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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 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 it kā to uz 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,* 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 moasures 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 diflicult 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.
* See Vol. I. p. 162.
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.
The first settlers of these States, having come chiefly from England, brought with them the measures and weights of that country. These alone are generally established among us, either by law or usage; and these, therefore, are alone to be retained and fixed. We must resort to that country for information of what they are, or ought to be.
This rests, principally, on the evidence of certain standard measures and weights, which have been preserved, of long time, in different deposits. But differences among these having been known to exist, the House of Commons, in the years 1757 and 1758, appointed committees to inquire into the original standards of their weights and measures. These committees, assisted by able mathematicians and artists, examined and compared with each other the several standard measures and weights, and made reports on them in the years 1758 and 1759. The circumstances under which these reports were made entitle them to be considered, as far as they go, as the best written testimony existing of the standard measures and weights of England ; and as such, they will be relied on in the progress of this report.
MEASURES OF LENGTH.
The measures of length in use among us are :
The ell of a yard and quarter, The furlong of 40 poles or. The yard of 3 feet, perches,
The foot of 12 inches, and The pole or perch of 5) yards. The inch of 10 lines.
On this branch of their subject, the committee of 1757–1758, says that the standard measures of length at the receipt of the exchequer, are a yard, supposed to be of the time of Henry VII., and a yard and ell supposed to have been made about the year 1601; that they are brass rods, very coarsely made, their divisions not exact, and the rods bent; and that in the year 1742, some members of the Royal Society had been at great pains in taking an exact measure of these standards, by very curious instruments, prepared by the ingenious Mr. Graham ; that the Royal Society had had a brass rod made pursuant to their experiments, which was made so accurately, and by persons so skilful and exact, that it was thought not easy to obtain a more exact one; and the committee, in fact, found it to agree with the standards at the exchequer, as near as it was possible. They furnish no means, to persons at a distance, of knowing what this standard is. This, however, is supplied by the evidence of the second pendulum, which, according to the authority before quoted, is, at London, 39.1682 English inches, and, consequently, the second rod there is of 58.7523 of the same inches. When we shall have found, then, by actual trial, the second rod for 45° by adding the difference of their computed length, to wit: 13877 of an inch, or rather is of a line (which in practice will endanger less error than an attempt at so minute a fraction as the ten thousandth parts of an inch) we shall have the second rod of London, or a true measure of 58; English inches. Or, to shorten the operation, without varying the result,
Let the standard rod of 45° be divided into 587} equal parts, and let each of these parts be declared a line. 10 lines an inch,
51 yards a perch or pole, 12 inches a foot,
40 poles or perches a furlong, 3 feet a yard,
8 furlongs a mile, 3 feet 9 inches an ell,
3 miles a league. 6 feet a fathom,
Our measures of surface are, the acre of 4 roods and the rood of 40 square poles ; so established by a statute of 33 Edw. 1. Let them remain the same.
MEASURES OF CAPACITY.
The measures of capacity in use among us are of the following names and proportions :
The gill, four of which make a pint.
Eight gallons make a measure called a firkin, in liquid substances, and a bushel, dry.
Two firkins, or bushels, make a measure called a rundlet or kilderkin, liquid, and a strike, dry.
Two kilderkins, or strikes, make a measure called a barrel, liquid, and a coomb, dry; this last term being ancient and little used.
Two barrels, or coombs, make a measure called a hogshead, liquid, or a quarter, dry ; each being the quarter of a ton.
A hogshead and a third make a tierce, or third of a ton.
But no one of these measures is of a determinate capacity. The report of the committee of 1757–8, shows that the gallon is of very various content; and that being the unit, all the others must vary with it. The gallon and bushel contain224 and 1792 cubic inches, according to the standard wine
gallon preserved at Guildhall. 231 and 1848, according to the statute of 5th of Anne. 264.8 and 2118.4, according to the ancient Rumford quart,
of 1228, examined by the committee. 265.5 and 2124, according to three standard bushels pre
served in the Exchequer, to wit: one of Henry VII., without a rim ; one dated 1091, supposed for 1591, or 1601, and one dated 1601.