in cubic inches, which are converted into gallons by dividing by 282 for ale, and 231 for wine gallons.--Or, 2. To the square of the head diameter, add twice that of the bung diameter, and from that sum take of the square of the difference of the said diameters: then multiply the remainder by the length of the cask: then if the product be multiplied 1,00092837=002787 by x 3, will give the area. X 3, will give the area, } or divided by {1882;16=359,05 } EXAMPLES (38) What is the content of a cask, whose bung diameter, head diameter, and length, are 32, 26, and 40 inches, withinside, respectively? (39) Suppose the bung diameter of a cask to be 40 inches, head 36, and length 64: required the contents both in ale and wine gallons. QUESTIONS for EXERCISE in MENSURATION of Solids. (1) What is the difference between a solid half foot, and half a foot solid ? (2) What is the proportion, in space, between a room 25 feet 6 inches long, 20 feet two inches broad, 14 feet high, and two others of just half the dimensions ? (3) Another room is 17 feet 7 inches long within, 13 feet 10 inches broad, and 9 feet high; it has a chimney carried up straight in the angle, the plan whereof is just the half of 54 feet, by 4 feet 2 inches. The question is, How many cubic feet of air the same will contain, allowing the content of the fire-place and windows at 4 solid yards? (4) A ship's hold is 1121 feet long, 32 broad, and 5/ deep. How many bales of goods, 3 feet 4 inches long, 2 feet 2 inches broad, and 3 feet deep, may be stowed therein, leaving a gang-way 4 feet broad? (5) I want a rectangular cistern, that, at 16 lb. to the foot square, shall weigh just a fother of lead; it must be 8 feet long, and 41 over; how many hogsheads, wine measure, will this cistern contain, taking it at * of an inch from the top? (6) A Jog of timber is 184 feet long, 18 inches broad, and : 14 inches thick, die square all through. Now, if 2 solid feet and a balf be sawed off the end, how long will the piece then be? (7) The solid content of a square stone is found to be 1261 feet, its length is 8 feet. What is the area of one end, and what the depth, if the breadth assigned be 38.4 inches. (8) The dimensions of the circular Winchester bushel are 18.1. inches over, and 8 inches deep. How many quarters of grain will a square bin hold, that measures 7 feet 10 inches long, 3. feet. 10 broad, and 4 feet 2 inches deep, within (9) Taking the dimensions of the bushel as above, what must the diameter of a circular measure be, which at 12 inches deep will hold 9 bushels of sea coal struck? (10) A prism of two equal bases, and 6 equal sides, that measures 28 inches across the centre, from corner to corner; the superficial and the solid content is required, taking the length at 134 inches, (11) I have a rolling stone 44 inches in circumference, and am to cut off three cubic feet from one end. Where. abouts must the section be made? (12) I would have a syringe, 14 inch in the bore, to hold a pint (wine measure) of any fluid. What must the length of the piston, sufficient to make an injection with it, be? (13) I would have a cubic bin made capable of receiving just 131 quarters of wheat, Winchester measure ; what will be the length of one of its sides? (14) A Bath stone, 20 inches long, 15. over, and 8 deep, weighs 220 lb. How many cubic feet thereof will freight a ship of 290 tons ? (15) The common way of measuring timber being to girt a round straight tree in the middle, and to take of the girt for the side of a square, .equal to the area of the section there; if this be not considered in the price ap pointed, pray on which side lies the advantage ? (16) The solid content of a globe 20 inches in diameter, a cylinder of the same diameter, 20 inches long, and a cone 20 inches diameter at the base, and 20 inches high, are severally required; and also what they will cost painting at 8d. per yard. (17) Our satellite, the moon, is a globe, in diameter 2170 miles. I require how many quarters of wheat' she would contain, if hollow, 21502 solid inches being the bushel; and how much yard: wide stuff would make her a waistcoat,' were she to be clothed. (18) Suppose the atmosphere, or body of the air and vapours surrounding the globe of the earth and sea, to be 60 miles above the surface, and the earth is 7970 miles in diameter: how many cubic yards of air then hang about and revolve along with this planet? (19) A square pyramid, whose sides at the base measure 10 inches a-piece, and is 20 feet high by the slope in the middle of each side of the base, is to be sold at 78. per solid foot; and if the polishing the surface of the sides will be 8d. per foot more; I would know the cost of this stone when finished. (20) A round mash-vat measures at the top 72 inches over within, at the bottom 54, the perpendicular depth be ing 42 inches; the content in ale gallons is required. (21) The shaft of a round pillar, 16 inches in diameter at the top, is about 8 of the bottom diameters in height, whereof is truly cylindrical, and the other of swelling; but we will suppose it tapers straight, and that it is less at the top than at bottom; the price of the stone and workmanship is sought, at 3s. 0d, per cubic foot; and farther, the superficial content, including both ends, (22) A stick of square timber tapers straight; the side of the greater end is 19] inches, of the less 13 inches, the length 16 feet 6 inches; the value at 28. 6d. per foot solid, is demanded, (23) What quantity of brandy will the distiller's tun contain, that measures 40 inches within at the head, 52 at the bung, and 103 inches long; and how many barrels of London ale would fill it? (24) Suppose the globe or ball, on the top of St. Paul's Church, to be o feet in diameter; what did the gilding thereof come to at 3 d. per inch square? (25) The famous tan of Heidelberg, that being heretofore annually replenished with Rhenish, had in it some wine that was many ages old before the French de. molished it in the late war, It was 31 feet in length, and 21 in diameter, and pretty nearly cylindrical. Pray how many tons of wine would the same contain? LXXVII. SPECIFIC GRAVITY OF METALS. THE specific gravity of a body is the relation that the weight of a body of orre kind hath to the weight of an equal magnitude of a body of another kind; the knowledge of which is of great use in computing the weights of such bodies as are too unwieldy to have their weight discovered by other means. The following TABLE shows the specifie gravity, to rain water, of metals, and other bodies; and the weight of a cubic inch of each, in parts of a pound avoirdupois, and ounces troyand parts of an ounce. in Sp. Grav. | wt. Ib. Avoir. | wt. Oz. Troy. BODIES. Fine gold 19,640 0,7103587 10,459273 BODIES. Sp. Grav. wt. Ib. Avoir. wt, oz. Troy: Alabaster of brandy S 1,883 1,832 1,800 1,712 1,327 -1,255 1,150 1,063 1,030 1,033 1,000 0,993 0,995 0,932 0,0683061 0,0662606 0,0651042 0,0619213 0,0479962 0,0153921 0,0515943 0,0384475 0,0372530 0,0372530 0,0361690 0,0359158 0,0359881 0,0337095 0,0335503 0,0330946 0,0330222 0,0308883 0,0289352 0,0270182 0,0237630 0,0221715 0,0205801 0,0186805 0,0000434 0,988456 0,958489 0,949424 0.902498 0,699986 0,661959 0,606759 0,560691 0,543282 0,543742 0,527458 0,523766 0,524820 0,491591 0,489268 0,489008 0,481569 0,450 149 0,421966 0,394011 0,346539 0,323332 0,300123 0,126590 0,000633 0,927 0,800 0,747 0,657 0,613 0,569 0,240 0,0012 Case I. The linear dimensions, or solidity of any body being given, to find its weight. RULE. Multiply the cubic inches contained in that body by the tabular weight corresponding; the product will give the weight, in pounds avoirdupois, or ounces troy. EXAMPLES. (1) What is the weight of a piece of oak of a rectangular form, whose solidity is 12096' cubic inches? |