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 centres 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 the 31° of latitude, by about 1⁄679 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 inconveniences, 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 a 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 arcs, 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,[23] 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 to establish in their stead 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 to 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.
I. And first, on the supposition that the present measures and weights are to be retained but to be rendered uniform and invariable, by bringing them to the same invariable standard.