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resting to the left are acres, because 10 square four-pote chains make an acre, and the remaining figures are decimal parts of an acre. Multiply the five figures to the right by 4, cutting 5 figures from the product, and if any figure be to the left of them, it is a rocd, or roods; multiply the last cut off figures by 40, cutting off five or (which is the same thing) by 4, cutting off four; and the remaining figures to the left, if any, are perches.

1. The first part is plain, from considering that a piece of ground in a square form, whose side is a perch, must contain a perch of ground; and that 40 such perches make a rood, or stang, and four roods an acre; or which is the same thing, that 160 square perches make an acre, as before.

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2. A square four-pole chain (that is, a piece of ground four poles or perches every way) must contain 160 square perches; and 160 perches make an acre, therefore 10 times 16 perches, or 10 square four-pole chains make an acre.

Note, that the chains given, or required, in any of the following problems, are supposed two-pole chains, that chain being most commonly used ; but they must be reduced to four-pole chains or perches for calculation, because the links will not operate with them as decimals.


Plate I. fig. 17.

Let ABCD be à square field, whose side is 14C. 29 L. ; I demand the content in acrés.

Ch. L.
By problem 4. section 3. 14. 29 are equal to

29. 16 perches.
29. 16

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Ch. L.

Ch. L. 14. 29 are equal to 7. 29 of four-pole chains, by prob. 1. sect. S. 7. 29

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6561 1458 5103

A. R. P. Acres 5131441 content as bef. 5. 1. 10


Rood 1125764


Perches 1013056

It is required to lay down a map of this piece of ground, by a scale of twenty perches to an inch.

Take 29. 16 the perches of the given side, from the small diagonal on the common surveying scale, where 20 small, or two of the large divisions are an inch : make a square whose side is that length (by prob. 9. sect. 1.) and it is done.


To find the side of a square, whose content is given.

Extract the square root of the given content in perches, and you have the side in perches, and consequently in chains.


It is required to lay out a square piece of ground which shall contain 12A. 3R. 16P. Required the number of chains in each side of the square ; and to lay down a map of it, by a scale of 40 perches to an inch.

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Ch. L.
2056(45.34 perches 22. 33} by prob. 6.

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From a scale where 4 of the large, or 40 of the small divisions are an inch, take 45.34, the perches of the side, of which make a square.


To find the content of an oblong piece of ground.

Multiply the length by the breadth, for the content.


Plate I. fig. S.

Let ABCD be an oblong piece of ground, whose length AB is 14C. 25L. and breadth 8C. 37L. I demand the content in acres, and also to lay down a map of it, by a scale of 20 perches to an inch.

Ch. L. Perches.
14.25 = 29.00


8.37 =

17.48 f By prob. 4. sect. 3.


A. R. P.
150)506.9200(3. 0. 27. content.

26 perches, or near 27.

Or thus :

4 pole ch. Ch. L. Ch. L. 14. 25 = 7. 25


5057 2175 2900

Acres 3/16825

Rood 167300

Perches 26 9200

To draw the map.

Make an oblong (by schol. to prob. 9. seet. 1.) whose length, from a scale of 20 to an inch, may be 29 perches, and breadth, 17.48 perches.


The content of an oblong piece of ground, and one

side given, to find the other.

Divide the content in perches, by the given side in perches, the quotient is the side required in perches; and thence it may be easily reduced to chains.

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