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Note. — To multiply by }, we take ţ of the mu cand. - To divide by 161, we first reduce both the divisor and dividend to halves, and then divide; and the remainder being 25 half-feet, is equal to one half as many feet, or 12ft. bin. We adopt the same principle in dividing by 694; the remainder being 336 sixths of miles, is equal to one sixth as many miles, or 56 miles. As half a foot is equal to 6 inches we add them to the 3 inches, and have the 9 inches in the answer.
3. In 47 miles how
feet? 4. In 248160 feet how many miles ?
5. In 78deg. 50m. 7fur. 30rd. 5yd. 2ft. 10in. how many inches ?
6. How many degrees in 345056794 inches?
91. How do you reduce degrees to inches? The reason of the operation ? How do you reduce inches to degrees? The reason for the operation ? How do you multiply by ? How do you divide by 16} and find the true remainder? How do you obtain the true answer in examples of this kind ?
92. Surveyors' Measure is used by surveyors in measuring land, roads, &c.
TABLE. 78% Inches (in.)
make 1 Link,
p. 100 Links, 4 Poles, or 66 Feet,
cha. 10 Chains
1 Furlong, fur. 8 Furlongs, or 80 Chains,
NOTE. Gunter's chain, in length 4 poles, or 66 feet, and divided into 100 links, is that mostly used in ordinary land surveys ; but in locating roads, and like public works, an engineer's chain is usually 100 feet in length, containing 120 links, each 10 inches long.
1. In 2 poles how many links? In 4 poles ? In 7 poles ? 2. In 5 chains how many links ? In Scha.? In 10cha.? 3. How many poles in 50 links ? In 751. ? In 1251. ?
EXERCISES FOR THE SLATE.
1. How many links in 7m. 2. In 61630 links how many 5fur. 6cha. 301. ?
miles ? OPERATION. 7 m. 5fur. 6cha. 301.
100) 61 63 01. 8
10) 61 6 cha. 301. 6 1 furlongs. 10
8 ) 6 1 fur. 6cha.
7 m. 5fur. 61 6 chains. 100
Ans. 7m. 5fur. 6cha. 301. 61 6 3 0 links, Ans.
3. How many miles in 4386 chains ?
92. For what is surveyors' measure used ? Recite the table. How do you reduce miles to links? The reason for the operation ? How do you reduce inches to chains ? To miles? The reason of the operation ?
4. In 54m. 66cha. how many chains ?
SURFACE OR SQUARE MEASURE.
93. Square Measure is used in measuring surfaces of all kinds.
Note. - A square is a figure having four equal sides and four equal angles.
When the four lines are each 1 foot in length, the space enclosed is 1 square foot ; when I yard in length, 1 square yard; when i rod in length, 1 square rod; and so for any other dimension.
3ft = lyd.
In this diagram the large square represents a square yard, and each of the smaller squares within it represents one square foot. Now, since there are three rows of small squares, and three square feet in each row, there will be 3 sq. ft. X 3 9 sq. ft. in the large square.
But the large square is 3 ft. in length and 3 ft. in breadth ; hence,
To find the contents of a square, multiply the numbers denoting its length and breadth together.
93. For what is square measure used ? Repeat the table. What is a square ? A square foot? How may the contents of a square be found ? Explain by the diagram the reason of the operation.
MENTAL EXERCISES. 1. In 2 square feet how many square inches ? 2. In 3 square yards how many square feet? In 10 sq. yd. ? 3. In 5 roods how many poles ? In 20 roods ? In 30 roods ? 4. In 7 acres how
roods ? In 24 acres ? In 40 acres ?
EXERCISES FOR THE SLATE.
1. How many square inches in 12A. 3R. 24p. 144ft. 72in. ?
1 2 A. 3R. 24p. 144ft. 72in.
NOTE. To multiply by 4, we
take of the multiplicand.
5 1 6
5 6 2 0 68
144) 80 9 3 7 8 6 4 inches.
40) 2 0 6 4 poles. 576 +4=144ft.
4) 51 R. 24p.
Ans. 1 2 A. 3R. 24p. 144ft. 72in. Note. — To divide by the 2724, we first reduce the divisor and dividend to fourths, and then divide. The remainder obtained, being fourths, is reduced to whole numbers by dividing by 4.
93. How do you reduce acres to square inches? The reason for the operation? How do you reduce square inches to acres ? The reason for the operation ? How do you multiply by £?
3. In 49 A. 3R. 16p. how many square feet ? 4. In 2171466 square feet how many acres ?
5. What is the value of 365A. 3R. 17p. at $ 1.75 per square l'od or pole?
Ans. $ 102,439.75. 6. Sold a valuable piece of land, containing 3A. 1R. 30p., at $ 1.25 per square foot; what was received for the land ?
Ans. $ 187,171.875. 7. In a tract of land 12 miles square, how many square miles ? How many acres ?
Ans. 92160 acres. · 8. In 18A. OR. 16p. how many square feet?
feet. 9. Purchased 48A. 3R. 14p. of land for $ 2.25 per square rod, and sold the same for $3.15 per square rod; what did I gain by my bargain?
Ans. $ 7032.60.
CUBIC OR SOLID MEASURE.
94. Cubic or Solid Measure is used in measuring such bodies or things as have length, breadth, and thickness ; as timber,
Note 1.- A pile of wood 8ft. in length, 4ft. in breadth, and 4ft. in height, contains a cord.
One ton of timber, as usually surveyed, contains 50140cubic feet.
A perch of masonry is 164ft. long, ift. high, and ifft. thick, or 244 cubic feet.
93. How do you divide by 272£? Of what denomination is the remainder ? How is the true remainder found ? – 94. For what is cubic measure n-ed ? Recite the table. What are the dimensions of a pile of wood containing I cord? How many solid feet does a ton of timber contain, as usually surveyed ?