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MEASURE OF TIME.

98. Measure of Time is applied to the various divisions and sub-divisions into which time is divided.

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NOTE 1. - The true Solar or Tropical Year is the time measured from the sun's leaving either equinox or solstice to its return to the same again, and is 365d. 5h. 48m. 49sec. nearly.

The Julian Ycar, so called from the calendar instituted by Julius Cæsar, contains 3654 days, as a medium ; three years in succession containing 365 days, and the fourth year 366 days; which, as compared with the true solar year, produces a yearly error of 11m. 101% sec., or of 1 whole day in about

120 years.

The Gregorian Year, or that instituted by Pope Gregory XIII., in the year 1582, and which is now the Civil or Legal Year in use among the different nations of the earth, contains 365 days for three years in succession, and 366 days for the fourth, excepting centenniul years whose number cannot be exactly divided by 400. The Gregorian year gives an error of only 1 day in 3866 years.

A Common Year is one of 365 days, and a Leap or Bissextile Year is one of 366 days. Any year is Leap Year whose number can be divided by 4 without a remainder, except years whose number can be divided without a remainder by 100, but not by 400.

A Sidereal Year is the time in which the earth revolves round the sun, and is 365d. 6h. 9m. 91% sec.

Note 2. - The 12 calendar months, composing the civil year, are January, February, March, April, May, June, July, August, September, October, November, December, and the number of days in each may be readily remembered by the following lines :

98. To what is the measure of time applied ? Repeat the table. How is the true solar year measured ? How long is it? Why is the Julian vear so called ? Who instituted the Gregorian year? What is a Common year ? A Sidereal year ?

Name the months in their order.

“ Thirty days hath September,

April, June, and November;
And all the rest have thirty-one,
Save February, which alone
Hath twenty-eight; and this, in fine,
One year in four hath twenty-nine.”'

TABLE

SHOWING THE NUMBER OF DAYS FROM ANY DAY OF ONE MONTH TO THE

SAME DAY OF ANY OTHER MONTH IN THE SAME YEAR.

TO THE SAME DAY OF

FROM ANY
DAY OF

Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec.

January
February
March
April
May
June
July
August
September
October
November
December

365 31 59 90 120 151 181 212 243 273 304 334 334 365 28 59 89 | 120 150 181 212 242 273 303 306 337 365 31 61 92 | 122 153 184 214 245 275 275 306 334 365 30 61 91 122 153 183 214 244 245 276 304 335 365 31 61 92 123 153 184 214 214 215 273 304 334 365 30 61 92 122 153 183 184 215 243 274 304 335 365 31 62 92 123 | 153 153 184 212 243 273 304 331 365 31 61 92 122 122 153 181 212 242 273 303 334 365 30 61 91 92 123 151 182 212 213 273 304 335 365 31 61 61 92 | 120 | 151 181 212 242 273 304 334 365 30 31 62 90 121 151 182 | 212 243 274 304 335 365

For example, to find the number of days from April 4th to November 4th we look for April in the left vertical column, and November at the top, ana, where the lines intersect, is 214, the number sought. Again, to find the number of days from June 10th to September 16th, we fiud the difference between June 10th and September 10th to be 92 days, and ud 6 days for the excess of the 16th over the 10th of September, so we have 98 days as the exact difference.

If the end of February be included between the points of a time, a day must be added in leap year.

When the time exceeds one year, there must be added 365 days for each year.

MENTAL EXERCISES. 1. In 3 minutes how many seconds ? In 5 minu'es ? 2. In 2 hours how many minutes ? In 4 hours ? 3. In 4 weeks how many days? In 6 weeks? In 9 weeks? 4. In 2 days how many hours? In 3 days? In 7 days? 5. How many weeks in 21 days? In 30 days? In 50 days ? 6. How many calendar months in 2 years? In 8 years? In 10 years? In 12 years? In 20 years?

98. How many days has each month? How do yon find hi- the table the number of days from April 4th to November 4th? When the time sought for is more than one year, how many days must be added ?

EXERCISES FOR THE SLATE.

1. How many seconds in 365da. 2. In 31556929 seconds 5h. 48m. 49sec., or one solar year? how many days?

OPERATION.

OPERATION.

3 6 5 da. 5h. 48m. 49sec.

24

1 4 6 5
7 30
8 7 6 5 hours.

60
5 2 5 9 4 8 minutes.

60 315 5 6 9 2 9 seconds, Ans.

