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the 24th of February in ours. It was called the intercalary day, from the Latin intercalo, to insert.

The year in whch this day is added, is called Bisse.ctile, from the Latin bis, twice, and sextilis, the sixth. It is also called “ Leap Year," because it leaps over a day more than a common year.

3. The civil or legal year is often called the Julian year, from Julius Cæsar emperor of Rome, who adapted the calendar or register of the civil year to the supposed length of the solar year, by adding 1 day to every fourth year.

265. In process of time, as mathematical and astronomical science advanced, it was found that the length of a solar year was only 365 d. 5 hrs. 48 min. 48 sec., or 11 min. 12 sec. less than 3654 days, which in 400 years amounted to about 3 days; consequently, the Julian calendar was behind the solar time. This error at the time of Pope Gregory XIII., amounted to 10 days, which he corrected in 1582 by suppressing 10 days in the month of October, the day after the 4th being called the 15th. Hence this calendar is sometimes called the Gregorian calendor.

Obs. 1. This correction was not adopted in England till 1752, when the error amounted to 11 days. By Act of Parliament, 11 days, after the 24 of September, were therefore omitted; and the civil year by the same Act, was made to commence on the 1st of January, instead of the 25th of March, as it had done previously.

2. Dates reckoned by the old method or Julian calendar, are called Old Style ; and those reckoned by the new method, are called New Style.

To change any date from Old to New Style, we must add 11 days to it; and if the given date in Old Style, is between the 1st of January and the 25th of March, we must add 1 to the year in New Style.

Russia still reckons dates according to Old Style. The difference now amounts to 12 days.

266. To ascertain whether a year is LEAP YEAR.

Divide the given year by 4, and if there is no remainder, it is Leop year.

The remainder, if any, shows how many years have elapsed since a Leap year occurred. Thus, dividing the year 1847 by 4, the remainder is 3 ; hence it is 3 years since the last leap year, and the ensuing year will be leap year.

Obs. 1. To this rule there is an exception. For, we have seen, that a solar year is 11 min. and 12 sec. less than a Julian year, which is 365 days. This error, in 400 years, amounts to about 3 days; consequently, if 1 day is aaded

QUBST.-266. How do you ascertain whether a year is leap year ?

every fourth year; that is, if we have 100 leap years in 400 years, according to the Julian calendar, the reckoning would fall 3 days behind the solar time. Thus, reckoning from the commencement of the Christian era, when it was January 1st, 401 by the Julian time, it was January 4th by the solar time.

2. To remedy this error only 1 centennial year in four is regarded a leap year ; or, which is the same in effect, whenever the centennial year, or the number expressing the century, is not divisible by 4, that year is not a lear year, while the other centennial years are. Thus, 17, 18, 19, denoting 1700, 1800, and 1900, are not divisible by 4, consequently they are not leap years, though according to the rule above they would be; on the other hand 16 and 20, denoting 1600 and 2000, are divisible by 4, and are therefore leap years. There is still a slight error, but it is so small that in 5000 years it scarcely amounts to a day.

CIRCULAR MEASURE, OR MOTION. 267. Circular Measure is applied to the divisions of the circle, and is used in reckoning latitude and longitude, and the motion of the heavenly bodies. 60 seconds (")

make 1 minute, marked 60 minutes

1 degree, 30 degrees

1 sign, 12 signs, or 3600

1 circle, This measure is often called Angular Measure, and is chiefly used by astronomers, navigators, and surveyors.

900

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3600

1800

Obs. 1. The circumference of every circle is divided or supposed to be divided, into 360 equal parts, called degrees, as in the subjoined figure.

2. Since a degree is 3d part of the circumference of a circle, it is obvious that its length must depend on the size of the circle.

2700 Note.-The division of the circumference of the circle into 360 equal parts, took its origin from the length of the year, which, (in round numbers) was supposed to contain 360 days, or 12 months of 30 days each. The 12 signs

QUEST.-267. In what is Circular Measure used ? Repeat the Table. Obs. How is the circumference of every circle divided ? On what does the length of a degree depend ? correspond to the 12 months. The term minutes, is from the Latin minutum, which signifies a small part. The term seconds, is an abbreviated expression for second minutes, or minutes of the second order.

268. Since the earth turns on its axis from west to east once in 24 hours, it evidently revolves 15° per hour; or 1° in 4 minutes, and l' in 4 seconds of time. Hence,

When the difference of longitude between two places is 1', the difference in the time, or the hour of the day at these two places, is 4 seconds ; if the difference of longitude is 1°, the difference of time is 4 minutes ; if , the difference of time is 8 minutes, &c.

Thus, when it is noon at London, in Philadelphia, which is about 75° west from London, it is only 7 o'clock, A. M. For, if the earth revolves 1° in 4 minutes, to revolve 75°, it will require 75 times as long, and 4x75=300 min., or 5 hours.

