formed of an atom of carbon and an atom of hydrogen. (The atom of carbon is represented by C=6. The number of atoms of one element is expressed by an index, thus, C2 signifies two atoms of carbon.) 46. When phosphorus burns in the air, it produces phosphoric acid, formed of an atom of phosphorus, represented by Ph=32, and of 5 atoms of oxygen. Find the number and the form representing this acid. 47. For one atom of carbon there is one atom of water in sugar. Find the expression and the composition, in vulgar and decimal fractions, of this substance. 48. The analysis of an organic substance produced 60 parts of oxygen, 7.5 of hydrogen, and 45 of carbon. Find the atoms of each in the substance. 49. Bought, a quantity of cloth, for as many pence per yard as there were yards in the whole quantity; and by selling it again at 16 per cent. profit, I received for the whole £302. 1s. 8d. How many yards were there? 50. A owes B £360, which becomes due in 9 months; but in 3 months he pays him £80, and in three months after that £100. Required, how much longer than 9 months B should, in equity, defer demanding the balance. 51. A contractor, for digging a canal, when he had finished a mile in length, gave in his account to the proprietors. The canal was 20 feet broad at the top, 16 feet at the bottom, and 7 feet deep. How many cubic yards should be charged for, and what is the amount, at 1s. 3d. per yard? 52. If the end of the minute hand of a clock moves over a distance of 8 inches in 4 min, 30 sec., what is the length of the index? 53. How many trees may be planted on an English acre, at the distance of 6 feet from each other? 54. C barters with D 140 yards of cloth, at 24s. 8d. per yard, for 48 dozens of wine, at 28s. per dozen, and £40 in cash; the balance to be paid in stuff, at 2s. 6d. per yard. How many yards must be given? 55. A ship was bought for £1600. What must be charged for of of of her, to gain £350 on the whole? 56. I reckoned 8 pulsations during the fall of a stone from the top of a rock. What height did it fall, the pulse beating 72 times in a minute? 57. A cubical box, the diagonal of which is 16 inches, is filled with marbles, .60 inch in diameter. Required, the number it contains; and also the quantity of water, in feet, which might be poured into the cavities between the balls? 58. A general, detaching of his army to occupy a certain height, and of the remainder to watch the enemy's movements, had only 170 men left. The strength of his force is required. 59. In order to improve the quality of some home-made wine, which cost 4s. per gallon, I mixed in a cask, containing 45 gallons of it, 3 gallons of brandy, at 33s. per gallon, and 10 gallons of foreign wine, at 20s. per gallon. What is the price per gallon of the whole mixture? 60. What is the simplest vulgar fraction that is equivalent to .088134765625 ? 61. A bought some coffee; by selling it at 114d. per lb., he loses 3s. 3d.; by selling it at 131d., he gains 6s. 6d. How many lbs. were bought? 62. A cubic inch of glass is blown into the form of a globe, that will hold a pint of wine. What is the thickness of the glass? 63. A travels from P to Q, at the rate of 5 miles an hour. After 6 hours, B, who travels at the rate of 73 miles per hour, departs also from P, to overtake him. When will P be up to A? 64. A body weighs 12 lbs. 6 oz. in the air, and 7 lbs. 8 oz. in the water. Find its density, or its weight, compared to that of the same quantity of water. Weight lost 65. A stone weighs 15 oz. in the air; a vessel, filled with water, weighs 16 lbs. 6 oz.; the stone is plunged into it, and the weight is 16 lbs. 14 oz. Find the density of the stone. 66. The freezing point of water, by the centigrade thermometer, is 0°, and the boiling point 100°. In Reaumur's thermometer, the freezing point is 0°, and the boiling point 80°, Find what degree of the centigrade corresponds to 24° Reaumur. 67. In the thermometer of Fahrenheit, the freezing point is 32°, and the boiling point 212° Reduce 48° Fahrenheit into degrees centigrade. 68. Reduce 15 degrees centigrade to degrees Fahrenheit. 69. Bring 75° Fahrenheit into degrees Reaumur. 70. The expansion of iron is .0000122 of its length for every degree centigrade of increase in temperature. What will be the expansion of an iron ruler, 3 yards in length, for 32° of heat? 71. Mercury expands of its bulk for every degree of heat. 5 55 0 What will be the increase of 13 cubic inches of mercury, by raising the temperature from 16° to 48°? 72. To clothe 25000 men, it takes 125000 yards of stuff, wide. How many yards, wide, are required to clothe 3840 men? 73. Multiply of of 16 by of of 15; and divide of 27 by of 214. 