RULES FOR DETECTING ERRORS IN TRIAL BALANCES

ART. 135. The first rule of the book-keeper should be to make no error, but as all are fallible a few suggestions may not come amiss.

1st. If the error is found to be in one figure only it is probably an error of footing or copying.

2d. If it involves several figures it may have arisen from the omission of an entire entry or the entering of the same twice.

3d. If it be divisible by 2, without a remainder, it may have arisen by posting an item to the wrong side of the account, in which case the item would be half of the apparent error.

4th. If the error be divisible by 9, without a remainder, it may have arisen from transposition, three cases of which may be easily detected by rules founded on the peculiar property of the number 9. They are

First. When two figures are made to exchange places with each other, the orders in notation remaining the same: e. g., 372 made to read 327, or 732, or 273.

Second. When two or more figures are made to change their places in notation, their arrangement in respect to each other remaining the same: e. g., $4275 made to read $42750, or $42.75, or $427.50.

Third. When two significant figures are made to change position both with respect to themselves and also the orders of notation e. g., $14 made to read $0.41.

To detect the first and second cases of transposition divide the amount of the error in the trial balance successively by 9, 99, 999, 9999, &c., so far as possible without a remainder, rejecting all ciphers at the right of the last significant figure in the error.

The quotients that contain but one digit figure will express the difference between the two digit figures transposed, which will be adjacent to each other if the divisor contained but one 9, separated by one other figure if it contained two 9s, by two other figures if it contained three 9s, and so on.

Those quotients, which contain two or more figures will express the number itself, which is transposed in notation simply, the arrangement of the significant figures remaining the same. In either case the order of the last significant figure in the error will be the lowest order of the figures transposed. The orders of the other figures can be easily determined by referring to the error and applying the principles of no

tation.

To detect the third case, divide the error in the balance by as many 9s as is possible so as to give only a single figure in the quotient, and then the remainder in the same way, rejecting all ciphers at the right of the last significant figure in both dividends, after which there should be no remainder.

The first quotient will be the figure filling both the highest and lowest order in the transposition; the second quotient will be the other figure.

Note. If the error of the trial-balance be not divisible by 9 it cannot be the result of transposition alone. But whenever the error becomes so reduced as to be divisible by 9 without a remainder, a transposition being then possible, the above tests should be given.

To illustrate the application of the foregoing rules, four examples are given below, each one representing a balancesheet taken from the ledger, but erroneous, from the fact that the footings of the Dr. and Cr. columns do not agree.

The "errors" 63, 7425, 4455, and 34947 being each divisible by 9, transposition is possible. Taking the first example, we have 63÷9=7. As this is the only division we can perform, we conclude the transposition can occur only in those amounts where the digit figures expressing the units and tens of dollars differ by 7. In the Dr. column there are three numbers answering these conditions, and in the Cr. column two, viz.: $18.40, $7, $81.50, $981 and $92. The transposition could not have occurred in the third number for the footing is already too small. If, then, either of the other numbers had been transposed from $81.40, $70, $918, and $29 respectively, the error is accounted for, a question easily settled by reference to the ledger. In the second example, we have 7425÷9-825 and 7425÷99=75. The quotients containing two or more figures in the transposition must be in notation simply. By reference to the Dr. and Cr. columns it will be observed that these quotients occur four times in the former and once in the latter, viz. $0.75, 201.75, $8.25, $75, and $200.75. The transposition could not have occurred in the second number without displacing other significant figures, nor in the fourth, because the Dr. footing is already too small, nor in the fifth, because the Cr. footing is already too large. The only two numbers to be compared, therefore, are the first and third, which, perhaps, should have been $75 or $82.50, either of which would account for the error.

In the third example we have 4455÷9=495, 4455÷99 =45. Here the transposition must be in notation simply, and may be found in one of two places only, viz.: $495 and $450.

In the fourth example we have 34947÷9-3883, 34947÷ 99-353, 34947-9999 -3, with a remainder 495, which÷99 =5. We omit the division by 999, because the remainder is not divisible by 99 without a remainder. For the same reason we omitted it in the third example. In this case there could be no transposition in the notation of 3883, because the number does not occur. There may have been a transposition of $353 from $3.53, or the figure 3 and 5 may somewhere have

been made to change places with respect to themselves and notation also; as, when $0.53 had been made to read $350.

Remark.-In the use of these rules in practice, not only the balances of the ledger accounts as they appear on the balance sheet should be examined, but also all the separate postings, as a transposition there will equally affect the final balance.

STOCKS AND BONDS.

ART. 136. Capital is a term applied to the property invested, by an individual or company, in trade, manufactures, railroads, banking, &c. The capital of an incorporated company is generally called its capital stock, and is divided into equal parts of convenient size called shares: the persons owning one or more of these shares being called stockholders.

The management of such companies is generally vested in officers and directors, who are elected by the stockholders, each stockholder being entitled to as many votes as the number of shares he holds.

It not unfrequently happens that the capital stock considerably exceeds the actual capital paid in, which occurs when it is made payable in installments, and is called in only as the wants of the company demand. The profits which are distributed among the stockholders are called dividends, and when "declared" are a certain per cent. of the par value of the shares.

Certificates of stock are issued by the company, signed by the proper officers, indicating the size and number of shares each stockholder is entitled to. These are transferable, and may be bought and sold like any other property.

When their marketable value equals their nominal value they are said to be at par. When they sell for more than their nominal value or face they are above par, or at a premium; when for less, they are below par, or at a discount.

Quotations of their marketable value are generally made by a percentage of their par value.

When States, cities, railroad companies, and other corporations borrow large amounts of money, instead of giving common promissory notes, they issue bonds, in denominations of convenient size, payable at a specified time, with interest usually payable semi-annually.

When issued by governments these bonds are frequently called government stocks or State stocks, but the terms should be carefully distinguished from the capital stock of business corporations.

To these bonds are attached what are called coupons, each of which is a due bill for the interest on the bond to which it is attached, representing the amount of the periodical dividend or interest, and the time of payment, which coupons are severally cut off and presented for payment as they become due.

These bonds and coupons are signed by the proper officers, and, like certificates of capital stock, are negotiable by delivery, being made payable "to bearer." The loan is made by the sale of the bonds, with coupons attached, but they are rarely negotiated at par. Their value depends upon the degree of certainty of their being paid at maturity, and the market rate of interest compared with the rate drawn by the bond.

Treasury notes are also issued by the United States government for the purpose of effecting temporary loans, which more nearly resemble bank notes, and are made payable with interest, but without coupor

con

Consols is a term abbreviated from the expression solidated annuities," the British government having at various times borrowed money at different rates of interest, and payable at different times, consolidated the stock or bonds thus issued, by issuing new stock drawing interest at three per cent. per annum, payable semi-annually, and redeemable only at the option of the government, becoming practically perpetual annuities. With the proceeds of this the old stock was redeemed. The quotations of these three per cent. perpetual annuities or *Coupon, pronounced koo-pong'.