Introduction. The problem; definitions, page I.--I. The expansion of a single bank, page 3.--II. The expansion of the aggregate of commercial banks, page 15.--III. Observations on the single-bank and system coefficients, page 26. To Follow in Next Issue IV. The effect of central banking; the ratio of commercial bank credit to gold. --V. Observations on the member-bank system coefficients.--VI. Summary; conclusions.