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No. 1 represents a square yard; that is, each of its four sides is one yard in length. Each of the sides are divided into three parts, representing feet, by lines running across the figure, which is thus divided into nine equal surfaces, each representing one square foot. Now, if we take the whole length, 3 feet, and one foot in breadth, we shall have 3x1=3 square feet. Taking 2 feet broad, and 3 feet long, we have 2X3=6 square feet. And, taking the whole figure, we have 3X3=9 square feet. By using a similar process in No. 2, it will appear that there are 144 square inches in one square foot. The figures also distinctly show why 3 square feet are only f of 3 feet square; and 12 square inches of 12 inches square.
VI. MEASURE OF SOLIDITY.
For solid or cubic Measures. 1728 cubic inches (c. i.)=12x12x12,
that is, 12 long, 12 broad, and 1 cubic foot. .
12 deep, make 27 cubic feet=3X3X3
1 cubic yard. C. yd. 40 cubic feet of round timber, or
T. 50 of square timber, 42 cubic feet of shipping
T. 16 cubic feet.
1 cord foot.
A pile of wood 8 feet long, 4 feet wide, and 4 feet high, contains just one cord, since 8X4X4=128.
By this measure, firewood, timber, stone, and other articles which have the dimensions of length, breadth, and thickness, and are of regular form, are measured. It has been shown that a square yard, or yard of surface, by
having two dimensions, contains 3X3 =9 square feet. In like manner, a cubic, or solid yard, having three dimensions, contains 3X3X3=27 cubic feet, as will evidently, appear from an inspection of the figure. The difference between a cube of 3 feet and 3 cubic feet, will also be
apparent, the one being only $ of the other.
This measure is used for estimating latitude and longitude, and also in meas
easuring the motions of the heavenly bodies. Every circle, whether great or small, is supposed to be divided into 360 equal parts, called degrees. A degree of a great circle of the earth contains 60 geographical miles, equal to 693 statute miles.
VIII. MEASURE OF TIME.
hr. 24 hours
day. 7 days
1 week. wk.
Four weeks are sometimes called a month. In computing interest, 30 days are considered a month, when no particular ones are named. The calendar months are 12 in number. Their length is as follows:
When the hundreds of any centennial year, and when the tens and units of any other year, are divisible by 4, every such year is called leap-year, and then February has 29 days. The number of days in each calendar month will be more easily remembered by committing to memory the following lines :
Thirty days hath September,
The solar, or true year, consists of 365 days, 5 hours, 48 minutes, and 48 seconds. The Julian year consists of 365 days and 6 hours. The calendar year consists of 365 days for three successive years; every fourth year, which is called bissextile, or leap-year, having 366. The calendar year is thus adjusted to the Julian year. By the omission of the odd day of the first year of the century (which would always be leap-year) for three out of four centuries, the calendar year is so nearly adjusted to the true, or solar year, that the only correction it will require will be the suppression of a day and a half in five thousand years.
IX. Books. A sheet folded in 2 leaves is called a folio. 4
quarto, or 4to. 8
octavo, or 8vo. 66 12
duodecimo, or 12mo. 16 18
octodecimo, or 18mo. 66 24
1 great gross. 20 things
1 score. 24 sheets of paper
1 quire. 20 quires (19 good, 1 broken) 1 ream. [or salmon. 200 pounds
1 barrel of pork, beef, shad, 196 pounds.
1 barrel of flour. 30 pounds
1 barrel of anchovies. 112 pounds
1 barrel of raisins. 256 pounds
1 barrel of soap. 71 pounds
1 gallon of train oil. 11 pounds ·
1 gallon of molasses. 14 pounds
1 stone of iron or wood. 8 pounds .
1 stone of meat. 28 pounds
1 tod. 56 pounds
1 firkin of butter. 94 pounds
1 firkin of soap. 112 pounds
1 quintal of fish. 30 gallons
1 barrel of fish. 364 pounds
1 sack. 191 cwt..
1 fother of lead. 32 gallons
1 barrel of cider. 8 bushels of salt
1 hhd. at sea. 71 bushels of salt
1 hhd. on shore.
Specimen of the mode of questioning the classes, after they have recited a table.-1. How many mills make a cent? How many cents make a dollar ? How many mills in a dollar, then ? How many dollars make an eagle? How many mills in an eagle, then? How many cents in an eagle? 2. How many farthings in a penny? How many pence in a shilling? Then how many farthings in a shilling? How many shillings in a pound? How many farthings in a pound ? How many pence in a pound? 3. How many grains in a pennyweight? How many pennyweights in an ounce ? Then how many grains in an ounce ? and so on throughout the tables, till they are thoroughly committed to memory.
a. Change of Form. [It has already been shown, when treating of Common Fractions, p. 193, 4, that it is sometimes extremely convenient to change their form, without altering their value, and that this is effected by multiplying or by dividing both terms by the same number. Such a change of form is equally convenient and necessary in the case of Determinate Fractions, and it is effected in precisely the same manner. This we shall readily perceive if we only notice that the sole difference between them is, that the denominations of the one are limited in number, and expressed in words or signs, while those of the other are unlimited in number, and expressed by figures written under them. Thus, if a pound sterling is considered the unit, 5 shillings is the same thing as zo. If we wish to change the sum into pence, by multiplying by 12 (the number of pence in a shilling), we have 60 pence, or . Here the intimate connection of determinate with common fractions is too evident to escape notice. By multiplying the denominator (shillings) by 12, it is changed to pence, reducing the value of the determinate fraction twelve fold, just as, by multiplying the denominator of the common fraction, zo, by 12, we change it to zko, reducing its value twelve fold. And as, by multiplying the numerator in both fractions by 12, we increase their value twelve fold, it is evident that by multiplying both terms in either fraction by the same number, the value of the fraction is unchanged.
Again : if a bushel be considered the unit, 8 quarts is the same as . If we wish to change the quarts to gallons, dividing both terms by 4 (the number of quarts in a gallon), the 8 quarts become 2 gallons, and the common fraction becomes . In neither case is there the slightest change of value. For, by dividing the denominator of the determinate fraction by 4, the quarts are changed into gallons, thus enhancing the fraction four fold; and by dividing the numerator by 4, thus diminish