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 accurate 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 lands 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 were laid down, your reason will be sufficient to direct you

THE

VARIATION OF THE COMPASS.

And how to find it by Amplitudes or Azimuths of the

Sun.

1.

IT T was before observed, that the needle does 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 axis in twenty-four hours from west to east, and hence alt 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.

4. If a circle be supposed to pass round the globe of the earth, so as to be equidistant from each pole, it is called the equator, or equinoctial line, and by some the line only.

And if the plane of the equator be produced to the heavens, it will lay out the celestial equator.

5. The latitude of any place, is its nearest distance to, and counted from the equator in degrees and minutes; and is north or south as it lies on the north or south side of the equator.

6. The poles are 90 degrees from the equator: therefore the complement of the latitude of any place, is the latitude taken from 90 degrees, or the distance of the place from its nearest pole.

7. The declination of the sun, is the nearest distance thereof from the celestial equator counted in degrees and minutes; and is north or south, as it lies on the north or south side of the equator.

8. The sun's declination taken from 90, leaves the complement thereof; or its distance from the nearest celestial pole.

9. The sun's altitude, is the number of degrees and minutes the sun is above the horizon, and is easily

10. What the sun's altitude wants of 90, or the sun's distance from the zenith, or point of the heavens perpendicularly over you, is the complement of the altitude.

11. The magnetical amplitude, is the complement of the sun's bearing at rising or setting, taken by the quarter'd compass; on it is the number of degrees the sun is from the east or west point of the compass, at rising or setting.

12. The true amplitude, is the complement of degrees the sun would rise or set on if the compass did not vary; or it is the number of degrees the sun is from the east to the west point of the horizon, at rising or setting; and this true amplitude is always north, if the sun's declination be north; or south if the sun's declination be south.

To find the variation by the amplitudes.

Having the latitude of the place, and the sun's declination given, the true amplitude is found by this astronomical proportion, viz.

As the co-sine or sine complement of the latitude, Is to the sine of the sun's declination,

So is radius

To the sine of the true amplitude.

Then if both amplitudes be north or both south, their difference is the variation, but if one be north and the other south, their sum is the variation.