TO obtain uniformity in Measures, Weights and Coins, it is necessary to find some measure of invariable length, with which, as a standard, they may be compared.

There exists not in nature as far as has been hitherto observed, a single subject or species of subject, accessible to man, which presents one constant and uniform dimension.

The globe of the earth itself, indeed, might be considered as invariable in all its dimensions, and that its circumference would furnish an invariable measure; but no one of its circles, great or small, is accessible to admeasure­ment through all its parts; and the various trials to measure definite portions of them, have been of such various result, as to shew there is no de­pendance on that operation for certainty.

MATTER then, by its mere extension, furnishing nothing invariable, its MOTION is the only remaining resource.

The motion of the earth round its axis, though not absolutely uniform and invariable, may be considered as such for [...] [...]uman purpose. It is measured obviously, but unequally, by the departure of a given meridian from the sun, and its return to it, constituting a solar day. Throwing to­gether the inequalities of solar days, a mean interval, or day, has been found, and divided, by very general consent, into 86,400 equal parts.

A Pendulum, vibrating freely, in small and equal area, may be so adjusted in its length, as, by its vibrations, to make this division of the earth's mo­tion into 86,400 equal parts, called seconds of mean time.

Such a Pendulum then, becomes itself a measure of determinate length, to which all others may be referred, as to a standard.

But even the Pendulum is not without its uncertainties.

1. The difficulty of ascertaining, in practice, its center of oscillation, as depending on the form of the bob, and its distance from the point of sus­pension; the effect of the weight of the suspending wire towards displacing the center of oscillation; that center being seated within the body of the bob, and therefore inaccessible to the measure, are sources of considerable uncertainty.

[Page 8]2. Both theory and experience prove, that to preserve its isochronism, it must be shorter towards the equator, and longer towards the poles.

3. The height of the situation above the common level, as being an increment to the radius of the earth, diminishes the length of the Pendulum.

4. The pendulum being made of metal, as is best, it varies its length with the variations in the temperature of the atmosphere.

5. To continue small and equal vibrations, through a sufficient length of time, and to count these vibrations, machinery and a power are necessary, which may exert a small, but constant effort to renew the waste of motion: And the difficulty is, so to apply these, as that they shall neither retard nor accelerate the vibrations.

1. In order to avoid the uncertainties which respect the center of oscilla­tion, it has been proposed by Mr. Leslie, an ingenious artist of Philadelphia, to substitute, for the pendulum, an uniform cylindrical rod, without a bob.

Could the diameter of such a rod be infinitely small, the center of oscilla­tion would be exactly at two thirds of the whole length, measured from the point of suspension. Giving it a diameter which shall render it sufficiently inflexible, the center will be displaced, indeed; but, in a second rod not the (1.) 600,000th part of its length, and not the hundredth part as much as in a second pendulum, with a spherical bob of proper diameter. This displacement is so infinitely minute then, that we may consider the center of oscillation, for all practical purposes, as residing at two thirds of the length, from the center of suspension. The distance between these two cen­ters might be easily and accurately ascertained in practice. But the whole rod is better for a standard, than any portion of it, because sensibly defined at both its extremities.

2. The uncertainty arising from the difference of length requisite for the second pendulum, or the second rod, in different latitudes, may be avoided by fixing on some one latitude, to which our standard shall refer. That of 38°, as being the middle latitude of the United States, might seem the most convenient, were we to consider ourselves alone; but connected with other nations by commerce and science, it is better to fix on that parallel which bids fairest to be adopted by them also. The 45th, as being the middle term between the equator and pole, has been heretofore proposed in Europe; and the proposition has been lately renewed there, under circumstances which may very possibly give it some effect. This parallel is distinguished with us also, as forming our principal northern boundary. Let the com­pletion of the 45th degree, then, give the standard for our union, with the hope that it may become a line of union with the rest of the world.

The difference between the second rod for 45° of latitude, and that for 31°, our other extreme, is to be examined.

The second pendulum for 45° of latitude, according to Sir Isaac Newton's computation, must be of (2.) 39.14912 inches English measure; and a rod, to vibrate in the same time, must be of the same length between the centers [Page 9] of suspension and oscillation, and consequently its whole length 58.7 (or more exactly 58.72368) inches. This is longer than the rod which shall vibrate seconds in 31° of latitude, by about 1/670 part of its whole length; a difference so minute that it might be neglected, as insensible, for the com­mon purposes of life: But in cases requiring perfect exactness, the second rod, found by trial of its vibrations in any part of the United States, may be corrected by computation for the (3.) latitude of the place, and so brought exactly to the standard of 45°.

3. By making the experiment in the level of the ocean, the difference will be avoided, which a higher position might occasion.

4. The expansion and contraction of the rod with the change of tem­perature, is the fourth source of uncertainty before mentioned. According to the high authority so often quoted, an iron rod, of given length, may vary, between summer and winter, in temperate latitudes, and in the com­mon exposure of house clocks, from 1/1728 to 1/2592 of its whole length, which, in a rod of 58.7 inches, will be from about two to three hundredths of an inch. This may be avoided by adjusting and preserving the standard in a cellar, or other place, the temperature of which never varies. Iron is named for this purpose, because the least expansible of the metals.

5. The practical difficulty resulting from the effect of the machinery and moving power, is very inconsiderable in the present state of the arts; and, in their progress towards perfection, will become less and less. To estimate and obviate this, will be the artist's province. It is as nothing when com­pared with the sources of inaccuracy hitherto attending measures.

Before quitting the subject of the inconveniencies, some of which attend the pendulum alone, others both the pendulum and rod, it must be added that the rod would have an accidental, but very precious advantage over the pendulum in this country, in the event of our fixing the foot at the nearest aliquot part of either; for the difference between the common foot and those so to be deduced, would be three times greater in the case of the pendulum, than in that of the rod.

Let the standard of measure then be an uniform cylindrical rod of iron, of such length, as, in latitude 45°, in the level of the ocean, and in a cellar, or other place, the temperature of which does not vary through the year, shall perform its vibrations, in small and equal ares, in one second of mean time.

A standard of invariable length being thus obtained, we may proceed to identify, by that, the Measures, Weights and Coins of the United States: But here a doubt presents itself, as to the extent of the reformation meditated by the House of Representatives. The experiment made by Congress in the year one thousand seven hundred and eighty-six, by declaring that there should be one money of account and payment through the United States, and that its parts and multiples should be in a decimal ratio, has obtained such general approbation, both at home and abroad, that nothing seems wanting, but the actual coinage, to banish the discordant pounds, shillings, pence, and farthings of the different States, and so establish in their stead, [Page 10] the new denominations. Is it in contemplation with the House of Repre­sentatives to extend a like improvement to our Measures and Weights, and to arrange them also in a decimal ratio? The facility which this would in­troduce into the vulgar arithmetic, would, unquestionably, be soon and sen­sibly felt by the whole mass of the people, who would thereby be enabled to compute for themselves whatever they should have occasion to buy, to sell, or m measure, which the present complicated and difficult ratios place beyond their computation, for the most part. Or, is it the opinion of the Representatives that the difficulty of changing the established habits of a whole nation opposes an insuperable bar to this improvement? Under this uncertainty the Secretary of State thinks it his duty to submit alternative plans, that the House may, at their will, adopt either the one or the other, exclusively, or the one for the present, and the other for a future time, when the public mind may be supposed to have become familiarized to it.