G/2P + S/2 = to a pound troy fine silver, in sterling currency.
S/2 × P + G/2 = to a pound troy fine gold, in sterling currency.
This will be a rule for the mint, to keep the price of the metals constantly at par with the price of the market; and coinage may be imposed as has been described, by fixing the mint price of them at a certain rate below the value of the fine metals in the coin.
13. When to change the mint price.
13. As long as the variation of the market price of the metals shall not carry the price of the rising metal so high as the advanced price of the coin above the bullion, no alteration need be made on the denomination of either species.
14. Rule for changing the denomination of the coins.
14. So soon as the variation of the market price of the metals shall give a value to the rising species, above the difference between the coin and the bullion; then the King shall alter the denominations of all the coin, silver and gold, adding to the coins of the rising metal exactly what is taken from those of the other. An example will make this plain.
Let us suppose that the coinage has been made according to the proportion of 14.5 to 1; that 20 shillings, or 4 crown pieces, shall contain, in fine silver, 14.5 times as many grains as the guinea, or the gold pound, shall contain grains of fine gold. Let the new proportion of the metals be supposed to be 14 to 1. In that case, the 20 shillings, or the 4 crowns, will contain 1⁄29 more value than the guinea. Now since there is no question of making a new general coinage upon every variation, in order to adjust the proportion of the metals in the weight of the coins, that proportion must be adjusted by changing their respective denominations according to this formula.
Let the 20 shillings, or 4 crowns, in coin, be called S. Let the guinea be called G. Let the difference between the old proportion and the new, which is 1⁄29, be called P. Then say,
S - P/2 = a pound sterling, and G + P/2 = a pound sterling.