3. With regard to the figures of the ratios there is great difference and divergence among the various authorities. The declared ratio may be of a double nature--(1) mercantile, as calculated on the purchase price of gold and silver in the open market; (2) legal, as settled by law in the terms prescribed for Mint purchase and issue. The former is comparatively simple, but it is not until a quite recent date, the opening of the eighteenth century, that it is statistically determinable. The table of the commercial ratio (pp. 157-9 infra.) is taken from Soetbeer, and was by him calculated on the Hamburg exchange and London market rates. The competing figures of the commercial ratio drawn up by Ingham in his Report to the Senate of the United States (4th May 1830), and by John White, of the same date (see _United States Report of the International Monetary Conference of 1878_, pp. 583, 647), I regard as comparatively untrustworthy.
With regard to the legal or Mint ratio (see infra., tables, pp. 40, 69-70, 157) there is the greatest discrepancy, and I print the figures with much trepidation and every mental reserve. The differences in the results arrived at by the various authorities are due to the difference in method of calculation, according as the issue price or the purchase price at the Mint is taken (i.e. with or without allowance of seigniorage and remedy), or according as the pure or gross content of the piece is calculated from (i.e. with or without allowance for alloy). As a matter of fact, hardly any two authorities or sets of calculations agree. See, for instance, duplicate sets of figures for Holland in Appendix 1. to Schimmel's _Geschiedkundig overzicht_; or again, compare Soetbeer's figures with those deduced by Köhler in his _Grundliche Nachricht_; or by Dr. Arnold Luschin, in the _Proceedings of the Congrés International de Numismatique_, 1880, p. 443; or with those deducible from Le Blanc's tables (infra., Appendix VI.). It is to this difference that must be attributed the discrepancy in the statement of the ratio by the French Mint authorities in 1640 (see text, infra., p. 92 and note, ibid.). The difficulty of calculating the European Mint ratio at any moment can be judged from the experience and statements of persons so widely apart as Sir Isaac Newton in England, Mirabeau and Calonne in France, and Morris and Hamilton in the United States (see infra., pp. 172-3, 229-30, and 251).