logarithm of the quotient, as here where 96 must be divided

by 12.

quotient 80.90309

Again, divide 90 by 6, and the quotient by 5.

Logarithm of 90 is 1.95424

60.77815 subtract

In these examples the great utility of logarithms cannot be very apparent, because only such small numbers as come within the specimen of the tables are chosen: but when considerable numbers are employed, as in the following examples, the advantages of logarithms will be evident. Suppose it were required to multiply 98730 by 5865; by logarithms the operation is performed very speedily, in this way.

This multiplication done in common numbers is not only tedious but subject to mistakes, which can scarcely occur in the above short operation.

As all quantities and magnitudes may be expressed by numbers, tables have been calculated applicable to geometrical operations, founded on the nature and proportions of certain parts of circles and triangles, such as sines, tangents, and secants: but the nature and uses of these last tables must be reserved for the introduction to Practical Geometry.

CHAP. VI.

BOOK-KEEPING.

BY

Y Book-keeping or merchants' accounts is meant the method of recording, with order and accuracy, all mercantile or commercial transactions.

By book-keeping the merchant or trader obtains a particular and complete statement of every brauch of his affairs, exhibiting the profit or loss arising from each separate transaction, as well as from the whole course of his business, and affording satisfactory information on all matters in which, as a man of commercial or mercantile business, he is concerned.

A merchant's books should contain an account of the whole amount of his property employed in trade, consisting in cash, bills, public funds, goods in hand, ships, houses, lands, debts due to him, &c. By comparing the state of these several sorts of property, from time to time, he will learn the true situation of his affairs, discover whether they be prosperous or the contrary, and thence be enabled to manage them to the best advantage.

Various modes of book-keeping have been adopted in the mer-cantile world: but that which is generally followed is book-keeping by double entry. This is usually called the Italian method, having been carried into other countries from the northern parts of Italy.

To Italy the other states of Europe are indebted for the first principles of reli gion and literature, of science and of art. The inbabitants of the northern parts of Italy, known by the general name of Lombardy, comprehending the powerful commercial republics of Genoa, Pisa, and Venice, travelled to and established themselves in all those countries where mercantile transactions promised the due recompense of their labour and risk. Occupying particular quarters or streets of the places where they fixed their abode, the name of Lombard street is still preserved in Loudon, Paris, and other principal towns of Europe. Exhibiting their wares for sale an a bench (in Italian, banco) these traders came to be called bankers; and when they were unable to discharge their debts, their bench was broken, or at least taken from them: bence the Italian danco-retto, the French banque-route, and the English bankrupt. By lending money for interest upon goods, particularly upon gold and silver vessels, jewels, &c. deposited in their hands, they obtained the appellations of silver-smiths and pawn-brokers. The golden or blue balls adopted in many pla ces, as the emblems of their shops, have a reference to the arins of the Grand Duchy of Tuscany in Italy, from which many known as Lombards originally came.

In books of single entry, only such articles are recorded as are bought or sold on credit; no account being kept of those bought or sold for ready money or other immediate payment. The consequence of this is that the books can furnish no complete statement of the trader's concerns, unless assisted by taking the stock of goods remaining unsold, and so calculating the amount of gain or loss on his transactions. Single entry is therefore applicable only to small dealings or retail business. Book-keeping by double entry is, on the contrary, adapted to large, extensive and complicated commercial transactions: for it possesses this great advantage, that by merely inspecting each account, or the periodical balances of his whole concerns, the merchant can at once form a correct notion of the state of his affairs.

In keeping accounts by single entry two books are required, the Day-book and the Ledger. The day-book contains a statement of the trader's property in business, followed by a description of each transaction in the order in which it occurs. The Ledger comprises in one account, under the name of each person, the several occurrences of the day-book in which that person is concerned; the different articles in which he may be debtor or creditor, being entered in opposite pages, and thus furnishing a state of the trader's affairs with that person. The manner of keeping these two books will be readily understood from the following specimen of accounts kept by single entry.

On the 11th of April 1814, I purchase, on credit, from Richard Wilson, 124 yards of silk at 5s. 8d. per yard; value in all £35.. 2..8. On the 15th of the same month I sell to Joseph Andrews, on credit, 85 yards of that silk at 7s. 1d. per yard, amounting to £30..5..7. On the 18th Joseph Andrews pays to me £20.. 5..7, in part of his account for silk. On the 20th of the same month, 1 pay to Richard Wilson £15..2..8 in part of my debt to him. In the day-book these articles appear in this way.

2 By Silk, for 124 yards, at 5s. 8d. per yard..[ 35

2 .8

2 To Silk, for 85 yards, at 7s. 13d. per yard.. 30 5.73

In the Ledger these articles will appear in the following man

ner.

Y

Here it is to be observed that as the person who receives any money or article of merchandise becomes the debtor, and the person who gives away any money or article of merchandise becomes the creditor; having purchased silk on credit from Richard Wilson, I become his debtor and he becomes my creditor for the value of the goods: his name is therefore entered in the day-book as creditor for a certain quantity of silk at a certain value, and the amount is placed in the money columns.

In the next transaction where a part of that silk is sold on eredit to Joseph Andrews, he is entered as debtor to me for the value: and in the following occurrence when he pays me a part of his debt, I give him credit for that partial payment; that is, he appears in the book as creditor for that amount.

In the last transaction, by paying to Richard Wilson a part of what I owe him, that by giving him a sum of money, he is entered as debtor to me, or he is debited for that amount.

In this way is the day-book filled up; but in the Ledger a separate account is allotted for each person with whom I have dealings: room being left to enter all the transactions expected