How to enlarge or diminish a Map, or how to reduce a Map from one Scale to another: Also the Manner of uniting Separate Maps of Lands which join each other, into one Map of any affigned Size.

AY the Map you would enlarge, over the Paper on which you would enlarge with a fine protracting Pin, prick thro' every angular Point of your Map, join these Points on your Paper, (laying the Map you copy before you) by pencilled or popped Lines, and you have the Copy of the Map you are to enlarge: In this Manner any Protraction may be copied on Paper, Vellum, or Parchment for a fair Map.

If you would enlarge a Map to a Scale which is double, or treble, or quadruple to that of the Map to be enlarged; the Paper you must provide for its Enlargement must be two, or three, or four Times as long and broad as the Map; for which Purpose in large Things you will find it neceffary to join feveral Sheets of Paper, and to cement them with white Wafer or Pafte, but the former is best.

Then pitch upon any Point in your copied Map, for a Center; from whence if Diftances be taken to its extream Points, and thence if thofe Diftances be fet in a right Line with (but from) the Center, and

thefe

these last Points fall within your Paper, the Map may be encreased on it to a Scale as large again as its own; and if the like Diftances be again fet outwards in right Lines from the Center, and if these last Points fall within your Paper, it will contain a Map encreased to a Scale three Times as large as its own, &c.

Plate XII. Fig. 2.

Let the pricked or popped Lines represent the Copy of a Down or old Survey, laid down by a Scale of 80 Perches to an Inch, and let it be required to enlarge it to one laid down by 40 to an Inch.

Pitch upon your Center as O, from whence thro' a lay the fiducial Edge of a thin Ruler, with a fine pointed pair of Compaffes, take the Distance from a to the Center O, and lay it by the Ruler's Edge from a to A: In the like Manner take the Distance from the next Station b to the Center, and lay it over in a right Line from b to B, and join the Points A and B by the right Line AB: In the like Manner fet over the Distance from every Station to the Center, from that Station outwards, and you will have every Point to enlarge to; the joining of these conftantly as you go on by right Lines, will give you the enlarged Map required.

In taking the Distances from every Station to the Center, fet one Foot of the Compaffes in the Station, and the other very lightly over the Center-Point, fo lightly as fcarcely to touch it, otherwife the Center-point, will become fo wide that it may occasion several Errors in the enlarged Map: For if you err from the exact Center but a little, that Error will become double, or treble, or qua

druple,

druple, 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 miffing a Station, or in laying your Ruler over one Station twice.

From what has been faid it is plain, that if a Map is to be enlarged to one whofe Scale is double the given one, that the Distances from the respective Stations to the Center, 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 muft be Half of thofe 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 Center, being set twice beyond the faid Stations, will mark out the feveral Points required, for thefe Points will be three Times farther from the Center than the ftationary Points of the. Map are.

In the fame Manner, if you would enlarge a Map from a Scale of 160, to one of 40 Perches

10

to the Center, being fet three Times beyond faid Stations, will lay out the Points for your enlarged Map, for thefe Points will be four Times farther from the Center than are the Stations of the Map.

When a Map is enlarged to another, whofe 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. thofe of the given one, for it must be eafy to conceive that thofe Maps are like: But the Area, if the Scale be double, will be four Times; if treble, nine Times; if quadruple, fixteen Times that of the given Figure; that is, it will contain four, nine, or fixteen Times as many fquare Inches as the given one (for it has been shewn that like Polygons are in a duplicate Proportion with their homologous Sides.) Yet these Figures being caft up by their refpeive Scales, will produce the fame Content.

Thus much is fufficient 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 Center, will mark out Points, which, if joined, will compofe a Map fimilar to the given one, whofe Scale will be four Times, three Times, or twice as fmall 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 Center will give Points requifite 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 Distance to the Center, will give the Points for the Map: And if we would reduce

from

from 40 to 160, from 20 to 80, from 10 to 40 Perches to an Inch, &c. one fourth of the Diftances to the Center, 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 confifted of 224 feparate Divifions, without the leaft Confufion from the Lines; for none can arife if the Methods here laid down be strictly obferved.

I have alfo from the fame 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 thefe Methods for reducing Maps to be much more accurate than any of the Methods commonly used, fuch as fquaring of Paper, ufing a Parallelogram, proportional Compaffes, or any other Method I ever met with, though the Figures to be reduced were ever fo numerous, irregulr, or complicated.

How to unite Separate Maps of Lands which join each other, into into one Map of any af Signed Size.

If there be feveral large Maps contained in a Book, each of which fuppofe to take up a Skin of Parchment, or a Sheet of the largest Paper; which Maps of Lands join each other; and it be required to reduce them to fo fmall a Scale, that all of them when joined together may be contained

in