The Average Term of Credit is the time the debts due at different times have to run, before they may be equitably settled by one payment.

To find the Equated Time of Payment when the Terms of Credit begin at the Same Date.

RULE.

Multiply each debt by its term of credit, and divide the sum of the products by the sum of the debts. The quotient will be the average term of credit.

Add the average term of credit to the date of the debts, and the result will be the equated time of payment.

To find the Equated Time when the Terms of Credit begin at Different Dates.

RULE. Find the date at which each debt becomes due. Select the earliest date as a standard.

Multiply each debt by the number of days between the standard date and the date when the debt becomes due, and divide the sum of the products by the sum of the debts. The quotient will be the average term of credit from the standard date.

Add the average term of credit to the standard date, and the result will be the equated time of payment.

RATIO

Ratio is the relation one number bears to another of the same kind.

The Terms of the ratio are the numbers compared.

The Antecedent is the first term.

The Consequent is the second term.

The antecedent and consequent form a couplet.
PRINCIPLES.-See Fractions.

PROPORTION

A Proportion is formed by two equal ratios.
The Extremes of a proportion are the first and last terms.
The Means of a proportion are the second and third terms.

PRINCIPLES. The product of the means is equal to the product of the extremes.

Either mean equals the product of the extremes divided by the other mean.

Either extreme equals the product of the means divided by the other extreme.

RULE FOR PROPORTION. Represent the required term by x. Arrange the terms so that the required term and the similar known term may form one couplet, the remaining terms the other. If the required term is in the extremes, divide the product of the means by the given extreme.

If the required term is in the means, divide the product of the extremes by the given mean.

PARTNERSHIP

Partnership is an association of two or more persons for business purposes.

The Partners are the persons associated.

The Capital is that which is invested in the business.

The Assets are the partnership property.

The Liabilities are the partnership debts.

To find the Profit, or Loss, of Each Partner when the Capital of Each is Employed for the Same Period of Time.

RULE.

Find the part of the entire profit, or loss, that each partner's capital is of the entire capital.

To find the Profit, or Loss, of Each Partner when the Capital of Each is Employed for Different Periods of Time.

RULE. -Find each partner's capital for one month, by multiplying the amount he invests by the number of months it is employed; then find the part of the entire profit, or loss, that each partner's capital for one month is of the entire capital for one month.

INVOLUTION

A Power of a number is the product obtained by using that number a certain number of times as a factor.

The First Power of a number is the number itself.

The Second Power of a number, or the Square, is the product of a number taken twice as a factor.

The Third Power of a number, or the Cube, is the product of a number taken three times as a factor.

An Exponent is a small figure written a little to the right of the upper part of a number to indicate the power.

Involution is finding any power of a number.

To find the Power of a Number.

RULE.

Take the number as a factor as many times as there are units in the exponent.

EVOLUTION

A Root is one of the equal factors of a number.

The Square Root of a number is one of its two equal factors. The Cube Root of a number is one of its three equal factors.

Evolution is finding any root of a number.

Evolution may be indicated in two ways: by the Radical Sign, V, or by a fractional exponent.

The Index of a root is a small figure placed a little to the left of the upper part of the radical sign, to indicate what root is to be found. In expressing square root, the index is omitted.

In the fractional exponent, the numerator indicates the power to which the number is to be raised; the denominator indicates the root to be taken of the number thus raised.

To find the Square Root of a Number.

RULE.-Point off in periods of two figures, commencing at units. Find the greatest square in the first period and place the root in the quotient. Subtract this square from the first period, and bring down the next period.

Multiply the quotient figure by two, and use it as a trial divisor. Place the second figure in the quotient, and annex it also to the trial divisor. Then multiply the figures in the trial divisor by the second quotient figure, and subtract.

Bring down the next period, and proceed as before until the square root is found.

To find the Square Root of a Fraction.

RULE. Reduce the fraction to its simplest form, and find the square root of each term separately.

To find the Cube Root of a Number.

RULE.- Point off in periods of three figures each, beginning at

units.

Find the greatest cube in the first period and place the root in the quotient. Subtract this cube from the first period, and bring down the next period.

Multiply the square of the first quotient figure by three and annex two ciphers for a trial divisor. Place the second figure in the quotient. Then, to the trial divisor add three times the product of the first and second figures, also the square of the second. Multiply this sum by the second figure and subtract.

Bring down the next period, and proceed as before until the cube root is found.

To find the Cube Root of a Fraction.

RULE. Reduce the fraction to its simplest form, and find the cube root of each term separately.

STOCKS AND BONDS.

Capital Stock is the money or property employed by a corpora

tion in its business.

A Share is one of the equal divisions of capital stock.
The Stockholders are the owners of the capital stock.

The Par Value of stock is the face value.

The Market Value of stock is the sum for which it may be sold.

Stock is at a premium when the market value is above the par value; at a discount, when below par.

Bonds are interest-bearing notes issued by a government or a corporation.

A Dividend is a percentage apportioned among the stockholders. A Stock Broker is a person who deals in stocks.

Brokerage is a percentage allowed a stock broker for his services. In Stocks and Bonds,

The par value is the base.

The rate per cent premium, or discount, is the rate.
The premium,

discount, or is the percentage.

dividend

The market value is the { amount, or

difference.

NOTES, DRAFTS, AND CHECKS.

A Promissory Note is a written promise to pay a specified sum on demand, or at a specified time.

The Face of a note is the sum named in the note.

The Maker is the person who signs it.

The Payee is the person to whom the sum specified is to be paid.

The Indorser is the person who signs his name on the back of the note, thus becoming liable for its payment in case of default of the maker.

An Interest-bearing Note is one payable with interest.

If the words "with interest" are omitted, interest cannot be collected until after maturity.

A Demand Note is one payable when demand of payment is made.

A Time Note is one payable at a specified time.

A Joint Note is one signed by two or more persons promise to pay.

who jointly