REDUCTION DESCENDING? REDUCTION ASCENDING? Rule reduction descending. Write, perform, and explain an example, illustrating it. Rule for reduction ascending. Illustrate it. How can you prove examples in reduction descending? in reduction ascending?

2. What are the denominations in UNITED STATES MONEY? the coins? How are the gold coins hardened? the silver? Give the table of U. S. or Federal Money. From what are the names of the denominations derived? Which place from the decimal point do the mills occupy? How will you write forty-five thousand three hundred twenty-five mills? How many dollars in the above number of mills? how many cents?

Give the table of ENGLISH MONEY. Name the denominations. What is a guinea? a crown? a sovereign? value of a pound English money in Federal money?

3. Name the tables of WEIGHT. Repeat the table of Troy Weight; of Apothecaries' Weight; of Avoirdupois Weight. Which is in most common use? By which would you buy and sell coal? iron? silver? salt? quinine? fish? emeralds? flour? gold? opium? What is a long ton? Which is the most, a lb. Avoirdupois or a lb. Troy or Apothecaries' Weight? an oz. Avoirdupois, or an oz. Troy or Apothecaries' Weight? 1 lb. Avoirdupois = how many grs. Troy or Apothecaries' Weight?

4. Name the table of EXTENSION IN LENGTH. Repeat the table of Long Measure. Draw a line that you think to be 1 inch leng. Divide it into lines. Mark off one foot on your slate or paper. Measure the distance from your home to the school-house. What is a land league? How many English miles 1° on the earth's surface? how many geographical? How is cloth usually measured? Give the denominations of Surveyors' Measure. Repeat the table. Denominations of Mariners' Measure; the table? Which is longer, a land or sea league?

5. What are the denominations of SQUARE MEASURE? Repeat the table. Draw a square 1 inch each way; inch each way. What part of the first square is the second? Difference between 5 square inches and 5 inches square? Define a rectangle ; a

square. Show why you multiply the length of a rectangle by the breadth to obtain the surface. Can you multiply feet by yards? When the length of one side of a rectangle is given in feet, and the other in rods, how do you find the surface? When the square contents and one dimension are given, how do you find the other? Find the area of the top of your desk.

6. Give the denominations of CUBIC MEASURE;- the table Give the table for Wood Measure. Define a parallelopiped. How do you find its contents? Illustrate. When the solid contents and two dimensions are given, how do you find the third? How many faces has a cube? How many edges? How many cubic feet of air would your school-room contain if there were nothing else in it? Suppose the average number of pupils who attend your school were shut in the school-room without any means of ventilation, how long before they would all die, if each person should render 20 cubic feet of air per hour unfit to sustain life? 7. Repeat the denominations of LIQUID MEASURE; ble.

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What is the common size of barrels and hogsheads? 8. Repeat the denominations of DRY MEASURE; the table. Which is the larger, 1 quart Liquid or 1 quart Dry Measure? 1 bushel Dry Measure how many gallons Liquid Measure?

9. Where is CIRCULAR MEASURE used? Define circle; circumference; arc; radius; diameter; degree; minute; second; semicircumference; quadrant; sextant; sign. Give the table.

Define an angle; the vertex.

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Read the annexed angle, «<;

How is an angle measured? Does the size of an angle depend at all upon the length of its sides? What is a right angle? How are its sides in regard to each other? What is an obtuse angle? an acute angle? How many right angles can you have at the centre of a circle? Draw a right angle; an obtuse angle; an acute angle; a circle; a semi-circle; an arc; a radius; a diameter; a sextant; a quadrant.

10. What is an astronomical day? a solar day? Which is the longer? How is the solar day divided? Give the denominations of time. Repeat the Table. Give the reason for leap

year; the rule. What are the seasons of the year, and how divided? Give the number of days in each calendar month. Repeat the helping lines. Repeat the table of numbers under the head of Miscellaneous; of Paper; of Books. What measures are sometimes used for animals?

11. How do you reduce a fraction of one denomination to whole numbers of lower denominations? How do you reduce whole numbers of lower denominations to the fraction of a higher!

12. What is COMPOUND ADDITION; SUBTRACTION; MULTIPLICATION; DIVISION? How do these operations differ from similar operations upon simple numbers? Give an example in each, and repeat the rule. How can you prove these operations? 13. How do you find the difference of latitude between two places upon the same side of the equator? upon different sides? Give, in your own words, a rule for finding the difference of longitude between any two places. Suppose two places are in different longitudes, and in your operation the number of degrees between them is found to exceed 180°, what will you do?

14. How do you add or subtract denominate fractions? 15. When the difference of time between any two places is given, how do you find the difference of longitude? When the difference of longitude is given, how do you find the difference of time? For places east of any given point, must the difference of time be added or subtracted to give the true time? For places west, what must be done?

