Since there are 360 degrees in every circumference, a degree of arc is always 30 of a complete circumference, regardless of the size of the circle. As a circumference may be an inch, a foot, a yard, a mile, or 25,000 miles in length, one degree of arc will represent as many different distances as there are different circumferences, because the number of inches, yards, etc., in a degree varies with the size of the circle, but the number of degrees in every circumference always is 360 regardless of the size of the circle. Remember that a circumference 1 inch in length contains just as many degrees as one 25,000 miles in length. For making the more accurate measurements in surveying and astronomy each degree is divided into 60 equal parts called minutes, and each minute is divided into 60 equal parts called seconds. Exercise 4-Oral. 1. Draw a circle. How many degrees are there in your circle? 2. If each one in the class draws a circle, does each circle contain 360°? 3. Does the size of the circle make any difference? 4. How many degrees are there in of a circle? In of 1? 5. One degree is what part of a circumference? 6. If the circumference is 25,000 miles, 1° of that is found how? 7. If the circumference is 9 inches, how do you find the length of 1°? The "horizon" is the line where the sky and earth seem to meet. 8. How many degrees of arc are there in the entire horizon? 9. How many degrees of arc are there in the horizon between points exactly east and exactly west? How many degrees between points exactly north and exactly south? 10. Point with your arm toward the eastern horizon. What is the position of your arm while pointing? The point directly overhead is called the "zenith." 11. How many degrees of arc are there between any point on the horizon and the zenith? 12. From horizon to horizon through the zenith is how many degrees? Does the direction of such an arc make any difference? 13. Point with your arm toward the zenith. What is the position of your arm while it is pointing toward the zenith? 14. How many degrees are there between the hands of the clock when it is 3 o'clock? 15. If a star is 30° from the zenith on an arc toward the southern horizon, how many degrees is it from the southern horizon? Point with your arm in the direction where such a star would be. What is the position of your arm while it is pointing toward this star? Exercise 5-Written. 1. How many degrees of arc are there in ference? How many minutes of arc? many seconds of arc? 2. Reduce 35,745" to °'". 3. 28.800 MILES circum How Circumference = 28,800 miles; 1° = ? For making the more accurate measurements in surveying and astronomy each degree is divided into 60 equal parts called minutes, and each minute is divided into 60 equal parts called seconds. Exercise 4-Oral. 1. Draw a circle. How many degrees are there in your circle? 2. If each one in the class draws a circle, does each circle contain 360°? 3. Does the size of the circle make any difference? 4. How many degrees are there in of a circle? In of ? 5. One degree is what part of a circumference? 6. If the circumference is 25,000 miles, 1° of that is found how? 7. If the circumference is 9 inches, how do you find the length of 1°? The "horizon" is the line where the sky and earth seem to meet. 8. How many degrees of arc are there in the entire horizon? 9. How many degrees of arc are there in the horizon between points exactly east and exactly west? How many degrees between points exactly north and exactly south? 10. Point with your arm toward the eastern horizon. What is the position of your arm while pointing? The point directly overhead is called the "zenith.' 11. How many degrees of arc are there between any point on the horizon and the zenith? 180° east or west of Greenwich, since, if it were 190° east it would be only 170° west and it would be so called. There are other imaginary lines running parallel to the equator to show distances north and south of the equator, and these are called "parallels of latitude.” All places on the same meridian have the same longitude; all places on the same parallel have the same latitude. Exercise 6—Oral. Follow Harry's imaginary trips and troubles. 1. He is traveling on an imaginary circle equally distant from the poles; what imaginary circle is this? 2. He has a trip of how many degrees if he tries to reach either of the poles? 3. Longitude is distance east or west of the Prime Meridian. If he is where the Prime Meridian crosses the equator, write the longitude of his place. 4. If he travels the circumference of the equator how many degrees does he travel? 5. How many longitude? longitude? O can he travel to the greatest east How many to the greatest west 6. Why is it wrong to say 260° East? 7. He visits several cities that have east longitude. Name 3. 8. Follow him to 3 cities in west longitude. Name them. |