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Extract from a law of the territory of Missouri, concerning weights and
measures. 66 SEC. 1. The several courts of common pleas (circuit courts] within this territory, shall provide for their respective counties, and at the expense of their said counties, one measure, of one foot, or twelve inches, English measure, so called : also, one measure of three feet, or thirty-six inches, English measure, as aforesaid, to be denominated one yard ; also, one half bushel measure, which shall contain one thousand seventy five and one fifth solid inches, to be denominated dry measure : also, one gallon measure, which shall contain two hundred and thirty-one solid inches ; one half gallon measure, which shall contain one hundred and fifteen and one half solid inches; and one quart measure, which shall contain fifty-seven and three fourths solid inches; which measures are to be of wood, or any metal the court shall think proper: also, one set of weights, commonly called avoirdupois weights; and one seal, with the initial of the county inscribed thereon, which measures, weights, and seal, shall be kept by the clerk of the court of common pleas (circuit court] in each county, for the purposes of trying and sealing the measures and weights used in their counties.” L. M. T. July sess. 1813.
PARIS, 16th July, 1817. SIR: I had the honor to receive your letter dated London, the 5th of May last, together with the resolution of the Senate of the 3d of March, 1817, on the subject of weights and measures.
I accordingly enclose, in relation to those of France, Tarbe's Manuel, which is considered as the best elementary practical work on the subject; the Annuaire of the Board of Longitude, for the present year, in which you will find a very concise exposition of the principles of the system ; the third volume of Delambre's Base du Systeme metrique decimal, which explains them at large; the Connoissance des
Tems, for the year 1816, in which are found, pages 314 to 332, and particularly page 330, some subsequent observations on the pendulum ; and some sheets of a journal now printing, which contains an additional note of De Prony, on the ratio of the metre to the English foot.
I have not sent the two first volumes of Delambre's work, which contain the details of the measurement of the meridian, from Dunkirk to Barcelona, as all the results are found in the third volume. The fourth volume, edited by Biot and Arrago, which, besides other mat. ter, will give the measurement of the meridian from Barcelona to Formentera, its northern extension, to Greenwich, and through a part of Great Britain, and Biot's observations of the pendulum at several places, is not yet printed.
You requested that I might add such observations as might occur to me. The following are made, less on account of their intrinsic value, than because they may assist in explaining some points of the works enclosed.
The legal metre, or unit of the French linear measures, is presumed to be arrotory of the quarter of the meridian, from the equator to the pole, and has been deduced from the actual measurement of the arch from Formentera to Dunkirk, compared in order to calculate the flattening of the earth with the former measurement in Peru. This standard metre, such as it is definitively adopted by law, is equal to 443 204 lignes (or 12th parts of an inch) of the old French measures. Doubts have however arisen whether it is truly the , 72 ans of the quarter of the meridian. Delambre, in his third volume, deducing the car or from the measurement of the arch from Barcelona to Dunkirk alone, had made it equal to 443106 lignes. The calculations of the flattening of the earth, as deduced solely from theory, would give a result nearer to the legal metre. The measurement made in England of an arch of the meridian, would seem to affect those conclusions. But it must be observed that an error of two seconds in the latitude observed, would, in the long arch measured from Formentera to Dunkirk, produce a difference in the length of the metre, equal to the difference between Delambre's calculation and the legal metre; that the same error would, in the much shorter arch measured in England, produce a much greater difference; and that the most candid astronomers acknowledge that, with the instruments now in use, such an error (of two seconds of latitude) is possible. Although, therefore, it seems probable that the legal metre is a little too short, and it seems to be regretted that it was not made equal to 443 lignes, it is, upon the whole, nearly as exact as was practicable in the present state of science. But, should more extensive measurements of the meridian, greater improvements in the instruments, and a more precise knowledge of all the elements which affect the observations, lead to a still more correct calculation of the true length of the quarter of the meridian, the standard, or legal French metre, would remain as it now is, the unit or basis of the system of French measures, and the only difference would be, that, in- . stead of being, as now presumed, tooobron, it might be found to be
totoo, or some other not far distant fraction of the quarter of the meridian. And this difference would be less than the errors which will always take place in the confection, not of a standard metre executed with every possible care, but of the measures used for common purposes.
For the purpose of ascertaining the ratio of the length of the metre to that of the pendulum, observations have been made with great
care in several places ; but those at Paris by Borda and Cassini, inserted in Delambre's third volume, are the only ones (with the exception of those mentioned in the Connoissance des Tems, page 314 to 322) which are given in detail by the French writers. Those of Biot and others will appear in Delambre's fourth volume: but their general result is given in the Connoissance des Tems, and it thereby appears that the length of the pendulum making 100,000 oscillations in 24 hours (in vacuo and at the freezing point of water) and referred to the level of the sea, is at Paris, in latitude 48° 50' 14", equal to 16707 of the metre ; at Bordeaux, in latitude 44° 50' 25', equal to 141677; and at Formentera, in latitude 33° 39' 56", equal to
2017. The final calculation of Borda for Paris, of the second pendulum (which makes 86,400 oscillations in 24 hours) is 1938 137 of the metre, and 44044307 lignes old French measure.
