rator and denominator are surds,) and save the trouble of extracting the root of two numbers.

6

81? 144

13. What is the square root of? #? 1/8 ? ? ? ? ? {? :? 85? ?? ? 11? 1888? 4858?

25

8

??

123

43

14. What is the cube root of root of 4? ?!? (1?? 3921417 927888 ? 12? 13 ? 38 ?

947436

Remark.-Dr. Hutton has given a RULE for extracting the roots of high powers, which he thinks most convenient; but we are satisfied, nothing can be gained by departing from the General Rule.

SQUARE AND CUBIC MEASURE.

When

Boards and scantling, are measured by SQUARE, or suPERFICIAL MEASURE, and sold by CUBIC MEASURE. A FOOT of BOARDS is 1 foot long, 1 foot wide, and 1 inch, or 12 of a foot thick. A FOOT of SCANTLING is 1 foot long, 4 inches, or of a foot wide, and 3 inches, or of a foot thick. boards are less than 1 inch thick, or scantling less than 3 by 4 inches, no difference is made in the price; but when either EXCEEDS these dimensions, the price is varied in proportion. When we wish to calculate the quantity of boards necessary to cover any particular surface, we simply compare the dimensions of that surface with the dimensions of a foot of boards, without reference to the thickness. A cord of wood, or bark, is sold on the same principle. A PILE 8 feet long, 4 feet wide, and 4 feet high, is called a CORD.

MISCELLANEOUS QUESTIONS.

1. A lumber merchant sold 2348 square feet of siding, at $30 per thousand, what did it amount to?

NOTE. Here the cost of 1000 feet is given, equal to $30, and 2348 feet required, from which QUANTITIES the EQUATION is easily formed.

2. How many feet of boards in a pile 16 feet long, 18 inches wide, and 14 of an inch thick?

Here 1 foot long, 1 foot wide, 2 of a foot thick, are the GIVEN dimensions, equal to 1 foot of boards, and 16 feet long. 18 inches to }} = to of a foot wide, and 14 inches

= to

inches

to of a foot thick, the REQUIRID dimensions;

hence, the solution is

feet feet feet feet of long. thick. wide. boards. 1 1 1

Thus:

1

3. What is the cost of a pile of boards, closely packed, measuring 16 feet, 5 inches long, 12 feet 7 inches wide, and 10 feet 8 inches high, at $17 per thousand?

Thus: 1000ft. long, 1ft. wide, ft. thick, GIVEN, equal to $17, and 197 ft. long, ft. wide, 128 ft. high, REQUIRED,

4. How many cords are there in a pile of wood 28 feet 5 inches long, 13 feet 7 inches wide, and 16 feet 9 inches high?

NOTE. This may be calculated in the same manner as the above, since the dimensions of a cord are known.

5. What is the cost of a pile of wood 10 feet long, 8 feet wide, and 5 feet high, at $3.50 per cord?

6. If 1 FOOT of SCANTLING cost 1 cts., what will 1000 FEET Cost? What will be the cost of a pile, measuring 37ft. 6in. long, 12ft. 4in. wide, and 7A. 3in. high?

7. How many square feet of boards will be required to lay a floor 25 feet 3 inches long, and 18 feet 4 inches wide?

8. How many square feet of siding will cover the sides of a house 40 feet front, 36 feet deep, and 20 feet high?

NOTE. It is the same as if there were one surface 152 feet long, and 20 feet wide.

9. What would the siding of the above house come to at $15 per thousand.

10. How many perches of stone will be required to build a house 30 feet high, and 80 feet square, walls 24 feet thick, allowing a solid perch to be 16 feet long, 1 feet thick, and 1 foot high?

build the walls of the above

11. How many bricks would house, allowing the brick walls to be 18 inches thick, each brick to be 9 inches long, 4 thick?

inches wide, and 2 inches

12. What would the bricks above referred to cost, at $7.50 per thousand?

13. A lumberman purchased a raft of boards, and having piled them on his wharf, found the solid mass, measured 56 feet 4 inches, by 48 feet 6 inches, and 18 feet 9 inches high; how many feet of boards did he purchase? What would be the cost at $20 per thousand?

14. A lumberman sold a quantity of wood, closely piled, measuring 75 feet 9 inches, by 68 feet 6 inches, and 9 feet 8 inches high, at $4.75 per cord; what did the sale amount to? allowing the clear gain on each cord to be 25 cents, what did he gain per cent?

15. If of a set of compositors of 24 hands to a set, will compose of a thousand lines, of 84 m's to a line in of a week, by working of each day of 12 hours long; how many sets, 12 hands each, must be employed to compose of a thousand lines of 72 m's each, in 1⁄2 of a week, by working of each day of 9 hours long?

THE END.

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