MISCELLANEOUS EXERCISES. 1. Pestalozzi was born on the 12th of January, 1746, and died February 17th, 1827. How old was he when he died, and how long is that ago? 2. From May 1st to October 15th, 1851, the time that the Great Exhibition was open, the number of visitors was 6167944. How many went on an average daily, Sundays not included? 3. If 17 pieces of cloth, 23.75 yards long and .77 yard wide, are to be lined with stuff, yard wide. How many yards will be required? 4. There were 3300 iron pillars in the Crystal Palace, on the average 18 feet in length and 8 inches in diameter. If laid side by side, what surface of ground would they cover; and what would be their length, if placed lengthwise? 5. At the opening of a dock, which measures 870 yards by 166 yards, the water was admitted at an average of 4500 gallons per second, and continued to flow in for 12 hours. What was the depth of water? 6. How much further will a man's head travel than his feet, in going round any great circle, supposing his height to be 6 feet? 7. If 100 oranges are bought at 3 a penny, and 100 more at 2 a penny, at what price must they be retailed, so as to gain 25 per cent.? 8. Two travellers sat down to dinner, one had 5 loaves and the other 3; a stranger passing by asked to eat with them, to which they consented. The stranger dined, laid down 8 pieces of money, and departed. How much must each traveller receive? 9. What is the weight of a block of marble, specific gravity 2700, length 63 feet, and breadth and thickness each 12 feet (being the dimensions of one of the stones in the walls of Balbec)? 10. A gentleman dying left in his will a certain amount, to be disposed of as follows: 1st, for funeral expenses £500; 2nd, doctor's bill 150 guineas; 3rd, to each of his two executors £500; 4th, lawyers' bills 300 guineas; 5th, to each of his 13 servants £50: 6th, to his wife he left money for an investment, which, at 4 per cent., would produce her an income of £1000 a year; 7th, the remainder of his property to be divided among his five sons, in such a manner that B shall have 10 per cent. less than A; C, 10 per cent. less than B; D, 10 per cent. less than C; and E, 10 per cent. less than D. Now, E's income, at 4 per cent. from his fortune, was £656.2 per annum. Required, the fortune of each son, and the total amount of property the gentleman left. 11. A could do a work in 16 days, B in 15, and C in 18. Required, the time they will do it in together. 12. How many moidores, guineas, marks, nobles, and crowns are there in £1598. 14s., when there is an equal number of each? 13. If 60 gallons of water, in one hour's time, runs into a cistern, containing 240 gallons, and by a pipe in the same cistern, there runs out 42 gallons per hour. In how many hours will it be filled, supposing there is no water in the cistern, and both taps are open at the same time; the rate of influx and efflux being uniform? 14. The difference of income for one day, between the common and leap year, is 1.346972 farthings. Required, the income per annum. 15. If a solid inch of mould candle will burn 28 minutes, how long will a whole one last, the length of which is 9 inches and diameter .75 inch, supposing the candle to burn uniformly? 16. A body is immersed in a cylindrical vessel of water, the diameter of which is 3 feet 6 inches; and on taking it out, I found the fall of water to be .8 of an inch. What was the solidity of the body? 17. Three merchants form a partnership: A and B together put in £1300, and C 700. A gained £5 more than B, and C £5 more than A. The whole gain was £600. What was the gain of each, and what stock had A and B respectively? 18. A druggist bought 24 cwt. avoirdupois of Epsom salts for £7. 16s. How should he sell 1 oz. Troy to gain 250 per cent.? 19. A man of war displaces 64240 cubic feet of sea water. The weight of the vessel is required. 20. Divide £229.6 among A, B, and C, so that for every 5§ shares taken by A, B takes up 43; and for every 4 shares taken by B, C takes 3.2. What did each receive ? 21. If 12 oxen be worth 29 sheep, 15 sheep worth 25 hogs, 17 hogs worth 3 loads of wheat, and 8 loads of wheat worth 15 loads of barley, how many loads of barley must be given for 24 oxen? 22. At what time, between 4 and 5 o'clock, will the hour and minute hands of a watch make an angle of 180 degrees? 23. In a shoal of herrings, 6 miles in length, 24 in breadth, and 240 yards in depth, how many herrings, allowing 184 to the solid foot; and how many casks would they fill, each cask containing 875 ? 