From the metre are immediately deduced, by a descending and ascending decimal ratio, all the French measures, linear, superficial, and of capacity, such as they are found every where, and which require no observation.
The unit of weight, which is in fact the kilogramme or 1000 grammes, has been determined by ascertaining the weight in vacuo of the tooo part of a cubic metre of distilled water at its maximum of density, which is 4o of the centigrade thermometer above the freezing point, corresponding to 39.6 of Fahrenheit. The experiments, which in every system of measures which may be adopted, are extremely important, were made with great care and skill by Lefevre Gineau ; the substance is found in Delambre's third volume, but the detailed account appears to have been unfortunately lost. The old French pound, poids de marc, is 480g of the kilogramme.
From the kilogramme or gramme has been deduced, by a decimal ratio, the whole system of French weights, including also that of moneys, in the manner stated in all the elementary works.
The ratio of the English foot to the old and new French measures, may have been lately ascertained in England, where a correct standard metre of platina has been sent. By de Prony's experiments the metre is equal to 39.3827 English inches, and the old French foot to 12.1232 English inches.
It is probable that the second pendulum will, at Washington, be found nearly equal to 1.036 of a metre, and to 39.107 English inches.
The great advantages of the French system seems to consist, ist. In having an unit from which derives the whole by a decimal ratio ; 2dly. In having ascertained the ratio of that unit to constant quantities, (the quarter of the meridian, and the length of the pendulum) so as to be able to perpetuate, and, in case of accident, to make new standard measures, perfectly similar to those now established by law : 3dly. In the great correctness of the experiments by which this ratio has been ascertained, and in the similar care bestowed on the confection of the standard measures and weights.
These advantages are, in a great degree, independent of the substitution of new to ancient measures, which bas in practice met with
such difficulties. Provided the ratio of the old French foot to the natural and constant measures of the earth and of the pendulum, kad been ascertained, that foot might have been preserved, introducing only its decimal subdivision.
I will, for the present, only add, that as one of the first steps, if any plan is adopted on that subject in the United States, must be to ascer tain the ratio of our foot to natural measures, it will be important to obtain the observations (not yet printed) of Biot, which, together with those of Borda, give all the information necessary for correct experiments of the length of the pendulum. As we will not probably very soon measure with sufficient correctness a considerable arch of the meridian, the best mode to obtain at once the ratio of our foot, both to the quarter of the meridian and to the French measure, will be to cause a metre of platina to be made here by Fortin. I could, I think, prevail on Mr. Arrago, or some other member of the board of longitude, to superintend the execution. Two have been completed for the Royal Society of London, and one is now on hand for the king of Prussia. The price will be about one hundred guineas. The brass metre made by order of Mr. Hassler, and which belongs to the United States, was executed by young Le Noir, and is not sufficiently correct for the purpose.
I am, &c.
Mr. Russell to the Secretary of State.
STOCKHOLM, 31st July, 1818. Sir: The duplicate of your letter (No. 3.) of the 25th of May last, reached me on the 15th inst. but the original is not yet received. I have now the honor, in compliance with your request therein expressed, to communicate such information as I have been able to collect, “ relative to the proceedings of this country for establishing uniformity in weights and measures," and which was required by the resolution of the Senate, to which you refer.
Not being made acquainted with the object of the Senate in franing that resolution, either by the resolution itself or by your letter, 1 have felt some uncertainty with regard to the precise import of the term “uniformity,” as therein used. It may relate to the proceedings of any foreign country to establish, within itself, one sole standard for weights and measures respectively; or it may relate to the proceedings of several foreign countries to establish such a standard in common, or to the regulations of each particular country, for preserving the constancy of its weights and measures, by an exact conformity to one or more standards, respectively, which may there exist, and thus, in regard to those respective standards, establishing uniformity throughout such country.
Were I to confine myself to either of these constructions, singly, I might err in my selection, and furnish information altogether inapplicable to the real object of the resolution. I have believed it safer, therefore, to communicate all the information which I have collected on the subject, considered in the three points of view above suggested. I shall even present some details, which, although obviously not called for by the resolution of the Senate, may be useful on some other occasion.
Throughout Sweden there is but one measure, which was last established by the royal ordinance of King Frederick, in 1739. This measure appears, like many others now in use in Europe, to have been originally taken from the human foot and thumb. The Swedish foot is divided into twelve work inches (werktums) or decimally into ten inches. The work inches are used in building, handifraft, and commerce, and the decimal, inches for geometrical mensuration.
Long measure. To the foot thus divided into inches are all the Swedish measures of length, superficies, or capacity referrible :
2 Swedish feet = 1 Swedish (aln) ell; 3 ells = 1 fathom (famm); 5 ells = 1 perch (stang); 36,000 Swedish feet = 18,000 Swedish ells = i Swedish mile.
56,000 Swedish square feet = 14,000 ells = 1 Swedish (tunnland) acre of land ; 1 tunnland - 2 spannlands = 4 half spannlands = 32 kapplands = 56 kannlands.
i Swedish cubic foot = 1,000 Swedish decimal cubic inches = 10 Swedish (kannor) cans ; 5,600 decimal cubic inches = 1 tunna (ton) = 2 span = 8 quarts (fjerdinger) = 32 kappar = 56 cans (kannor); 7 cans = 4 kappe,