PART III. DENOMINATE NUMBERS. Linear Measure. NOTE.-Pupils who have mastered the Elementary Book and the preceding pages of this book have had much practice in the use of denominate numbers. In part to provide for ready reference and in part to give further application of the principles already presented, the subject is here treated as a whole. 331. The English and United States standard unit of length is the Imperial yard arbitrarily fixed by Act of Parliament and afterward adopted in the United States. It is about 399999 of the length of a pendulum that vibrates once a second at the level of the sea in the latitude of . London. It is 3600 of a meter. 391393 3937 1 fathom (used in measuring the depth of the sea) 1 knot (used in navigation) 1 league (used in navigation) 1 hand (used in measuring the heights of horses) 1 chain (used by civil engineers) 1 chain (used by land surveyors) 1 pace (used in measuring approximately) 1 barleycorn (used in grading length of shoes) 1 furlong (a term nearly obsolete) = 6 feet. = 1.15+ miles. = 3 knots. = 4 inches. = 100 feet. Denominate Numbers Linear Measure. EXERCISE. 1. Mont Blanc is 15810 feet, or about 2. Mt. Everest is 29000 feet, or about 3. Commodore Dewey opened fire on the distance of 5000 yards, or about or miles. miles high. miles high. enemy at a 4. My horse, measured over the front feet, is 161 hands, 5. The vessel seemed to be about three leagues, or miles distant. 6. On sounding, they found the depth of the water to be 15 fathoms, or feet. 7. The cruiser made 20 knots, or about hour. 8. The length of the lot was 36 paces, or about miles, an rods. 1. A seven-foot drive wheel of a locomotive makes how many revolutions to the mile? 2. Which is the longest distance, 5 miles 319 rods 16 feet 6 inches, 5 miles 319 rods 5 yards 1 foot 6 inches, or 6 miles? 3. Reduce 40 rd. 4 ft. 5 in. to inches. Denominate Numbers-Surface Measure. 332. The standard unit of surface measure is a square yard which is the equivalent of a 1-yard square. This unit, like the square foot, square inch, square rod, and square mile, is derived from the corresponding unit of linear measure. TABLE. 144 square inches (sq. in.) = 1 square foot (sq. ft.). 1. Show by a drawing that there are 144 square inches in a 1-foot square. 2. Show by a drawing that there are 9 square feet in a 1-yard square. 3. Show by a drawing that there are 304 square yards in a 1-rod square. 4. Estimate the number of square yards of blackboard in the room; the number of square feet of blackboard. 5. Estimate the number of square feet in the floor of the schoolroom; the number of square yards. 6. Estimate the square yards of plastering on the walls of the schoolroom. 7. Estimate the number of square rods in the schoolhouse lot. Is the lot more or less than of an acre? Denominate Numbers-Surface Measure. 333. In the measurement of land it is more convenient to use a decimal scale; hence the invention of the Gunter Chain. This chain is 4 rods long and is divided into 100 links. Observe that links are hundredths of chains. Observe that square chains are tenths of acres. 1. Land, 3 chains by 4 chains contains 2. Land, 5 chains by 4 chains contains 3. Land, 3 chains by 8 chains contains 4. Land, 5 chains by 7 chains contains 5. Land, 8 chains by 6 chains contains 6. Two chains 35 links equals acres. acres. acres. acres. acres. chains. 12. Make a rule and find the number of acres in each of the following: (1) Land, 12 chains 35 links by 9 chains 50 links. (2) Land, 21 chains 8 links by 12 chains 30 links. (3) Land, 32 chains 25 links by 15 chains 6 links. (a) Find the sum of the area of the ten pieces of land described on this page. TO THE TEACHER.—A rod is exactly 25 links. A foot is about 1 links. Hence rods and feet can be easily changed to chains and links by regarding each 4 rods as 1 chain and each additional rod as 25 links and each additional foot as 1 links. The error in any one measurement never exceeds 2 inches. 9 rd. 12 ft. : (25+18) links. = 2 chains 43 Denominate Numbers-Surface Measure. 334. To determine the amount of carpet necessary for a given room several minor problems must be solved which can be best studied by means of an EXAMPLE. 1. How many yards of carpet must be purchased for a room 16 ft. by 20 ft. if the carpet is 1 yd. wide? (1) How many breadths will be necessary if the carpet is put down lengthwise of the room? How much must be cut off or turned under from one breadth in this case? (2) How many breadths will be necessary if the carpet is put down crosswise of the room? How much must be cut off or turned under from one breadth in this case? (3) Make two diagrams of the room on a scale of 1 inch to the foot and show the breadths of carpet in each case. (4) How many yards must be purchased in each case? (5) If in the first case there is no waste in matching the figure and in the second case there is a waste of 8 inches on each breadth except the first, which plan of putting down the carpet will require the greater number of yards? (6) If the carpet costs 90¢ a yard and the conditions are as stated in No. 5, what is the cost of the carpet in each case? 2. How many yards of carpet must be purchased for a room 16 ft. by 20 ft. if the carpet is of a yard wide and there is no waste in matching the figure? 3. How many yards of carpet must be purchased for a room that is 15 ft. 6 in. by 16 ft. 4 in. if the carpet is of a yard wide, is put down lengthwise of the room, and there is no waste in matching the figure? |