Note 2. — The mariners of Great Britain and the United States reckon longitude from the meridian of Greenwich in England, as do the nautical books of both countries for the most part. American maps, however, very generally have longitude reckoned both from the meridian of Greenwich, and from the meridian of Washington. 159. To find the difference of longitude of any two places. Ex. 1. What is the difference of longitude between Boston, which is 71° 4' west, and Detroit, which is 82° 58' west. Ans. 11° 54'. Operation. The two places being Long, of Detroit = 8 2° 5 8' both in west longitude, we Long, of Boston =7 1° 4' subtract the less longitude from the greater. If, how Dif. of Longitude =11° 5 4' ever, one of the places had been in east longitude, and the other in west, we should have added the two longitudes together for the difference required. Hence, When the longitudes of two places are either both east or both west, subtract the less longitude from the greater for their difference; ami when the longitude of the one place is east, and that of the other icest, add the longitudes together for their difference. Note. — In adding together two longitudes, should their sum exceed 180 degrees, subtract it from 360 degrees, and the remainder will be the correct difference of longitude. Examples. 2. What is the difference of longitude between the city of Washington, whose longitude is 77° 16' west, and Paris, whose longitude is 2° 20' east? Ans. 79° 36'. 3. The United States extend from the St. Croix River, longitude 67° 2' west, to Cape Flattery, longitude 124° 43' west. Over how many degrees of longitude does the Union extend? 4. What is the difference of longitude between Raleigh, whose longitude is 78° 48' west, and Sacramento City, whose longitude is 120° west? Ans. 41° 12'. 5. What is the difference of longitude between Hartford, whose longitude is 72° 40' west, and Fort Leavenworth whose longitude is 94° 44' west? 6. The longitude of Honolulu is 157° 52' west, and that «,f Canton 113° 14' east. What is their difference of longitude? Ans. 88° 54'. LONGITUDE AND TIME. Hkh To find the time corresponding to degrees and min utes of longitude. Ex. 1. The difference of longitude between Boston and London being 71° 4', what is their difference of time? Ans. 4h. 44m. 16sec. Operation. gmce J' 0f longitude Dif. of longitude = 71° 4' corresponds to 4sec. of 4 time, and 1° of longitude n.f P .. 77 to 4m. of time (Art. 143, Dif. of time = 284m. 16sec. Note 2), 4/ corresponds 284m. 16sec. = 4h. 44m. 16sec. Ans. to I6sec, and 71° to 284m.; and 284m. 16sec. = 4h. 44m. 16sec, the answer required. The apparent motion of the sun being west, the time at Boston is as much earlier than that of London as the difference of time between them. Thus, when it is noon at London, it wants 4h. 44m. 16sec. of noon at Boston (Art. 143, Note 2). Therefore, to find the time corresponding to degrees and minutes of longitude, Multiply (lie minutes of longitude by 4, for seconds of time. Note 1. — Should the seconds of time, when found, be 60 or more, they maybe reduced to minutes; and should, also, the minutes be 60 or more, they may be reduced to hours. The difference of time between two places is exactly aa much as the true clock time of the one is fast or slow as compared with that of the other. Examples. 2. Galveston in Texas is 14° 43' west of Pittsburg. When it is 12 o'clock at Galveston, what is the time at Pittsburg? 3. The longitude of Valparaiso is 71° 37' west, and the longitude of Rome is 20° 30' east. When it is llh. 15m. A. M. at Valparaiso, what is the time at Rome? Ans. 23m. 28sec. past 5 o'clock, P. M. 4. The longitude of Jerusalem is 35° 32' east, and the longitude of Baltimore 76° 37' west. When it is 9 o'clock, A.M. at Jerusalem, what time is it at Baltimore? Ans. lh. 31m. 24sec. A. M. 161. To find the longitude corresponding to hours, minutes and seconds of time. Ex. 1. The difference of time between Boston and London is 4h. 44m. 16sec.; what is the difference of longitude? Ans. 71° 4'. OPERATION. Since lh. of time corresponds to 1 5° X 4 = 6 0° 15° of longitude, 4m. of time to 1° 44-5-4=11° of longitude, and 4 sec. of time to 16-5-4= 4' 1' of longitude (Art. 143, Note 2), 4h. corresponds to 60°, 44m. to 11°, Dif. of longitude = 7 1° 4' and 16sec. to 4'; and 60° + 11° -f 4' = 71° 4', the answer required. Hence, to find the longitude corresponding to hours, minutes, and seconds of time, Multiply the hours of time by 15, and divide the minutes of time by 4, for degrees of longitude; and divide the seconds of time by i,for minutes of longitude. The several results added together will be the difference of longitude. Examples. 2. The difference of time between Washington and Cincinnati is 29m. 36sec.; what is the difference of longitude? 3. A ship-captain sailing from New York to Europe, after being at sea some days, on taking an observation, found that the sun at noon was 2h. 20m. 40sec. earlier than the New York time, as shown by his chronometer. How many degrees east had he sailed? Ans. 35° 10'. 