NOTE. In add.ng two longitudes, if their su.n exceed 180 degrees, f must be subtracted from 360 degrees for the correct difference of longitude 1. From what is latitude reckoned? From what is longitude 1eckoned ? 2. What is the greatest latitude a place may have? What is the greatest longitude a place may have? 3. What places have no latitude? What places have no longitude? What place has neither latitude nor longitude? 4. What is the use of latitude and longitude? Has every place a meridian of longitude? 5. What is the latitude of the equator? the latitude of the poles? the longitude of the poles? 317. From the above "inciples, to find the difference of latitude or longitude, we have the following rule: Rule. When the latitudes or longitudes are both of the same name, subtract the less from the greater; when they are of different names, take their sum. EXAMPLES FOR PRACTICE. 1. The latitude of Richmond, Va., is 37° 20' north, and of Savannah 32° 4′ 56′′ north; what is the difference of latitude? Ans. 5° 15' 4". 2. The latitude of Charleston, S. C., is 32° 46′ 33′′ north, and of Quito, 13′ 27′′ south; what is the difference of latitude? Ans. 33°. 3. The longitude of Portland is 70° 13′ 34′′ W., and of Mobile, 88° 1' 29" W.; what is the difference of longitude? Ans. 17° 47′ 55′′. 4. The longitude of New Orleans is 90° W. and of Geneva 6° 9'5" E.; what is the difference of longitude? Ans. 96° 9' 5". 5. The longitude of St. Paul, Minn., is 95° 4′ 55′′ W., and of Berlin 13° 23′ 45′′ E.; what is the difference of longitude? Ans. 108° 28′ 40′′. 6. The longitude of Paris is 2° 20′ E., and of New York 74° 3′ W.; what is the difference of longitude? Ans. 76° 23'. LONGITUDE AND TIME. 318. The earth revolves on its axis from west to east once in 24 hours, and this causes the sun to appear to revolve around the earth from east to west in the same time. Places on the east of a certain point have later time, those on the west earlier time, since the sun appears to those on the east first. 319. The circumference of a circle contains 360°, hence the sun appears to travel through 360° in 24 hours, and in 1 hour it travels 24 of 360°=15°; in 1 minute it travels of 15°15′, and in 1 second it travels of 15′=15′′. Hence the following table : TABLE OF LONGITUDE AND TIME. 1. In what time does the earth revolve on its axis? What part of a revolution does it make in 12 hours? in 6 hours? 2. How many degrees of the earth's surface pass under the sun's rays in 24 h.? in 12 h.? in 4 h.? 3. How many degrees of longitude make a difference of 1 hour in time? 2 hours? 3 hours? 4 hours? 4. In what direction does the earth turn on its axis? In what direction does the sun appear to move? 5. Does the sun appear first to places east or west of a given point? 6. When it is noon with us, is it earlier or later east of us? west of us? 7. When it is noon at Boston, what is the time 15° east of Boston? 15° west? 30° cast? 30° west? 8. What difference in longitude makes a difference of 1 hour of time? of 1 minute? of 1 second? 9. What is the difference of longitude between two cities, if the difference of time is 1 hour? 1 h. 30 min.? 2 h.? 2 h. 45 min.? 10. If I start at New York and travel until my watch is 1 h. 30 min. too fast, in what direction and how far do I go? 11. If I start at Chicago and travel until my watch is 2h. 15 min too slow, how far and in what direction do I travel? CASE I. 320. To find the difference of time of two places when their difference of longitude is given. 1. The difference of longitude between two places is 40° what is their difference of time? SOLUTION. Since 15° of longitude correspond to 1 h. of time, and 15′ of longitude to 1 min. of time, of the number of degrees and minutes will equal the number of hours and minutes difference in time. Dividing by 15 we have 2 h. 40 min. Hence the following OPERATION. 15)40° 0' 2 40 Rule. Divide the difference of longitude expressed in • " by 15; the result will be the difference of time in н. MIN. SEC. EXAMPLES FOR PRACTICE. 