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SECOND OPERATION.

The same result, however, Min. 1857 3 4 could be obtained, as some preSub. 1819 5 16 fer, by reckoning the number

of the given months instead of Rem. 37 9 18 the number of months that have

elapsed since the beginning of the year, which would require the numbers to be written as in the second operation. Written either way, the earlier date, being placed under the later, is subtracted from it.

NOTE. — In finding the difference between two dates, and in computing interest for less than a month, 30 days are considered a month. In legal transactions, however, a month is reckoned from any day in one month to the corresponding day of the following month, if it has a corresponding day, otherwise to its end. The above process, which is that ordinarily used by business men, does not give always the exact time between two different dates. The result obtained by it may deviate sometimes a day, and, less often, two days, from the exact difference. But for practical purposes it is generally regarded as sufficiently accurate.

EXAMPLES.

1857 ;

2. What is the time from June 30, 1854, to April 19th, 1857? 3. A note was given October 26th, 1856, and paid June 12th,

how long was it on interest? 4. The Pilgrims landed at Plymouth December 22d, 1620, N.S., and the Declaration of Independence was made July 4th, 1776; what is the difference of time between these events ?

5. General Washington was born February 22d, 1732, and died December 14th, 1799; how long did he live?

Ans. 67y. 9mo. 22d. 154. To find the exact number of days between two different dates.

Ex. 1. How many days from January 28 to July 30, common year?

Ans. 183 days. January to July = 6mo.

6 x 31

18 6 days. For Feb. 3d., April 1d., June 1d., 3+1+1

5

181 For difference between 30 and 28, 30 28

2

Ans. 18 3 days. The difference between January and July we find to be 6mo., which, multiplied by 31, the greatest number of days in any month in the year, gives 186 days. But since in the interval of time included between the given dates several months end that do not con

OPERATION.

66

tain 31 days, we make deductions for these, which, in all, amount to 5 days, and have left 181 days; and as the difference between the given dates is the difference between 30 and 28 more than exactly 6mo., we add 2 to the 281 days, thus obtaining 183 days, the difference of time required. Hence, to find the number of days between two different dates,

Find the number of months ending between the giren dates, and multiply that number by 31, and from the product make the necessary deduction for the months counted that do not contain 31 days, if any. Should the later date end later in the month than the earlier, add the difference of days; but should it end earlier, subtract the same.

NOTE. The exact difference in days between two different dates can also be obtained by use of the table in Note 2, Art. 142.

EXAMPLES. 2. How many days has a note to run dated November 15, 1856, and made payable February 13, 1857 ? Ans. 90 days.

3. How many days from June 18, 1855, to May 1, 1856 ?

4. How many days from March 4 to May 3 of the same year?

5. From November 4, 1856, to April 4, 1857, how many days?

Ans. 151 days. 6. In a leap year, how many days are there from the 7th of January to the 11th of December?

Ans. 339 days. 155. To find the day of the week corresponding to any given day of the month, when the day of the week of some other date is given.

Ex. 1. If the 16th day of May be on Saturday, what day of the week will the next 25th of December be?

Ans. Friday. From May 16 to December 25 223 days = 7

31 weeks and 6 days. 6 days after Saturday = Friday, Ans. Having found the difference of time in days between the given dates, we bring the days to weeks by dividing by 7, and obtain 31 weeks and 6 days. The 25th of December, therefore, must come 6 days after Saturday, or on Friday. Hence, we

Reduce the days between the given dates to weeks. Should there be no remainder, the day given will be the same as that sought, but should there be a remainder, it will indicate the number of days that the day sought is after the day given.

OPERATION.

223 days.

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 68100 miles; and the 89th degree about 69100 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 5 1° 31' N. both in north latitude, we Lat. of Boston 42° 23' N.

subtract the less latitude

from the greater. If the Dif. of Latitude go 8' N. latitude of the one place

had been north and that of

OPERATION.

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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.

EXAMPLES

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 lati. tude was he then in ?

Ans. 23° 9' north. 6. Philadelphia is 9° 15' of latitude north of Mobile, whose latitude is 30° 41' north ; what is the latitude of Philadelphia ?

Ans. 39° 56' north.

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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 692 statute miles, and, in general, a degree is 365 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.)

OPERATION.

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.

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'.

The two places being Long, of Detroit 8 2°

5 8' both in west longitude, we Long. of Boston 71° 4

subtract the less longitude

from the greater. If, howDif. of Longitude 11° 54'

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.

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 of Canton 113° 14' east. What is their difference of longitude ?

Ans. 88° 54'.

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