Banks having accounts with other banks find it necessary to make frequent reconciliations; that is, they must check the figures of their correspondent's account, as shown in the statement, with their own books. This process is especially necessary where the two banks are located in different cities and where their transactions with each other are numerous. It is obvious that under such conditions the debit balance of the account shown for example by this bank in the account "Due from Tenth National Bank, New York," will not be the same at a given moment as the credit balance shown to be due this bank on the New York bank's books. This is on account of the items in transit for which one has been charged, and for which the other has not as of a given date been credited, or vice versa. In other words, as at the close of business June 30:

A. Our balance according to our books, plus

B. Items for which they credit us, but which we do not as of June 30 charge, minus

C. Items for which they debit our account, but which we do not credit, equals X. Our balance according to their books, plus Y. Our "in transit" debits which they do not credit, less Z. Items which we credit, but which they do not debit.

This seems complicated, but it will be clear if it is taken at first in simpler form. Assume that all entries originate with our bank, that is, that no debits or credits are made by the New York bank on their own books until they are instructed by our bank to do so. That situation may be illustrated thus:

If A, The debit balance on our books equalled $100 and Y, Items which we had charged and which they had not credited us for were $40, and Z, Our credits which they have not yet received were $30, thus A, $100 less Y $40, plus Z $30 would equal $90, and $90 would be X, the credit balance on their books according to their statement. This must be obvious because our debit balance must have been recently increased by Y. which are debit items and decreased by Z credit items and if Y and Z have not as yet reached the New York bank's books, it must be proper, in order to ascertain what their balance should be, to take Y and Z out again. That is done by the following:

This $90 must be X, namely the balance of the New York bank's books. So then we have the simple rule that:

A

Y +Z = X or A=X+Y - Z

In accordance with the old arithmetic rule if an item is transferred from one side of the equality sign to the other, its plus or minus sign must change.