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cular 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, bridges, 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 graving, 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. Leta 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 INCLOSING ANY GIVEN QUANTITY.
PL. 12. fig. 1.
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 of DG, and the quotient 4 will be a perpendicular for a triangle whose base is 70, and the area 140P. Let HI be drawn parallel to DG, at ihe 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; alt 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 dependance on the map and scale.
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.
IA N. 62°+ W. 59 27.5
71.7 Area, 8722.3 perches:129.6129.6 1123.9 123.9
Merid dist. &c.
152A. TR. 25.9P.=24385.9 perch.
= 3470.6 perches.
Merid. dist. &c
Area, 6522.1 per. (109.1 109.1 122.9 123.9
Then, ICDI: CD :: ICNI: CN
Th. 18 6522.1 : 115 :: 3470.6: 61.19 Sec. 1 which determines the point N in CD.
As dif. lat. 54.6 As S. Bear 61°15' : Radius S. 90 deg.
: Depart. 99.5 :: Depart. 99.5 :: Radius S. 90 deg. : Tang. Bear. 61°15' : Distance 113.49 IN runs N. 61.15' E.
113.5 NI runs S. 61 15 W.
per. 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 content is obtained, as already taught, without the bearing or length of the line CI.
For the triangle ICDI, the diff. 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 inclosed.
Now the student or practitioner may calculate the content of the part ABCNIA (the bearing and distance, or the diff. 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.
P4. 12. fig. 3.
It is proposed to cut off 38A. 16Pų, to the south end of this tract, by a line running from E due West 40 perches to a well at 0, 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 2d.
M from H, north, 43.23