4. A gentleman travelling west from Philadelphia, whose longitude is 75° 10' west, found, on arriving at St. Louis, that his watch, an accurate timekeeper, which was right when he left Philadelphia, was lh. 20sec. earlier than the time at St. Louis. What, then, is the longitude of St. Louis? Ans. 90° 15' west. 5. The difference of time between Baltimore and New Orleans is 53m. 30sec.; what is the difference of longitude? 6. When it is noon at St. Paul's, longitude 93° 5' west, it is at Bangor lh. 37m. 12sec. P.M.; what is the longitude of Bangor? Ans. 68° 47' west. 7. When it is 11 A. M. at a place 30° east of Greenwich, it is 3h. 44m. 20sec. A.M. at Buffalo; what is the longitude of Buffalo? Ans. 78° 55' west. 8. The difference of time between Cambridge Observatory and Greenwich is 4h. 44m. 32sec.; what is the difference of longitude? Ans. 71° 8'. MISCELLANEOUS EXAMPLES. 1. If the population of the world be as follows: America, 57,650,000; Europe, 263,517,490; Asia, 626,400,000; Africa, 100,000,000; Australia, 1,445,000; Polynesia, 1,500,000; and the average length of life be 33 years, what must be the average number of deaths annually? Ans. 31,833,712. 2. A farmer has in 3 bins 755 bushels of grain; there being in the first 125 bushels, and in the second 96 bushels, more than in the third; how many bushels in the second and third? Ans. 363 in the second, 267 in the third. 3. There is a certain island 30 miles in circumference. If A and B commence travelling round it, A at the rate of 3 miles an hour, and B at the rate of 5 miles an hour, how far apart will they be at the end of 30 hours? 4. Having money to invest, I purchased two farms at $ 1,750 each, and 19 shares of bank stock at $ 103 per share, and have left $ 113; how much money had I? Ans. $ 5,570. 5. It has been agreed by 12 men to gather 960 bushels of cranberries, and receive for their labor one half of the quantity gathered; after one half was gathered, one third of the men withdrew, leaving the others to complete the job. How many bushels should each man receive? Ans. Those who left, 20 bushels each; those who remained, 50 bushels each. 6. A drover made $ 652.00 by selling a lot of sheep, at a profit of 50 cents each; how many did he sell? 7. What will it cost to carpet a floor that is 18 feet wide and 27 feet long, provided the carpeting cost $2.25 per sq. yd.? 8. If a young man, by early rising and economy of time, can save for study and improvement of mind two and a halt hours a day, how many years' study, of 12 hours per day, can thus be gained in 20 years? Ans. 4y. 60d. lOh. 9. From 4 piles of wood, the first containing 7c. 76ft. 1671in., the second 16c. 28ft. 56in , the third 29c. 127ft, 1000in., the fourth 29c. 10ft. 1216in., I have sold 45 cords and 6 cord feet; how much remains? Ans. 37c. 19ft. 487in. 10. Boston is in north latitude 42° 21'; Portland is in latitude 1° 15' north of Boston; and Charleston is in latitude 10° 40' south. of Portland. What is the latitude of Charleston? Ans. 32° 56'north. 11. If 1 cubic foot of anthracite coal weighs 54 pounds, how many cubic feet of space are required to stow 2 tons of 2000 pounds each? Ans. 74^ cubic feet. 12. Two engineers, A and B, surveyed a certain house-lot. A made its contents 3R. 18p. 0yd. 6ft. 64sq. in., but B made its contents 3R. 17p. 30yd. 8ft. lOOsq. in. How much did the one differ from the other? 13. The products of the industry of 250,000 persons in Massachusetts, during the year 1855, amounted to $ 295,300,000. What was the average amount to each individual, and how much was added to the capital of the State, if one fourth of the whole amount was saved? Ans. $1,181.20 to each individual; $ 73,825,000 added to the capital. 14. The capacity of a certain cistern is 216 cubic feet; how many hogsheads of water will it contain? 15. What day of the month and what day of the year is the second Monday of May, in a common year commencing on Thursday? Ans. 11th day of May; 131st day of the year. 16. Purchased 18T. 17cvvt. 3qr. 201b. of copperas, at 4 cents per pound. I sold 4T. 6cwt. lqr. 141b. at 5 cents per pound, and 7T. lcwt. 3qr. 101b. at 6 cents per pound. Moses Atwood purchased one fourth of the remainder at 6 cents per pound. One half of what then remained I sold to J. Gale at 10 cents per pound. The remainder I sold to J. Smith at 12 cents per pound; but he has become a bankrupt, and I lose half my debt. What have I gained by my purchase? Ans. $ 894.07 17. The distance between Boston and San Francisco is 2691 miles. If Nathan Swift of San Francisco and Oliver Fleet of Boston, on Thursday, the first day of January, 1857, set out to meet each other, Swift travelling 3 miles 7 furlongs 29 rods 15 feet per hour, and Fleet 5 miles 10 rods and 1£ feet per hour, both travelling 6£ hours per day, commencing at 8 o'clock, A. M., provided they rest on the Sabbath, in what year and month, and on what day of the month, and at what time of the day, will they meet, and how far will each have travelled? Ans. On Monday, February 23, 1857, 2h. 30m. P. M. Swift, 1186m. lfur. 22rd. 13ft. 6in.; Fleet, 1504m. 3fur. 17rd. 3ft. |