and requires the fourth term to be greater than the second.

Rule. State the question, and if necessary, reduce the terms as before. Multiply the first and second terms together, and divide the product by the third; the quotient will bear such proportion to the second, as the first does to the third.

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Example. If a certain quantity of work be executed in 28 days by five men, how inany men will do the same in 10 days?

COMPOUND PROPORTION, or Double Rule of Three, or Rule of Five, is a rule in which more than three terms are given to find another dependent upon them.

Rule. Place the terms of supposition one above another in the first place. Set down in the middle, the term which is of the same nature with the answer sought. Place the terms of demand one above another in the third place. Multiply the numbers standing under each other on the left hand side of the middle term; and in like manner multiply together all those on the right hand side of it. Then multiply the middle term by the latter product, and divide the result

by the former product; and the quotient will be the answer required.

Example. If 8 men can reap 40 acres in 7 days, how many acres may be reaped by 23 men in 28 days?

24×28×40=26880
26880-7 x8 = 56

Product 480 acres

which is the answer.

PRACTICE, SO called from its general use in business, is a short method of working the rule of three direct; that is, whenever the first term of the questions is unity.

All questions in this rule are performed by taking aliquot parts. The aliquot parts of any quantity or number; are such as will exactly divide it without remainder. Thus three and six are aliquot parts of eighteen, six-pence is an aliquot part of a shilling; and four shillings is an aliquot part of a pound.

Example. Bought 3428 lbs. of beef at 84d per lb. what is the amount?

TARE AND TRET are a set of practical rules which teach how to deduct certain allowances

made by wholesale dealers, on selling their goods by weight.

INTEREST is the sum of money paid or allowed for the loan of some other sum lent for a certain time, according to some fixed rate.

The sum lent is called the principal.

The sum which is paid for every hundred pound lent, by the year, is called the rate.

The principal and rate added together" is called the amount.

Simple interest is that which is reckoned on the principal only, during the whole time it is lent.

Compound interest, is that which is reckoned not only on the principal, but also upon the interest, which may remain unpaid; and which consequently must be continually augmenting, until payment of the amount be made.

All the operations of calculating interest are carried on by rules of proportion, in which three quantities are given to find a fourth. The usual proportion is, as £100 is to the sum proposed, so is the interest, or value, of £100 to the required interest or value of the proposed

sum.

COMMISSION or brokerage, is an allowance of a certain sum, upon every hundred pounds, to an agent for buying and selling goods; or to a banker for drawing bills.

BUYING AND SELLING STOCKS.

Stock is a general name for the capital of any

trading company. It signifies, also, any sum of money lent to government, on condition of receiving a certain interest, till the money shall be repaid.

The price of stocks, or the rates per cent, are the several sums for which £100, of the respective stocks sell at any time.

INSURANCE is the obtaining a security for goods or possessions of any kind, in consideration of paying a premium of so much per cent. The insurers engage to answer for damage or loss by fires, casualties at sea, or other accidents.

DISCOUNT is an interest allowed by the debtor to the creditor, when a bill or draft is given instead of ready money, or when long credit is granted.

Rebate signifies a reduction made by the creditor to the debtor, when a payment is made before the time when it becomes due, or when a bill or draft payable at a future date is exchanged for ready money.

PROFIT AND Loss. This rule teaches to ascertain how much is gained or lost, on the prime cost in the purchase and sale of goods; it shows also how to fix the price of goods so as to gain a certain sum per cent.

FELLOWSHIP, is a rule, by which any sum or quantity may be divided into any number of parts, which shall be in a given proportion to one another. This is a very useful rule; as by it, the gains or losses of partnerships; the ef

fects of bankrupts; or legacies, in case of a deficiency, in the assets; or the shares of prizes, are arranged and settled.

ALLIGATION teaches how to mix together simples of different natures, so that the composi tion may be of some intermediate quality or

rate.

EXCHANGE is the receiving of money in one country for the same value paid in another.

POSITION is a method of working certain questions which cannot be resolved by the common direct rules. It is sometimes called the rule of false, because it makes a supposition of false numbers to work with, as if they were the true numbers, and, by this means, discovers the true numbers sought.

INVOLUTION is the raising of powers from any given number as a root.

A power is a number produced by multiplying any given number, called the root, a certain number of times continually by itself. Thus, 22 is the root or first power of 2

1

2×24 is the second power or sq.of2 2×2×28 is the third power or cube of 2 2×2×2×2 = 16 is the fourth power of 2, &c. The number denoting the power is called the index or exponent; and it is more than the number of multiplications used in producing the

same.

Thus 1, is the index of the first power; 2, of the second power; 3, of the third power; 4, of the fourth power, and so on. Powers that are to be raised, are usually denoted by placing the index above the root, or first power.