The Theory of Free Banking, Selgin, 1988, chapter 5, Increased Money Demand :
To summarize, a general increase in the demand for inside money is equivalent to a general decline in the rate of turnover of inside money. Bank notes change hands less frequently, and holders of demand deposits write fewer (or perhaps smaller) checks. As a result, bank liabilities pass less frequently into the hands of persons or rival issuers who return them to their points of origin for redemption. The reduction in turnover of liabilities leads directly to a fall in the volume of bank clearings. When this happens banks find they have excess reserves relative to the existing level of their liabilities, and so they are able to increase their holdings of interest-earning assets, which they do by expanding the supply of inside money in a manner that accommodates the growth in demand for it. In standard textbook terminology, there is an increase in the reserve multiplier. Liability expansion continues so long as there are unfilled reservoirs of demand. Any issues in excess of demand, however, will lead to additions to the stream of payments, causing an increase in bank clearings and reserve requirements.
He could hardly be more clear, I guess.