Q. How did the United States government obtain the funds for carrying on its war with England? When did the last war begin? When end? How much money was borrowed? What security did the United States give? (Its own stock.) Was it generally above or below par? When is stock par? When below par? When above par? How much stock at 95 per cent. must be given for $100 cash? How much for $1000 cash? How much stock at 90 per cent. must be given for $100 cash? How much at 80? What is $1000 stock worth at par? At 5 per cent. above par? At 10 per cent, above par? At 20 per cent.? 6. By a treaty with the French in 1831, to indemnify the United States for spoliations upon their commerce, the French agreed to pay 25,000,000 of francs, in 6 annual instalments, bearing interest at 4 per cent,; what was the amount of each payment in federal currency? Ans. 7. The last United States Bank was chartered by Congress in 1816, for 20 years, with a capital of 35,000,000 of dollars, the United States government holding 70,000 shares at $100 each; what advance per cent. would there be in the stock to make the capital of the government $8,000,000? Ans. 8. In 1829, a dividend of 34 per cent. was declared upon the capital stock of the United States Bank, for the previous 6 months; what amount of dividend was paid to the United States, its total amount in stock being $7,000,000? Ans. $245,000. 9. By the law of Congress establishing the last Bank of the United States, a bonus of $1,500,000 was stipulated to be paid to the United States; what per cent. of the capital stock did the sum amount to? Ans. 10. What distance will sound travel in 1 minute through the following media, its rate per second being as follows: Through air, .... 1143 ft, per sec. Ans. 12.7 miles per m. water,.. 4900 Ans. 66 steel, 17000 Ans. 66 glass,. 18000 **** Q. Through what media does sound travel most rapidly? 11. The best bell-metal contains 80 per cent. of copper, and 20 per cent. of tin: how many pounds of each substance would be in the following bells, supposing the bells to be made in the above proportion? Q. What metals compose bell-metal? What proportion of each? What are some of the largest bells in the world? 12. The steam-ships British Queen and President are stated to have cost £90,715 each. The total receipts of the British Queen for 9 voyages amounted to £82,001 2s. 6d., and the total expense £70,691. The total receipts of the President for 9 voyages were £25,234 6s. 7d., and the expenses £21,833 38. 7d. What was the average profit per voyage in federal currency, and what rate per cent. was the profit upon the first cost? Ans. 13. The first voyages from Great Britain to New York by steam were made simultaneously by the steam-ship "Sirius" from Cork, and the Great Western from Bristol, in 1838. The former travelled 3,300 miles, and performed the voyage in 19 days. The Great Western travelled 3,223 miles, and performed the voyage in 15 days 5 hours. What was the average rate per hour of each vessel? Ans. S Sirius' rate per hour, 7.2+ miles. 14. The total amount of debt of Great Britain in 1836, was £787,638,816 8s. 94d.: what is the annual charge to that government, estimating the interest at 3 per cent. in federal money? Ans. 15. By the act of Congress of 1835, the standard of the gold and silver coins of the United States was fixed as fol lows. That of 1000 parts by weight, 900 shall be pure metal and 100 parts alloy; the alloy of the silver coins being copper; that of the gold coins, equal parts of silver and copper. The dollar weighs 412 grains; dollar, 2064 ; dollar, 103; the dime, 414; and the dime, 20g grains. The eagle weighs 258 grains; eagle, 129; and the eagle, 64 grains. The copper coins, composed of pure copper, as follows: the cent weighs 168, and the cent 84 grains. How much gold, silver, and copper, by weight, were used in the coinage at the United States Mint, Philadelphia, in 1842, the number of pieces of each kind being as follows: Ans. 3870.0 lbs. 93188.6 lbs. 80060.9 lbs. Q. What are the coins of the United States? By whom is their weight fixed? What metals compose the gold coins? The silver? How much alloy to the 1000 parts? What is the weight of the eagle? Dollar? Cent? Is the weight determined by the pound avoirdupois or troy? DUODECIMALS. 213. DUODECIMALS are numbers in which the unit has been divided into twelfths, or some multiple of twelve. The name is derived from the Latin word duodecim, which means twelve. As usually applied, the unit which is thus divided is the foot. When 1 foot is divided into 12 equal parts, each of these parts is called primes, or more commonly inches, and is denoted by the sign'. The inch or prime being again divided into twelve equal parts, each of these parts is called seconds, and is denoted by the sign ". In like manner, the second being divided into twelve other equal parts, the name of thirds is given to them, and they are denoted by the sign "", and so on. The number 1 ft., 5', 10", 6", is read, 1 foot, 5 inches, 10 seconds, and 6 thirds. Q. What are duodecimals? From what is the name derived? To what unit is this division usually applied? When the foot is divided into twelve equal parts, what is each of these parts called? How denoted? When the inch is divided into twelfths, what is each of the equal parts called? How denoted? What name is given to the twelve equal parts into which the seconds are divided? How denoted? How would you read the expression 5 ft. 2' 3" 4? How would you write the number 4 feet, 3 inches, 4 seconds, 2 thirds? 214. From the manner in which these divisions of the foot are formed, it follows that Q. What part of 1 foot is 1 inch? What part of 1 inch is 1"? What part of 1 foot is 1"? What part of 1" is I"? What part of 1 foot is 1'"'? 215. When 1. foot is multiplied by 1 foot, the product is 1 square foot. When 1 foot is multiplied by 1 inch, since l' of a foot, the product is 1×2 of a foot=1'. When 1 inch is multiplied by 1 inch, since 1'=' of a foot, the product is of a foot=1". When 1 inch is multiplied by 1", since l' of a foot, and 1" of a foot, the product is of a foot= = 1728 of a foot=1"". Hence we conclude that Feet multiplied by feet give square feet in the product. Feet multiplied by inches give inches in the product. Inches multiplied by inches give seconds in the product. 1 Inches multiplied by seconds give thirds in the product. Q. When feet are multiplied by feet, what will the product be? Why? Feet by inches? Why? Inches by inches? Why? Inches by seconds? Why? ADDITION AND SUBTRACTION OF DUODECIMALS. 216. Addition and subtraction of duodecimals are performed like the corresponding operations in compound numbers. 2. From 11 ft. 3′ 1′′ 4′′ take 5 ft. 8′, 2′′, 3"". In this example, 3"" from 4" gives 1""; 2" from 1" we cannot, but borrowing 12", 2" from 13′′ gives 11"; carrying 1' to the next higher unit, and proceeding as in subtraction of compound numbers, the result is 5 ft. 6' 11" 1"". OPERATION. W43 1 5 8 2 Ans. 5 6 11 1 13. Add 4 ft. 0′ 2′′ 3′′′′ and 5 ft. 9′ 3" 9" together. Ans. 9 ft. 9' 6" 0". 4. From 8 ft. 0′ 0′′ 2′′′′ take 2 ft. 1′ 0′′ 3′′′′. Ans. 5 ft. 10' 11" 11". Q. How are addition and subtraction of duodecimals performed? MULTIPLICATION OF DUODECIMALS. 217. Multiplication of Duodecimals is frequently used to determine the contents of solid bodies, such as timber and the like, when the dimensions of its sides are known in feet and parts of a foot, since the number of solid feet will be equal to the product of the length, breadth, and thickness. |