Those indeed who have preferred the other element, do justice to the certainty, as well as superior facilities of the pendulum, by proposing to recur to one of the length of their standard, and to ascertain its number of vibrations in a day. These being once known, if any accident impair their standard it is to be recovered by means of a pendulum which shall make the requisite number of vibrations in a day. And among the several commissions established by the Academy of Sciences for the execution of the several branches of their work on measures and weights, that respecting the pendulum was assigned to Messrs. Borda, Coulomb & Cassini, the result of whose labors, however, I have not learned. Let our unit of measures then be a pendulum of such length as in the latitude of 45°, in the level of the ocean, and in a given temperature, shall perform its vibrations, in small and equal arcs, in one second of mean time. What ratio shall we adopt for the parts and multiples of this unit? The decimal without a doubt. Our arithmetic being founded in a decimal numeration, the same numeration in a system of measures, weights and coins, tallies at once with that. On this question, I believe, there has been no difference of opinion. In measures of length, then, the pendulum is our unit. It is a little more than our yard, and less than the ell. Its tenth or dime, will not be quite 4 inches. Its hundredth, or cent, not quite .4 of an inch; its thousandth, or mill, not quite .04 of an inch, and so on. The traveller will count his road by a longer measure. 1,000 units, or a kiliad, will not be quite two-thirds of our present mile, and more nearly a thousand paces than that. For measures of surface, the square unit, equal to about ten square feet, or one-ninth more than a square yard, will be generally convenient. But for those of lands a larger measure will be wanted. A kiliad would be not quite a rood, or quarter of an acre; a myriad not quite 2½ acres. For measures of capacity, wet and dry, The cubic Unit = .1 would be about .35 cubic feet, .28 bushels dry, or ⅞ of a ton liquid. Dime = .1 would be about 3.5 cubic feet, 2.8 bushels, or about ⅞ of a barrel liquid. Cent = .01 about 50 cubic inches, or ⅞ of a quart. Mill = .001 = .5 of a cubic inch, or ⅔ of a gill. To incorporate into the same system our weights and coins, we must recur to some natural substance, to be found everywhere, and of a composition sufficiently uniform. Water has been considered as the most eligible substance, and rain-water more nearly uniform than any other kind found in nature. That circumstance renders it preferable to distilled water, and its variations in weight may be called insensible. The cubic unit of this = .1 would weigh about 2,165 lbs. or a ton between the long and short.