2. The gable ends of a barn are each 28 feet wide, and the perpendicular height of the ridge above the eaves is 7 feet; how many feet of boards will be required to board up both gables? Ans. 196 feet.

CASE V.

476. To find the circumference or the diameter of a circle.

477. A Circle is a figure bounded by one uniform curved line.

478. The Circumference of a circle is the curved line bounding it.

479. The Diameter of a circle is a straight line passing through the center, and terminating in the circumference.

It is proved in geometry that in every circle the ratio between the diameter and the circumference is 3.1416+.

RULE. I. To find the circumference.-Multiply the diameter by 3.1416. II. To find the diameter.-Multiply the circumference by .3183.

EXAMPLES FOR PRACTICE.

1. What length of tire will it take to band a carriage wheel 5 feet in diameter? Ans. 15 ft. 8.4+ in.

2. What is the circumference of a circular lake 721 rods in diameter ? Ans. 7 mi. 25 rds. 1.54+ ft.

3. What is the diameter of a circle 33 yards in circumference ? Ans. 10.5+yards.

CASE VI.

480. To find the area of a circle.

From the principles of geometry is derived the following

RULE. I. When both diameter and circumference are givenMultiply the diameter by the circumference, and divide the product by 4. II. When the diameter is given;— Multiply the square of the diame ter by .7854.

III. When the circumference is given ;— Multiply the square of the circumference by .07958.

EXAMPLES FOR PRACTICE.

1. The diameter of a circle is 113, and the circumference 355; what is the area? Ans. 10028.75. 2. What is the diameter of a circular island containing 1 square mile of land? Ans. 1 mi. 41 rd. 1.4+ ft. 3. A man has a circular garden requiring 84 rods of fencing to inclose it; how much land in the garden? Ans. 3 A. 81.5+ P.

481. The Metric System of Weights and Measures has now received the sanction of law among more than half the inhabitants of the civilized world. Up to this date it has been adopted in France, Germany, Austria, the Netherlands, Southern Europe, and South America, and has been legalized in Great Britain, Germany, and the United States.

* The Metric System, as it was presented in all the editions of this book, printed previous to 1877, was useless, because the symbols and applications did not correspond with present usage.

This will be a sufficient reason for substituting in place of the former matter, a condensed and practical treatise of the system, together with some useful miscellaneous tables.

482. The Metric System of weights and measures is based upon the decimal scale.

483. The Meter is the base of the system, and is the one ten millionth part of the distance on the earth's surface from the equator to either pole, or 39.37079 inches.

From the Meter are made the Ar (are), the Liter (leeter), and the Gram; these constitute the primary or principal units of the system, from which all the others are derived.

484. The Multiple Units, or higher denominations, are named by prefixing to the name of the primary units the Greek numerals, Deka (10), Hecto (100), Kilo (1000), and Myra (10000).

485. The Sub-Multiple Units, or lower denominations, are named by prefixing to the names of the primary units the Latin numerals, Deci (1), Centi (180), Milli (1000).

Hence, it is apparent from the name of a unit whether it is greater or less than the standard unit, and also how many times.

Meter means measure; and the three principal units are length, capacity or volume, and weight.

The Meter, like our yard, is the unit used in measuring cloths and short distances.

The Kilometer is commonly used for measuring long distances, and is about g of a common mile.

The Centimeter and Millimeter are used by mechanics and others for minute lengths. The Dekameter, Hektometer, and Myriameter are seldom used.

The Square and Cubic Measures are only the squares and cubes of the measures of length, as shown in the following tables.

The Square Meter is the unit for measuring ordinary surfaces of small extent.

The Ar is the unit of land measure, and is a square whose side is 10 meters, equal to a square dekameter, or 119.6 square yards.

1000 Cu. Decimeters (cu. dm.) 1 Ster =35.316 cu. ft.

10 Decisters

10 Sters

(ds.)
(8.)

=1 Dekaster=13.079 cu. yd.

The Cubic Meter is the unit for measuring ordinary solids.

The Ster is the unit of wood measure, and is equal to a cubic meter, or .2759 cord.

A Cubic Meter of water weighs 1000 kilos, or a metric ton.

The scale for the meter, liter and gram is uniformly 10; but in the scale for the square meter, 100 units of any order make one unit of the next higher; and in the scale for the cubic meter, 1000 units of any order make one of the next higher.

The Liter is commonly used in measuring liquids in moderate quantities; the dekaliter, for large quantities and for fruits, etc.

The Hektoliter is used for measuring grain, fruit, roots, etc., in large quantities, also for casks of wine.

The Kilogram, or Kilo, is the unit of common weight in trade and is a trifle less than 2 lb. Avoirdupois.

The Ton is used for weighing very heavy articles, and is about 204 lb. more than a common ton. The other denominations, larger than the gram, are seldom used.