A pile of wood 8 feet long, 4 feet wide, and 4 feet high, contains just one cord, since 8X4×4-128.

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.

G

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 appar ent, the one being only of the other.

This measure is used for estimating latitude and longitude, and also in measuring 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 691⁄2 statute miles.

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,
April, June, and November;
February hath twenty-eight alone;
All the rest have thirty-one;
Except in leap-year, when, in fine,
February's days are twenty-nine.

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.

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 shillings in a

how many farthings in a shilling? pound? How many farthings in a pound? How many pence in a pennyweight? How Then how many grains in

in a pound? 3. How many grains many pennyweights in an ounce? 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. 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 40. 60 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, %, by 12, we change it to go, 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.

5

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

ing the fraction four fold, the one effect completely counterbalances the other, and leaves the value of the fraction unchanged.

It is evident, then, whether these numbers be considered as fractions or as compound numbers, that, when we wish to change their form from one of a greater to one of a less value, it must be performed by multiplication; because the greater number of less value will be equivalent to the less number of greater value. And, on the contrary, when we wish to change their form from a denomination of less value to one of greater, it must be performed by division, since the smaller number of greater value will be equivalent to the greater number of less value. Thus, to change 4 pounds to shillings, the 4 must be multiplied by 20 (the number of shillings in a pound), since 80 shillings 4 pounds. And, to change 80 shillings into pounds, the 80 must be divided by 20, since 4 pounds=80 shillings. Hence, also, it results that questions of this sort may be proved by changing the number back to its original denomination.]

Federal money being arranged on the decimal scale, no other operation is necessary, in changing a number from one denomination to another, than a mere change of the separatrix. Thus, to change 5 eagles through all the inferior denominations, and vice versa,

e. $ d. C.

m.

C.

d. $

e.

5=50'=500'=5000=50,000-5000'0=500'00—50'000=5'0000

Exemplification for the Black-board.

1. Change £3 5s. 6d. 3q. to farthings.

Suggestive Questions.-How many farthings in one pound? Why, then, are the three pounds multiplied by 960? Of what denomination, then, is the 2880? How many farthings in one shilling? Why, then, are the 5s. multiplied by 48? denomination, then, is 240? How many farthings in ny? Why, then, are the pence multiplied by 4?

Of what one penOf what