TO COMPUTE TOLL.

What is the toll on 6000 pounds, for 289 miles, at 4 mills per mile per 1000 pounds?

Place the 4 opposite 1000: opposite 6 is 024 (two cents four mills). Now place this opposite 1: then opposite 289 is $6.936, the answer.

TO MEASURE SUPERFICES.

RULE 1. Place the width in inches opposite 12: then opposite the feet in length, is the answer in feet and tenths of a foot.

Example.-Give the contents of a board 6 inches wide, 14 feet long.

Place 6 opposite 12: then opposite 14 (the length), is the answer, 7 feet.

RULE 2. Place the width in feet opposite 1: then opposite the length in feet, is the answer in feet.

How many square feet in a floor 20 by 20? 20×20=400, the answer.

How many square feet in a garden 96 by 54 feet?

96X54-5184 feet, answer.

NOTE.-If one side be inches and the other feet, place the given number of inches opposite the number of inches

in a foot, viz. 12: then opposite the length in feet, will be the answer in feet. If one side be feet and the other rods, the answer will be in rods by placing the feet opposite the number of feet in a rod; &c., &c.

In a lot of land 120 rods long and 60 rods wide, how many acres?

Place 60 opposite 160 (the number of rods in an acre) then opposite 120, is 45 acres, the answer.

If a board be 8 inches wide, how much in length will make a square foot?

Place the width, 8 inches, opposite 1: then opposite 144 (the number of square inches in a foot) is the answer, 18 inches.

If a piece of land be 5 rods wide, how many rods in length will make an acre?

Place 5 opposite 1: then opposite 160 (the number of rods in an acre) is the answer, 32 rods.

SQUARE YARDS.

How many square yards of carpeting will it require to cover a floor 20 feet long and 14 feet wide?

Place 20 found on the circular opposite 9 (the gauge point for yards square): then opposite 14 on the fixed part is 31 yards, the answer.

THE WIDTH AND CONTENTS GIVEN, TO FIND THE LENGTH.

RULE-Place the contents on the circular opposite

:he width in feet: then opposite 9, on the fixed part, is the length in feet.

Fxample.-I have a room containing 20 square yards: I wish to cover it with a piece of carpeting 2 feet wide: how many feet in length will it require?

Place 20 on the circular opposite 2·5 (24): then opposite 9, on the fixed part, is 72 feet, the answer.

TO MEASURE LAND IN CHAINS AND LINKS.

RULE. Place one of the sides in chains and links, opposite 1: then opposite the other side, in chains and links, are the number of acres and parts of an

acre.

Example.-To find the acres in 7 chains and 50 links by 6 chains and 40 links.

Place 750 opposite 1: then opposite 640 is 4.80 (48%) acres, the answer.

To find the acres in 7 chains and 75 links by 9 chains and 64 links.

Place 775 opposite 1: then opposite 964 is 70 acres, the answer.

To find the amount of land in 1 chain and 80 links by 2 chains and 50 links.

Place 180 opposite 1: then opposite 250 is 45 (f) of an acre, the answer.

TO MEASURE SQUARE TIMBER.

RULE. Place the product of the width by the thickness, opposite 144: then opposite the length is the answer in feet and tenths.

Example.-What is the solid contents of a stick 4 inches by 7, and 20 feet long?

4x7=28. Place 28 opposite 144: then opposite the length, 20 feet, is 39 feet, the answer, -31% feet.

What is the solid contents of a stick of timber 18 inches by 18 inches, and 13 feet long?

The product of 18 by 18, is 324. Now place 324 opposite 144: then opposite 13 (the length) is 29.3, (29,) the answer.

N. B.-If it be desired to have the answer in inches, instead of placing the product of the width by the thickness, opposite 144, place it opposite 1: then opposite the length in inches, will be the solid contents in inches.

NOTE.-Any bale, box, or chest may be measured by the preceding rule.

TO MEASURE A HYPOTENUSE.

B

A

C

75

AB hypotenuse, BC perpendicular, ac base.

RULE.-Square each of the sides and add their

products together, the square root of which is the

answer.

Example. What is the hypotenuse of a rightangled triangle, one side of which is 3 feet, the other 4 feet?

3X39 and 4×4-16: these two added together, make 25, the square root of which is 5 feet, the answer.

Δ

TO MEASURE A TRIANGLE.

Place half the base opposite 1: then opposite the perpendicular height, is the area.

Example.-What is the area of a triangle whose base is 32 inches, and perpendicular height 14 inches ?

Place 16 (of 32) opposite 1: then opposite 14 is 224 square inches, the answer.

TO FIND THE SOLID CONTENTS OF A PYRAMID.

RULE.-Multiply the area of the base by of the perpendicular height, whether it be a

square, triangular, or circular pyramid.

Example.-What is the solid contents of a pyramid whose base is 4 feet square, and perpendicular height 9 feet?

4 X 416, the base. Place this opposite 1. Now of 9 is 3. Opposite 3 is the solid contents, 48 feet.