Explanation of Foregoing Table.

The transposition of figures is a frequent cause of errors in proving accounts and balance sheets. This table is founded on the fact that all differences between transposed numbers are multiples of nine. The difference between the figures misplaced is equal to the quotient of the resulting error when divided by nine; thus, 91 - 19 = 72; 72 ÷ 9 = 8; 9 - 1 = 8, and the labor of searching for it may be confined to examining those figures the transposition of which would make the difference, as they are the only ones that can cause the error. Thus: if the error in the balance-sheet be 81 cents, it is possibly caused by a transposition, and the clerk can first examine the cents column of his books for items of 90 cents, or 09 cents, alone, with a strong probability of finding the cause of the error without further revision. Transpositions may occur in any decimal or integer place, and the differences caused thereby are divisible by nine without a remainder; but, beyond this table, the numbers ascend in regular progression, each difference increasing by nine, as follows:

108{120;117{130;126{140;etc.
121314

The quotient of the difference in a regular progression, when divided by nine, gives the figures transposed, thus: 130 - 13 = 117 ÷ 9 = 13, which are the figures to be sought for when a discrepancy of 117 is shown; but this will not apply to differences below 81, nor to mixed transpositions. An error divisible by two may be caused by posting an item to the wrong side of the ledger.