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DIFFERENCE BETWEEN DATES.
153. To find the time between two different dates. Ex. 1. What is the difference of time between May 16,
Ans. 37y. 9mo. 18d.
Commencing with January, the first month in the year, and counting the months and days in the later date up to March 4th, we find that 2mo. and 4d. have elapsed. Wc therefore write th« numbers for subtraction as in the first operation.
1819, and March 4, 1857?
y. mo. d.
Min. 1 8 5 7 2 4
Second Operation. The same result, however,
Min. 1 8 5 7 3 4 could be obtained, as some pre-
of the given months instead of
Rem. 3 7 9 1 8 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.
2. What is the time from June 3d, 1854, to April 19th, 1857?
3. A note was given October 26th, 1856, and paid June 12th, 1857; 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 = 1 8 6 days.
For Feb. 3d., April Id., June Id., 3 + 1 + 1 = 5"
1 8 1
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 days. But since in the interval of time included between the given dates several months end that do not contain 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 (iino., 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, the other south, we should have added the two latitudes together for the difference required. Hence
Find the number of months ending between the given 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.
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 clays are there from the 7th of January to the 11th of December? Ans. 339 days.
155i 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?
From May 16 to December 25 = 223 days.
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 (i days after Saturday, or on Friday. Hence, we
Reduce the days between the given dates to iveeks. 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.
2. If the 2d day of April be on Wednesday, what day 01 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?
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 68,80 statute miles in length; the 40th degree, about 68155 miles; and the 89th degree about 69,^ 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 lati
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 Li 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 9° 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 69j statute miles, and, in general, a degree is 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.)