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3. Milton was born Dec. 9th, 1608, and died Nov. 8th 1675; what was his age ? Ans. 66 yr. 10 mo. 29 da.

4. Franklin was born Jan. 6th, 1706, and died April 17th, 1790; required his age.

Ans. 84 yr. 3 mo. 11 da. 5. Wuat is the exact time a note has to run, dated Dec 30th, 1862, and payable Jan. 16th, 1864 ? Ans. 1 yr. 17 da.

6. The Revolution was commenced the 19th of April, 1775, and terminated January 20th, 1783; how long did it continue ?

Ans. 7 yr. 9 mo. 1 da. 7. The Civil War began April 11, 1861, and closed April 9, 1865; how long did it last ? Ans. 3 yr. 11 mo. 28 da.

8. How many years, months, and days, from your birthday to the present date ?

SUPPLEMENTARY PROBLEMS,

To be omitted unless otherwise directed. 9. A man was born the 29th of Feb., 1824, and died the 3d of March, 1860; how many birthdays did be see, and what was his exact age ?

Ans. 10; Age, 36 yr. 4 da. 10. Two men were born on the first day of January, one in the year 1756, the other in 1822; both died 37 years after they were born, upon the 1st of January; required the difference of their ages ?

An8. 1 day. 11. What is the exact time from 45 min. and 25 sec. past 12 o'clock noon, May 20, 1874, to 24 min. 36 sec. past 4 o'clock P. M., July 4, 1876?

Ans. 2 yr. 1 mo. 15 da. 3 h. 39 min. 11 sec.

CASE II. 314. To find the day of the week upon which any given day of the month will fall, the day of the week of some other date being given.

NOTE.-A common year ends on the same day it begins, hence each year begins one day later than the preceding year. A year following leap year begins two days later.

1. If the 3d of April, 1876, occur on Monday, on what day of the week will the next 29th of August be ?

SOLUTION.-By the table we find the difference of tinue to be 148 days: dividing by 7, the number of days in a week, we have 21 weeks and 1 day; the

148--7=21,+1 29th of August must therefore be one day after Monday or Tuesday.

OPERATION.

Rule. Find the number of days between the two dates, reduce this number to weeks; the number of days remaining will be the number of days from the given day of the week to the required day.

NOTE.-In solving the problems after the 2d, the date in a previous problem may be assumed as the starting-point.

WRITTEN EXERCISES.

2. If the year 1776 began on Monday, on what day of the week was the 4th of July following ? Ans. Thursday.

3. What day of the week was the surrender of Burgoyne, Oct. 17, 1777 ?

Ans. Friday. 4. On what day of the week was Daniel Webster born, Jan. 18, 1782?

Ans. Friday. 5. On what day of the week was the battle of Waterloo fought, June 18, 1815 ?

Ans. Sunday. 6. On what day of the week was President Lincoln assassinated, April 14, 1865 ?

Ans. Friday. 7. On what day of the week was General Grant inaugurated the first time, March 4, 1869 ? Ans. Thursday.

SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed. 8. The Centennial opened on Wednesday, May 10, 1876; on what day will the next open on the same date? Ans. Monday.

9. Suppose a letter should be published purporting to have been written at New Orleans on the day of the battle, and dated Wednes. day, Jan. 8, 1815 ; would it be genuine ?

10. Let the pupils now determine, from the above principles, the day of the week upon which they were born.

LATITUDE AND LONGITUDE.

315. The Latitude of a place is its distance from the equator, north or south. It is reckoned in degrees, minutes, and seconds, and cannot exceed 90°, or a quadrant.

316. The Longitude of a place is its distance, east or west, from a given meridian. It is reckoned in degrees, minutes, and seconds, and cannot exceed 180°, or a semicircumference.

NOTE.-In- adding two longitudes, if their sum exceed 180 degrees, it must be subtracted from 360 degrees for the correct difference of longitude.

MENTAL EXERCISES. 1. From what is latitude reckoned ? From what is longitude reck. oned ?

2. What is the greatest latitude a place may have? What is the greatest longitude a piace may have ?

3. What places have no latitude? What places have no longituile.“ What place has neither latitude nor longitude ?

4. What is the use of latitude and longitude ? Has every place 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 principles, 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.

WRITTEN EXERCISES.

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. 33o. 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 th , 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 14 of 360°=15°; in 1 minute it travels to of 15°=15', and in 1 second it travels of of 15'=15''. Hence the following table :

TABLE OF LONGITUDE AND TIME. 15° of longitude

1 hour of time. 15 of

1 minute of time. 15" of

1 second of time.

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MENTAL EXERCISES. 1. In what time does the earth revolve on its axis ? What part of & 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 di. rection 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° east? 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 2 h. 15 min coo slow, how far and in what direction do I travel ?

CASE I.

OPERATION,

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 ! min. of time,

15)40° 0 15 of the number of degrees and minutes will equal the number of hours and minutes difference in time.

2 40 Dividing by 15 we have 2 h. 40 min. Hence the following

Rule.- Divide the difference of longitude expressed in 01" by 15; the result will be the difference of time in a MIN. SEC.

WRITTEN EXERCISES. 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 Washington 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. 384 sec. past 9 A. M. 6. Vienna is 160 23' east long.; what is the time there at 9 A. M. in Philadelphia ?

Ans. 3 h. 6 min. 83 sec. P. M. SUPPLEMENTARY PROBLEMS.

To be omitted unless otherwise directed. 7. The long. at Washington is 760 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 20 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 120 27' east, and San Francisco 1220 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.

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