; and as you go round the land, to make a note on the side of your field-book at every station where the boundary of any particular field or holding intersects or meets the surround; then proceed from any one of those stations, and in your field-book say, “proceed from such a station,” and when you have gone round that field or division, insert the station you close at, and so through the whole: a little practice only can render this sufficiently familiar, and the method of protraction must be evident from the fieldnotes. When the whole is protracted, and you are satisfied of the closes of the particular divisions, cast up each severally, and if the sum of their contents be equal to the contents of the whole first found, you may safely conclude that all is right.
The protraction being thus finished and cast up, transfer it on clean paper, vellum, or parchment as before ; be careful to draw your lines with a fine pen, write on it the names of the circumjacent lands, and set No. 1, 2, 3, 4, &c. in every particular field or division; let every tenant's particular holding be distinguished by a different coloured paint being run finely along the boundaries; let all the roads, rivulets, rivers, bogs, ponds, houses, castles, churches, beacons, or whatever else may be remarkable on the ground, be distinguished on the map. Write the title of the map in a neat compartment, either drawn or done from a good copper-plate engraving, with the gentleman's arms. Prick off one of your parallels with the map, and on it make a mariner's compass, and draw a flower-de-luce to the north, and this will represent the magnetical north; after which set off the variation, which express in figures, and through the centre of the compass let a true meridian line be drawn of about 3 inches long, by which write True Meridian. Let a scale be drawn, or it is sufficient to express the number of perches to an inch the map was laid down by. Draw a reference table of three or, if occasion be, of four or more columns: in the first insert the number of the field or holding; in the next its name, and by whom occupied; in the third the quantity of acres, roods, and perches it contains; if you have unprofitable land, as bog or mountain, let the quantity be inserted in the fourth column; and if it be required, you may make another column for statute measure, and then the map is completed.
THE METHOD OF DIVIDING LAND, OR OF TAKING OFF OR ENCLOSING ANY GIVEN QUANTITY.
LET ABCD, &c. be a map of ground containing 11 acres; it is required to cut off a piece, as DEFGID, that shall contain 5 acres.
Join any two opposite stations, as D and G, with the line DG (which you may nearly judge to be the partition line), and find the area of the part DEFG, which suppose may want 3R. 20P. of the quantity you would cut off; measure the line DG, which suppose to be 70 perches. Divide 3R. 20P., or 140P., by 25, the half of DG, and the quotient 4 will be a perpendicular for a triangle whose base is 70 and area 140P. Let HI be drawn parallel to DG, at the distance of the perpendicular 4, and from I, where it cuts the boundary, draw a line to D, and that line DI will be the division line; or a line from G to H . will have the same effect; all which must be evident from what has been already said. But if hills, trees, &c. obstruct the view of the points D and I from each other, it will be necessary, in order to run a partition line, to know its bearing; and it may be proper on some occasions to have its length; both these may be easily calculated from the common field-notes only, as in the following example, without the trouble of any other measurement on the ground, or any dependence on the map and scale.
EXAMPLE II. PL. 12, fig. 3. Let ABCDEFGHIA be a tract of land to be divided into two equal parts by a right line from the corner I to the opposite boundary CD; required the bearing and length of the partition line IN, by calculation, from the following field-notes, viz.
In the part IABCI, the difference between the northings and the southings of the three lines IA, AB, and BC (109.1) is the difference of latitude, and that of their eastings and westings (71.7) the departure of the line CI, which is placed thereto, so as to balance the columns; see theo. 1, sect 5: hence the contents are obtained, as already taught, without the
bearing or length of the line CI.
For the triangle ICDI, the dif, lat. and dep. of IC are taken from the preceding table, which in going from I to C will be northing and easting: those of CD are found by the bearing and distance, and of DI by balancing the columns, as before for CI.
The difference of latitude (54.6) and departure (99.5) of the line NI, in the third table, are found by balancing those of IC and CN; and as they are the base and perpendicular of a right-angled triangle, of which the line NI is the hypothenuse, and the angle opposite to the departure the bearing, we have the answer by two trigonometrical statings, as above; and thus may any tract be accurately divided, or any proposed quantity readily cut off or enclosed.
Now the student or practitioner may calculate the contents of
the part ABCNIA (the bearing and distance, or the dif, lat. and dep. of CN and of NI being known), and if it be found equal to the intended quantity, it proves the truth of the operation.
EXAMPLE III. Pl. 12. fig. 3. It is proposed to cut off 38A. 164P. to the south end of this tract, by a line running from E due west 40 perches to a well at O, and from thence a right line to a point M in the boundary HI; the place of M and the bearing and length of the line OM are required, the field-notes being as in example second.
As HI happens to be a meridian, the area of HOMH divided by half OV (19.1) quotes HM (42.23), without finding the area of HOIH, as we did of ICDI in example second, and
HM-HV=VM-8.03= dif, lat. of OM, which with its dep. VO=38.2, gives the bearing and distance as before.
A trapezoidal field ABCD, bounded as under specified, is to be divided into two equal parts by a right line EF parallel to AB or CD; required AF or B.F.