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NOTE 1. — By the table, it is evident that each of the measures of capacity is a species of cubic measure; and to change cubic measure, expressed in cubic inches, to any denomination of either dry, liquid, or beer measure, divide by the number of cubic inches required to make a unit of the proposed denomination. Thus, to reduce 14ft. 294in. cubic measure to gallons of liquid measure: 14 cu. ft. 294 cw.in. 24486 cu. in.; 24486 cu. in. ; 231 = 106 gallons, liquid measure.

NOTE 2. – To change a quantity from one measure of capacity to its equive alent in another, reduce the given quantity to cubic inches, and then find their value in denominations of the proposed measure.

EXAMPLES.

1. Change 4hhd. 15 gal. beer measure to liquid measure ? 2. Change 4hhd. 30 gal. liquid measure to beer measure ?

3. If a milkman buy 2820 gallons of milk at 4 cents per quart, beer measure, and sell the same at 6 cents per quart, liquid measure, what will he gain?

Ang. $ 375.0244 4. If 2538 gallons of milk have been purchased by liquid measure, at 4 cents per quart, and the same has been sold by beer measure at 6 cents per quart, what has been the gain?

Ans. $ 92.88. 5. A merchant bought 385 bushels of seed peas at $ 4.00 per bushel, dry measure. He sold the same at 20 cents per quart, liquid measure.

What did he gain by the purchase ?

Ans. $ 1327.20. 6. J. Day bought 1000 bushels of corn at $ 1.05 per bushel, dry measure, and sold the same at $ 1.12 per bushel, liquid

Did he gain or lose by the operation, and how much ?

7. My hogshead contains 30 cubic feet. How many more gallons of dry measure will it contain, than of beer measure ?

8. Bought of my neighbor, John Smith, 365 gallons of milk, at 5 cents per quart; but by mistake he measured it in his liquid measure. How much did I lose ?

measure.

MEASURE OF TIME.

142. This measure is applied to the various divisions and subdivisions into which time is divided.

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W.

TABLE. 60 Seconds (sec.)

make 1 Minute, 60 Minutes

1 Hour, 24 Hours

1 Day, 7 Days

1 Week, 3654 Days, or 52 weeks 14 days, 1 Julian Year, 12 Calendar Months (mo.)

1 Year, sec.

m. 60

1 3600

60

1

d. 86400

1440

24

1 604800

10080
168

7 31557600

525960 8766 3651

y: y.

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W.

y. 1

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. 491/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 129 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 most nations of the earth, contains, like the Julian year, 365 days for three years in succession, and 366 for the fourth, excepting centennial years whose number cannot be exactly divided by 400. 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.

The manner of reckoning time according to the Julian Calendar is termed Old Style, and that according to the calendar of Gregory, New Style. England did not adopt the new style till 1752, when, according to an act of Parliament, the difference between the two styles, which then amounted to 11 days, was removed, by the day following the 2d of September of that year being accounted the 14th day. The difference now between old and new style is 12 days.

A Coinmon 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.

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;
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."

96 sec.

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

SAME DAY OF ANY OTHER MONTH IN THE SAME YEAR.

89

FROM ANY

TO THE SAME DAY OF NEXT DAY OF

Jan. Feb. Mar. Apr. May. June July. Aug. Sept. Oct. Nov. Dec. JANUARY 365

31

59 90 120 151 181 212 243 273 304 334 FEBRUARY 334 365 28 59

120 150 181 212 242 273 303 MARCH 306 337 365 31 61 92 122 153 184 214 245 275 APRIL 275 306 334 365 30 61 91 | 122 153 183 214 244 MAY 245 276 304 335 365 31

92 123 153 184 214 JUNE

214 245 273 304 334 365 30 61 92 122 153 183 JULY 184 215 243 274 304 335 365 31 62 92 123

153 AUGUST 153 184 212 243 273 304 334 365 31 61 92 122 SEPTEMBER 122 153 181 212 242 273 303 334 365 30 61 91 OCTOBER 92 123 151 182 212 243 273 304 335 | 365 31 61 NOVEMBER 61 92 | 120 151 181 212 242 273 304 334 365 30 DECEMBER 31 62 90 121 151 182 212 243 274 | 304 335 365

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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 for 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, and 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.