Obs. 1. Since the earth revolves from west to east, it is manifest, that the time is earlier as we go eastward, and later as we go westward.

2. This principle affords navigators and others a convenient and useful method of ascertaining the difference of time between two places, when the difference of their longitude is known; also, for ascertaining the difference of longitude between two places, when the difference in their time is known.

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MISCELLANEOUS TABLE. 269. The following denominations not included in the preceding Tables, are frequently used. 12 units

make 1 dozen, (doz.) 12 dozen, or 144

1 gross. 12 gross, or 1728

1 great gross. 20 units

score. 56 pounds

1 firkin of butter. 100 pounds

1 quintal of fish. 30 gallons

1 bar. of fish in Mass. 200 lbs. of shad or salmon

1 bar. in N. Y. and Conn. 196 pounds

1 bar. of flour. 200 pounds

1 bar. of pork.
14 pounds of iron or lead

stone.
21. stone
8 pigs

1 fother. Note.- Formerly it was customary to allow 112 lbs. for a quintal. QUEST.-268. When the difference of longitude between two places is l' what is the difference of time? When 19, what is the difference of time ?

1 pig.

PAPER AND BOOKS.

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270. The terms folio, quarto, octavo, &c., applied to books, denote the number of leaves into which a sheet of paper is folded. 24 sheets of paper

make 1 quire. 20 quires

1 ream. 2 reams

1 bundle.
5 bundles

1 bale.
A sheet folded in two leaves forms a folio.
A sheet " four leaves

a quarto, or 4to.
A sheet eight leaves

an octavo, or 8vo. A sheet " twelve leaves

a duodecimo, or 12mo.
A sheet eighteen leaves

an 18mo.
A sheet
thirty-six leaves

a 36mo.

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DIMENSIONS OF DIFFERENT KINDS OF ENGLISH PAPER.

Writing.

Names,

Drawing. Printing. Pott,

151 by 12in. 154 by 12; in. Small Post,

161 by 13in. Fool's Cap,

164 by 134 in. 164 by 13% in. Crown,

20 by 15 in. 20 by 15 in Demy,

20 by 154 in. 22 by 17 in. Medium, 221 by 171 in.

23 by 18 in Royal,

24 by 194 in. 24 by 194 in. 26 by 20 in. Super Royal, 273 by 194 in. 271 by 194 in. Elephant,

28 by 23 in. Double Crown,

30 by 20 in. Imperial,

301 by 22 in. 30} by 22 in. Atlas,

34 by 264 in. Columbier,

341 by 231 in. Double Demy,

38} by 26 in Double Elephant,

40 by 261 in. Antiquarian,

52 by 31 in. Double Atlas,

55 by 314 in. Emperor,

68 by 48 in. Note.-American paper is usually rather larger than English paper of the

Bame name.

QUEST.—270. What do the terms, folio, quarto, &c., denote, when applied to books ! What is a folio? A quarto ? An octavo? A duodecimo ? An 18mo.? A 36mo. ?

FRENCH MONEY, WEIGHTS, AND MEASURES. 271. The new system of Money, Weights, and Measures of France, adopted in 1795, was formed according to the decimal Notation.

FRENCH MONEY.

272. The Franc is the unit money of the new system of French currency. It is a silver coin, consisting of to pure silver, and to of alloy.

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Note.—The value of a franc by Act of Cor ess in 1843, is $.186. The value of the livre tournois, the former unit of money, is $.185.

FRENCH LINEAR MEASURE.

273. The standard unit of the French Linear Measure, is the Metre. Its length, according to the mean of the several comparisons of Troughton, Nicollet and Hassler, is equal to 39.3809171 English, or United States inches.

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10 metres make 1 decametre = 32.817431 U. S. feet.
10 decametres 1 hectometre 328.17431
10 hectometres 1 kilometre 3281.7431
10 kilometres 1 myriametre = 32817.431

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Note.-1. The standard by which the new French measures of length are determined, is the quadrant of a meridian of the earth, or the terrestrial arc from the equator to the pole, in the meridian of Paris. The ten-millionth part of this arc is called a metre, which is equal to 39.381 U. S. in., nearly.

2. The melre is divided into 10 decimetres; the decimetre into 10 centimetres; the centimetre into 10 millimetres.

3. The denominations of the old system of linear measure were the toise, foot, inch, line, and point. 12 points=1 line; 12 lines=1 inch ; 12 in.=1

6 ft.=1 toise. The old French foot was equal to 1.066 U. S. feet. 4. By a decree of 1812, the Toise, Aune, Foot, &c., are allowed to be used, having the following ratios to the metre, viz: the toise=2 metres; the foot= 4 metre; thè inch=ita metre; the aune or ell=1} metre; the bushel=hectolitro.

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