183. A passenger on a moving train observes that it takes him just 45 sec. to pass a freight train 1320 ft. long, standing on a side track. At what rate in miles per hour is his train running? 184. Simplify: (1 − 1) × (1 + 1) ÷ (1 + 1) × (1 − 1). 185. A, B, and C invested jointly $3100. A's capital was invested 8 mo., and his gain was $360; B's capital was invested 9 mo., and his gain was $450; C's capital was invested 12 mo., and his gain was $720. Find the capital of each. 186. Write all the numbers possible each with the figures 5, 6, 7. What two numbers of one figure each will divide each of the numbers? 187. A contractor has workmen enough to divide into groups of 12 men or 14 men, and in each case have one man left for overseer. How many workmen has he? 188. If one fourth of the sum a boy received for matches was gain, what was the gain per cent? 189. Of 225 weight tests of groceries purchased recently in one of our large cities, 158 showed a shortage in weight. What per cent of them were short in weight? 190. To a kitchen 18 ft. long and 16 ft. wide, an addition is built 12 ft. long and 16 ft. wide. What is the distance around the enlarged kitchen? 191. Find the number of acres in the field ABCDEF having given the following measurements: Bm, Cn, Fs, and Er are perpendiculars drawn to the diagonal. 192. If a merchantman sailing 10 knots an hour is chased by a battleship sailing 133 knots an hour, how far ahead must the merchantman be to escape by four knots into a port which is 12 knots distant at the beginning of the race? 193. A piece of work was to be performed by 8 men in a certain time, but 3 of them failing to come, the work was prolonged 4 days; in what time would the work have been done had all come? 194. Assuming the radius of the earth to be 4000 mi., find the weight of a body 8000 mi. above the earth's surface if the body weighs 200 metric tons at the surface. [The weight of a body varies inversely as the square of its distance from the center of the earth.] SUPPLEMENT LATITUDE AND LONGITUDE 1. To locate places on the surface of the earth, a circumference, called the meridian of Greenwich, is supposed to be drawn through Greenwich, England, and the north and south poles of the earth. Halfway, or 90°, from either pole another circumference, called the equator, is supposed to be drawn east and west around the earth. These two circumferences divide each other into two equal parts of 180° each. 2. The meridian of a place is the half circumference supposed to be drawn from pole to pole through the place. It is divided by the equator into two equal parts of 90° each. 3. The meridian of Greenwich is called the prime meridian, and its opposite meridian, or the other half of the circumference of which the prime meridian is one half, is the 180th meridian. 4. The latitude of a place is its distance from the equator measured in degrees upon the meridian of the place, and is north or south according as the place is north or south of the equator. 5. The longitude of a place is the distance in degrees on the equator from the prime meridian to the meridian of the place, and is east or west according as the place is east or west of the prime meridian. 6. Parallels of latitude are circumferences extending east and west around the earth parallel to the equator. 7. The following truths are evident: 1. All places on the equator have no latitude. 2. All places on the same parallel of latitude have the same latitude. 3. All places on the prime meridian have no longitude. 4. All places on the same meridian have the same longitude. 5. The greatest latitude that a place may have is 90°. 6. The greatest longitude that a place may have is 180°, being the distance from the prime meridian to the 180th meridian. Exercise 1 How far and in what direction by the shorter arc is: 13. The latitude of A is 60° 55′ N., and of B on the same meridian, 30° 20' N. How far and in what direction is B from A? 14. The longitude of St. Paul, Minn., 93′ 5′ W. 15. Portland, Me., is 70° 15' 40" W., and of The longitude of Vienna is 16° 23′ E., and of New York, 74° 3" W. Find their difference in longitude. 16. The latitude of Portland, Me., is 43° 39' 28" N., and of Boston, 42° 21' 28" N. Find their difference of latitude. 17. The latitude of Savannah, Ga., is 32° 4′ 52′′ N., and of Seattle, Wash., 47° 35' 54" N. Find their difference of latitude. 18-26. Find the difference in longitude between each city in the first table and each city in the second table. LONGITUDE AND TIME 8. The earth rotates on its axis from west to east in 24 hours. This makes the sun appear to revolve about the earth from east to west once in the same time. Since the sun appears to revolve through 360° in 24 hours, its apparent motion is 15° per hour, 15' per minute, and 15" per second. It is noon at any place when the sun is on the meridian of that place, and since the sun apparently moves 15° from east to west in 1 hour, it is then 1 P.M. 15° east of that place, 11 A.M. 15° west of it, 2 P.M. 30° east of it, 10 A. M. 30° west of it, and so on. From this we see that a difference of 15° in the longitude of two places makes a difference of 1 hour in their time. Similarly, a difference of 15' in their longitude makes a difference of 1 minute in their time, and a difference of 15" in their longitude makes a difference of 1 second in their time. Hence : 9. of the number of degrees, minutes, and seconds in the difference of longitude of two places equals the number of hours, minutes, and seconds in the difference of their time. 10. 15 times the number of hours, minutes, and seconds in the difference of time of two places equals the number of degrees, minutes, and seconds in the difference of their longitude. REMARK. It is evident from § 8 that places east of any given meridian have later time and those west of it earlier time than places on the meridian. 11. This figure shows the times on different given meridians when the time is noon on the meridian of Greenwich. MIDNIGHT |