24. A, B, and C can trench a field in 14 days; C, D, and A in 12 days; and D, A, and B, in 18 days. In what time will it be done by them together, and by each singly? 25. Required, the prime cost of a ream of paper, weighing 16 lbs., made from rags at £42. 10s. per ton; waste in manufacturing 25 per cent., expenses 7s. 6d. per ream, and a duty of 3d. per lb. on the paper. 26. It has been computed that the weight of the atmosphere is 1371977266659000000 lbs. The carbonic acid gas is part of its whole weight; and in every 100 lbs. of air there are 23 parts of oxygen, and 77 nitrogen. How much nitrogen is in combination with oxygen in the air? 27. It is found that 61.024 cubic inches of air weigh 20.0624 grains, it is required to determine the weight of the same quantity of oxygen, nitrogen, hydrogen, and chlorine gas, in the same circumstances. (See table of specific gravities.) 28. It has been ascertained that bodies falling freely in space, describe distances increasing as the square of the number of seconds thus in 1 second a body falls 16 feet, in 2 seconds 2× 16 or 64 feet, in 3 seconds 32 × 16 or 1443 feet, &c. What is the space traversed by a stone which has been 7 seconds in falling? 29. The time of oscillation of a pendulum increases as the square root of its length, in the latitude of London, the length of a pendulum which vibrates seconds is 39 inches. Find the length of a pendulum that vibrates 4 times in a second. 30. How many oscillations will a pendulum 75 inches long make in a minute? 31. A merchant received 18 guineas for a piece of cloth, by which he gained 3s. 6d, per yard, at the rate of 16 per cent. Required the length of the piece and the invoice price per yard. 32. When will the hour and minute hands of a clock be at right angles with each other, after 2 o'clock? 33. If by selling goods at 2s. 3d. per lb. I clear 100 per cent., what shall I gain per cent. by selling them at 9 guineas per cwt.? 34. In common air, sound travels at the rate of 1142 feet per second. What is the depth of a well, in which the sound of a stone arriving at the bottom is heard 4 seconds after its being dropped? 35. How long after firing a gun will the report be heard, at the distance of 5 miles? 36. In a storm, thunder was heard 3 seconds after the flash of lightning. At what distance was the cloud from which it proceeded? 37. Light travels at the rate of 192500 miles per second, and the light from the sun is 8 min. 13 sec. in reaching us. What distance is the earth from the sun? 38. What would be the difference of income made by the transfer of £4500 stock from the 3 per cent., at 84, to the 4 per cent., at 96 ? 39. Suppose a wolf could devour a sheep in an hour, a tiger in 20 min., and a lion in 30 min. ; and suppose the wolf eats 10 min. by himself, after which the tiger arrives, and eats along with him ten minutes more; then the lion arrives, and they all eat together. Find the time in which the sheep will be devoured. 40. If a factor's commission, at 3 per cent., be £16. 14s. 6d., what money has he disbursed on his employer's account? 41. On starting for a walk, I found the hour and minute hands of my watch exactly together, between 2 and 3 o'clock. On my return, having walked at the rate of 3 miles an hour, the hands were again together, between the hours of 5 and 6. How many miles did I walk ? 42. Bought, 23 bags of hops, at £3. 17s. 6d. per bag, by which I expected to clear 22 per cent.; but when I had sold 12 bags at that rate, the price lowered, and I could only sell the remainder at 4 guineas per bag. How much did the whole gain fall below my expectations? 43. A stationer sold pencils at 2s. 6d. per 100, by which he gained 25 per cent.; but afterwards, the pencils becoming very scarce, he raised the price to 5s. per 100. What did he gain per cent. by the latter price? 44. In the atomic theory, substances are supposed to combine with each other by atoms, and the weights of these atoms express the proportion in which they are combined; thus, taking the weight of an atom of hydrogen, or H=1; the weight of an atom of oxygen, or 0=8. Now, since the atom of water consists of one atom of hydrogen and one of oxygen, it follows that the weight of one atom of water, or HO=1+8=9. Find the weight of hydrogen and of oxygen in 50 gallons of water. 45. Express the weight of one atom of the three following gases: 1st, the oxide of carbon, which is formed of 2 atoms of carbon and 1 of oxygen; 2nd, carbonic acid, formed of an atom of carbon and 2 atoms of oxygen; and 3rd, carburetted hydrogen, |