213. MISCELLANEOUS EXAMPLES.

1. If coal is worth $9 a ton, what is the expense of a coal fire for a week, allowing it consumes 25 lbs. a day, coal being sold by the long ton?

2. What will be the cost of freighting 50 bbls. of flour, at $.382 per bbl.?

3. A quantity of gold weighed 4 lb. 10 oz. 3 pwt. before refining, and 3 lb. 11 oz. 2 pwt. 9 gr. afterwards. What was lost in the process?

4. If £69 12s. be paid for 6 cwt. of tobacco, what is the price per pound?

5. An apothecary mixed 3 lb, 10 3, 2 3, 29, 14 gr.

1 lb, 43, 13, 29, 17 gr.

2 tb, 73, 63, 19, 13 gr.

and divided the mixture into 100 equal parts. What was the weight of each part?

6. What is the duty on 6 lb. 4 oz. of essence of lemon, at $.50 per pound?

7. What is the cost of 137 gall. 2 qts. of molasses at 12 cts per quart?

8. If a bird fly 1° in 1 h. 8 m. 15 s., in what time will it fly round the world at the same rate?

9. How many times will a wheel 3 ft. 4 in. in circumference turn in crossing a bridge that is 40 rd. 1 yd. 2 ft. long?

10. What will be the cost of 125 pieces of delaine, averaging 33 yards in length and 22 inches in width, at 25 cts. per yard in length, and 2 cts. per sq. yard for duties? Ans. $1081.66.

11. How many busheis will a bin contain which is 10 ft. long, 8 ft. wide, and 5 ft. deep?

12. At $6.00 a cord, what cost a pile of wood 33 ft, long, 8 ft. 10 in. high, and 4 ft. wide?

13. Divide an arc of 15° 12' 3" by 73.

14. Reduce of a great gross to integers of lower denomina. tions.

15. What will be the cost of fencing a lot of land 20 rods by 260 rods, at 12 cts. per foot?

16. A farmer divided one half of his estate of 350 A. 3 R. 20 rd. equally between his two daughters, and the balance, after setting off 17 A., equally between his two sons. What was the share of each son and daughter?

17. How many cords of wood in 25 loads. each measuring 1 cd. 1 cd. ft. 12 cu. ft.?

18. What would be the cost of the above at $4.50 per cord? 19. How many yards of carpeting 14 yd. wide will cover a floor 18 ft. sq.?

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20. If a cotton mill can make 1200 yds. of cloth per hour, many yards could be made by working 10 hours a day from July 7th to January 4th, allowing for 26 Sabbaths?.

21. Charge 15 lb. 8 oz. Av. to pounds and ounces Troy.

22. How many cakes of ice 1 ft. sq. by 1 ft. thick may be contained in a building measuring in the inside 105 ft. long, 60 ft. wide, 31 ft. 3 in. high?

23. How many bricks 8 in. by 4 in. will cover a court 75 ft. by 50 ft.?

24. How many sq. ft. does the surface of a box contain, which is 3 ft. long, 2 ft. wide, and 6 ft. deep?

25. What is the price of 250 tons of lead at $0.11 per pound? 26* I have imported 1 T. 5 cwt. 1 qr. 15 lbs. of black lead, wich cost me at New York $200.00 a ton, and on which I have also paid $10.00 a ton for duties; for what must I sell it per pound to gain $150.00 on the lot, if I buy and import by the long ton? Ans. $.141.

27. At $6.50 for two dozen pints of olive oil, what cost 1 qt.? 28. What is the difference between 37 f. 8 rd. 0 yd. 1 ft. 3 in., and 37 f. 7 rd. 5 yd. 2 ft. 9 in. ?

29. I have sold 71⁄2 tons of chalk for $75.30. What do I receive per pound?

30. A regiment of troops that enlisted for 9 months was not discharged till July 20th, 1863, which was 1 mo. 26 d. after the term of service had expired. When did they enlist?

31. Divide 60 miles by 7, carrying out the quotient to the lowest denomination.

32. From a pile of wood 48 ft. long, 4 ft. high, and 4 ft. wide, was sold at one time 3 cd. 5 cd. ft.; at another 2 cd. 32 cu. ft.; what is the remainder worth at $4 per cord?

33. What is the value of 7 cd. 7 cd. ft. and 5 cd. 112 cu. ft. of wood, at $7 per cord?

34. If a man saves 1 hour 50 minutes a day by habits of order, 1 hour 30 minutes by promptness in business, and half an hour by early rising, how much time is saved in 25 years of 3651 days each?

35. A floor 30 ft. by 12 ft. is to be covered with carpeting of a yard wide. Required the number of yards.

36. Bought 7 tons of coal for $75.30; what was the cost per ewt.?