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EXAMPLES 2. If the 2d day of April be on Wednesday, what day of the week will the following 4th of July be?
Ans. Friday 3. If a leap year commence on Tuesday, on what day will the 17th of June, the anniversary of the battle of Bunker Hill, happen?
4. If in a common year the 25th of December, or Christmas, be on Tuesday, on what day did the year commence ?
Ans. Monday. 5. If the 4th day of November be on Tuesday, what day of the next February will be the second Monday of that month?
Ans. The 9th. 6. A bill was dated on Thursday, December 20th, 1855, and made payable 90 days after date. In what year and month, and on what day of the month and week, did it become due ?
Ans. Wednesday, March 19, 1856.
DIFFERENCE OF LATITUDE.
156. LATITUDE is the distance of any place from the equator, north or south. It is reckoned in degrees, minutes, and seconds, from the equator to either pole of the earth ; and cannot exceed 90 degrees, or one fourth of the earth's circumference. Places north of the equator are said to be in north latitude, and those south of the equator, in south latitude.
NotE. — The shape of the earth not being that of a perfect sphere, but somewhat flattened toward the poles, the degrees of latitude differ a little from each other in length toward either pole. Thus the 1st degree is about 68% statute miles in length; the 40th degree, about 68180 miles; and the 89th degree about 6918 miles.
157. To find the difference of latitude of any two places.
Ex. 1. The latitude of London is 51° 31' north, and that of Boston is 42° 23' north. What is their difference of latitude ?
Ans. 9° 8'.
The two places being Lat. of London = 51° 31' N. both in north latitude, we Lat. of Boston 4 2° 23' N.
subtract the less latitude
from the greater. If the Dif. of Latitude 9° 8' N latitude of the one place
had been north and that of
the other south, we should have added the two latitudes together for the difference required. Hence
When the latitudes of two places are either both north or both south, subtract the less latitude from the greater for their difference; and when the latitude of the one place is north and the other south, add the latitudes together for their difference.
Note. — In north latitude, when the sailing is southerly, or in south latitude, when the sailing is northerly, if the difference of latitude be subtracted from the latitude LEFT, the remainder will be the latitude in; or, in north latitude, when the sailing is northerly, or in south latitude, when the sailing is southerly, if the difference of latitude be added to the latitude LEFT, the sum will give the latitude in.
2. The latitude of Quebec is 46° 48' north, and that of New Orleans 29° 57' north, What is their difference of latitude ?
Ans. 16° 51'. 3. The latitude of Washington City is 38° 53' north, and that of Cape Horn 55° 58' south. What is their difference of latitude ?
Ans. 94° 51'. 4. Valparaiso is in latitude 33° 2' south, and San Francisco 37° 48' north. What is their difference of latitude ?
5. Captain James Francis, sailing southerly from New York City, whose latitude is 40° 42' north, found on reaching Havana that his latitude differed 17° 33' from that he left. What latitude was he then in ?
Ans. 23° 9' north. 6. Philadelphia is go 15' of latitude north of Mobile, whose latitude is 30° 41' north ; what is the latitude of Philadelphia ?
Ans. 39° 56' north.
DIFFERENCE OF LONGITUDE.
158. LONGITUDE is the distance of any place from a given meridian, east or west. It is reckoned in degrees, minutes, and seconds, and cannot exceed 180 degrees, or one half of a circle.
Note 1. — A degree of longitude on the equator is about 693 statute miles, and, in general, a degree is 3io of any circle of latitude. The meridians all converge from the equator to the poles to a point, so that the degrees of longitude under different parallels of latitude vary, diminishing with the circles of latitude, till at the poles the longitude becomes nothing. (Art. 133, Note 4.)
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 ineridian of Washington.
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'.
The two places being Long, of Detroit 8 2° 58 both in west longitude, we Long. of Boston 71° 4'
subtract the less longitude
from the greater. If, howDif. 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; and when the longitude of the one place is east, and that of the other west, 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.
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 of Canton 113° 14' east. What is their difference of longitude ?
Ans. 88° 54'.
LONGITUDE AND TIME.
160. 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. 16 sec.
Since 1' of longitude Dif. of longitude 71° 4
corresponds to 4sec. of 4
time, and 1° of longitude
to 4m. of time (Art. 143, Dif. of time
Note 2), 4 corresponds 284m. 16 sec. 4h. 44m. 16sec. Ans.
to 16 sec., 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 the minutes of longitude by 4, for seconds of time. Multiply the degrees of longitude by 4, for minutes of time. Note 1.- Should the seconds of time, when found, be 60 or more, they may be 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 as much as the true clock time of the one is fast or slow as compared with that of the other.
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 11h. 15m. A. MI, 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'.
Since 1h. of time corresponds to 1 5° X 4 = 60° 150 of longitude, 4m. of time to 1° 44 54
11° of longitude, and 4sec. of time to 16 ; 4
41 1' of longitude (Art. 143, Note 2),
4h. corresponds to 60°, 44m. to 11°, Dif. of longitude = 71° 4' and 16 sec. to 4'; and 60° +11° +
4 = 710 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 4, for minutes of longitude. The several results added together will be the difference of longitude.
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. 12 sec. 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'.