fhare. At what distance from the centre muft the line be struck, the diameter being 40 inches? Anf. 4 inches, or A will cut off 15 of the diameter. 27. A leaden pipe of 4 inches bore weighs 20 lb. averdupois per foot in length;-required the thickness, the fpecific gravity of lead being 11325. Auf..3014 inches. 28. If fimilar folids be to one another in the triplicate ratio of their homologous fides, and the weight of an iron ball of 4 inches diameter be 9 lb.-required the weight of a ball of 6 inches diameter. Anf. 32.025 lb. 29. If water iffue through an orifice with the fame velocity that a heavy body would acquire in falling freely from the furface of the water to the level of the orifice; and fupposing a ship 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. Suppofing three wheels, A, B, and C, fo combined that three revolutions of A will drive B five times round, and feven revolutions of B will drive C nine times round, it is required to find the least number of teeth neceffary to regulate the above motion. Anf. A 15, B9, and C 7 teeth. 31. Upon the fame fuppofition, 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 ftrikes feconds; how many miles would fhe run upon edge at the fame rate in feven days? Anf. 1799 miles 2 f. 93 p. 33. The fame conditions being given, in what time would fhe go found the terraqueous globe, its diameter being 7958 miles? Anf. 97 days 6 hours 20 min 48 fec. 34. Suppofing 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 furface furface an orifice of a fquare yard ought to be, to discharge an equal quantity. Anf. 3249 feet. 35. The times in which pendulums vibrate are as the square root of their lengths; and if a pendulum of 39.128 inches vibrate feconds, how many fwings will a pendulum of 156.512 inches take in an hour? Anf. 30. 36. Required the length of a pendulum that vibrates half seconds. Anf. 9.782 inches. 37. My plumber has fold me 600 yards leaden pipes, of 4 inches bore and thick, at 16s. per cwt. at the fame time he purchased a garden in the form of a rightangled triangle, of fuch dimensions that the difference between the hypothenuse and the fum of the two other fides was 50 yards. I, being a gardener, have undertaken to make a circular fish-pond in the garden to touch the three fides, at 6d. per folid yard, and find, upon the balance, 731. 13s. 9d. 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. 60 ells 39. If a pipe of 4 inches diameter is fufficient to supply a town with water, required the diameter of a pipe, fimilarly fituated with the former, that fhall ferve, after the town is encreased by one half. Anf. 4.899 inches. 40. The fame town, after being so encreased, to fave expences, intends to be fupplied from the old pipe; at what depth in the reservoir muft it be placed, it being formerly 4 feet deep? Anf. 9 feet. 41. Given the two fides of an acute angled triangle 40 and 60 poles; required the included angle, and the third fide, 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 ftrong beer between them, at a draught each. Now the first having drank till the furface of the liquor touched the oppofite 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 fhares, fuppofing the pot was the fruftum 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 feconds of time elapfed before the found from the bottom was heard. It is required to find the depth of the pit. Anf. 1273 feet. 44. If a heavy sphere, whofe diameter is 4 inches, be put into a conical glafs full of water, whofe 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 fide measured 500 feet, the other 433 feet; required the expence of levelling it, one part with another, at 3d. per cubic yard. Anf. 2712l. 10s. 3 d. 46. The fame bowling-green being levelled, required the expence of drefling it at d. per square foot. Anf. 102. 175. 2 d. 47. An old mathematician bought a field in the form of a parabola, the length of the bafe or ordinate being 3000 links, and of the axis or abfciffa 2500. He built a fummer-house 9 chain-lengths diftant from the ordinate, and 2 chain-lengths from the abfciffa; and ordered by his will, that the field fhould be divided between his two fons, by the leaft line that could be drawn through the fummer-house, terminating both ways by the parabolic curve; required how much land each of the fons fhall have. The one will have 25 ac. 2 r. 16 falls. 24 ac. I r. 24 falls. 48. If a ciftern 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? An. 4 hours 48 min. 49. The paving of a fquare court, at 6d. a yard, cost as Anf.The other, much much as the inclosing at 5s. a yard; required its extent. Anf. 40 yards. 50. An army being drawn up in a fquare, there were 79 0ver; but in attempting to enlarge each fide of the fquare by one man, there was a deficiency of 80; required the number. of men. Anf. 6241 men. 51. An oblong pond was furrounded by a terrace-walk 7 yards broad; the pond measured 1500 fquare yards, and the walk 3696 fquare yards; required the length and breadth of the pond. Anf. 100 by 150 feet. 42. A gardener and his fervant being at work, each digs a fquare piece of ground, whofe fide is as many feet long as the labourer is years old. The gardener digged four times the quantity the fervant digged. The fum of their ages was 45 years. Required their ages, and the quantity dug by each. The lad's age is 15-the gardener's 30 years. Anf. {The lad dug 225 {quare feet-the gardener 900. 53. A rectangular plantation of 360 acres, contains 435600 trees; required the diftance of the trees. Anf. 6 feet. 54. How many trees can be planted in the fame area, at the diftance of 12 feet? Anf. 108900. 55. The fanctuary at Butis in Egypt is formed of one stone, in the form of a cube of 60 feet, open at the top, and hollowed fo as to leave the ftone 6 feet thick; required the weight, at the rate of 2520 averdupois ounces per cubic foot. Anf. 6439 tons. 56. Two neighbouring gentlemen, A and B, had a circular piece ground, containing 785 acres 1 rood 24 poles, whereof A has two-thirds and B the reft. They agreed with a mason to build a mutual wall on the march at a guinea per yard, and that each fhould pay the expence in proportion to his share of the ground. It is required to find the mason's charge against A pays 1484.49841. B pays 742.25921. each of the genticmen. Anf. { 37. A circular pond occupies half an English acre; required the perimeter of a fquare circumfcribed about the pond. Anf. 1009 links. 58. Three farmers, A, B, and C, had each an inclosure. B's inclosure contains 100 English acres. A's inclofure, and that of B's, are together 1 times as large as that of C's; and B's and C's are together 3 times as large as that of A's ;-required the extent of A's and C's Anf. A had 60 acres and C 120. 59. Suppofing A's inclosure, as in last question, to be in the form of a rhombus, and one of its acute angles 30°, required the expence of inclofing it with a wall 6 feet high, 14 feet thick, at 5 guineas per rood, ftandard measure. Anf. 423 391 guineas. 6c. The pit wheel of a meal-mill contains 60 cogs, and makes 16 revolutions in a minute. It drives a trundle of 8 teeth. How many revolutions will the ftone make per minute? Anf. 120 revolutions. 61. The advantage gained by water-falls of different heights is as the fquare root of the heights. Now, fuppofing a fall of 4 feet fufficient to overcome 10 cwt. 3 qr. 7 lb. of friction, what friction will the fame quantity of water overcome from a fall of 16 feet? Anf. 1 ton 1 cwt. 2 qrs. 14 lb. 62. A wright engaged to build a common corn-mill under the following restrictions. The ftone must revolve 75 times per minute; the trundles to have 8 rungs, the driver 80 cogs, and the fall 16 feet high. Required the diameter of the waterwheel to produce the greateft effect poffible, Anf. 13 feet 6 inches 11 pts. 8". Note. The greatest effect is obtained when the float-boards move with one-third the velocity of the impinging fluid. 63. A tapering round tree 10 feet long, whofe diameter at the greater end is 3 feet, at the lefs 2 feet, being hurled down a regular declivity defcribes a fegment of a circle. How far diftant |