11. On what day will happen July 4, 1857? Ans. Saturday. 12. On what day will March begin in the year 1890 ? Ans. Saturday. 13. On what day of the week was our Independence declared? 14. There will be a "Transit of Venus," on what day of the week will it happen? Ans. Thursday. December 8, 1874, Ans. Tuesday. 15. On what day of the week were you born? SECTION LXXXIV. MISCELLANEOUS QUESTIONS. 1. What number must 73 be multiplied by, that the product may be 63 ? Ans. 5. 2. What number is that, which, being multiplied by half itself, the product shall be 44? 3. What fraction is that, which, being divided quotient shall be 5? 4. What part of 72 is 94 ? 19 to a simple fraction. 6. Add of a ton to of a cwt. Ans. 3. by 11, the Ans. 574. Ans. 2 or 17. Ans. Ans. 12cwt. 1qr. 84lb. 7. If the earth make one complete revolution in 23 hours 56 minutes 3 seconds, in what time does it move one degree? of § be added the Ans. . 11. A certain gentleman, at the time of his marriage, agreed to give his wife of his estate, if, at the time of his death, he left only a daughter, and, if he left only a son, she should have of his property; but, as it happened, he left a son and a daughter, by which the widow received in equity $2400 less than if there had been only a daughter. What would have been his wife's dowry if he had left only a son? Ans. $2100. 12. A gentleman being asked what o'clock it was, said that it was between 5 and 6; but, to be more particular, he said that the minute hand had passed as far beyond the 6 as the hour hand wanted of being to the 6; that is, that the hour and minute hands made equal acute angles with a line passing from the 12 through the 6. Required the time of day. Ans. 32m. 18 sec. past 5. 13. A, B, and C are to share $100,000 in the proportion of ,, and, respectively; but C's part being lost by his death, it is required to divide the whole sum, properly, between the other two. Ans. A's part is $ 57,1429, and B's $ 42,8574. 14. A father devised of his estate to one of his sons, and of the residue to the other, and the remainder to his wife. The difference of his sons' legacies was found to be 257£. 3s. 4d. What money did he leave for his widow ? Ans. 635£. Os. 103gd. 15. In the walls of Balbec, in Turkey, the ancient Heliopolis, there are three stones laid end to end, now in sight, that measure 61 yards in length; one of which is 63 feet long, 12 feet thick, and 12 feet broad; what is its weight, supposing its specific gravity to be 3 times that of water? Ans. 759 tons. 16. A burden of 200lbs., suspended on a pole 4ft. in length, the point of suspension being 6in. from the middle, is carried by two men, the ends of the pole resting on their shoulders; how much of this load is borne by each man? Ans. 125lbs. and 75lbs. 17. The new court-house in Boston has 8 pillars of granite, each 25ft. 4in. in length, 4ft. 5in. in diameter at one end, and 3ft. 5in. in diameter at the other end. How many cubic feet do they contain, and what is their weight, allowing a cubic foot to weigh 3000 ounces? Ans. 2455.03 cubic feet, 205.4 tons. 18. A father, dying, left his son a legacy, of which he spent in 8 months; of the remainder lasted him 12 months longer; after which he had only $410 left. What did his father bequeathe him? Ans. $956.663. 19. A butcher, wishing to buy some sheep, asked the owner how much he must give him for 20; on hearing his price, he said it was too much; the owner replied, that he should have 10, provided he would give him a cent for each different choice of 10 in 20, to which he agreed. How much did he pay for the 10 sheep, according to the bargain? Ans. 1847.56. 20. A merchant sold goods to a certain amount, on a commission of 4 per cent., and, having remitted the net proceeds to the owner, he received per cent. for prompt payment, hich amounted to $ 15.60. What was the amount of his comon ? Ans. $260.00. 21. A, of Boston, remits to B, of New York, a bill of exchange on London, the avails of which he wishes to be invested in goods on his account. B having disposed of the bill at 71⁄2 per cent. advance, he received $9675.00, and having reserved for himself per cent. on the sale of the bill, and 2 per cent. for commission, what will remain for investment, and for how much was the bill drawn? Ans. For investment, $9461.58; the bill was £2025. 22. Bunker Hill Monument is 30ft. square at its base, and 15ft. square at its top; its height is 220ft. From the bottom to the top, through its centre, is a conical avenue 15ft. in diameter at the bottom and about 11ft. at the top. How many cubic feet are there in the monument? Ans. 86,068.518+ft. 23. A hired a house for one year for $300; at the end of 4 months he takes in M as a partner, and at the end of 8 months he takes in P. At the end of the year what rent must each pay? Ans. A pays $1831; M pays $83; P pays $ 33. 24. A merchant receives on commission three kinds of flour; from A he receives 20 barrels, from P 25 barrels, and from C 40 barrels. He finds that A's flour is 10 per cent. better than B's, and that B's is 20 per cent. better than C's. He sells the whole at $6 per barrel. What in justice should each man receive? Ans. A receives $1391; B, $ 15817; C, $211. 25. Bought 100 barrels of flour, at $5 per barrel, and immediately sold it on a credit of 6 months. The note which I received for pay, I got discounted at the Suffolk Bank, and, on examining my money, I found that I had gained 20 per cent. on my purchase. What did I receive per barrel for the flour? Ans. $6.1818. 