The Trial Balance.—In Chapter XIV the trial balance was defined as a list of account totals, debit and credit, or account balances, debit or credit, for all the open accounts in the ledger. This list is set up in two columns, debit and credit, and if the original entries in the journals and the postings to the ledger have been done correctly, the totals of these two columns should be the same.

Neither method of showing the trial balance has any inherent advantage over the other. Some concerns desire the account totals to be shown in the trial balance, as that indicates to some extent the volume of business. This would be true of all accounts which had been opened during the current period. As to those carried over from a previous period little current information would be given. As a general thing, however, the status of customers’ accounts is better indicated when both total charges and total credits are shown. Where only the balance is shown, it does not provide any basis for determining whether that balance is normal for that particular account. In judging a request for a further extension of credit there is a rather close relationship between the volume of trade with a customer and the amount of his unsettled balance.

Sometimes, even the totals of accounts that balance are shown in the trial balance, thus giving the status of all accounts appearing in the ledger. Again, concerns desirous of knowing the net amount owing on customers’ accounts and the net amount owed on creditors’ claims, require balances of all personal accounts and cash, but debit and credit totals of all other accounts. No unalterable rule can be given. The manner of showing the accounts in the trial balance is governed by the way in which the trial balance is to be used and the purpose it is to serve. Manifestly, however, the trial balance cannot give information of every kind desired by a manager. As personal accounts are usually handled by canceling offsetting credits against corresponding debits and carrying only balances forward, the trial balance cannot well show at the same time both total transactions and outstanding balances. Only in small concerns could the trial balance give the information which in larger concerns would be gathered statistically and furnished in addition to the trial balance.

The tendency in modern accounting is to make the ledger record so detailed that all accounts are currently “uniphase,” i.e., have entries on but one side, and in connection with such accounts the two methods of entering them in the trial balance are identical, because the total of the one side of the account is at the same time the balance of the account. It must be observed that as a matter of course this modern tendency does not apply to personal accounts nor to adjustment and closing accounts.

Errors in the Trial Balance.—The manner of entering the small pencil footings of both sides of each account and also the account balances previous to taking the trial balance, was explained in an earlier chapter. This preliminary work should be done carefully so as to reduce errors to a minimum.

It is not purposed here to discuss all the kinds of errors that find their way into the accounting records. Errors are frequently made in the original analysis and classification of the transaction, which, as previously stated, result in an entirely incorrect showing of financial condition. Such errors do not affect the balance of the books and are not detected by the trial balance. Their detection is one phase of the professional auditor’s work. This discussion has been qualified by saying that if the work of original and secondary entry has been done correctly, then the ledger should prove. Some points in connection with errors which often occur in posting will be treated here.

The equality of the two totals of the trial balance proves that for every debit entry on the books there has been made an equal credit, or at any rate that the sum of all debit entries equals the sum of all credit entries; i.e., it proves only the mathematical correctness of the work.

It might happen that an item, though posted to the correct side of the ledger, has been entered in the wrong account. The trial balance would not detect an error of this kind. For example, John Doe’s account might be debited with a charge belonging to Richard Roe, both being customers. This of course would make the books show wrong balances in those particular accounts, but would not cause an incorrect showing in the total assets. However, more serious results may come from an error caused by posting to the wrong account.

According to the schedules shown earlier, all transactions bring about increases and decreases in the three main groups of accounts, viz., assets, liabilities, and proprietorship. A transaction resulting in an increase of assets may have its credit in any of the three classes—decrease of assets, increase of liabilities, or increase of proprietorship. A credit entry in any one of these would result in an exact offset to the debit and would therefore so far as that transaction was concerned, result in equal debits and credits in the trial balance; but were entry made to the wrong group of accounts, it would bring about absolutely false results. This would be the case if a proprietorship account were credited, resulting in an increased profit, when the credit should have been to the liability group with a resulting increase of the liabilities—two divergent results.

Thus, while the trial balance does not detect errors in posting to the wrong account, it has great value in that its equality is considered as good evidence of the correctness of the books. This is so because errors of the kind just referred to are not of so frequent occurrence as those involving only the mathematics of the work.

Suggestions for Locating Errors.—Where trial balance totals do not agree, it is certain that one or more errors have been made somewhere. The following suggestions may be useful in locating them:

1. If there is a difference of 1 in any column, i.e., .01, .10, 1.00, 10.00, etc., the error very likely results from wrong addition. Check additions of the trial balance and if the error is not located there, those of the ledger accounts must be checked as well.

2. If the difference between the two trial balance totals is an even number, divide this difference by two and look through the trial balance for an item of that amount but entered as a debit instead of a credit or vice versa. The amount of the error must be divided by two because the placing of a given item in the wrong column would result in a difference of twice this amount in the totals of the trial balance. If the error is not located in the trial balance, it may be necessary to look through the ledger accounts because the wrong placing may have occurred there.

In checking through the ledger for an error of this kind, some aid is afforded by the fact that all postings from even pages in the cash book (i.e., the cash receipts) appear on the credit side of the ledger accounts, and all postings from the odd pages in the cash book appear on the debit side of the ledger accounts. If, therefore, in any of the credit reference columns in the ledger is seen a reference like “C 13” or “C 29,” or in any of the debit reference columns an index like “C 40” or “C 58,” it is probable that the error is due to posting to the wrong side.

3. If the mistake has not been found in this way, the trial balance should be checked against the ledger to be sure that no open accounts have been omitted. Examine all closed accounts to see that they balance.

