Postscript to the Report on Weights and Measures
It is scarcely necessary to observe that the measures, Weights, and Coins, proposed in the preceding report, will be derived altogether from mechanical operations; viz: A rod, vibrating seconds, divided into five equal parts, one of these subdivided, and multiplied, decimally, for every measure of length, surface and capacity, and these last filled with water, to determine the weights and coins. The Arithmetical estimates in the report were intended only to give an idea of what the new measures, weights, and coins would be nearly, when compared with the old. The length of the standard or second rod therefore was assumed, from that of the pendulum; and as there have been small differences in the estimates of the pendulum by different persons, that of Sir Isaac Newton was taken, the highest authority the world has yet known. But if even he has erred, the measures, weights, and coins proposed will not be an Atom the more or less. In cubing the new foot, which was estimated at .978728 of an English foot, or 11.744736 English inches, an arithmetical error of an unit happened in the fourth column of decimals, and was repeated in another line in the sixth column, so as to make the result one ten thousandth, and one millionth of a foot too much. The thousandth part of this error (about one ten millionth of a foot) consequently fell on the metre of measure, the ounce weight, and the unit of money. In the last it made a difference of about the twenty fifth part of a grain Troy in weight, or the ninety third of a cent in value. As it happened, this error was on the favorable side, so that the detection of it approximates our estimate of the new unit exactly that much nearer to the old, and reduces the difference between them to 34 instead of 38 hundredths of a grain Troy; that is to say, the money unit, instead of 375.64 Troy grains of pure silver, as established heretofore, will now be 375.98934306 grains, as far as our knowledge of the length of the second pendulum enables us to judge: and the current of authorities since Sir Isaac Newton's time gives reason to believe that his estimate is more probably above than below the truth: consequently future corrections of it will bring the estimate of the new unit still nearer to the old.
The numbers in which the arithmetical error before mentioned shewed itself in the table, at the end of the report, have been rectified, and the table reprinted.
The head of superficial measures in the last part of the report, is thought to be not sufficiently developed. It is proposed that the rood of land, being 100 feet square (and nearly a quarter of the present Acre) shall be the unit of land measure. This will naturally be divided into tenths, and hundredths, the latter of which will be a square decad. Its multiples will also, of course, be tens, which may be called double Acres, and hundreds which will be equal to a square furlong each. The surveyor's chain should be composed of 100 links of one foot each.
Secretary of State
January 10, 1791.
FC (DNA: RG 59, SDR). Printed text (DLC: TJ Papers, 65: 11262–5); consisting only of p. 47– of the Report (N.Y., Childs & Swaine, 1791; Evans No. 23910) and, in addition to the postscript, containing the table reprinted. PrC of Tr (DLC: TJ Papers, 65: 11258–60); in the hand of George Taylor, except for date at end in TJ's hand, without signature: “Jan. 10. 1791.”