EXAMPLES.

1. How many seconds in a solar year?
2. In 31556929 seconds how many days?

3. How many seconds from the deluge, which took place 2348 years before Christ, to the year 1856, a year being 3651 days?

Ans. 132636592800. 4. In 74726807872 seconds how many solar years ?

Ans. 2368 years. 5. How long did the last war with England continue; it having commenced June 18th, 1812, and ended February 17th, 1815?

Ans. 974 days 2 years 244 days.

CIRCULAR ANGULAR MEASURE.

143. Circular Angular 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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60 Seconds (0)

make 1 Minute, 60 Minutes

1 Degree, 30 Degrees

i Sign, 12 Signs, or 360 Degrees,

The Circle of the Zodiac,

S. C.

1

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210

300

330

210

360

180

30

150

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60 3600

60

1

S. 108000

1800

30

1

C. 1296000

21600

360
12

1 NOTE 1. - A Circle is a plane figure 270

bounded by a curve line, all parts of which are equally distinct from a point called its center.

T'he 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 center to its circumference;

as CA, CB, or CD. 06

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 900; 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 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 = 1200 is the measure of the angle ACD, and AB 900, the measure of the angle ACB; hence the one is called an angle of 1200, and the other an angle of 900.

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 3600 of longitude every hour, or 150 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, when it is noon at any place, it is 1 hour earlier for every 15° of longitude westward, and 1 hour later for every 150 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.

EXAMPLES 1. How many minutes in 27S. 27° 43' ? 2. In 50263 minutes how many signs ? 3. How many seconds in 44S. 18° 57' 23" ? 4. How many signs in 4820243"? 5. How many seconds in 360° ? 6. How many degrees in 1296000" ?

MISCELLANEOUS TABLE.

1 gross.

12 gross

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8 pigs

144. The following denominations, frequently used, are not embraced in the preceding tables. 12 units

make 1 dozen. 12 dozen

1 great gross. 20 units

1 score. 24 sheets of Paper

1 quire. 20 quires

1 ream. 2 reams

1 bundle. 5 bundles

1 bale. 14 pounds of Iron or Lead

1 stone. 211 stone

1 pig.

1 fother 18 inches

1 cubit. 243 cubic feet of Stone

1 perch. 60 pairs Shoes

1 case. 25 pounds of Powder

1 keg: 56 pounds of Butter

1 firkin. 100 pounds of Fish

1 quintal. 196 pounds of Flour

1 barrel. 200 pounds of Beef or Pork

1 barrel. 100 pounds of Grain

1 cental. 200 pounds of Shad or Salmon, in N. Y. & Ct.“ 1 barrel. 220 pounds of Fish, in Md.

1 barrel. 256 pounds of Soap

1 barrel. 300 pounds of Hydraulic Cement

1 barrel. 30 gallons of Fish, in Mass.

1 barrel. 5 bushels of Shelled Corn, in Southern States “ 1 barrel. 8 bushels of Salt

1 hogshead. NOTE 1. — A sheet of paper folded into 2 leaves forms a folio; a sheet folded into 4 leaves, a quarto; a sheet folded into 8 leaves, an octavo; a sheet folded into 12 leaves, a 12mo; a sheet folded into 18 leaves, an 18mo; a sheet folded into 24 leaves, a 24mo.

NOTE 2. - Of shoemaker's measure, No. 1 of small size is 4} inches in length; and No. 1, large size, is 854 inches in length; and each succeeding number of either size is f of an inch additional length.

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EXAMPLES

many sheets ?

1. In 4 bales 4 bundles 1 ream 10 quires of paper how

Ans. 23760. 2. In 23760 sheets of paper how many bales ? 3. In 10 fothers 6 pigs 8 stones of iron how many pounds ? 4. In 25998 pounds of iron how many fothers ?

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