The author acknowledges the helpful and stimulating discussions on this subject with W. Philip Gramm, former student, now colleague and teacher, and with Thomas R. Saving while the author was a Visiting Professor of Economics at Texas A&M University

¹ Carothers, Neil, Fractional Money, Reprints of Economic Classics (New York: Augustus M. Kelley, 1967), First Edition, John Wiley, 1930, pp. 188–189.Google Scholar

² For example, Smith, Adam, Wealth of Nations, Cannan, Edwin, ed. (New York: Modem Library, Random House, 1937), pp. 307–309.Google Scholar Also, Thornton, Henry, The Paper Credit of Great Britain, Hayek, F. A. v., ed. (New York: Rinehart 1939), p. 189.Google Scholar

³ See forthcoming paper by W. Philip Gramm, “The Optimum Nominal Stock of Money and ‘Cheap Money’ Movements in the United States.”

⁴ Dunbar, Charles F., The Theory and History of Banking (New York: G. P. Putnam's Sons, 1922), pp. 62–63.Google Scholar

⁵ Dewey, Davis R., State Banking Before the Civil War, National Monetary Commission, Sen. Doc. No. 581, 61st Cong., 2d Sess. (Washington, 1910), p. 64.Google Scholar

⁶ Mints, Lloyd W., History of Banking Theory (Chicago: University of Chicago Press, 1945), p. 148.Google Scholar

⁷ See Dewey, State Banking, pp. 65 and passim. See also Hepburn, A. B., A History of Currency in the United States (New York: Macmillan, 1924), pp. 84, 90, 94, 163, 181, 308.Google Scholar

⁸ Adam Smith, Wealth of Nations, p. 308.

⁹ Henry Thornton, Paper Credit, p. 189.

¹⁰ Smith, Wealth of Nations, p. 306 (note).

¹¹ Viner, Jacob, Studies in the Theory of International Trade (New York: Harper and Brothers, 1937) p. 179,Google Scholar and Ricardo, David, Economic Essays (Gonner, E. C. K., ed.) (London: G. Bell and Sons, Ltd. 1923), p. 213.Google Scholar

¹² Viner, Studies, p. 182.

¹³ Knox, John Jay, United States Notes (New York: Charles Scribner's Sons, 1884), pp. 37–38.Google Scholar

¹⁴ Hepburn, History of Currency, p. 89. (Italics supplied.)

¹⁵ American State Papers Finance, Vol. III. See also Timberlake, Richard H. Jr, “Treasury Note Issues and Treasury Policies in the United States, 1812–1820,” In ternational Review of Banking History, Librarie Droz (Geneva, 1969), p. 212.Google Scholar

¹⁶ Hepburn, History, p. 163. The use of the word “barter” by Hepburn is revealing. Silver was undervalued at the mint and therefore a commodity during this period. Without bank-issued small notes, many transactions undoubtedly were barter.

¹⁷ Dewey, State Banking, pp. 66–73, and Hepburn, History, pp. 166–167.

¹⁸ A few writers recognized this truth. See, Hildreth, Richard, Banks, Banking and Paper Currencies, Whipple and Damrell (1840), reprinted by Greenwood Press (1968).Google Scholar

¹⁹ Carothers, Fractional Currency, pp. 76–78. A common device was to cut the half dollar into four more-or-less equal pieces (p. 81).

²⁰ Ibid., p. 92.

²¹ Ibid., pp. 110–111.

²² Ibid., p. 160. This example should have proven beyond all doubt that the inflation and disappearance of metallic currency came first and were followed by innovations of substitute paper currency. Knox also reported that premiums of ten to twelve percent over its commodity value were offered for small amounts of silver coin “by businessmen who desired it for convenience in making change.” (U.S. Notes, p. 100.)

²³ Hepburn, History, p. 308.

²⁴ U.S. Congress, Annual Report of the Comptroller of the Currency, 1872, House Executive Document #1562, pp. 96–97. The Alabama notes were in five denominations which read: “The State of Alabama: Receivable as ― dollars in payment of all dues to the State. Montgomery, May 1, 1867.” They were signed by the Governor and the Comptroller of Public Accounts.Google Scholar

²⁵ Report of the Comptroller, 1873, House Executive Document #1603, p. 109.

²⁶ Ibid.

²⁷ House of Representatives, 43d Congress, 1st Session, Miscellaneous Document No. 48, Dec. 19, 1873, “Memorial of Bankers and Merchants of Columbia, South Carolina, PRAYING Congress to prohibit by law the issuance of an irredeemable currency by certain corporations,” p. 1.

²⁸ Ibid., p. 2.

²⁹ U.S. Congress, Treasurer's Report, 1874, House Executive Document #1641, p. 353.

