(b.) The calendar year is divided as follows. ❝ C. 1 century, Season. Months. No. of Days. Abbreviations. (c.) Nores.—1. The exact length of the solar year is 365 days 5 h. 48 min. 49 sec.; but, for convenience, it is reckoned 11 min. 11 sec. more than this, or 365 da. 6 h.=365 days. This day in four years makes day, which every fourth year, (called Bissextile or leap year,) is added to the shortest month, giving it 29 days. The numbers denoting leap years are exactly diyisible by 4; as, 1856, 1860, 1864; except years whose number can be divided without a remainder by 100, but not by 400. 2. The pupil should carefully commit to memory the names of the months in their order, and the number of days in each. He should associate the name of each month with the number of days it contains, independently, rather than rely on the common rhyme to assist the memory. Many persons through their whole lives are obliged to repeat, “Thirty days hath September," &c., whenever they wish to recall the number of days in any particular month, 3. In most business transactions 30 days are called a month and 52 weeks a year. era 4. The centuries are numbered from the commencement of the Christian ; the months from the commencement of the year; the days from the commencement of the month; and the hours from the commencement of the day (12 o'clock midnight), and from mid-day or noon. A. M. denotes time before noon, M., at noon, and P. M., after noon. Thus, 9 o'clock A. M., May 23, 1860, is the end of the ninth hour of the 23d day of the fifth month of the 60th year of the 18th century. LESSON XLIII. PROB. How may seconds in 12 yr. 11 mo. 22 da. 12 h. 51 min. 3 sec. ? 349. How many years in 40783064 seconds? LESSON XLIV. 356. How long will it take to walk 3 mi. 7 fur. 30 rd. 8 ft., if it takes 1 second to walk 6 ft.? 357. How long will it take a cannon ball to fly 5 miles, if it flies at the uniform rate of 1500 feet per second? 358. How long will it take a cannon ball to fly 4 mi. 7 fur. 36 rd., if the uniform rate is 1500 feet per second? 359. How long will it take a railroad car to run 138 miles, if it runs 3 rods per second ? 360. How long will it take a railroad car to run 397 miles 14 fur. 29 rd., if it runs 2 rods per second? 361. How long will it take a fox to run 39 miles, if he runs 22 feet each second? LESSON XLV. CIRCULAR OR ANGULAR MEASURE. 100. This Measure is used to measure angles or the REVIEW.-What is an analysis? (27.) What is an analytical step? (28.) What is the order of solving problems? (29.) What is the rule for addition? (29., e.) What is the proof? (29., f.) Define subtraction. (31.) What is the minuend? (32.) What is the subtrahend? (33.). What is the remainder? (34.) What is the difference in subtraction? (35.) What is the sign of subtraction? (36.) What are the axioms in subtraction? (37.) What is the rule for subtraction? (88., d.) How may subtraction be proved? (33., e.) What does the parenthesis show? Define multiplication. (41.) Multiplicand. (42.) Multiplier. (43.) Product. (44.) Which are factors? (45.) What is the sign of multiplication? (46.) What are the axioms? (47.) Recite the rule. (49., d.) State the method of proof. (49., e.) arcs of circles. It is used in astronomy, geography, navigation, and surveying, and for calculating differences of time. D 71 right angle, UMFERE 15/30° C R QUADRANT RIGHT ANGLE DIAMETER or circle. (b.) NOTES.-1. The greatest distance across a circle is called its diameter. The distance around it is called its circumference. Any part of the circumference is called an arc. 2. If any circumference, whether large or small, be divided into 360 equal arcs, each arc is called a degree. The degree is divided into 60 minutes, and the minute into 60 seconds. The length of a degree, minute, or second, depends on the size of the circle. If the size of the circle is increased or decreased, the length of the degree, minute, or second is also increased or decreased. 3. The greatest circumference of the earth's surface is about 24,930 miles; 1° of that circumference is one 360th of 24,930 miles, which is 694 miles. 4. A geographical or nautical mile is equal to 1' of the earth's greatest circumference, which is found to be a little more than 1 statute mile and 49 rods. 5. Latitude is measured north or south from the equator on any meridian, and is expressed in degrees, minutes, and seconds; thus, 43° 17′ 31′′ north lat. denotes a position 43° 17′ 31" north from the equator. 6. Longitude is measured east or west from any given meridian, Washington being generally used in the United States, Greenwich in England, and Paris in France; thus, 43° 17′ 13′′ east long. from Greenwich denotes a position 43° 17′ 13" east from the meridian which passes through Greenwich. 7. The linear extent of a degree of longitude depends upon the latitude, and diminishes as the latitude increases; thus, at latitude 10° its extent is 359640 feet; at lat. 40° it is 280106 feet; and at lat. 80° it is only 63612 feet. 8. Since the sun apparently goes around the earth once in 24 hours, in 1 hour it must pass over one 24th of 360°, which is 15°; hence, if in the sun's apparent motion 15° of long. require 1 hour, or 60 minutes of time, one deg will require one 15th of 60 minutes, which is 4 minutes. Since 1° or 60' long. requires 4 min., or 240 sec. of time, 1' long will re quire one 60th of 240 sec., which is 4 sec.; therefore, 15° long. require 1 hour of time; 1° long. requires 4 minutes of time; 1' long. requires 4 seconds of time. 362. How many signs in 878374'? 363. How many minutes in 48° 38'? 364. How many minutes of time does the sun require to pass over 3483° of longitude? 365. How many circles in 41837° ? 366. How many seconds in 12 cir. 12′ 14′′? 367. How many degrees in 4187834" ? 368. How much time will the sun require to pass over 13° 4' of longitude? |