resting to the left are acres, because 10 square four-pole 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 rood, 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.

2. A square four-pole chain (that is a piece of ground four-poles or perches every way) must contain 16 square perches; and since 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 twopole 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.

EXAMPLES.

Plate I. fig. 17.

Ch. L.

Let ABCD be a square field, whose side is 14. 29; I demand the content in acres.

By

Ch.L.

By problem 4. section 3. 14.29 are equal to 29.16 perches

29.16

17496

2916

26244

5832

A. R. P.

160)850.3056(5. 1. 10. content.

14.29 are equal to 7. 29 of four-pole chains, by

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.

PROB. II.

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.

EXAMPLE.

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.

A. R. P. 12. 3. 16.

4

51

40

2056(45.34 perches-22. 33, by prob. 6.

Ch. L.

[sect. 3.

85)456

003)3100

9064(39100

Το

A a

To draw the map.

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.

PROB. III.

To find the content of an oblong piece of ground.

Multiply the length by the breadth, for the

content.

Plate I. fig. 3.

EXAMPLE.

I

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

160)506.9200(3. 0. 27. content.

26 perch, or near 27.

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

PROB. IV.

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 required side in perches; and thence it may be easily reduced to chains. EXAMPLE.