To Dr. Robert Patterson Monticello, November 10, 1811
-- Your favor of September 23d came to hand in due time, and I thank you for the nautical almanac it covered for the year 1813. I learn with pleasure that the Philosophical Society has concluded to take into consideration the subject of a fixed standard of measures, weights and coins, and you ask my ideas on it; insulated as my situation is, I am sure I can offer nothing but what will occur to the committee engaged on it, with the advantage on their part of correction by an interchange of sentiments and observations among themselves. I will, however, hazard some general ideas because you desire it, and if a single one be useful, the labor will not be lost.
The subject to be referred to as a standard, whether it be matter or motion, should be fixed by nature, invariable and accessible to all nations, independently of others, and with a convenience not disproportioned to its utility. What subject in nature fulfils best these conditions? What system shall we propose on this, embracing measures, weights and coins? and in what form shall we present it to the world? These are the questions before the committee.
Some other subjects have, at different times, been proposed as standards, but two only have divided the opinions of men: first, a direct admeasurement of a line on the earth's surface, or second, a measure derived from its motion on its axis. To measure directly such a portion of the earth as would furnish an element of measure, which might be found again with certainty in all future times, would be too far beyond the competence of our means to be taken into consideration. I am free, at the same time, to say that if these were within our power in the most ample degree, this element would not meet my preference. The admeasurement would of course be of a portion of some great circle of the earth. If of the equator, the countries over which that passes, their character and remoteness, render the undertaking arduous, and we may say impracticable for most nations. If of some meridian, the varying measures of its degrees from the equator to the pole, require a mean to be sought, of which some aliquot part may furnish what is desired. For this purpose the 45th degree has been recurred to, and such a length of line on both sides of it terminating at each end in the ocean, as may furnish a satisfactory law for a deduction of the unmeasured part of the quadrant. The portion resorted to by the French philosophers, (and there is no other on the globe under circumstances equally satisfactory,) is the meridian passing through their country and a portion of Spain, from Dunkirk to Barcelona. The objections to such an admeasurement as an element of measure, are the labor, the time, the number of highly-qualified agents, and the great expense required. All this, too, is to be repeated whenever any accident shall have destroyed the standard derived from it, or impaired its dimensions. This portion of that particular meridian is accessible of right to no one nation on earth. France, indeed, availing herself of a moment of peculiar relation between Spain and herself, has executed such an admeasurement. But how would it be at this moment, as to either France or Spain? and how is it at all times as to other nations, in point either of right or of practice? Must these go through the same operation, or take their measures from the standard prepared by France? Neither case bears that character of independence which the problem requires, and which neither the equality nor convenience of nations can dispense with. How would it now be, were England the deposit of a standard for the world? At war with all the world, the standard would be inaccessible to all other nations. Against this, too, are the inaccuracies of admeasurements over hills and valleys, mountains and waters, inaccuracies often unobserved by the agent himself, and always unknown to the world. The various results of the different measures heretofore attempted, sufficiently prove the inadequacy of human means to make such an admeasurement with the exactness requisite.
Let us now see under what circumstances the pendulum offers itself as an element of measure. The motion of the earth on its axis from noon to noon of a mean solar day, has been divided from time immemorial, and by very general consent, into 86,400 portions of time called seconds. The length of a pendulum vibrating in one of these portions, is determined by the laws of nature, is invariable under the same parallel, and accessible independently to all men. Like a degree of the meridian, indeed, it varies in its length from the equator to the pole, and like it, too, requires to be reduced to a mean. In seeking a mean in the first case, the 45th degree occurs with unrivalled preferences. It is the mid-way of the celestial ark from the equator to the pole. It is a mean between the two extreme degrees of the terrestrial ark, or between any two equi-distant from it, and it is also a mean value of all its degrees. In like manner, when seeking a mean for the pendulum, the same 45th degree offers itself on the same grounds, its increments being governed by the same laws which determine those of the different degrees of the meridian.
