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ruple, as you enlarge to a scale that is double, or treble, or quadruple of the given one; therefore great accuracy is required in enlarging a map. When
you have done with a station, give a dash with a pen or pencil to it, such as at the station a and b; by this means you cannot be disappointed in missing a station, or in laying your ruler over one station twice.
From what has been said it is plain, that if a map is to be enlarged to one whose scale is double the given one, that the distances from the respective stations to the centre, being set over by the ruler's edge, will give the points for the enlarged one. And thus may a map be enlarged from a scale of 160 to one of 80, from one of 80 to one of 40, from one of 20 to one of 10 perches to an inch, &c. For to enlarge to a scale that is double, the number of perches to an inch for the enlarged map, must be half of those to an inch for that to be enlarged: to enlarge to a scale that is treble the given one, the number of perches to an inch for the enlarged map, will be one third of those for the other; if to a scale that is quadruple the given one, the number of perches to an inch for the enlarged map, will be one fourth of those for the other, &c. therefore if you would enlarge a map which is laid down by a scale of 120 perches to an inch, to one of 40 perches to an inch, the distance from the several stations to the centre, being set twice beyond the said station, will mark out the several points required, for these points will be three times further from the centre than the stationary points of the map are.
In the same manner, if you would enlarge a map from a scale of 160, to one of 40 perches to an inch, the distance from the several stations
to the centre, being set three times beyond sạid stations, will lay out the points for your enlarged map, for these points will be four times further from the centre than are the stations of the
When a map is enlarged to another, whose scale is double, or treble, or quadruple, &c. of the given one, every line, as well as the length and breadth of the enlarged map, will be double, or treble, or quadruple, &c. those of the given one, for it must be easy to conceive that those maps are like: but the area, if the scale be double, will be four times; if treble, nine times : if quadruple, sixteen times that of the given figure; that is, it will contain four, nine, or sixteen times as many square inches as the given one (for it has been shewn that like polygons are in a duplicate proportion with the homologous sides.) Yet these figures being cast up by their respective scales, will produce the same content.
Thus much is sufficient for enlarging maps, and from hence, diminishing of them will be obvious ; for one fourth, one third, or half the distances from the several stations to the centre, will mark out points, which if joined, will compose a map similar to the given one, whose scale will be four times, three times, or twice as small as the given one.
Thus, if we would reduce a map from 40 to 80, from 20 to 40, from 10 to 20 perches to an inch, &c. half the distance of the stations from the centre will give the points requisite for drawing the map; if we would reduce from 40 to 120, from 20 to 60, from 10 to 30 perches to an inch, &c. one third of the distances to the centre, will give the points for the map; and if we would reduce
from 40 to 160, from 20 to 80, from 10 to 40 perches to an inch, &c. one fourth of the distances to the centre, will give the points for the map.
By the methods here laid down I have reduced a map from a scale of 40 to one of 20 perches to an inch, which contained upwards of 1200 acres, and consisted of 224 separate divisions, without the least confusion from the lines; for none can arise if the methods here laid down be strictly observed.
I have also from the same methods reduced a large book of maps, each of which was an entire skin of parchment, and the whole contained upwards of 46000 acres, to a pocket volume; and afterwards connected all these maps into one map, which was contained in one skin of parchment: therefore upon the whole I do recommend these methods for reducing maps to be much more accu. rate than any of the methods commonly used, such as squaring of paper, using a parallelogram, proportional compasses, or any other method I ever met with, though the figures to be reduced were ever so numerous, irregular, or complicated.
How to unite separate maps of lands which join each other, into one map of any assigned size.
If there be several large maps contained in a book, each of which suppose to take up a skin of parchment, or a sheet of the largest paper ; which maps of land join each other; and it be required to reduce them to so small a scale, that all of them when joined together may be contained
in one skin, half a skin, or any assigned sized piece of parchment, or paper.
Having pricked off and copied the several maps on any kind of paper, unite them by cutting with scissors along the edge of one boundary which is adjoining the other, but not cutting by the edge of both, and throw aside the parts cut off ; then lay these together on a large table, or on the floor, and where the boundaries agree, they will fit in with each other as indentures do; and after this manner they are easily connected: measure then the length and breadth of the entire connected maps, and, 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 will your map 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.
VARIATION OF THE COMPASS.
And how to find it by Amplitudes or Azimuths of
1. IT was before observed, that the needle does IT
not point truly to the north or south points of the horizon: the number of degrees therefore, that the points of the needle are from the north or south points of the horizon, is called the variation of the needle, or compass.
This variation differs widely in many places; for in some, the needle will point several degrees on the west side of the north ; at others there will be little or no variation, and again, , at others it will point several degrees on the east side; in the same place it differs sensibly in a few years : the true cause or theory of which, has not hitherto been discovered or explained for want of a sufficient number of observations.
2. The globe of the earth revolves round its axes in twenty-four hours from west to east, and hence all celestial bodies seem to move from east to west.
3. The extremities of the axis are called the poles ; the one the north or arctic, and the other the south or antarctic. And if the axis be produced to the heavens, it will point out the celestial poles.