if such a wheel were 3 feet 4 inches in diameter, one rotation would be 10 feet, which is half a plantation perch; and because 320 perches make a mile, therefore 640 rotations will be a mile also: and the machinery is so contrived, that by means of a hand, which is carried round by the work, it points out the miles, quarters, and perches, or sometimes the miles, furlongs, and perches.

Or roads may be measured by a chain more accurately; for 80 four-pole, 160 two-pole chains, or 320 perches, make a mile as before: and if roads are measured by a statute chain, it will give you the miles English, but if by a plantation chain, the miles will be Irish. Hence an English mile contains 1760, and an Irish mile 2240) yards; and because 14 half yards is an Irish, and 11 half yards is an English perch, therefore 11 Irish perches, or Irish miles, are equal to 14 English ones.

Since some surveys are taken by a four-pole, and others by a two-pole chain; and as ground for houses is measured by feet, we will shew how to reduce one to the other, in the following pro*blems.

PROB. I.

To reduce two-pole chains and links to four-pole

ones.

If the number of chains be even, the half of them will be the four-pole ones, to which annex the links given, thus,

i. In

Ch. L.

1. In 16.

four-pole ones?

37 of two pole chains, how many

Ch. L.

Answer 8. 37.

But if the number of chains be odd, take the half of them for chains, and add 50 to the links, and they will be four-pole chains, and links, thus,

Ch. L.

2. In 17. 42 of two-pole chains, how many four-pole ones?

Ch. L.

Answer 8. 92.

PROB. II.

To reduce four-pole chains and links, to two-polé

ones.

Double the chains, to which annex the links, if they be less than 50; but if they exceed 50, double the chains, add 1 to them, and take 50 from the links, and the remainder will be the links, thus,

Ch. L.

1. In. 8. 2

37 of four-pole chains, how many two pole ones?

16 37

Ch. L.

2. In 8.

82 of four-pole chains, how many two-pole ones?

2. 50

To reduce four-pole chains and links, to perches and decimals of a perch.

The links of a four-pole chain are decimal parts of it, each link being the hundredth part of a chain; therefore if the chains and links be multiplied by 4 (for 4 perches are a chain) the product will be the perches and decimal parts of a perch. Thus,

Ch. L.

How many perches in 13. 64 of four-pole

chains?

4

Answer 54.

56 perches,

PROB. IV.

To reduce two-pole chains and links, to perches and decimals of a perch.

They may be reduced to four-pole ones (by prob. 1.) and thence to perches and decimals (by the last.) or,

Τ

If the links be multiplied by 4, carrying one to the chains, when the links are, or exceed 25; and the chains by 2 adding one, if occasion be: the product will be perches, and decimals of a perch. Thus,

Ch. L.

1. In 17, 21 of two pole chains, how many perches?

2. 4

2. In 15.

2.

38. of two-pole chains, how many 4 perches?

Answer 31. 52 perches.

PROB. V.

To reduce perches, and decimals of a perch, to four-pole chains and links.

Divide by 4, so as to have two decimal places in the quotient, and that will be four-pole chains and links. Thus,

In 31. 52 perches, how many four pole chains and links.

Ch. L.

4)31.52(7. 88 Answer.

35

32

PROB. VI.

To reduce perches and decimals of a perch, to two-pole chains and links.

The perches may be reduced to four-pole chains (by the last) and from thence to two-pole chains (by prob. 2.) or,

Divide the whole number by 2, the quotient will be chains; to the remainder annex the given decimals, and divide by 4, the last quotient will be the links, Thus,

In 31.52 perches, how many two-pole chains and links?

Ch. L.

2)31.52(15. 38 Answer.

11

4)152(38

32

PRO B. VII.

To reduce chains and links to feet and decimal parts of a foot.

If they be two-pole chains, reduce them to four-pole ones: (by prob. 1.) these being multi

plied