was broke by a tempestuous wind, so that the upper part of it struck the ground 30 feet from its root ;-required the length of the part broke off. Anf. 54 feet. 11. A square within a circle contains 16 square yards ;-required the area of a square circumscribed about the same circle. Anf: 32 square yards. 12. The cubical altar at Delphos was i cubit ;-required the fide of the new altar, which was to be twice that size, and of the same form. Ans: 1.259921 cubits. 13. The ceiling of a room, at 6d. per square yard, amounted to 21. 10s. ; the breadth is 22 feet ;-required the length. Anf. 40 feet. 14. A man left two daughters ; ordered by his will that the eldest should have annually the rent of a square field, and the younger the rent of a circular one; the rent of each field, at 205. per acre, would exactly surround it in shillings, allowing one inch to each shilling ;-required the portion of each of the daughters. The first's annual income is 250905l. 125. -197061l. 55. 2d. 15. A gentleman had a garden surrounded by a terrace walk; the length of the garden is 500 yards, and the breadth 400 yards; the walk was equal to of the garden ;-required the breadth of the walk. Anf. 13.6809 yards. 16. A gentleman has a garden 100 feet long and 80 broad, but intends to make a walk half round it that shall take up half the ground ;--required the breadth of the walk. Anf. 25.96876. 17. The length of a room is 40 feet, and breadth 30 feet; the expence of painting the walls, at 6d. per square yard, is 7!. -required the height of the room. Anf. 18 feet high. 13. The diameter of a malt bushel is 18 inches, and its depth 8,5 inches; what ought to be the depth when the diameter is 19 inches ? Anj. 6.8448 inches. 19. Three 19. Three farmers, A, B, and C, had each an equal share of a triangular field, whose base, being a river, measured half an English mile, its content being 120 acres : the marches were drawn parallel to the base. Now C had his share next the river, B the middle division, and A the rest. They agreed with an undertaker to dig a ditch from the top of A's division perpendicular to the river side. The breadth of the ditch at a medium is 6 feet, and depth 41 feet. Required the undertaker's charge against each of the three farmers, at 4d. per folid yard. A pays 381. 25 2d. Anf. 3 B pays 151 155.71d. (Cpays 121. 2s. 2d. 20. One horse chaise, in turning round a ring, it was ob, served that the outer wheel made three turns for every two of the inner wheel. The height of the wheels being 47 feet, and distance 5 feet, required the area of the space or ring included betwixt the tracts of the wheels. Anf. 392.7 square feet. 21. The gilding of a ball, at 3d. per square inch, cost as much as the buying of it at id. per cubical inch : It is required to find its diameter, · Anf. 18 inches. 22. A cone, whose height is 40 inches, is to be divided into three equal parts, by sections parallel to the base ;-required the height of each. The upper part is 27.73. Ans. The middle part 7.21. The lower part 5.06. 23. What length of a plank, that is 10 inches broad, will make 41 square feet? Anf. 5 feet 4 inches. 24. What length of a log of wood, that is 15 inches broad and 11 inches thick, will be equal to 10 cubical feet? Anf. 8 feet 844'inches. 25., What length of a cord will strike off one-third part of a circular pond, whose diameter is 40 yards ? Anf. 38.5696 yds. 26. Two men, A and B, bought a round piece of wood, co qually thick throughout. A paid one-third share, B the rest. A proposes to have a flip the whole length of the tre, for his 3C fhare. Mare. At what distance from the centre must the line be Itruck, the diameter being 40 inches ? Anf. 41': inches, or A will cut off 151 of the diameter, 27. A leaden pipe of 4 inches vore weighs 20 ib. averdupois per foot in length ;-required the thickness, the specific gravity of lead being 11325. Auf .3014 inches. 28. If similar solids be to one another in the triplicate ratio of their homologous fides, and the weight of an iron ball of 4 inches diameter be 95 lb.-required the weight of a ball of 6 inches diameter. Anf. 32.025 lb. 29. If water issue through an orifice with the fame velocity that a heavy body would acquire in falling freely from the surface of the water to the level of the orifice; and fupposing a fhip to have been bored through by a 32 pounder, 8 feet below water; it is required to determine what weight of water she will draw in 10 minutes. Anf. 13 ton 2 cwt. 3 qr. 24 lb. 30. Supposing three wheels, A, B, and C, so combined that three revolutions of A will drive B five times round, and seven revolutions of B will drive C nine times round, it is required to find the least number of teeth necessary to regulate the above motion. Ans. A 15, B9, and C 7 teeth. 