The so called money your referring to isn't constitutional money. Its not even evidence of wealth, its evidence of debt.
The Constitution for the United States says 'No state shall make anything but gold and silver a tender in the payment of debts.'
The Coinage Act of April 2, 1792
(1 Stat. 246)
Statute I.
Mint established at the seat of government.
Chapter XVI.--An Act establishing a Mint, and regulating the coins of the United States.
Section I. Be it enacted by the Senate and House of Representatives of the United States of American in Congress assembled, and it is hereby enacted and declared, That a mint for the purpose of a national coinage be, and the same is established, to be situate and carried on at the seat of the government of the United States, for the time being; and that for the well conducting of the business of the said mint, there shall be the following officers and persons, namely, --a Director, an Assayer, a Chief Coiner, an Engarver, a Treasurer....
Section 9. And be it further enacted, That there shall be from time to time struck and coined at the said mint, coins of gold, silver, and copper, of the following denominations, values and descriptions, viz.
Eagles --each to be of the value of ten dollars or units, and to contain two hundred and forty-seven grains and four eighths of a grain of pure, or two hundred and seventy grains of standard gold.
Half Eagles--each to be of the value of five dollars, and to contain one hundred and twenty-three grains and six eighths of a grain of pure, or one hundred and thirty-five grains of standard gold.
Quarter Eaglesc--each to be of the value of two dollars and a half dollar, and to contain sixty-one grains and seven eighths of a grain of pure, or sixty-seven grains and four eighths of a grain of standard gold.
Dollars or Units--each to be of the value of a Spanish milled dollar as the same is now current, and to contain three hundred and seventy-one grains and four sixteenth parts of a grain of pure, or four hundred and sixteen grains of standard silver.
Half Dollars--each to be of half the value of the dollar or unit, and to contain one hundred and eighty-five grains and ten sixteenth parts of a grain of pure, or two hundred and eight grains of standard silver. Quarter Dollars--each to be of one fourth the value of the dollar or unit, and to contain ninety-two grains and thirteen sixteenth parts of a grain of pure, or one hundred and four grains of standard silver.
Dismes--each to be of the value of one tenth of a dollar or unit, and to contain thirty- seven grains and two sixteenth parts of a grain of pure, or forty-one grains and three fifths parts of a grain of standard silver.
Half Dismes--each to be of the value of one twentieth of a dollar, and to contain eighteen grains and nine sixteenth parts of a grain of pure, or twenty grains and four fifths parts of a grain of standard silver.
Cents--each to be of the value of the one hundredth part of a dollar, and to contain eleven penny-weights of copper.
Half Cents--each to be of the value of half a a cent, and to contain five penny-weights and a half a penny-weight of copper.
It continues as to shape of coin, what's to be imprinted on it etc.