³⁰ See, for example, U.S. Congress, Congressional Record, 43d Congress, 1st Session, speech by W. Loughridge of Iowa in the House of Representatives, April 9, 1874. Virtually any speech on currency questions cited the per capita values per state in the United States, as well as similar values for most European countries.

³¹ Moran, Charles, Money, Currencies and Banking (New York: no publisher, printed by S. W. Green, 1875), p. 4.Google Scholar

³² Ibid., p. 39. While Moran was correct in his evaluation of denominational factors, he was an anti-bullionist and wrong in his assessment of quantitative factors. His case demonstrates how quantity of the total can get mixed up with quantities of specific denominations. The former could be overabundant, while a specific denomination could be distressingly short, e.g. small denominations in 1862.

³³ Selden, Richard, “Monetary Velocity in the United States,” in Studies in the Quantity Theory of Money, Friedman, Milton, ed. (Chicago: University of Chicago Press, 1956), pp. 189Google Scholar and passim. Also, Warburton, Clark, “The Secular Trend in Monetary Velocity,” The Quarterly Journal of Economics, LXIII (Feb. 1949), 68–91,CrossRefGoogle Scholar [reprinted in Warburton, Clark, Depression, Inflation and Monetary Policy (Baltimore: Johns Hopkins Press, 1966), pp. 199–209].Google Scholar Selden's data sources for his V-39 velocity values are noted to be the same as those for his V-27 estimates. These latter were taken from Warburton's study, and made use of income data compiled by Martin, Robert F. in his book, National Income in the United States, 1799–1938 (New York: NICB, 1939).Google Scholar (Warburton, Depression, Inflation and Monetary Policy, p. 201, note 3.)

³⁴ Friedman, Milton and Schwartz, Anna J., A Monetary History of the United States, 1867–1960, NBER (Princeton: Princeton University Press, 1963).Google Scholar See also, Warburton, Depression, p. 212.

³⁵ Friedman and Schwartz treat at length the question of the secular trend in velocity. Their data show a slight downward trend from 1900 to 1914, a rough constancy from 1914 to 1929, a sharp decline in the early 1930's followed by a rise to 1941, another sharp decline to 1946, and then a constant rise to 1960 (pp. 136, 197, 494, 641). The post-World War II figures, they note, show a “clear upward trend” (p. 643). Later studies on velocity measurement indicate that the upward trend has continued through the 1960's and into the 1970's. Therefore, no clear-cut secular decline can be inferred for the twentieth century, the sharp effects of the depression and World War II notwithstanding.

³⁶ Let M be the stock of money, P the price index value for goods and services exchanged for money, R the volume of goods and services exchanged for money, r the volume of goods and services bartered or exchanged by means of unaccounted money, apparent velocity, and V_R real velocity. Then, apparent velocity is , while real velocity is . Obviously, . But over time as barter exchange is replaced by monetary transactions, PR will come to include the value of goods and services formerly valued as Pr, and .

³⁷ Warburton, Depression, pp. 208–210.

³⁸ The reliability of Martin's estimates of income, cited in note 33, are subject to some serious doubts. Aside from questionable methods and some obviously spurious results, he gives no indication of how much non-monetary income is included in his estimates. In all fairness, it was not his intention to do so. Therefore, his income estimates are for the value of that income but do not give any indication of how much of this income was exchanged for money. Selden unaccountably reports that Martin's estimates (not identified by name, but just by reference to Warburton) exclude nonmonetary income (Studies, p. 244), but Martin clearly does not make any such adjustment. His estimates are simply projections of production figures from the Census of Manufactures multiplied by price relatives.

³⁹ Fractional currency is not included here. The fractional, paper currency in existence from 1862 to 1876, although explicitly recorded in Treasurers' reports, is subject to an extraordinary amount of error due to unaccounted losses and destructions (e.g. the Chicago fire). After 1877, metallic fractional currency replaced the paper currency of the earlier years. The totals of this latter currency are not readily calculable because of the re-importations after 1876 of millions of U.S. coins that had been exported in 1861 and 1862. No constraints on fractional currency were noticeable after resumption. Also, these data include neither the very largest denominations ($100 and over), nor state and national bank deposits. However, the denominations listed in the table contain about ninety percent of the highpowered money stock.

⁴⁰ The price data are Warren and Pearson's Wholesale Price Index (1910–14 = 100). This index is very sensitive, so it may exaggerate somewhat the fluctuation in the general price level.

⁴¹ The data for 1879 are counted as the end values for the first period and as the beginning values for the second period.

⁴² Growth of real output and the behavior of velocity do not lend themselves to accurate measurement before 1890. See Milton Friedman and Anna Schwartz, A Monetary History, pp. 36–44, 87 and passim.