He will also be taught to balance; that is, to find the difference between two sums by addition instead of subtraction. Thus, if the two sums be .£1,347 16s. 3d. and £4,834 19s. 8d., he will be apt at first to put one under the other and subtract, in this way:-

 £4,834 19 8 1,347 16 3 Difference . . . £3,487 3 5

But he must be taught to proceed by a mental process, and will add the difference to the smaller number, thus:-

 £1,347 16 3 - 4,834 19 8 Difference . . . 3,487 3 5 £4,834 19 8

He performs this operation by beginning with the pence, saying, or rather, thinking, " three and five make eight," and so on. And thus the two sides of an account are made to balance; that is, both sides are of the same amount.

The principle of balancing pervades the whole system of book-keeping. For example, we know that if to the amount of cash in the bank last night we add the amount received to-day, and deduct the amount paid to-day, the remainder will show the amount on hand to-night; and a novice would very naturally put it down in this form:-

 £ Cash on hand last night....... 100,000 Received to-day........ 60,000 160,000 Paid to-day............ 80,000 Cash on hand to-night................. 80,000

But an accountant would arrange these four items in such a way as to form a balance, thus :-

 £ £ Cash paid away to-day . 80,000 Cash on hand last night 100,000 Cash on hand to-night . 80,000 Cash received to-day 60,000 £160,000 Balance . . £160,000

In keeping the Progressive Ledger, the principle of balancing is of constant occurrence. The ledger-keeper brings out a new balance every time he turns to an account. But he never deducts-always adds. And if he posts several articles at the same time, the method is the same, thus:-

 If the credit balance is........................ £1,214 3 7 And he posts the following sums to the debit of the account. . £141 2 4 8 7 6 49 3 11 305 4 2 £710 5 8

he will add up these items, and mentally add a sum that will make the whole equal to £1,214 3s. 7d., bringing out this sum as a new balance, and placing it under the former one as he goes on. Thus he will say, or rather think,-"4 and 6 are 10, and 11 are 21, and 2 are 23, and (here he must supply the figure) 8 are 31 = 7 and carry 2; " and he puts down the 8 in the pence division of the balance column; and goes on in the same way to the shillings, and afterwards to the pounds. "When he has placed this sum, £710 5s. 8d., he adds up the whole, including this sum, in order to check the operation, and to be sure that he is right.

He will then acquire a knowledge of the names and functions of the different books, and of the terms and phraseology used in book-keeping. The same book is sometimes called by different names in different banks, and different terms are employed to describe the same operations. But every clerk should use the language of the office in which he is placed. He should call every book by its proper name, and employ the phrases which are used by others. For instance, if the word "money" is used to denote coin, he must always use it in that sense; and not say "money" when he means bank notes.

It will be of great advantage to a sensible youngster, if one of the senior clerks should take the trouble to give him a general notion of the system of book-keeping, and show him the connection that exists between the books that he keeps and the other books of the office.

II. "We shall now describe the system of Banking Book-keeping, as published in the former editions of this work.

Every person, on opening an account with a London banking-house, enters his name in a book called the Signature-Book, and this book is referred to whenever a draft is presented having a doubtful signature. The person is supplied free of cost-stamps excepted-with a book of printed drafts and a cash-book, called in some houses a Pass-Book, in which is entered an account of his debits and credits, as often as he thinks proper to leave it for that purpose.

London bankers do not usually give receipts for money paid into their hands, but they enter the amount into the customer's book. A person paying money on account of a country bank, will sometimes recpuire a receipt, and he may then be given a simple acknowledgment.

Before explaining the banking system of book-keeping, I will define a few terms which are often used in connection with the subject. By the word bill is always meant a bill of exchange not yet due. The word cash denotes the various items included in a credit or cash entry, and may denote due bills, cheques, bank notes, country notes, or coin. The terms cheque and draft are used synonymously, and denote an order on a banker, payable on demand. The word draft is never used in London to denote a bill of exchange, though this use of the term is very common in the country. Both bills and drafts are often called articles; and if they are cash, they are styled cash articles. An addressed bill is a bill made payable at a banking-house. A discounted bill is usually called a discount. By money is always meant coin. To post an article is to place or enter it in the ledger. One book is said to mark against another when the same entry is made in both books. One book is checked by another, when any error in one book would be detected by some operation in another. To check a book, or an account, is to examine it, and prove it correct, or make it so. To cast, or cast up, means to add together. The balance of an account is the difference between the credit and the debit side. An account is said to balance when the credit and the debit side are of the same amount. To balance an account is to enter the balance, and to add up both sides, and then to bring down the balance as a new amount. The credit side of an account, or that on which the cash received is placed to the credit of a customer, is the right-hand side as you face the ledger; the debit side is the left-hand side. In London, the establishments of bankers are usually called banking-houses, not banks. A person who has an account at a banking-house is said to keep a banker.

I shall now describe the various books in the order of the different departments to which they belong.