NOTES.-1. Circular Measure is used by surveyors in surveying land; by navigators in determining latitude and longitude at sea; and by astronomers in measuring the motion of the heavenly bodies, and in computing difference in time. 2. The portion of surface represented by the annexed figure is a circle. The curved line which bounds the circle is its circumference. Any portion of a circumference is an arc. 3. One half of a circumference is called a semi-circumference. '30° One fourth of a circumference is called a quadrant. One third of a quadrant is called a sign. A semi-circumference contains 180°; a quadrant, 90°; and a sign, 30°. 4. Every circumference is divided into 360 equal parts, called degrees, and, hence, the length of a degree depends upon the size of the circle. A degree of the earth's surface at the equator contains 69 statute miles, or 60 geographical miles- a minute of space being a geographical or nautical mile. 1. How many minutes in 5 degrees? 5. How many signs in of a circumference? WRITTEN EXERCISES. 6. How many seconds in 15° 30'? 7. Reduce 15° 33' to minutes. I. A.-11. 8. Reduce 5 signs to minutes. 9. Reduce 10800" to degrees. 10. The sun appears to revolve around the earth once a day: how many degrees does it appear to pass over in an hour? In 6 hours? NOTES.-1. The exact length of a solar year is 365 d. 5 h. 48 min. 48 sec., which is nearly 6 hours, or of a day, longer than the common year. Since the common year lacks of a day of the true time, an additional day is added to every fourth year, making leap year. This additional day is given to February, and hence this month in leap year contains 29 days. The leap years are exactly divisible by 4; as, 1860, 1864, 1868, 1872, etc. 2. The names and order of the calendar months and the number of days in each are as follows: 3. The following couplet will assist in remembering the months which have 30 days each: Thirty days hath September, April, June, and November. 4. In most business transactions 30 days are considered a month, and 360 days a year. 5. The year is divided into four seasons of three months each, as follows: 1. How many seconds in 5 minutes? In 10 min utes? In 20 minutes? 2. How many minutes in 4 hours? In 8 hours? 3. How many hours in 120 minutes? In 240 minutes? In 300 minutes? 4. How many hours in 3 days? In 5 days? 5. How many days in 48 hours? In 72 hours? In 240 hours? In 480 hours? 6. How many days in 6 weeks? In 8 weeks? In 10 weeks? In 15 weeks? 7. How many weeks in 35 days? In 49 days? 8. How many weeks in 5 lunar months? In 12 lunar months? 9. How many lunar months in 16 weeks? In 32 weeks? 44 weeks? 60 weeks? 10. How many calendar months in 5 years? In 7 years? 10 years? 12 years? WRITTEN EXERCISES. 11. How many seconds in 15 hours? 14. Reduce 31 d. 30 min. 45 sec. to seconds. 17. How many minutes in a leap year? 18. How many seconds in the solar year, which contains 365 d. 5 h. 48 min. 48 sec.? 19. How many seconds in a common year? 20. The age of a certain man is 64 yr. 45 d. 12 h.: how many hours has he lived, allowing 365 the year? days to 21. How many hours in the three Spring months? In the three Summer months? 22. How many minutes will there be in the month of February, 1880? In February, 1882? 23. If your pulse beat 75 times a minute, how many times will it beat in 5 weeks? 24. How many days will it take a steamship to sail 3744 miles, if it sail at the rate of 12 miles an hour? |