TABLE. 1 gram, 6. 10 grams, 10 milligrams (mg.) equal 1 centigram, cg. 1 decigram, dg. 1 decagram, DG. 10 decagrams 1 hectogram, HG. 10 hectograms 1 kilogram, KG., or K. 10 kilograms 1 myriagram, MG. Notes. -1. The gram is used in weighing letters, and mixing and compounding medicines, and in weighing all very light articles. The new 5 cent coin (dated 1866) weighs 5 grams. 2. The kilogram is the ordinary unit of weigbt, and is generally abbre Vlated into kilo. It equals about 24 pounds avoirdupois. Meat, sugar, etc., are bought and sold by the kilogram. 3. In weighing heavy articles, two other weights, the quintal (100 kilo grams) and the tonneau (1000 kilograms), are used. The tonneau is be tween our short ton and long ton. 4. The avoirdupois ounce is about 28 grams; the pound is a little less than is kilo. MENTAL EXERCISES. 1. How many grams is a kilogram? 2. How many milligrams in a gram? 3. How many decigrams in a kilogram? 4. How many hectograms in a myriagram? MEASURES OF VALUE. 798. The Franc is the French money unit. It equals $0.193. The principal gold coin is the 20-franc piece; the principal silver coins are the franc and the B-franc piece. TABLE. 1 franc. NOTE.-It has been suggested that the American dollar and the English pound be so modified that we shall have the following money table : 5 francs 1 dollar. 5 dollars 1 pound. The franc equals about 19.3 cents of our present money. NUMERATION AND NOTATION. 799. In the Metric System the decimal point is placed between he unit and its divisions, the whole quantity being regarded as an integer and a decimal. Thus, 3 decagrams, 5 grams, 6 decigrams, 8 centigrams, are written 35.68 grams. 800. The initials of the denomination may be placed either before or after the quantity, though they are most frequently placed after it; thus, 27 grams may be written 627, or 276. EXERCISES IN NUMERATION. 1. Read 48.05M. SOLUTION.—This is read 48 and 5 hundredths meters; or it may be read 4 decameters, 8 meters and 5 centimeters. Read the following: 2. 12.06M. 5. 807.005L. 8. 28.66A. 6. 5062.0356. 4. 204.06S. 7. 20760.5086. EXERCISES IN NOTATION. 1. Write 6 meters and 5 centimeters. SOLUTION.- We write the 6 meters with a decimal OPERATION, point to the right, and then, since there are no deci 6.05M meters, we write a naught in the tenths place, and then write the 5 centimeters in the place of centimeters. 2. Write 17 meters, 4 decimeters, 8 centimeters. 3. Write 7 decameters, 2 decimeters, 5 centimeters. 4. Write 15 ares, 9 deciares, 8 milliaręs. 6. Write 4 hectares, 8 ares, 5 centiares. 6. Write 12 decasteres, 6 decisteres, 8 centisteres. 7. Write 9 kilosteres, 7 decasteres, 5 centisteres. 8. Write 3 hectoliters, 8 liters, 7 deciliters. 9. Write 16 grams, 4 decigrams, 8 centigrams. 10. Write 8 myriagrams, 7 hectograms, 6 centigrams, and 6 milligrams. REDUCTION OF THE METRIC SYSTEM TO THE COMMON SYSTEM. MEASURES OF VALUE. 1. How many dollars in 25 francs ? Ans. $4.825. 2. How many dollars in 47.50 francs ? Ans. $9.16. 3. How many francs in $15.50 ? Ans. 80.31 fr. 4. How many francs in $37.75? Ans. 195.595 fr. MEASURES OF WEIGHT. 5. How many grains in 12 grams? Ans. 185.184 gr. 6. Pounds Troy, in 480.5 grams? Ans. 1 lb. 8 oz. 8 pwt. 237. gr. 7. Pounds Av., in 976.25 grams ? Ans. 2 lb. 2 oz. 190.49 gr. 8. Grams in 480 grains ? Ans. 31.1046. 9. Grams in 12 Troy pounds? Ans. 4479.0046. 10. Grams in 12 Av. pounds ? Ans. 5443.2346. MEASURES OF LENGTH. 11. How many feet in 24.5 meters ? Ans. 80.38 ft. 12. Yards in 136.54 meters? Ans. 149.3216 yd. 13. Meters in 120 yards? Ans. 109.73M. 14. Meters in 2 mi. 120 rd. ? Ans. 3822.199M. 16. Miles in 4000 meters? Ans. 2 mi. 155 rd. 5 ft. 10 in. 16. Meters in 3 mi. 272 rd. ? Ans. 6195.9867M. MEASURES OF SURFACE. 17. How many ares in 360 sq. yd. ? Ans. 3.01A. 18. Sq. yd. in 142.5 ares ? Ans. 17043 sq. yd. 19. Acres in 505.6 ares ? Ans. 12 A. 78.1312 P. 20. How many ares in 30 acres? Ans. 1214.574A. 21. How many ares in 5 A. 104 P. ? Ans. 228.744A. MEASURES OF VOLUME. How many cu. ft. in 46 steres ? Ans. 1624.5636 cu. ft. 23. Cu. ft. in 214.78 steres ? Ans. 7585.2993 cu. ft. 24. How many steres in 128 cu. ft. ? Ans. 3.6248. 