If interest were not considered, the above account could be balanced as follows:

Had no credit been given, the debits should be increased by the following items of interest: (See Table, ART. 76, and Rule, ART. 114.)

On $100 for 182 days at 7 per cent. 100 x 182 × 97.

66

=400 x 106 × 107.

(6 400" 106 66 In like manner the credits should be increased by interest:

On $50 for 153 days at 7 per cent. 50 × 153 × 0. "375" =375 × 78×07

78

66

66

But, since 30 days credit is given on all sums, it follows that by the above, we should increase the debits by an excess of interest equal to the interest of the sum of debits, $500, for 30 days=500 × 30×907. In like manner we should increase the credits by an excess of interest equal to the interest of sum of credits, $425, for 30 days 425 x 30 x

Now if, instead of diminishing the debit items of interest by 500 × 30×7, and the credit items of interest by 425 ×30×907, we merely diminish the debit items of interest by the interest on merchandise balance, $75, for 30 days, which is 75×30×907, the result will be the same. And since taking any sum from one side of a book account has the same effect as adding the same sum to the other side, it follows, that instead of diminishing the

debit items of interest by 75 × 30×907, we may increase the credit items of interest by this same quantity.

From which we see that the difference between 100 × 182×+ 400 × 106 × 7 and 50 × 153×907+ 375×78×7+75×30×907 is the interest balance. The operations indicated in the foregoing work may be exhibited in a more condensed form, as follows:

7 of 21450-$4.11=interest balance.

Hence the foregoing account will become balanced as

Place such sum on the debtor or credit side as may be necessary to balance the account, which sum may be regarded as MERCHANDISE BALANCE. Then multiply the number of 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.

Dr.

EXAMPLES.

1. Suppose A has the following account with B :

1848.

Jan. 1. To Merchandise,

Merchandise balance $150

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.?

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 cash balance is $150-$1.49 $148.51 in favor of A.

2. Suppose A's account with B to have been as follows:

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 entries, 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.

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

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 be done? How is the interest balance found? In favor of which side of an account 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 Thus, 3×39: the number 9 is the square

number. 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 used 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