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debit items of interest by 75 x 30 x 7, we may increase the credit items of interest by this same quantity.

From which we see that the difference between 100 x 182x+400 x 106x7 and 50x153x+ 375×78x+75 x 30 x fg is the interest balance. The operations indicated in the foregoing work may be exhibited in a more condensed form, as follows:

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of 21450-$4.11-interest balance.

Hence the foregoing account will become balanced as

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Place such sum on the debtor or credit side as may necessary to balance the account, which sum may be regarded as MERCHANDISE BALANCE. Then multiply the number o dollars in each entry by the number of days from the time such entry was made, to the time of settlement; observing to multiply the merchandise balance by the number of days for which credit is given.

Multiply the difference between the sum of the debit products, and the sum of the credit products, by the interest of $1 for 1 day; the product will be the number of dollars in INTEREST BALANCE, which will be in favor of the debit side of account, when the sum of debit products exceeds the sum of credit products; but in favor of the credit side when the sum of credit products exceeds the sum of debit products. If, then, the interest balance be added to, or subtracted from, the merchandise balance, as the case may require, it will give the cash balance.

EXAMPLES.

1. Suppose A has the following account with B:

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What is the cash balance of the above account on the 1st of July, 1848, provided each individual is allowed 90 days time on his purchases, if interest is estimated at 7 per cent.?

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hence $1.49 is the interest balance, which balance is in favor of the credit side; but $150, the merchandise balance, was in favor of the debtor side; consequently the casă balance is $150-$1.49 $148.51 in favor of A.

2. Suppose A's account with B to have been as fol· lows:

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What is the cash balance, and in whose favor, on the 1st of August, 1848, provided 6 months, or 180 days' time is given, interest being 6 per cent.?

NOTE. In practice, when the cents in any of the en ries, as in this example, are less than 50, we may, without sensible error, omit them; but when they are 50, or greater, we may consider them as an additional dollar.

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fog of 112154=18.44 nearly; hence $18.44 is the interest balance, which balance is in favor of the debtor side. The merchandise balance of $80.48 was also

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in favor of the debtor side, consequently the cash balance is $80-48+$18·44-$98.92 in favor of A.

What is meant by a cash balance? What is meant by merchandise balance? Instead of diminishing one side of a book account by a certain sum, what may done? How is the interest balance found? In favor of which side of an account be will the interest balance be? Repeat the Rule. In practice, what may be done with the cents in any of the entries ?

INVOLUTION.

129. THE product arising from multiplying a number into itself is called the second power, or the square of that number. Thus, 3x3=9: the number 9 is the square of 3.

If the square of a number be again multiplied by that number, the result is called the third power, or the cube of the number. Thus, 3×3×3=27: the number 27 is the cube of 3.

The word power denotes the product arising from multiplying a number into itself a certain number of times; and the number thus multiplied is called the root. Thus, 9 is the second power of 3, and 3 is the square root of 9. In the same manner 27 is the third power of 3, and 3 is the cube root of 27.

The product arising from multiplying a number into itself is called what? If it be ed as a factor three times, what power is it? The number 9 is what power of 3? The number 27 is what power of 3? What is the square root of 9? What is the cube root of 27?

130. Involution is the method of finding the powers of numbers.

To denote that a number is to be raised to a power, a

small figure is placed above, a little to the right of the number whose power is to be found.

The small figure is called the index, or exponent.

Thus, 42-4x4-16; here the exponent is 2, and 42 de notes the second power of 4.

31 =

32=3x3=

=

In the same way we have

3 the first power of 3.

9 the second power of 3.

33 3x3x3 27 the third power of 3. 34 3x3x3x3= 81 the fourth power of 3. 35=3x3x3x3x3=243 the fifth power of 3.

&c.,

The second power of a number is called the square of that number, because it may be represented by means of a geometrical square. Thus, in the adjacent figure if the side of this square is 12 linear units, as 12 inches long, its entire surface will be denoted

by 12 x 12 144 square units,

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which in this case will be 144 square inches.

For a similar reason, the

third power of a number is called the cube of that number, since it can be represented by the geometrical cube, as in the adjacent figure, where the side of the cube is supposed to be 3 linear feet, consequently each face will be 3x3=9 square

3 feet.

3 feet.

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feet, and its volume will be 3x3x3=27 cubic feet.

3 feet.

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