31. Upon the same supposition, it is required to determine the number of revolutions each must take before the fame teeth be in conjunction. Anf. A takes 21, B 35, and C 45. 32. A milftone of 5 feet diameter strikes feconds; how many miles would she run upon edge at the same rate in seven Ans. 1799 miles 2 f. 9} p. 33. The fame conditions being given, in what time would she go round the terraqueous globe, its diameter being 7958 miles ? Anf. 97 days 6 hours 20 niin 48 sec. · 34. Supposing Loch Tay to be supplied fo as to discharge a river 100 yards broad and 3 yards deep, flowing at the rate of 3 miles per hour, it is required to determine how far below the surface days? Anf. 30. surface an orifice of a square yard ought to be, to discharge an equal quantity. Anf. 3249 feet. 35. The times in which pendulums vibrate are as the square foot of their lengths; and if a pendulum of 39.128 inches vie brate seconds, how many swings will a pendulum of 156.512 inches take in an hour ? 36. Required the length of a pendulum that vibrates half fee conds. Anf. 9-782 inches. 37. My plumber has sold me 600 yards leaden pipes, of 4 inches bore and thick, at 16s. per cwty at the fame time the purchased a garden in the form of a rightangled triangle, of fuch dimensions that the difference between the hypothenuse and the sum of the two other fides was 50 yards. I, being a gardener, have undertaken to make a circular filh-pond in the garden to touch the three fides, at 6d. per solid yard, and find, upon the balance, 731. 135. od. due to him ; required the depth of the pond. Anf. 3 yards, or 9 feet. 38. What length of a ridge 6 ells broad will make 10 falls ? Anf. 65 ells 39. If a pipe of 4 inches diameter is susficient to supply a town with water, required the diameter of a pipe, fimilarly lituated with the former, that shall serve, after the town is ercreased by one half. Anf. 4.899 inches. 40. The fame town, after being so encreased, to save expen, ces, intends to be supplied from the old pipe ; at what depth in the reservoir must it be placed, it being formerly 4 feet deep? Anf. 9 feet. 41. Given the two sides of an acute angled triangle 40 and 60 poles; required the included angle, and the third side, that the triangle may contain 4 acres of land. Anf. 32° 14', and 33.84 poles. 42. Two porters agreed to drink off a quart of strong beet between them, at a draught each. Now the first having drank till the surface of the liquor touched the opposite edge of the bottom 3 C2 bottom of the quart pot, and gave the remaining part of it to the other, what was the difference of their shares, supposing the pot was the frustum of a cone, the depth being 5.7 inches, the diameter at the top 3.7 inches, and that of the bottom 4.23 inches? Anf. 7.07 cubic inches. 43. A heavy body is dropt into an empty pit; ten seconds of time elapsed before the sound from the bottom was heard. It is required to find the depth of the pit. Anf. 1273 feet. 44. If a heavy sphere, whose diameter is 4 inches, be put into a conical glass full of water, whose diameter is 5 inches and depth 6 inches, how many cubic inches of water will run over? Anf. 26.1674336 inches. 45. A gentleman has a rectangular piece of ground which he intends for a bowling-green. It being a regular declivity of 30°, the flant lide measured 500 feet, the other 433 feet; required the expence of levelling it, one part with another, at 3d. per cubic yard. Anf. 27121. 1os. 31d. 46. The same bowling-green being levelled, required the expence of dressing it at Ad. per square foot. Anf. 1021. 175. 2 d. 47. An old mathematician bought a field in the form of a parabola, the length of the base or ordinate being 3000 links, and of the axis or abscissa 2500. He built a summer-house 9 chain-lengths distant from the ordinate, and 2 chain-lengths from the abscissa ; and ordered by his will, that the field should be divided between his two sons, by the least line that could be drawn through the summer-house, terminating both ways by the parabolic curve ; required how much land each of the fons fnail have. The one will have 25 ac. 2 r. 16 falls. 24 ac. I r. 24 falls. 48. If a cistern can be filled with water from one cock in 12 hours, and from another in 8 hours, in what time will it be filled by both cocks running together? Anf. 4 hours 48 min. 49. The paving of a square court, at 6d. a yard, cost as much Anf } The other, |