2. The sitting-room with yard-wide three ply carpet, laid lengthwise, @954, 3 inches on each strip being lost to match.

3. The library with China matting, 36 in. wide, @ 604, there being no loss to match. (Allow 11⁄2 in. at each end of each strip for turning in.)

4. The dining-room with China matting, 36 in. wide, @ 504, to be laid with least loss, no loss to match. (Three in. on each strip being allowed for turning in, as above.).

5. The reception-room with Brussels carpet, 27 in. wide, @ $1.60, to be laid lengthwise, 6 in. being lost on each breadth to match.

6. The hall with Moquette carpet, 27 in. wide, @ $1.75.

7. What will be the cost of a rug for the dining-room, that is 3 yd. 1 ft. 6 in. by 4 yd., @ 85¢ per □ yard, with a border in addition, @ 65¢ per lineal yard? (Allow 1 yard of border for turning corners.)

8. Find the cost of carpeting a stairway having 20 steps, and each one having 11/4 in. tread and 634 in. rise, 1 yard being allowed for the landing, 12 yard for the turning, and 1⁄2 yard for moving up when the edges are worn. Carpet, $1.50 per yard.

1. A sidewalk 4 ft. wide and 63 ft. long, @ 214 per foot. 2. A courtyard 19 ft. x 19 ft. 6 in. with brick laid flat in sand, @75¢ a yard.

3. A sidewalk 37 ft. long 4 ft. 6 in. wide with brick, @ $1.36 a yard, the bricks to be laid on edge.

4. A cellar with cement, @ 39¢ a □ yard; dimensions, 27 ft. 'X 31 ft.

5. Find which would be the cheaper: to brick a sidewalk 4 ft. wide and 275 ft. long, @ 114 a foot, or to lay a stone walk 3 ft. 6 in. wide and of the same length, @ $1.89 per □ yard.

Bins, Tanks, and Cisterns.

It must be remembered that

2150.42 cubic inches the contents of a bushel measure.

1. How many bushels of wheat may be contained in a box measuring 5 ft. long, 5 ft. wide, and 5 ft. deep?

Note. If any number of cubic feet be diminished by '/, of itself, the remainder will represent very nearly an equivalent in bushels, stricken measure.

Thus, the box above mentioned contains 125 cubic feet, 1/ being deducted the remainder is 100, which is the number of bushels to within less than 1/2 bu. (.44).

2. First estimate and then compute exactly the number of bushels of grain in a box measuring 3 by 5 by 6 feet; also in one measuring 21 by 6 by 7 feet. What is the difference between the estimated and exact contents in each case?

3. What would be the difference between the estimated and exact number of bushels in a bin 8 by 7 by 5 feet?

4. I wish to build a tank 4 ft. square to contain 700 gallons; how deep must it be?

5. How many gallons will fill a circular reservoir 155 ft. in diameter and 15 ft. deep? (The contents of a circular reservoir or cistern is .7854 of a square one of equal depth and having sides equal to the diameter.) 6. How many gallons of water in a cistern 9 ft. in diameter and 10 ft. deep?

Estimating the Weight of Hay in a Mow.

272. The average weight of 450 cubic feet of meadow hay, or 550 feet of clover, dry and well settled in large mows or stacks, is about one ton.

1. The average height of the hay in a mow is 11% ft., the length of the mow is 30 ft., and the width 18 ft. What is the estimated weight of the hay? How much heavier than clover -occupying the same space?

2. The length, width, and height of a stack of clover average 12 by 12 by 10 ft. What is its estimated weight ?

Miscellaneous.

1. The pumping-engine at the Saratoga water-works in one week pumps 15,307,558 gallons of water. How long should a reservoir 150 wide and 35 ft. deep be to hold that quantity of water?

2. At $2.80 per M, what must be paid for the shingles for a barn having a gable roof 37 ft. 6 in. long, and each slope being 16 ft. 6 in. wide? (1000 shingles of good quality, laid 4 in. to the weather, cover 120

feet.)

3. How many cords of wood can be piled under a shed 45 ft. long, 48 ft. wide, and 12 ft. high, and what would the wood be worth at $4.75 a cord?

4. How many gallons will fill a water-tank 82 X 6 X 5? How many bushels of wheat would the tank contain? How many bushels of potatoes or apples?

