TIME. 108. TIME is used in measuring duration. The natural divisions of time are days, months (moons), seasons, and years. The artificial divisions are seconds, minutes, hours, weeks, etc. 13 Months, 1 Day, and 6 Hours" 12 Calendar Months (= 365 or 366 Days), 1 Civil Year, 1 Julian Year, J. yr. c. yr. 100 Years make 1 Century, C. 1. m. 1 J. yr. = 4 = 28 = 1 = 131f2 = 5238 = 672 = 40320 2419200 3651 8766 52596031557600 NOTE 1. The twelve calendar months have the following number of days: January (Jan.) has 31 days; February (Feb.), 28 (in leap year, 29); March (Mar.), 31; April (Apr.), 30; May, 31; June, 30; July, 31: August (Aug.), 31; September (Sept.), 30; October (Oct.), 31; November (Nov.), 30; December (Dec.), 31. NOTE 2. The number of days in each month may be easily remembered by committing the following lines: "Thirty days hath September, April, June, and November; NOTE 3. A solar year, i. e. a year by the sun, is very nearly 365 days, 5 hours, 48 minutes, and 50 seconds. 108. For what is time used? What are its natural divisions? Artificial divisions? Table? Scale? What are the names of the calendar months? How many days in each? Length of a solar year? 3. Reduce 1 wk. 4 d. 16 h. 8 m. to minutes. Ans. 16808 m 4. Reduce 376487 seconds to higher denominations. 5. Reduce 365 d. 5 h. 48 m. 50 sec. to seconds. 6. In 342698 minutes how many days, hours, etc.? 7. In 5 C. 56 yr. 8 m. how many calendar months? 8. Reduce 37846 calendar months to centuries, years, etc. 9. Reduce 2419199 seconds to weeks, days, etc. 10. Reduce 34 d. 20 h. 40 m. 50 sec. to seconds. CIRCULAR MEASURE. 109. CIRCULAR MEASURE is used in surveying, navigation, geography, astronomy, etc., for measuring angles, determining latitude, longitude, etc. 109. For what is Circular Measure used? Table? Scale? Д B NOTE. A Circle is a figure bounded by a curved line, all parts of the curve being equally distant from the center of the circle. The Circumference is the curve which bounds the circle. An Arc is any portion of the circumference, as A B or B D. An arc equal to a quarter of the circumference, or 90°, is called a quadrant. A Radius is a line drawn from the center to the circumference, as CA or C B. A Diameter is a line drawn through the center and limited by the curve, as A D. Ex. 1. How many seconds in 5 s. 25° 48' 54"? OPERATION. 5 s. 25° 48' 54". 30 175° 60 10548' 60 632934", Ans. Ex. 2. Reduce 632934" to higher denominations. OPERATION. 60)632934" 60)10548'54" 3. Reduce 9 s. 20° 55' 47" to seconds. Ans. 5 s. 25° 48' 54". Ans. 1047347". 4. In 7484925" how many circumferences, signs, etc.? 5. In 3 quadrants, 10° 8' 5" how many seconds? 6. Reduce 984627" to quadrants, degrees, etc. 110. MISCELLANEOUS TABLE. This table embraces a few terms in common use, and may be indefinitely extended. 109. What is a Circle? Circumference? Arc? Quadrant? Radius? Diameter? Ex. 1. How many dozen bottles, each bottle holding 1 qt. 1 pt. 3 gi., will be sufficient to bottle 61 gal. 3 qt. 1 pt. of wine? 2. How many sheets of paper in 3 reams, 18 quires, and 23 sheets? MISCELLANEOUS EXAMPLES IN REDUCTION. 1. Reduce 27 £. 14s. 6 d. 3 qr. to farthings. 2. Reduce 18 bush. 3 pk. 7 qt. 1 pt. to pints. 3. Reduce 7 t. 14 cwt. 2 qr. 12 lb. 8 oz. 6 dr. to drams. 4. How many tons, etc., in 574692 ounces ? 5. Reduce 1577048 seconds to minutes, hours, etc. 6. Reduce 24838 grains to scruples, drams, etc. 7. Reduce 2 circ. 4 s. 20° 25′ 30′′ to seconds. 8. Reduce 3 m. 5 fur. 7 ch. 2 rd. 20 li. to links. 9. Reduce 14 lb. 7 oz. 15 dwt. 23 gr. to grains. 10. Reduce 6. 4 3. 3 3. 19. 6 gr. to grains. 11. Reduce 2548 square inches to higher denominations. 12. Reduce 411 nails to quarters and yards. 13. Reduce 7432 farthings to pence, etc. 14. Reduce 18469874 drams, Avoirdupois, to ounces, etc. 15. Reduce 54896 grains to pennyweights, etc. 16. Reduce 4 sq. m. 25 a. 3 r. 34 sq. rd. to square rods. 17. Reduce 8 c. yd. 1727 c. in. to cubic inches. 18. Reduce 4 sq. yd. to square inches. 19. Reduce 4 gal. 1 pt. to gills. 20. Reduce 2 wk. 6 d. 8 h. 16 sec. to seconds. 21. Reduce 4 m. 7 fur. 39 rd. to rods. 22. Reduce 3795 rods to furlongs, etc. 23. Reduce 17 yd. 2 qr. 3 na. to nails. 24. Reduce 10881 links to miles, furlongs, etc. 29. Reduce 310556 square rods to roods, acres, and miles. NOTE. This subject will receive further attention in the articles or: Fractions. DEFINITIONS AND GENERAL PRINCIPLES. 111. All numbers are even or odd. An EVEN NUMBER is a number that is divisible by 2 without remainder (Art. 74); as 2, 4, 8, 12. An ODD NUMBER is a number that is not divisible by 2 without remainder; as 1, 3, 5, 11, 19. 112. All numbers are prime or composite. A PRIME NUMBER is a number that is divisible by no whole number without remainder except itself and one; as 1, 2, 3, 5, 7, 11, 19. NOTE 1. Two is the only even prime number, for all even numbers are divisible by 2. NOTE 2. Two numbers are mutually prime (i. e. prime to each other) when no whole number but one will divide each of them without remainder; thus, 8 and 9 are mutually prime, although neither 8 nor 9 is absolutely prime. A COMPOSITE NUMBER is a number (Art. 61) that is divisible by other numbers besides itself and one; thus, 6 is composite, because it is divisible by 2 and by 3; 12 is composite, because it is divisible by 2, 3, 4, and 6; 25 is composite, because it is divisible by 5 and 5. NOTE 3. A composite number that is composed of any number of EQUAL factors is called a power, and the equal factors are called the roots of the power; thus, 9, which equals 3 X 3 is the second power or square of 3, and 3 is the second or square root of 9; 64, which equals 4 × 4 × 4, is the third power or cube of 4, and 4 is the third or cube root of 64. NOTE 4. The power of a number is usually indicated by a figure, called an index or exponent, placed at the right and a little above the number; thus, the second power or square of 4 is written 42, which equals 4 X 4 = 16; the third power or cube of 4 is 43, which equals 4 × 4×4=64. NOTE 5. A root may be indicated by the radical sign, ✅; thus, ✅9 indicates the second or square root of 9, which is 3. So 3/8 indicates the third or cube root of 8, which is 2. The square root of a number is one of its two equal factors; the cube root is one of the three equal factors of the number. NOTE 6. Every number is both the first power and the first root of itself. 111. What is an Even Number? An Odd Number? 112. A Prime Number? What is the only even prime number? When are numbers mutually prize? What is a Composite Number? A power? A root? How is a power indicated? A root? A number is what power of itself? What root? |