Page images
PDF
EPUB

NOTE 1. — The Standard Unit of Dry Measure adopted by the United States government is the Winchester bushel, which is in form a cylinder, 184 inches in diameter, and 8 inches deep, containing 2150 16% cubic inches. The Standard Imperial bushel of Great Britain contains 2218100% cubic inches, so that 32 Imperial bushels equal about 33 Winchester bushels. The gallon in Dry Measure contains 268 cubic inches.

NOTE 2. — 1gal. Dry Measure=268fcu. in. = 1gal. 1pt. 1}gi. Wine Measure=3qt. 114 pt. Beer Measure ; 1gal. W. M. 231cu. in. = 3 qt. $pt. D. M. = 3qt. 2 pt. B. M. ; 1gal. B. M.= 282cu. in. = 1gal. 1pt. 33gi. W. M.=lgal. 2kpt. D. M. ; 1qt. D. M.=67}cu. in. 1qt. 13}gi. W. M. ; 1qt. W. M.=574cu. in.=13pt. D. M. ; 1pt. D. M. = 33 cu. in. =1pt. 17 gi. W. M. ; 1pt. W. M. = 28/cu. in.={{pt. DM.

MENTAL EXERCISES. 1. In 2 quarts how many pints? In 5 quarts ? In 7 quarts? 2. In 3 pecks how many quarts ? In 6 pecks? In 9 pecks? 3. In 5 bushels how many pecks ? In 10 bushels ? 4. How many pecks in 16 quarts ? In 25 quarts ?

EXERCISES FOR THE SLATE. 1. How many quarts in

2. In 56731 quarts how 49ch. Sbu. 3pk, and 3qt.?

many chaldrons ?

OPERATION

OPERATION.

49 ch. Sbu. 3pk. 3qt. 8) 56 731 qt.
36

4)7091 pk. 3qt.
302
147

36) 1772 bu. 3pk.
177 2 bushels.

49 ch. Sbu. 4

Ang. 49ch. Sbu. 3pk. 3qt. 7091 pecks.

8
Ans. 5 6 7 31 quarts.

3. Reduce 97ch. 30bu. 2pk. to quarts.
4. In 112720 quarts how many chaldrons ?
5. How many pints in 35bu. Ipt. ?
6. Reduce 2241 pints to bushels.
7. Reduce 18qr. Bpk. 5qt. to quarts.
8. How many quarters in 4637 quarts ?
9. In 19bu. Bpk. 7qt. 1pt. how many pints ?
10. In 1279 pints how many bushels ?
QUESTION. — What is the standard unit of Dry Measure ?

m.

}

m.

h.

[ocr errors]

MEASURE OF TIME. Art. 98. This measure is applied to the various divisions and subdivisions into which time is divided.

TABLE. 60 Seconds (sec.)

make 1 Minute, 60 Minutes

1 Hour,

h. 24 Hours

1 Day,

da. 7 Days

1 Week,

W 3654 Days, or 52 weeks

1 Julian Year, 14 days,

y 12 Calendar Months (mo.) “ 1 Year.

sec 1

60 d. 1 60

3600 1 24 1440

86400 1

7
168
10080

604800 1 52

3654 8766 525960 31557600 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. 4917 sec.

The Julian Year, 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 an average yearly error of 11m. 101% sec., or a difference that would amount to 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, like the Julian year, 365 days for three years in succession, and 366 days for the fourth, excepting the last year of the odd centuries. The Gregorian year is so nearly correct as to err only 1 day in 3866 years, a difference so little as hardly to be worth taking into account.

A Common Year is one of 365 days, and a Leap or Bissextile Year is one of 366 days. Any year, excepting the last year of the odd centuries, that can be divided by 4 without a remainder, is Leap Year.

A Sidereal Year is the time in which the earth revolves round the sun, and is 365d. 6h. 9m. 93 sec.

NOTE 2. — The names of 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 :

Thirty days hath September,

April, June, and November ; QUESTIONS. Art. 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 year so called? Who instituted the Gregorian year? What is a Common year ? What is a Sidereal year ?

And all the rest have thirty-one,
Save February, which alone
Hath twenty-eight; and this, in fine,
One year in four bath 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

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

Jon., Feb. Mar., Apr. May. June. July. Aug. Sept. Oct., Nov., Dec. 365 31 59 90 120 151181 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 245267 / 304 335 | 365 31 61 92 123 153 184 214 214 245 273 304 334 365 30 61 92 | 122 153 183 184 215 243 274 304 335 | 365 31 62 92 | 123 153 153 184 212 243 273 304 334 365

61 92 122 122 | 153 | 181 212 242 273 303 334 365 30 61 91 92 123 151 182 212 243 273 304 335 365 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

31

For example, suppose we wish to find the number of days from April 4th to November 4th, we look for April in the left-hand vertical. column, and November at the top, and, where the lines intersect, is 214, the number sought. Again, if we wish the number of days from June 10th to September 16th, we find the difference between June 10th and September 10th to be 92 days, and add 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 time, a day must be added in leap year.

When the time includes more than one year, there must be added 365 days for each year.

MENTAL EXERCISES.

1. In 3 minutes how many seconds? In 5 minutes ? 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?

QUESTIONS. — Name the months in their order. How many days has each month? How do you find by 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 ?

[blocks in formation]

3 6 5 da. 5h. 48m. 49 sec. 60) 31556 929
24

60) 525948 m. 49seo 14 6 5

24) 8 765 h. 48m. 7 30

3.6 5 da. 5h. 8 7 6 5 hours. 60

Ans. 365da. 5h. 48m. 49 sec 5 2 5 9 48 minutes.

60

Ans. 3 15 5 6 9 29 seconds.

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.

QUESTIONS. — How do you reduce years to seconds ? Give the reason for the operation. How do you reduce seconds to days ? To years ? Give the reason for the operation.

CIRCULAR MEASURE.

Art. 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.

TABLE. 60 Seconds (“)

make 1 Minute, 60 Minutes

1 Degree, 30 Degrees

1 Sign, 12 Signs, or 360 Degrees,

The Circle of the Zodiac, C.

socio

[ocr errors]
[ocr errors]
[ocr errors]

A 360

80

330

300

60

270

06

240

120

D

OLO

091

1

60 1 60

3600 0. 1 30 1800

108000 1 12 360 21600

1296000 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 centre.

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

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

A Radius of a circle is a straight line drawn from its centre to its circumference;

as CA, CB, or CD. 081

Every circle, large or small, is supposed to be divided into 360 equal parts, called

degrees. A Quadrant is one fourth of a circle, 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 circle be drawn around the vertex of an angle as a centre, 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= 90°, the measure of the angle ACB ; hence the one is called an angle of 120°, and the other an angle 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 24 of 360° of longitude every hour, or over 15° of longitude in 1 hour's time, or 1° in 4 minutes of time, and 1' in 4 seconds of time ; so that, for instance, at any place, when it is noon, it is 1 hour earlier for every 15° of longitude westward, or 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.

QUESTIONS. — Art. 99. To what is circular measure applied ? Recite the table. What is a circle? What is an angle ?

« PreviousContinue »