In a pendulum loaded with a Bob, some difficulty occurs in finding the centre of oscillation; and consequently the distance between that and the point of suspension. To lessen this, it has been proposed to substitute for the pendulum, a cylindrical rod of small diameter, in which the displacement of the centre of oscillation would be lessened. It has also been proposed to prolong the suspending wire of the pendulum below the Bob, until their centres of oscillation shall coincide. But these propositions not appearing to have received general approbation, we recur to the pendulum, suspended and charged as has been usual. And the rather as the the laws which determine the centre of oscillation leave no room for error in finding it, other than that minimum in practice to which all operations are subject in their execution. The other sources of inaccuracy in the length of the pendulum need not be mentioned, because easily guarded against. But the great and decisive superiority of the pendulum, as a standard of measure, is in its accessibility to all men, at all times and in all places. To obtain the second pendulum for 45 degrees it is not necessary to go actually to that latitude. Having ascertained its length in our own parallel, both theory and observation give us a law for ascertaining the difference between that and the pendulum of any other. To make a new measure therefore, or verify an old one, nothing is necessary in any place but a well-regulated time-piece, or a good meridian, and such a knowledge of the subject as is common in all civilized nations.
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 recoved 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 degrees, 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 arithmatic 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 2 1/2 acres.
For measures of capacity, wet and dry,
The cubic Unit =.1
would be about .35 cubic feet, .28 bushels dry, or 7/8 of a ton liquid.
Dime = .1
would be about 3.5 cubic feet, 2.8 bushels, or about 7/8 of a barrel liquid.
Cent = .01
about 50 cubic inches, or 7/8 of a quart.
Mill = .001 = .5 of a cubic inch,
or 2/3 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.
|The Dime =||.1 a little more than 2. kentals.|
|Cent =||.01 a little more than 20 lb.|
|Mill =||.001 a little more than 2 lb.|
|Decimmil =||.0001 about 3 1/2 oz. avoirdupoise.|
|Centimmil =||.00001 a little more than 6 dwt.|
|Millionth =||.000001 about 15 grains.|
|Decimmillionth =||.0000001 about 1 1/2 grains.|
|Centimmillionth =||.00000001 about .14 of a grain.|
|Billionth =||.000000001 about .014 of a grain.|
With respect to our coins, the pure silver in a dollar being fixed by law at 347 1/4 grains, and all debts and contracts being bottomed on that value, we can only state the pure silver in the dollar, which would be very nearly 23 millionths.
I have used loose and round numbers (the exact unit being yet undetermined) merely to give a general idea of the measures and weights proposed, when compared with those we now use. And in the names of the subdivisions I have followed the metrology of the ordinance of Congress of 1786, which for their series below unit adopted the Roman numerals. For that above unit the Grecian is convenient, and has been adopted in the new French system.
We come now to our last question, in what form shall we offer this metrical system to the world? In some one which shall be altogether unassuming; which shall not have the appearance of taking the lead among our sister institutions in making a general proposition. So jealous is the spirit of equality in the republic of letters, that the smallest excitement of that would mar our views, however salutary for all. We are in habits of correspondence with some of these institutions, and identity of character and of object, authorize our entering into correspondence with all. Let us then mature our system as far as can be done at present, by ascertaining the length of the second pendulum of 45 degrees by forming two tables, one of which shall give the equivalent of every different denomination of measures, weights and coins in these States, in the unit of that pendulum, its decimals and multiples; and the other stating the equivalent of all the decimal parts and multiples of that pendulum, in the several denominations of measures, weights and coins of our existing system. This done, we might communicate to one or more of these institutions in every civilized country a copy of those tables, stating as our motive, the difficulty we had experienced, and often the impossibility of ascertaining the value of the measures, weights and coins of other countries, expressed in any standard which we possess; that desirous of being relieved from this, and of obtaining information which could be relied on for the purposes of science, as well as of business, we had concluded to ask it from the learned societies of other nations, who are especially qualified to give it with the requisite accuracy; that in making this request we had thought it our duty first to do ourselves, and to offer to others, what we meant to ask from them, by stating the value of our own measures, weights and coins, in some unit of measure already possessed, or easily obtainable, by all nations; that the pendulum vibrating seconds of mean time, presents itself as such an unit; its length being determined by the laws of nature, and easily ascertainable at all times and places; that we have thought that of 45 degrees would be the most unexceptionable, as being a mean of all other parallels, and open to actual trial in both hemispheres. In this, therefore, as an unit, and in its parts and multiples in the decimal ratio, we have expressed, in the tables communicated, the value of all the measures, weights and coins used in the United States, and we ask in return from their body a table of the weights, measures and coins in use within their country, expressed in the parts and multiples of the same unit. Having requested the same favor from the learned societies of other nations, our object is, with their assistance, to place within the reach of our fellow citizens at large a perfect knowledge of the measures, weights and coins of the countries with which they have commercial or friendly intercourse; and should the societies of other countries interchange their respective tables, the learned will be in possession of an uniform language in measures, weights and coins, which may with time become useful to other descriptions of their citizens, and even to their governments. This, however, will rest with their pleasure, not presuming, in the present proposition, to extend our views beyond the limits of our own nation. I offer this sketch merely as the outline of the kind of communication which I should hope would excite no jealousy or repugnance.
