LATITUDE AND LONGITUDE 179 1. Taking the equatorial radius of the earth to be 4,000 mi., what is the length of the equator? 2. How many degrees are there in any circle? What is the length (to the nearest mile) of 1° (one degree) on the equator? 3. The radii of the tropics may be taken to be 3,600 mi., TROPIC OF CAPRICORN and of the polar circles 1,400 mi. ; how many miles are there in 1° on each circle? Meridians. The circles whose diameters lie in the axis connecting the north and south poles of the earth are called meridianal circles. Each half circle from pole to pole is called a meridian. 4. Are meridians large or small circles? Find the length of a meridianal circle. 5. What is the length of a meridian? Of 1o on a meridian? In the study of geography it is seen that the location of a point on the earth's surface may be indicated by stating its distance north or south of the equator and east or west of a given meridian. Latitude. Distance in degrees north or south of the equator is called latitude. To say that a place is in latitude 42° N. means that it is 42° north of the equator. Longitude. Distance measured in degrees east or west of a given meridian is called longitude. The meridian of Greenwich, a suburb of London, is usually taken. That of Washington is sometimes used. To say that a place is in longitude 87° W. means that it is 87° west of the meridian of Greenwich. 6. If you walk straight north, how does your latitude change? Your longitude? If you walk east? West? 180 DIFFERENCE OF LONGITUDE Angular Measure. 1° is divided into 60 equal parts called minutes, and 1 minute is divided into 60 equal parts called seconds. Notation. Minutes and seconds are denoted by' and " respectively. Thus, 12 degrees, 14 minutes and 17 seconds would be written 12° 14′ 17′′. 1. Write similarly 40 degrees, 30 minutes and 59 seconds; 84 degrees, 55 minutes and 43 seconds. 2. How many seconds are there in 1'? In 2'? In '? 3. How many minutes are there in 1°? In 11°? Numbers expressed in degrees, minutes, and seconds are best added by columns, and the usual tests applied to the work of each column. Similarly for subtraction. 30° 16′ 23′′ 37 50 19 6' 6′ 42′′ 68° 25.5′′ west 5. The longitude of New York is 73° 58′ and that of Chicago is 87° 36′ 42′′ west; what is the difference in longitude be When one place is in east longitude and the other in west, the difference in longitude between the two places is found by adding. 7. Find the difference in longitude between Berlin and each of the other places in the first column of the table: 8. Make and solve 10 other problems from the table. Oral, LONGITUDE AND TIME 181 1. How many hours are required by the earth to make one rotation on its axis? Through how many degrees does a point on the equator pass in 24 hours? In 1 hour? 2. In which direction does the earth rotate? 3. When it is sunrise in New York City, is it before or after sunrise in Boston? In Buffalo? In San Francisco? 4. How many hours elapse while a point of the earth's surface turns through 360°? 180°? 90°? 30°? 15°? 5. When it is noon in Chicago, what time is it in a place 15° west of Chicago? In one 15° east of Chicago? All places east of a given point have later time, all west of it have earlier time. This caused much confusion in railway travel, hence the country has been divided into sections corresponding to standard meridians, the time of the meridians being taken as the time throughout the sections. This is called standard time. The meridians used are 75°, 90°, 105°, 120°. The map shows the meridians and the corresponding time belts. 6. When it is noon, standard time at New York, what is the time at Boston? Albany? Philadelphia? Charleston? 7. Make and solve 10 other problems. 182 AREA OF SPHERES By winding a hemisphere closely with a string and then winding this string on the base of the hemisphere, it is found that twice as much string is required to cover the convex surface as to cover the base. 2. How does the radius of a sphere compare with that of one of its great circles? What represents the area of a circle of radius r? 3. What does 4772 express when r stands for the radius of a sphere? 4. Using the letter, state the area of a sphere of radius 3 in.; 6 in.; 4 ft.; 1 yd. Thus, for radius 3 in. the area is 36 π. Written. 5. Using 3.14 as the value of π, compute the area of each sphere of Exercise 4. 6. The radius of the base of the dome of this observatory is 45 ft. Find the perimeter of the base. 7. What is the cost of painting the outer surface of the dome at 24 a square foot, regarding it as a hemisphere? Oral. PROBLEMS-REVIEW 1. Name three bodies that are spherical in form. 183 2. What is a great circle of a sphere? A small circle? 3. State which of the following are great and which small circles: equator, meridians, tropical and polar circles. 4. Explain the meaning of east and west longitude. 5. What is the difference in longitude between two places: One 60° west and the other 95° west. 6. Find the difference in longitude between Paris, 2° 20′ 15′′ E. and New York 73° 58′ 25" W. 7. When it is noon in Chicago is it before or after noon. in New York? In San Francisco? In Salt Lake City? In Charleston? In Boston? 8. When it is noon on the 90th meridian west, what time is it at 75° W.? At 120° W.? At 105° W.? At 15° E.? At 0°? 9. What are the meridians used for standard time in the United States? How many hours difference is there in the standard time of Boston and San Francisco? 10. How is the area of a sphere found from its radius? II. What is the area of a sphere whose radius is 1 ft.? Written. 12. A hemispherical skylight is 12 ft. in diameter; how many square feet of glass are there in its surface, not allowing for sash? 13. A hemispherical ceiling 25 ft. in diameter is covered with steel at 30¢ a square foot; what did it cost? |