To find the weight of a body when its cubic content, or its volume, is given : Multiply its cubic content, in feet, by the specific gravity of the body, (disregarding the decimal point,) and the result will be its weight in avoirdupois ounces. EXAMPLES. 1. A cube of fine gold is two inches on a side; required its weight. Ans. 5 pounds 9.815 oz. avoirdupois. 2. A block of red Egyptian granite is 10 feet long, and its breadth and thickness each 20 inches; required its weight. Ans. 4607.5 pounds. 3. One of the stones in the walls of Baalbec was a square prism, 12 feet on a side and 63 feet long; required its weight, its specific gravity being 2.700. Ans. 683.44 tons. 4. What is the weight of a cylinder of cast brass, 7 feet in length and 7 inches in diameter ? Ans. 914.82 pounds. 5. Find the weight of a log of oak, 24 feet long, 3 broad, and 1 thick, the specific gravity being .925. Ans. 37 cwt. 18 lbs. 8 ounces. 6. How many fir-planks, 16 feet long, 9 inches broad, and 6 inches thick, will a ship of 400 tons burden carry ? Ans. 434433. To find the gauge point for the weight of any body :As the specific gravity of the body (disregarding the decimal point) is to 1728, so is the number of ounces in the required number of pounds (as 1 or 100 pounds) to the number of cubic inches required to weigh that number of pounds; then, (having found said number of inches,) extract the square root for the gauge point, when the length of the body is taken in inches; but if the length be taken in feet, extract the square root of onetwelfth of said number of inches for the gauge point. What is the gauge point for red Egyptian granite, when the length in feet is placed over the gauge point, to find the number of hundreds of pounds it will weigh? Ans. 9.317 on D. Solution. As 2654: 1728:: 1600 to the number of cubic inches required to weigh 100 pounds, viz. 1041.74, onetwelfth of which is 86.811, the square root of which is 9.317, the required gauge point. To find the gauge point for the weight of any solid in the cylindric form : Find the number of cubic inches required to weigh 1 or 100 pounds, as directed above; which number divide by.7854, and extract the square root of the quotient for the gauge point when the length is taken in inches, and the square root of one-twelfth of the said quotient when the length is taken in feet. What is the gauge point for a cylinder of cast brass, to find its weight in hundreds of pounds, the length in feet being placed over the gauge point? Ans. 6.12. The gauge point for a millstone is 10.878; for a grindstone 12.82; for a marble cylinder 10.44; for square marble blocks 9.25; for an octagonal prism of marble 4.21; for square iron bars 5.474; for square cast iron bars 5.59; for a wrought iron cylinder 6.20; for a cast iron cylinder 6.29; for a cast iron ball, the diameter in inches being placed over the gauge point, 2.667; for a leaden ball 2.16; for a square block of oak 15.78; for an elm log 20.917; for a cask of beer 15.318; for a cask of butter 6.1; for a cheese 5.78; for a body of well pressed hay 57.37; for a square ash stick 16.16; for a round ash log 18.69; for a square maple stick 17.47; for a round maple log 19.72; for a square stick of lignum-vitæ 13.22; for a round stick or log of lignum-vitæ 14.80; for a square walnut stick 18.6; for a round walnut log 20.91; for a square beech stick 18.82; for a round beech log 21.29; for fir when square 20.5; for a round log of fir 23.1; for apple-tree when square 17.04; for a round log of apple-tree 19.2; for water in a square form or prism, placing the depth in inches over the gauge point, 5.258; for water in a cylinder 5.93; for cider in a cask 5.88; for spermaceti oil in a cask 6.11; for mercury in a square prism 1.428; for mercury in a cylinder 1.610; for whale's oil in a cask 6.176; for loaf-sugar in a square form 4.131; for loaf-sugar when round 4.66; for proof spirit in a cask 6.18. Let the student perform the following examples with the sliding rule. 7. What are the weights of the following blocks of granite, the length of each being three feet, and one being 12 inches square, one 10 inches, one 7, one 6, one 4, one 31, one 2, and one 1 inch square? Place the length, 3 feet, found on C, over 9.317 on D, and over 12 found on D, will be found 500 pounds on C; over 10, 346 pounds; over 7, 170 pounds; over 6, 124.5; over 4, 55.5; over 34, 42.2; over 2, 13.75, and over 1, 3.46 pounds. 8. What are the weights of the following grindstones, the thickness of each being 5 inches, and the diameters 14, 18, 20, 30, 25, and 40 inches? Answers in order, -59.4; 98; 121.3;272; 190, and 486 pounds. A grindstone one inch thick and 12.82 inches in diameter, weighs 10 pounds; therefore, place the thickness in inches over 12.82 on D, calling the thickness so many tens, and over the diameter found on D, will be found the weight on C. 9. What is the weight of a ball of lead whose diameter is 4 Ans. 13.714 lbs. inches? 10. What is the weight of a cylinder of marble whose Ans. 330 lbs. length is 10 feet and diameter 6 inches? 11. What is the weight of an octagonal prism of marble, the side being 3 inches and its length 5 feet? Ans. 252.5 lbs. 12. What is the weight of a cast iron cylinder, its length being 6 feet, and its diameter 2 inches? Ans. 60.6 lbs. 13. What is the weight of a ball of iron 4 inches in diameter? Ans. 9 lbs. The solidities of balls being as the cubes of their diameters, the number of pounds in an iron ball may be found by multiplying the cube of its diameter by 9, and dividing the product by 64; and for a leaden ball multiply the cube of the diameter by 2, and divide the product by 9. 14. What is the weight of an iron ball whose diameter is 9 inches? Ans. 102.5 lbs. 15. What is the weight of an oak stick of timber, its length being 10 feet, and its ends 30 inches square? Ans. 3600 lbs. 16. What is the weight of an elm log, its length being 30 feet, and diameter 13 inches ? Ans. 1160 lbs. 17. What is the weight of a barrel of beer, its length being Ans. 614 lbs. 2 feet, and mean diameter 24 inches ? The gauge points for beer, water, and cider, in a cylinder, the length in inches being placed over the guage, are, for beer 5.31, for water 5.93, and for cider 5.88. 18. What is the weight of a mow of well-pressed hay, 6 feet square and 10 feet deep? Ans. 1575 lbs. 19. What is the weight of a mow of hay 6 feet deep and 200 inches square? Ans. 4325 lbs. To find the cubic contents of a body, its weight being given : Divide the weight of the body in ounces by its specific gravity, (disregarding the decimal point,) and the quotient will be its cubic contents in feet. EXAMPLES. Ans. 63.036. 1. How many cubic feet in a ton of fir? 2. What is the side of a cube of fine gold, its weight being one ounce avoirdupois? Ans. 0.44659 of an inch. 3. What is the diameter of a sphere of platinum, its weight being 1 pound ? Ans. 1.3492 inches. 4. Find the number of cubic feet in a ton of dry oak. Ans. 38.75 feet. To find the quantity of either of the ingrédients in a compound consisting of two ingredients, when the specific gravities of the compound and of the ingredients are given : Multiply each of the three specific gravities by the difference between the other two; then, as the greatest product is to each of the other products, so is the weight of the compound to the weight of each of the ingredients. EXAMPLES. 1. A composition weighing 56 lbs., and having a specific gravity of 8.784, consists of tin and copper of the specific gravities 7.320 and 9.000 respectively; what are the quantities of the ingredients ? Ans. 50 lbs. of copper and 6 lbs. of tin. One statement will be all that is required; for, having found one of the ingredients, if we deduct it from their sum, or the compound, the remainder will be the other. |