25. Steres in 16 cu. yd. 8 cu. ft. ? Ans. 12.458S. MEASURES OF CAPACITY. 26. How many gallons in 36.08 liters ? Ans. 9 gal. 2 qt. 27. Gallons in 45.05 liters ? Ans. 11 gal. 3 qt. 1 pt. 28. How many liters in 24 gallons ? Ans. 90.844L. 29. How many liters in 36 gal. 2 qt. ? Ans. 138.16L. 30. How many liters in 6 bu. 2 pk. ? Ans. 229.07L. 81. Bushels in 65.25 liters ? Ans 1 bu. 3 pk. 3 qt. MISCELLANEOUS PROBLEMS. 1. If a letter weighs 2.5 grams, how many such letters will it take to weigh a kilogram? Ans. 400. 9. A lady bought 11.5 meters of silk for a dress, at the rate of $4.75 a meter ; what did it cost her? Ans. $54.625. 3. My butcher's bill one month was 87.5 kilograms of beef, at 18 cents a kilo; what was the bill ? Ans. $16.40%. 4. How much must I pay for 56.25 liters of coal oil, at the rate of 18 cents a liter ? Ans. $10.546 +. 5. A kilogram weighs 2.2046 lb.; what is the weight of 561 tonneaux? Ans. 124559.9 lb. 6. A bought 2500 ares of land, at $4.50 an are, and sold it for $525 a hectare; what was the gain ? Ans. $1875. 7. If 15 steres of wood cost $22.50, wbat must I pay for 24.5 steres at the same rate ? Ans. $36.75. 8. If a kilogram of sugar is worth 214 cents, how many kilos can I buy for $100 ? Ans. 459.77 +. 9. The height of a pole is 68.325M; how long would it take a worm to climb to its top, at the rate of 15 meters a Ans. 4.555 days. 10. A kilometer is about g of a mile; how many kilometers from Lancaster to Philadelphia, 70 miles ? Ans. 112. 11. How much must I pay for 231 meters of silk, at 8 francs 25 centimes a meter ? Ans. 195.94— fr. 12. What cost 3 kilares, 7 hectares, 6 deciares of land, at $275.25 a hectare? Ans. $10185.90. 13. It is about 100 miles from Philadelphia to New York; bow many kilometers is it? Ans. 160. 14. How much will it cost to excavate 124 cubic meters of earth, at $37.25 a cubic meter ? Ans. $476.80. 15. What is the width of the Atlantic in kilometers, the width being about 3000 miles ? Ans. 4800 kilometers. 16. What must I pay for 25 steres, 2 decisteres, and 5 cen. tisteres of wood, at the rate of $2.65 a stere ? Ans. $66.917. 17. How long will it take a man to walk from Philadelphia New York, at 8 kilometers an bour ? Ans. 20 hours. day? 18. Two vessels are 432 kilometers apart, and sail toward each other, each at the rate of 18 kilometers an hour; in how many hours will they be together? Ans. 12 hours. 19. A block 3.5 meters long, .75 meters wide, and .8 meters thick, cost $12; what would a cubic meter of marble cost, at the same rate ? Ans. $5.71+. 20. A man bought 7000 grams of jewels, at 40 francs a gram, and sold them at $15 a pennyweight; how much was gained or lost ? Ans. $13475. PROBLEMS ON IMPORTS. 1. An importer bought 428.5 meters of silk in France, at 18 francs a meter, sent it to the United States, paying 25 cents a meter shipping and duty, and sold it for $5.25 a meter; what was his gain? Ans. $653.89. 2. A man bought a valuable gem in France which weigbed 325.75 grams, @ 10.25 francs; the duty on it was $6.25; how must be sell it a gram to clear $150 ? Ans. $2.46. 3. I bought 125.75 liters of wine in France, at 45.25 francs a liter, paid $1.25 a liter duty and freight, and sold it at $12.50 a liter ; how much did I gain? Ans. $316.48. 4. An importer bought 625.5 liters of French brandy, at 7.55 francs a liter, paid 15 cents a liter duty and freight, and sold it in New York at $1.65 a liter; how much did he gain ? Ans. $26.80. 5. A man bought 200 meters of cloth in France, at 16.25 francs a meter; he paid 121 cents a yard duty and freight, and sold it in Boston at $4.621, a yard; what was the gain ? Ans. $357. 6. An importer bought 480 grams of jewels, at 12.25 francs gram, said $5.25 an ounce shipment and duty, and sold them in Philadelphia at $102.75 an ounce; what was the Ans. $369.78. 7. A wine merchant bought 180 liters of brandy in Havre, at 32 decimes a liter; he paid 2 decimes a liter shipment, and $2.25 a gallon duty, and sold it in New York at $6.75 a gallon; what was his gain? Ans. $92.40. gain? |