Peculiar circumstances, however, would require letters of a more special character to the Institute of France, and the Royal Society of England. The magnificent work which France has executed in the admeasurement of so large a portion of the meridian, has a claim to great respect in our reference to it. We should only ask a communication of their metrical system, expressed in equivalent values of the second pendulum of 45 degrees as ascertained by Messrs. Borda, Coulomb and Cassini, adding, perhaps, the request of an actual rod of the length of that pendulum.
With England, our explanations will be much more delicate. They are the older country, the mother country, more advanced in the arts and sciences, possessing more wealth and leisure for their improvement, and animated by a pride more than laudable (*). It is their measures, too, which we undertake to ascertain and communicate to themselves. The subject should therefore be opened to them with infinite tenderness and respect, and in some way which might give them due place in its agency. The parallel of 45 degrees being within our latitude and not within theirs, the actual experiments under that would be of course assignable to us. But as a corrective, I would propose that they should ascertain the length of the pendulum vibrating seconds in the city of London, or at the observatory of Greenwich, while we should do the same in an equi-distant parallel to the south of 45 degrees, suppose in 38 degrees 29'.We might ask of them, too, as they are in possession of thestandards of Guildhall, of which we can have but an unauthentic account, to make the actual application of those standards to the pendulum when ascertained. The operation we should undertake under the 45th parallel, (about Passama-quoddy,) would give us a happy occasion, too, of engaging our sister society of Boston in our views, by referring to them the execution of that part of the work. For that of 38 degrees 29' we should be at a loss. It crosses the tide waters of the Potomac, about Dumfries, and I do not know what our resources there would be unless we borrow them from Washington, where there are competent persons.
Although I have not mentioned Philadelphia in these operations, I by no means propose to relinquish the benefit of observations to be made there. Her science and perfection in the arts would be a valuable corrective to the less perfect state of them in the other places of observation. Indeed, it is to be wished that Philadelphia could be made the point of observation south of 45 degrees, and that the Royal Society would undertake the counterpoint on the north, which would be somewhere between the Lizard and Falmouth. The actual pendulums from both of our points of observation, and not merely the measures of them, should be delivered to the Philosophical Society, to be measured under their eye and direction.
As this is really a work of common and equal interest to England and the United States, perhaps it would be still more respectful to make our proposition to her Royal Society in the outset, and to agree with them on a partition of the work. In this case, any commencement of actual experiments on our part should be provisional only, and preparatory to the ultimate results. We might, in the meantime, provisionally also, form a table adapted to the length of the pendulum of 45 degrees, according to the most approved estimates, including those of the French commissioners. This would serve to introduce the subject to the foreign societies, in the way before proposed, reserving to ourselves the charge of communicating to them a more perfect one, when that shall have been completed.
We may even go a step further, and make a general table of the measures, weights and coins of all nations, taking their value hypothetically for the present, from the tables in the commercial dictionary of the encyclopedia methodique, which are very extensive, and have the appearance of being made with great labor and exactness. To these I expect we must in the end recur, as a supplement for the measures which we may fail to obtain from other countries directly. Their reference is to the foot or inch of Paris, as a standard, which we may convert into parts of the second pendulum of 45 degrees.
I have thus, my dear sir, committed to writing my general ideas on this subject, the more freely as they are intended merely as suggestions for consideration. It is not probable they offer anything which would not have occurred to the committee itself. My apology on offering them must be found in your request. My confidence in the committee, of which I take for granted you are one, is too entire to have intruded a single idea but on that ground.
Be assured of my affectionate and high esteem and respect.