26. Purchased for a cloak 5 17 yards wide; to line this, I yard wide, but on being wet it yard in every 20 yards in length. was it necessary to buy? yards of broadcloth, that was purchased flannel that was shrunk 1 nail in width, and Î How many yards of flannel Ans. 12 yards. 27. How many bricks would it require to build the walls of a house 40 feet long, 30 feet wide, and 20 feet high, admitting the walls to be a foot thick, and that each brick was 8 inches long, 4 inches wide, and 2 inches thick? Ans. 73,440 bricks. 28. How many feet of boards would it require to cover a house, that was 40 feet square, and whose height to the top of the plate was 20 feet, the roof projecting 1 foot over the plate, and coming to a point over the centre of the house, 15 feet above the garret floor? Ans. 5367.7+ feet. 29. Lent a friend $700, which he kept 20 months. Some years after I borrowed of him $300; how long should I keep it to balance the favor? Ans. 46 months. 30. John Lee gave half of his estate to his wife, of the remainder to his oldest son, and of the residue to his oldest daughter, and of what then remained, which was $1500, to be equally distributed among his other children, who received $150 each; required the number of his children, and the value of his estate. Ans. 12 children; estate, $10,000. 31. A and B set out to travel round a certain island, which is 80 miles in circumference. A travels 5 miles a day, and B 7 miles a day. How far must B travel to overtake A ? Ans. 280 miles. 32. If 24.4 cubic inches of lead weigh 16 pounds, required the number of feet of lead pipe that can be made from 80 pounds of lead, the diameter of the pipe to be 1 inch, and the thickness of it of an inch. Ans. 124.26+ feet. 33. How long a tube can be made from a cylinder of lead 8 inches long and 2 inches in diameter, and through the centre of which is a hole of an inch in diameter; the tube or pipe to be of an inch in diameter, and 3 of an inch in thickness? Ans. 16.29+ feet. 34. Four men, A, B, C, and D, bought a stack of hay, containing 8 tons, for $100. A is to have 12 per cent. more of the hay than B, and B is to have 10 per cent. more than C, and C is to have 8 per cent. more than D. Each man is to pay in proportion to the quantity he receives. The stack is 20 feet high, and 12 feet wide at its base, it being an exact pyramid; and it is agreed that A shall take his share first from the top of the stack, B is to take his share the next, and then C and D. How many feet of the perpendicular height of the stack shall each take, and what sum shall each pay? Ans. A takes 13.22+ft., and pays $28.9313287; B takes 3.14+ft., and pays $25.8311927; C takes 2.06+ft. and pays $23.488; D takes 1.58+ft., and pays $21.7447966. 35. Suppose the rails of a railroad to be 5 feet 4 inches apart at the place of the wheels bearing, and on a curve line of 1200 feet radius for the outer rail. Suppose the wheels of the car running on the rails to be firmly fixed to the axle, and that it is 5 feet from the outside of the flange of one wheel to the outside of the flange of the opposite wheel; that from the outer side of one wheel to the outer side of its opposite wheel is 5 feet 8 inches; that the diameter of each wheel at the outside of the flange is 3 feet; the face of the wheels to be so bevelled that at the outside of each wheel the diameter of the wheel is 2 feet 11.5 inches, and that the axle will always be in a posi tion square across the two rails. In what part, between the two wheels, must the centre of gravity of the load be placed, so that the weight of the load shall bear equally on each rail? 5ft. 4in. OPERATION. 5ft.4in.; and 4in.÷22in. the place, beyond the flange, on the face of the wheel, where the wheel bears on the rail. The perpendicular width of the face of the wheel is 4 inches, and in that distance the wheel diminishes in diameter 3ft. 2ft. 11.5in. = .5in. Then, as 4in. : .5in. : : 2in. : .25in.; and so the diameter of the wheel at the bearing is 3ft.-.25in. 2ft. 11.75in. As the radius of the curve of the outer rail is to that of the inner rail, so is the diameter of the outer wheel at the place of bearing to that of the inner wheel ; viz. as 1200ft.: 1200ft.· 5ft. 4in. 1194ft. 8in. :: 2ft. 11.75in. : 2ft. 11.59iin. Then the difference of the diameters of the two wheels at the places of bearing is 35.75in. -35.591= .158in. Then, to see how much on the perpendicular face of the wheel this difference in diameter will vary the bearing; as 3ft. — 2ft. 11.5in.=.5in. : 4in. : : .158in. : 1.27iin. But this difference must be applied half to each wheel, viz. 1.27iin.÷ 2= .635in., which brings the place of bearing .635in. nearer to the flange on the outer wheel, and .635in. further from the flange on the inner wheel. And the middle point between the two bearings will be .635in. from the centre of the axle towards the inner curve; and in that place must the centre of gravity of the whole load be placed, to make the weight of the load bear equally on each rail; viz. .635in. from the middle of the axle towards the inner rail, Answer. 36. The dimensions of a bushel measure are 18 inches wide, and 8 inches deep; what should be the dimensions of a similar measure that would contain 8 bushels ? Ans. 37in. wide, 16in. deep. 37. What is the weight of a hollow spherical iron shell 5in. in diameter, the thickness of the metal being lin., and a cubic inch of iron weighing 2 of a pound? Ans. 13.2387lbs. 38. At a certain time between 2 and 3 o'clock, the minute hand was between 3 and 4. Within an hour after, the hour |