Your favor of Sep. 23. 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 in 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, & accessible to all nations, independantly of others, and with a convenience not disproportioned to it’s utility. what subject in nature fulfills best these conditions? what system shall we propose on this , embracing measures, weights & 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. 1. a direct admeasurement of a line on the earth’s surface. or 2. a measure derived from it’s motion on it’s 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 it’s degrees, from the Equator to the pole, require a mean to be sought,1 of which some equal part may2 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 expence required. all this too is to be repeated whenever any accident shall have destroyed the standard derived from it, or impaired it’s 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 independance 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 & vallies, mountains & waters, inaccuracies often unobserved by the agent himself, & 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 it’s axis from noon to noon3 of a mean solar day has been divided from time immemorial, and by very general consent, into 86400. 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 independantly to all men. like a degree of the meridian indeed it varies in it’s length from the Equator to the pole: and like that 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 midway 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 equidistant from it. and it is also a mean value of all it’s degrees. in like manner, when seeking a mean for the pendulum, the same 45th degree offers itself on the same grounds; it’s 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 center of oscillation; & 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 center of oscillation would be lessened. it has also been proposed to prolong the suspending wire of the pendulum below the Bob, until their centers of oscillation shall coincide. but these propositions not appearing to have recieved general approbation, we recur to the pendulum, suspended and charged as has been usual. and the rather as the laws which determine the center 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.4 the other sources of inaccu[ra]cy 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 it’s accessibility to all men, at all times, & in all places. to obtain the second pendulum for 45.° it is not necessary to go actually to that latitude. having ascertained it’s length in our own parallel, both theory & 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 regulated5 time piece, or a good meridian, and such a knolege 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 it’s 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 labours however I have not learned.

Let our Unit of measures then be a pendulum of such length, as in the Lat. of 45.° in the level of the ocean, and in a given temperature, shall perform it’s vibrations, in small & 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 & 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, & less than the ell. it’s 10th or dime will be not quite 4. inches. it’s hundredth, or cent not quite .4 of an inch; it’s thousandth, or Mill not quite .04 of an inch, and so on. the traveller will count his road by a longer measure. 1000 Units, or a Kiliad will be not quite ^⅔ of our present mile, and more nearly a thousand paces than that.

For measures of surface, the square unit, equal to about 10 square feet, or ^¹⁄₉ 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. cub. feet,	28. bushels dry, or ⅞ of a ton liquid.
	dime	=	.1		3.5 cub. f.	2.8 bush. 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 every where, and of a composition sufficiently uniform. water has been generally considered as the most eligible substance, and rainwater more nearly uniform than any other kind found in nature. that circumstance renders it preferable to distilled water, and it’s variations in weight may be called insensible.

The	cubic Unit of this	=	1. would weigh about 2165℔ or a ton between the long & short
the	dime	=	.1 a little more than 2. kentals.
	cent	=	.01 a little more than 20.℔.
	mill	=	.001 a little more than 2.℔.
	decimmil	=	.0001 about 3½. oz. avoirdupoise
	centimmil	=	.00001 a little more than 6. dwt
	millionth	=	.000001 about 15. grains
	decimmillionth	=	.0000001 about 1½ grain
	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 347¼ 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 & round numbers (the exact Unit being yet undetermined) merely to give a general idea of the measures & 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 marr our views, however salutary for all. we are in habits of correspondence with some of these institutions, and identity of character, & of object authorise 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.° 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, it’s 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 civilised country a copy of these tables, stating, as our motive, the difficulty we had experienced, & often the impossibility, of ascertaining the value of the measures, weights & 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; it’s length being determined by the laws of nature, and easily ascertainable at all times & places: that we have thought that of 45.° 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 it’s parts & multiples, in the decimal ratio, we have expressed, in the tables communicated, the values 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 & coins in use within their country, expressed in the parts and multiples of the same Unit. hav ing 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 knolege 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 a 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.° as ascertained by Messrs Borda, Coulomb & 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 it’s agency. the parallel of 45.° 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,6 while we should do the same in an equidistant parallel to the South of 45.° suppose in 38°–29′. we might ask of them too, as they are in possession of the standards 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 Passimaquoddy) 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°–29′ we should be at a loss. it crosses the tidewaters of the Patomac about Dumfries, and I do not know what our resources there would be, unless we borrow them from Washington, where there are competent persons.

Altho’ 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 & 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.° and that the Royal society would undertake the counterpoint on the North, which would be somewhere between the Lizard & Falmouth. the actual pendulums, from both of our points of observation, & not merely the measures of them, should be delivered to the Philosophical society to be measured under their eye & direction.

As this is really a work of common & equal interest to England and the US. 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 re-work.7 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 mean time, provisionally also, form a table adapted to the length of the pendulum of 45.° 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 compleated.

We may even go a step further, and make a general table of the measures weights & coins of all nations, taking their value, hypothetically for the present, from the tables in the Commercial dictionary of the Encyclopedie Methodique, which are very extensive, and have the appearance of being made with great labour & 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 & inch of Paris as a standard, which we may convert into parts of the second pendulum of 45.°

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 any thing 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.