4. Examine the posting index column of all books of original entry to see that no items have been omitted in posting.

5. When the totals of the trial balance are unequal, the error may lie either in the debit total or in the credit total, or both may be wrong. Even when the trial balance “proves,” both totals may contain the same error. In order to determine what is the correct footing, the following method may sometimes be applied: Take the total of the previous trial balance, add to it the current totals from the several journals, and deduct the total of all accounts closed during the period. The result shows the correct footing for the present trial balance. Where the number of accounts closed during the period is large, the work entailed by this method may be prohibitive. The method is of easy application only when the trial balance is taken by means of debit and credit totals.

It may be left to the student to prove why this is a correct method for determining the present trial balance total. Suffice it to say that it is based on the fundamental fact that for every credit item in any of the journals there is of necessity a debit or group of debits the total of which corresponds with the credit item. Duplicating entries in two or more journals must be eliminated from the journal total.

The following table will serve to illustrate the above method:

6. If the difference between trial balance totals is divisible by 9, the error may be due to a transposition of figures or to a transplacement, sometimes called a slide. A transposition is an interchange of figures, as 96 for 69, 215 for 512, 6,274 for 4,276, etc. The first is called a simple or one-column transposition, the second a two-column, and the last a three-column transposition. One-column transpositions may also occur in numbers of three or more figures, as 172 for 712, or 3,129 for 1,329.

Transpositions.—The following rules will be of help in locating errors of transposition. To determine divisibility by 9, the easiest way is to “cast out” the 9’s.

(a) If the difference between the trial balance totals is divisible by 9 and consists of less than three figures, i.e., 9, 18, 27, 36, a one-column transposition may be the cause of the error. Divide this difference by 9. If the quotient is 1, the difference between the two transposed figures is 1. If the quotient is 2 or 3 or 4, the difference between the transposed figures is 2 or 3 or 4, etc. For instance:

Thus the figures in the last column indicate the difference between the figures of the original item.

(b) If the difference is divisible by 9 and consists of two significant figures followed by one or more naughts, the error may be caused by a one-column transposition between columns of a higher order. For instance:

which divided by 9 gives 300. This indicates a transposition between figures in the “100” and “1,000” columns, the difference between these figures being 3. Reference to the example given will show this to be the case.

(c) When the difference between the trial balance totals is divisible by 9 and lies between 99 and 1,000, the error may be due to a two-column transposition. Here the middle figure of the error is always a 9, e.g., an error of 297 resulting from writing 512 as 215. Dividing the number (27) formed by the two outside figures of the difference by 9, the quotient (3) is the difference between the two transposed figures, i.e., the 5 and the 2. For instance:

Thus, the figures in the last column (1, 2, 8) indicate the difference between the two transposed figures in the correct item. Instead of dropping the middle figure of the difference and dividing by 9 as above, the entire difference figure may be divided by 99 with the same result.

(d) Similarly, when the difference is 999 or a four-figure amount with two 9’s in the middle, a three-column transposition may be indicated thereby. For instance:

the figures in the last column (1, 4, 6) again indicating the difference between the transposed figures in the original.

Instead of dividing the number formed by the outside digits (9, 36, 54) by 9, we might divide the full amount of the difference (999, 3,996, 5,994) by 999; this would give the same result.

The reason for the divisibility of this difference by 999 in an error of this kind is apparent when a number is given algebraic notation instead of Arabic. The Arabic number 2,197 expressed algebraically would be 2,000 + 100 + 90 + 7. Generalizing, we may formulate any number of four figures by 1,000a + 100b + 10c + d, in which a, b, c, and d may have values from 0 to 9 inclusive. A transposition between the thousands and units digits, the “a” and the “d,” would result in the following number: 1,000d + 100b + 10c + a. The error would therefore be:

This error is plainly divisible by 999, and the resulting quotient (a-d) is the difference between the two transposed digits.

It may be shown similarly why 99 is a divisor of the error cited under case (c) above.

Transplacements.—A transplacement or slide occurs when some or all of the digits of a number are moved one or more places to the right or left without change in the order of the figures; for instance, 736 written as 73.60, as 7.36, or as 700.36. The first is called a one-column slide, the second and third two-column slides. The error caused by a one-column slide is always divisible by 9, a two-column by 99, a three-column by 999, etc. The division by 9, 99, 999, etc., disregarding decimals, always gives the figures whose transplacement has caused the error. Thus the error caused by writing 736 as 73.60 is 662.40, which divided by 9 is 736; or 736 written as 7.36 produces an error of 728.64, which divided by 99 gives 736; or 736 written as 700.36 causes an error of 35.64, which divided by 99 gives 36, the part transplaced. The reason is similar to that given above for the transposition.

When a whole number of dollars is written as cents, the resulting error is divisible by 9 and moreover the cents added to the dollars gives 99 in each case. For instance in writing:

When the error in the trial balance is of this kind, the amount transplaced may be found by subtracting the cents of the error from 100. In the above examples this difference would be 100-27, 100 -42, 100-84, or 73, 58, and 16 respectively, which are in each case the figures of the transplaced amount as seen in the example. Having determined this, the trial balance and ledger accounts should be gone over to look for a slide of the given number.

Checking the Postings.—From the above discussion, the impossibility of determining in all cases the nature of the error is quite evident—particularly as to whether it is one caused by a transposition or a slide. Unless the kind of error is readily discernible, it is usually advisable to employ the method of checking, i.e., going over all the work of posting to determine its correctness—or other methods to be discussed in Chapter LI. After all, careful work in making the record with legible figures and in proving additions and subtractions, wherever possible, more than pays for itself in the time saved hunting for errors caused by slovenly and inaccurate work.