60) 315 5 6 9 29
6 0) 5 2 5 9 4 8 m. 49sec.
2 4) 8 7 6 5 h. 48m.

3 6 5 da. 5h. Ans. 365da. 5h. 48m. 49sec.

3. Reduce 296da. 18h. 32m. to minutes. 4. In 427352 minutes how many days?

5. How many seconds in 30 solar years 262da. 17h. 28m. 42sec. ?

6. In 969407592 seconds how many solar years ?
7. How many weeks in 684592 minutes ?
8. In 67w. 6d. 9h. 52m. how many minutes ?
9. How many days from June 5th to Dec. 11th ?

10. How many days from March 17th, 1856, to May 16th, 1857 ?

Ans. 425 days. 11. How many days from December 18th, 1856, to January 30th, 1857 ?

12. How many days from August 30th, 1857, to June 1st 1858 ?

13. How many days from July 4th, 1859, to July 4th, 1860 ?

14. How many days from April 25th, 1855, to August 20th, 1858 ?

Ans. 1213 days.

Note. — The last six examples are to be performed by aid of the table on

page 103.

98. How do you reduce years to seconds? The reason for the operation. How do you reduce seconds to days? To years? The reason for the operation.

CIRCULAR MEASURE.

99. Circular Measure is applied to the measurement of circles and angles, and is used in reckoning latitude and longitude, and the revolutions of the planets round the sun.

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360

30

330

300

60

270

90
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240

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091

Note 1.– A Circle is a plane figure bounded by a curve line, every part of which is equally distant from a point“ called its center.

The Circumference of a circle is the line which bounds it, as shown by the diagrain.

An Arc of a circle is any part of its circumference; as AB.

A Radius of a circle is a straight lino drawn from its center to its circumference; as CA, CB, or CD.

Every circumference is supposed to be divided into 360 equal parts, called de

grees. A Quadrant is one fourth of a circumference, or an arc of 90°; as AB.

An Angle, as ACB, is the inclination or opening of two lines which meet at a point, as C. The point is the vertex of the angle. If a circumference be drawn around the vertex of an angle as a center, the two sides of the angle, as radii of the circle, will include an arc, which is the measure of the angle; as the arc AD 120° is the measure of the angle ACD, and AB

900, the measure of the angle ACB; hence the one is an angle of 120°, and the other, of 90°.

NOTE 2 - As the earth turns on its axis from west to east every 24 hours, the sun appears to pass from east to west 4 of 360° of longitude every hour, or over 150 of longitude in 1 hour's time, or 1° in 4 minutes of time, and il in 4 seconds of time; so that when it is noon at any place, it is 1 hour earlier for every 15° of longitude westward, and 1 hour later for every 15° of longitude eastward. Thus, Boston being 71° 4' west of Greenwich, and San Francisco 51° 17' west of Boston, when it is noon at Boston, it is 4h. 44m. 16sec. past noon at Greenwich, and wanting 3h. 25m. 8sec. of noon at San Francisco.

99. To what is circular measure applied ? Recite the table. What is a circle ? An angle?

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3. In 27S. 19° 51' 28" how many seconds ?
4. How many signs in 2987488 seconds ?

MISCELLANEOUS TABLE.

100. This table embraces a variety of denominations frequently used in business.

66

12 gross

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12 units

make 1 dozen. 12 dozen

1 gross.

1 great gross. 20 units

1 score. 14 pounds of Iron or Lead

1 stone. 60 pounds of Wheat

1 bushel. 60 pounds of Clover-seed

1 bushel. 60 pounds of Beans

1 bushel. 60 pounds of Potatoes

1 bushel. 52 pounds of Onions

1 bushel. į 70 pounds of Corn on the Cob“ 1 bushel. 56 pounds of Shelled Corn

1 bushel. 56 pounds of Rye

1 bushel. 56 pounds of Flax-seed

1 bushel. 45 pounds of Timothy-seed

1 bushel. 20 pounds of Bran

1 bushel. 48 pounds of Barley

1 bushel. 52 pounds of Buckwheat

66

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1 bushel in Ky. 48 pounds of Buckwheat

1 bushel in Mass, and Pa. 32 pounds of Oats

1 bushel in Mass., Ill., 6., etc. 30 pounds of Oats

1 bushel in Me., N. H., Pa., etc.

99 How do you reduce signs to seconds ? Give the reason of the operation. How do you reduce seconds to degrees? To signs? Give the reason for the operation. How many degrees in a circle ? — 100. What is embraced in the miscellaneous table?

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