wants to pull down, and to build a new one that will dry three times as much at a time as the old one ; wbat must be the length of its side ? Ans. 28 feet 7 inches. 21. If a round cistern be 26'3 inches in diameter, and 52.5 inches deep, how many inches diameter must a cistern be to hold twice the quantity, the depth being the same ? Ans. 37.19 inches. 22. A may-pole, whose top was broken off by the wind, struck the ground at 15 feet distance from the bottom of the pole ; what was the height of the whole may-pole, supposing the length of the broken piece to be 39 feet? Ans. 75 feet. 23. What will the diameter of a globe be, when its solidity and superficial content are equal to each other, or rather when they are both expressed by the same number? Ans. 6. 24. How many three-inch cubes can be cut out of a 12-inch cube? Ans. 64. 29. A farmer borrowed part of a hay-rick of his neighbour, which measured 6 feet every way, and paid him back again by two equal cubical pieces, each of whose sides were three feet. Query, whether the lender was fully paid ? Ans. He was paid $ part only. 26. What will the painting a conical church spire come to at 8d. per yard ; supposing the circumference of the base to be 64 feet, and the altitude 118 feet ? Ans. 141. Os. 89d. 27. What will a marble frustum of a cone come to at 12s. per solid foct; the diameter of the greater end being 4 feet, that of the less end 14 feet, and the length of the slant side 8 feet? Ans. 301. Is. 10d. 28. The diameter of a legal Winchester bushel is 184 inches, and its depth 8 inches; what must the diameter of that bushel be whose depth is 71 inches Ans. 19:10671. 29. Three men bought a tapering piece of timber, which was the frustum of a square pyramid ; one side of the greater end was 3 feet, one side of the less I foot, and the length 18 feet; what must be the length of each man's piece, supposing they paid equally, and are to have equal shares ? Ans. first, 3.269 ; second, 4.559; and the third, 10:172 ; reckoning from the greater end to the less. 30. Supposing the ball at the top of St. Paul's Church to be 6 feet in diameter; what would the gilding come to at 3 d. per square inch ? Ans. 2371. 10s. Id. 31. A person wants a cylindric vessel of 3 feet deep, that shall hold twice as much as another of 28 inches deep, and 46 inches in diameter ; what must be the diameter of the required vessel ? Ans. 57.37 inches. 1. 32. Two porters agreed to drink off a quart of strong beer between them, at two pulls, or a draught each ; now, the first having given it a black eye, as it is called, or drank till the surface of the liquor touched the opposite edge of the bottom, gave the remaining part of it to the other; what was the difference of their shares, supposing the pot to be the frustum of a cone, the depth of which is 597 in ches, the diameter at the top 3.7 inches, and that of the bottom 4-28 inches ? Ans. 7.07 cubic inches. 33. Three persons having bought a sugar-loaf, want to divide it equally among them by sections parallel to the base; it is required to find the altitude of each person's share, supposing the loaf to be a cone, whose height is 20 inches ? Ans. 13.867 the upper part, 3.604 the middle part, and 2.528 the lower part. 34. How high above the surface of the earth must a person be raised to see a third part of its surface ? Ans. To the height of the earth's diameter. 35. A cubical foot of brass is to be drawn into a wire of 1-401h of an inch in diameter ; what will be the length of the wire, allowing no loss in the metal? Ans. 97784797 yards, or near 56 miles. 36. A bowling-green, 300 feet long, and 200 feet broad, is to be ra:sed one foot higher, by means of the earth to be dug out of a diich that goes round it; to what depth must the ditch be dug, supposing its breadth to be every where 8 feet? Ans. 7 feet 37. Of what diameter must the bore of a piece of ordnance be, which is cast for a ball of 24 lbs, weight, so that the diameter of the bore may be 1-10th of an inch more than that of the ball ? Ans. 5.757 inches. 38. If a sphere of copper, of one foot in diameter, was to be beat out into a circular plate of 1-20th of an inch thick, what would be its diameter ? Ans. 12 64 feet. 39. The perambulator, or surveying wheel, is so contrived as to turn just twice round, in the length of a pole, or 16. feet; what is its diameter ? Ans. 2.626 feet. 40. The ellipse in Grosvenor-square measures 840 links across the longest way, and 612 the shortest, within the rails : now the walls being 14 inches thick, it is required to find what ground they inclose, and what they stand upon ? Ans. They inclose 4 acres, o rood, 6 poles, and stand on 1760 square feet. 41. If a heavy sphere, whose diameter is 4 inches, be put into a conical glass, full of water, whose diameter is 5, and altitude 6 inches; it is required to find how much water will run over ? Ans. ** of a pint nearly. 42. Supposing it to have been found, by measurement, that a manof-war, with its ordnance, rigging, and appointments, displaces 50,000 cubic feet of water ; what is the weight of the vessel ? tons. 13. Supposing it were required to make a vessel of a foot deep, in the form of a frustum of a cone, that shall hold 13 ale gallons, and have its top and bottom diameters in proportion to each other, as 5 is to 3 ; what must be its dimensions ? Ans. The bottom diameter is 14:64017, and the top diameter 24:40028. Ans. 1395 56 LAND-SURVEYING Land-surveying is the art of measuring, planning, and finding the superficial content, of any field, or parcel of land. In this kind of measuring, the area or superficial content is always expressed in acres, or acres, roods, and perches; and the lengths of all lines, in the field, or parcel of land, are measured with a chain. A line, or distance on the ground, is thus measured.-Having procured ten small arrows, or iron rods, to stick in the ground at the end of each chain ; also some station-staves, or long poles with coloured fiags, to set up at the end of a station-line, or in the angles of a field ; two persons take hold of the chain, une at each end, the foremost, for the sake of distinction, is called the leader, the hindermost the follower. A station-staff is set up in the direction of the line to be measured, if there be not some object, as a tree, a house, &c. in that direction. The leader takes the ten arrows in his left hand, and one end of the chain by the ring, in his right hand, and proceeds towards the stationstaff, or other object. The follower stands at the beginning of the line, holding the other end of the chain, by the ring, till it is stretched straight, and laid, or held level, by the leader, whom he directs, by waving his hand to the right or left, till he see him exactly in a line , with the object towards which they are measuring. The leader then sticks an arrow upright in the ground, as a mark for the follower to come to, and proceeds forward another chain, at the end of which he is directed, as before, hy the follower ; or he may now, and at the end of every other chain, direct himself, by moving to the right or left, till the follower and the object measured from, be in one straight line. Having stuck down an arrow, as before, the follower takes up the arrow which the leader first stuck down. And thus they proceed till all the ten arrows are employed, or in the hands of the follower, and the leader, without an arrow, is arrived at the end of the eleventh chain length. The follower then sends or carries the ten arrows to the leader, who puts one of them down at his end of the chain, and proceeds with the other nine and the chain, as before. The arrows are thus changed from the one to the other, till the whole line is finished, if it exceed ten chains, and the number of changes sliows how many times ten chains the line contains. Thus, if the whole line measures 36 chains 45 links, or 3645 links, the arrows have been changed three times, the follower will have five arrows in his band, the leader four, and it will be forty-five links from the last arrow, to be taken up by the follower to the end of the line. |