74. How many revolutions will a wheel, 4 feet in circumference make, during a journey of 24 miles ? 75. What decimal of a pound is 1.045 of a shilling? 76. A clock, which gains 7 min. in 24 hours, is set right at noon on Monday. What will be the time by it at 6 o'clock in the evening of the following Saturday? 77. What income will arise from the investment of £2400 in the 3 per cent. stock, at 71 ? 78. If cloth, when sold at 14s. 3d. per yard, realises a profit of 14 per cent., at what price must it be sold to gain 20 per cent.? 79. A father divided his property among his three children, in the following manner: to the eldest, he gave to the youngest, ; and to the second, £3000. property left? of the whole; What was the 80. What sum will amount to £217. Os. 74d. in 3 years, at 4 per cent., S.I.? 81. What weight of water will a cistern contain, the depth of which is 3 feet 8 inches; its length, 5 feet 4 inches; and its breadth, 2 feet 6 in. ? 82. In how many years will 100 guineas amount to £140. 8s. 9d., at 33 per cent., S.I.? 83. Subtract of 5 guineas from 3 of £5. 17s. 9d. 84. A merchant sells goods for his correspondent at different times, for which he is to receive £64. 10s. 8d. at the end of 3 months, £72. 10s. at the end of 5 months, and £81. 10s. 6d. at the end of 6 months. What is the equated time to pay the whole? 85. Dr. L. Playfair states that in smelting iron 81 per cent. of the fuel is wasted by imperfect combustion, and this amounts, according to the present quantity of iron smelted, to the enormous waste of 5400000 tons, 4th of the whole quantity of coal annually consumed in the United Kingdom. How much coal is consumed in smelting the iron, and how much is consumed in the United Kingdom. 86. A and B at the opposite extremities of a wood, 248 yards in compass, begin to go round it the same way, at the same time, A at the rate of 25 yards in 2 minutes, and B at the rate of 38 yards in 3 minutes. How many rounds will each make before the one will overtake the other? 87. 35lbs. of tea being mixed with 20lbs. of a better quality, the mixture is found to be worth 7s. 4d. per pound. Find the value of each kind, the difference of their values being 1s. 10d. per pound. 88. Venus revolves round the sun in 224 days, 16 hours, 49 minutes, 11 seconds; and the earth in 365 days. 6 hours, 9 minutes, 12 seconds. Required the seven first approximate ratios of these periods. 89. A load of corn was sold for £14 17s., by which a loss of 17 per cent. was sustained, what should it have been sold for, to realize a profit of 12 per cent.? 90. If the interest of £250 amount to £50. 12s. 6d. in 4 years, what is the rate per cent.? 91. The weight of a bar of iron 3 feet long, 2 inches broad, and 1 thick, is 301 pounds, what is the weight of another bar 8 feet long, 4 inches broad, and 24 inches thick. 92. If a pound of tea be worth 2 of coffee, and a pound of coffee worth 3 of sugar, what will be the value of 56 pounds of tea when sugar is worth 7d. per pound? 93. By purchasing railway shares at 224 per cent. discount, and selling them again at 9 per cent. premium, I gained 300 guineas, what was the original sum I invested? 94. What per centage is gained on an article which is purchased for £10. 5s. and sold for 12 guineas? 95. If 4180 pounds of beef serve 176 men 19 days, how many days will 1991 pounds of beef serve 59 men. 96. Find the compound interest on £850 for 2 years, at 4 per cent.? 97. Suppose the surface of a man's body to contain 34 square feet, and that there are 784 pores in a square inch, what is the diameter of each pore, supposing it circular, and the membrane between the pores one quarter of the diameter, how many pores are there in the body? 98. If 464 men in 5 days, of 12 hours each, dig a trench 340 yards long, 3 wide, and 3 deep, in how many days of 9 hours each could 75 men dig a trench 720 yards long, 4 wide, and 2 deep? 99. If a person gain 81 per cent. by selling apples at the rate of 8 for 61d., how much does he gain per cent. by selling them at 3 for 24d.? 100. Three gentlemen contribute £164. 5s. towards the building of a church, at distance of 2 miles from the first, 23 miles from the second, and 34 miles from the third; and they agree that their shares shall be proportional to the reciprocals of the distances from the church. Required their subscriptions. 101. If beer which is brewed with 3 bushels of malt to the barrel, cost 1s. 3d per gallon when malt is at 62s. 8d. per quarter, how much will beer cost per gallon which is brewed |