When Tom left college he was taken into the bank, and before Bill's graduation had been advanced to the position of cashier, and had married a very fine young woman.

The cashier is the man that has charge of the money in the bank.
"It was thought best also for Bill to enter the bank, which he did a few months after his return from college, as assistant to his brother.
"Things went on very well until, one day, a man came to examine the bank and to see if all the money was safely there, and the examiner, as the man was called, discovered a shortage.

That is, there was not as much money in the bank as there should have been.

The shortage lay between the two brothers.

Tom, in terrible distress, admitted to Bill that he had 'just borrowed' the money to invest in stocks--which is a way people speak of one kind of gambling--but that the investment had failed, and he had lost it.
"You do not know, Partner, what stocks are, but I'll tell you some other time.
"When this happened Tom had a little baby boy at home, about two months old.