II. The most _easy ratio_ of multiplication and division is that by ten. Every one knows the facility of Decimal Arithmetic. Every one remembers, that, when learning Money-Arithmetic, he used to be puzzled with adding the farthings, taking out the fours and carrying them on; adding the pence, taking out the twelves and carrying them on; adding the shillings, taking out the twenties and carrying them on; but when he came to the pounds, where he had only tens to carry forward, it was easy and free from error. The bulk of mankind are school-boys through life. These little perplexities are always great to them. And even mathematical heads feel the relief of an easier, substituted for a more difficult process. Foreigners, too, who trade or travel among us, will find a great facility in understanding our coins and accounts from this ratio of subdivision. Those who have had occasion to convert the Livres, sols, and deniers of the French; the Gilders, stivers, and frenings of the Dutch; the Pounds, shillings, pence, and farthings of these several States, into each other, can judge how much they would have been aided, had their several subdivisions been in a decimal ratio. Certainly, in all cases, where we are free to choose between easy and difficult modes of operation, it is most rational to choose the easy. The Financier, therefore, in his report, well proposes that our Coins should be in decimal proportions to one another. If we adopt the Dollar for our Unit, we should strike four coins, one of gold, two of silver, and one of copper, viz. 1. A golden piece, equal in value to ten dollars: 2. The Unit or Dollar itself, of silver: 3. The tenth of a Dollar, of silver also: 4. The hundreth of a Dollar, of copper. Compare the arithmetical operations, on the same sum of money expressed in this form, and expressed in the pound sterling and its divisions. A bare inspection of the above operations, will evince the labor which is occasioned by subdividing the Unit into 20ths, 240ths, and 960ths, as the English do, and as we have done; and the ease of subdivision in a decimal ratio. The same difference arises in making payment. An Englishman, to pay £8 13s. 11d. 1/2qrs. must find, by calculation, what combination of the coins of his country will pay this sum; but an American, having the same sum to pay, thus expressed $38.65, will know, by inspection only, that three golden pieces, eight units or dollars, six tenths, and five coppers, pay it precisely. III. The third condition required is, that the Unit, its multiples, and subdivisions, coincide in value with some of the known coins so nearly, that the people may, by a quick reference in the mind, estimate their value. If this be not attended to, they will be very long in adopting the innovation, if ever they adopt it. Let us examine, in this point of view, each of the four coins proposed.