2. The difference of longitude of two places is 35°; what is their difference of time? Ans. 2 h. 20 min. 3. The longitude of Portsmouth is 70° 45', and of Wash ington 77° 0′ 15′′; required their difference of time. Ans. 25 min. 1 sec. 4. The long. of New York is 74° 3' west, and of New Orleans 90° west; required the difference in time. Ans. 1 b. 3 min. 48 sec. 5. The longitude of Philadelphia is 75° 9' 5" west, and of Cincinnati 84° 29′ 31′′ west; what is the time at Cincinnati when it is 10 A. M. at Philadelphia? Ans. 22 min. 38 sec. past 9 a. M. 6. Vienna is 16° 23′ east long.; what is the time there at 9 A. M. in Philadelphia? Ans. 3 h. 6 min. 8 sec. P. M. SUPPLEMENTARY EXAMPLES. To be omitted unless otherwise directed. 7. The long. of Washington is 76° 56′ west of London; what change must we make in our watches in coming from London to Washington? Ans. Set back 5 h. 7 min. 44 sec. 8. Paris is about 2° 20' east longitude; what change would a person have to make in his watch in going from New York to Paris? Ans. Set ahead 5 h. 5 min. 32 sec. 9. The longitude of Rome is 12° 27' east, and of San Francisco 122° 26' 15 west? what time is it in the latter place when it is 4 P. M. in the former? · Ans. 27 sec. past 7 A. M. CASE II. 321. To find the difference of longitude of two places when their difference of time is given. 1. The difference of time between two places is 26 minutes; what is their difference of longitude? SOLUTION. Since 1 h. of time corresponds to 15° of longitude, and 1 min. of time to 15' of longitude, 15 times the number of hours and minutes difference in time will equal the number of degrees and minutes difference in longitude. Multiplying by 15 we have 6o 30'. Hence the following OPERATION. h. min. 0 26 15 6° 30' Rule.-Multiply the difference of time expressed in н. MIN. SEC. by 15; the result will be the difference of longitude in ° !!!. EXAMPLES FOR PRACTICE. 2. The difference of time between Philadelphia and Cin cinnati is about 37 min. 20 sec.; what is the difference of longitude? Ans. 9° 20'. 3. The time at St. Louis is about 53 minutes earlier than the time at Washington; what is the difference in longitude? Ans. 13° 15'. 4. When it is noon at London it is about 7 o'clock, A. M., in Philadelphia; required the difference of longitude. Ans. About 75°. 5. In traveling from New York to Cincinnati I find my watch is 41 min. 32 sec. too fast; required the difference of longitude. Ans. 10° 23'. SUPPLEMENTARY EXAMPLES. To be omitted unless otherwise directed. 6. In coming from San Francisco to Philadelphia I find my watch is 3 h. 9 min. 8 sec. too slow; what is the longitude of San Francisco, that of Philadelphia being 75° 9′ 5//? Ans. 122° 26' 15'. 7. The longitude of Cambridge, England, is 5' 21' east, and the difference of time between it and Cambridge, Mass., is 4 h. 44 min. 50 sec.; required the longitude of the latter place. Ans. 71° 7/21/ vest. 8. The longitude of New York is 74° 3' west, and of Jerusalem is 35° 32 east; when it is 4 o'clock, A M., at New York, what is the time at Jerusalem? Ans. 48 min. 20 sec. past 11 A. M. DENOMINATE FRACTIONS. 322. A Denominate Fraction is one in which the unit of the fraction is denominate; as, of a pound. 323. Denominate Fractions may be expressed either as common fractions or as decimals. REDUCTION OF DENOMINATE FRACTIONS. 324. Reduction of Denominate Fractions is the process of changing them from one denomination to another without altering their value. 325. There are two general cases, reduction ascending and descending, which, for convenience of operation, are subdivided into several other cases. REDUCTION DESCENDING. CASE I. 326. To reduce a common denominate fraction to a fraction of a lower denomination. 1. Reduce of a shilling to farthings. SOLUTION. Since there are 12 pence in one shilling, 12 times the number of shillings equals the number of pence; and since there are 4 farthings in 1 penny, 4 times the number OPERATION. Xx far. of pence equals the number of farthings; hence of a shilling equals XX farthings, which by cancelling and multiplying becomes of a farthing. Therefore, etc. Rule.-Express the multiplication by the required multipliers, and reduce by cancellation. Reduce EXAMPLES FOR PRACTICE. 2. T of a bu. to the fraction of a pint. 4. 3 6. 1386 8. 64957 of a sq. rd. to the fraction of a sq. in. 9. T of a mile to the fraction of an inch. Ans. f. Ans. 1. Ans. 24. Ans. f. Ans.. Ans. 44. Ans. 37. Ans. 3. |