Note. In measuring grains the measure is stricken, or leveled, but in measuring potatoes, apples, etc., the measure is heaped. The bulk of a bushel stricken measure is 1/ less than of the heaped measure, and the bulk of the heaped is 1/4 greater than that of the stricken.

6. What will it cost to slate a gable roof, each slope being 35 ft. long by 18 ft. wide, @ $14.75 a square?

6. In a pile of wood 175 ft. long, 16 ft. wide, 7 ft. 6 in. high, how many wagon loads of cord-wood, 3/4 cord to a load, and what will it cost at $5.65 a cord, 504 a load being paid for hauling?

7. A surveyor, in measuring a road, finds that it is 873 chains long. How many miles is that? (See Table, page 202, Art. 203.)

8. On each side of a lane 17 chains long a farmer puts a fence. How many rods of fence does he build?

9. If a street vender buys chestnuts at $2 per bushel, and sells them at 104 per quart, liquid measure, how much does he gain per bushel ?

10. What was the cost of excavating a cellar 47 ft. 6 in. × 39 ft. 6 in. and 8 ft. 6 in. deep, @ 65¢ a cubic yard?

Original Problems.

Suggestions to Pupils.

1. Take measurements of the school-room for finding the cost of joists, flooring, plastering, etc. A comparison of the measurements taken will suggest corrections of errors.

2. Take the actual measurement of some rectangular room, give the dimensions with such other information as is necessary to find the cost of carpeting or papering it.

3. Give the dimensions of a bin or box to find the quantity of grain, or potatoes, or apples it will contain.

4. Give the dimensions of a lot, and such details of information as may be needed to find the cost of fencing it. An inspec tion of a fence already constructed and inquiries made of workmen will suggest the points needed.

5. Tell where some sidewalk about your school-house is needed, and ask the members of the class to find what its cost would be. The pupils may determine what kind of walk they would have, and learn what it would cost per square yard or foot.

6. Take the measurements of a load or pile of cord wood; report the same to the class and ask how many cords and what it would cost at prevailing prices.

7. Find how many cubic feet of coal, such as is commonly used in your neighborhood, are estimated to weigh a ton; report the same to the class with the size of some coal bin, and ask how many tons of coal may be put into it.

8. Give the thickness of ice formed at some place near by, and ask how many tons can be taken from any given space. (The weight of 1 cubic foot of ice, at 32° Farenheit, is 57.5 pounds.)

Note. It is not designed that all the pupils shall prepare questions on all the topics suggested, nor that they should be restricted to them alone. No pupil should present a question which he is not ready to answer if required.

Illustrations.-1. A farm hand, who works "on shares," receives from one farmer an offer of 7 bushels of corn out of every 16 bushels raised, another offers him 2 out of 5, another 5 out of 12. Which is the best offer?

Here it is difficult to determine which is the best offer, because the standards of comparison, 16, 5, and 12, are different.

105

Expressing the shares in the form of common fractions, we have 7/16, 2/5, and 5/12, and reducing these to fractions having a common denominator, we obtain 05/240, 96/240, and 100/240. Here 240 is the common standard of comparison, and the several offers arc respectively equivalent to 105, 96, and 100 out of 240 bushels produced, whence we see that the first offer is the best.

But the offer of 7 bushels out of 16, or 7/16 of a crop, is equivalent to the offer of 7/16 of each 100 bu., or at the rate of 43 3/4 bu. out of 100. Comparing all the offers with this standard, we find that they are equivalent to 43 3/4, 40, and 412/3 bushels per hundred, respectively; whence we readily see how the several offers compare with each other.

2. In like manner compare the value of two iron ores, one of which produces 52 tons of metal from 65 tons of ore, and the other 42 tons of metal from 56 tons of ore.

Suggestion. What common fractional part of each ore is metal? tons of metal can be produced from 100 tons of each ore?

How many

Note.-Because of its simplicity and convenience, 100 has been adopted as a standard of comparison in almost every department of business and by all civilized nations; hence we hear of a boy's spelling a certain per cent. of the words dictated, that is, at the rate of so many in a hundred, and in like manner of the merchant gaining or losing a certain per cent. of the money he lays out for his goods, of an increasing per cent. of children who are near-sighted, etc., etc.