29 Prairial An 7

The following translation appeared in the October and November 1799 issues of A Journal of Natural Philosophy, Chemistry, and the Arts, an English magazine edited by William Nicholson. The article originally appeared in the French Journal de Physique only a few months earlier, which suggests Nicholson had some sort of connection with his French counterpart. The article, written for an informed but not necessarily expert audience, is far more accessible than the French investigators' own reports, and the English translation, being contemporary, conveys much of the spirit of the enterprise. It is excellent evidence of the rapid diffusion of metrological knowledge between France and England at this time.

In this republication, the decimal separator has been changed to the period (or full stop). Footnotes are from the original but have been numbered.

The text is taken from the versions printed in

William Nicholson.
A Journal of Natural Philosophy, Chemistry, and the Arts. Volume III.
London: G. G. and J. Robinson, 1800.


Report made to the National Institute of Sciences and Arts (at Paris), on the 29th Prairial, in the seventh Year (June 17, 1799), in the Name of the Class of Physical and Mathematical Sciences, on the Measure of the Meridian of France, and the Results which have been deduced to determine the new Metrical System. 1, 2

Citizens,

To employ, as the fundamental unity of all measures, a type taken from nature itself—a type as unchangeable as the globe on which we dwell; to propose a metrical system, of which all the parts are intimately connected together, and of which the multiples and subdivision follow a natural progression, which is simple, easy to comprehend, and in every case uniform: this is most assuredly a beautiful, great, and sublime idea, worthy of the enlightened age in which we live. Accordingly, the Academy of Sciences, which, from its first establishment, had fixed its attention upon the experiments of Huyghens on the simple pendulum, did not fail to direct the meditations of men of science to the uniformity and invaribility of measures. That learned body was aware of the great importance of this object: the wishes of the mathematical world were well known to them in this respect, and they beheld one of their number, the celebrated Condamine, employ his talents with the greatest zeal, in destroying the objections which ignorance and prejudice did not cease at that time, any more than at present, to oppose against its establishment3. This academy did not fail to seize the moment when the people of France began to occupy themselves in their political and social regeneration to resume this interesting subject, the execution of which seemed to have waited till the period, when the impulse given to the spirits of men, induced them eagerly to seize every thing which could tend to the public good; and when the existing circumstances permitted them to attend them without constraint, and with the prospect of success. When consulted by the constituent assembly, whose attention was fixed, to this object by the proposition of Citizen Talleyrand4, and charged to determine the unities of measure and of weight, they employed, for good reasons, which were at that time developed5, as the base of the whole metrical system, the fourth part of the terrestrial meridian comprehended between the equator and the north pole. They adopted the ten millionth part of this arc for the unity of measure, which they denominated metre, and applied it equally to superficial and solid measures, taking for the unity of the former the square of the decuple, and for that of the latter the cube of the tenth part of the metre. They chose for the unity of weight the quantity of distilled water which the same cube contains when reduced to a constant state presented by nature itself; and lastly, they decided, that the multiples and sub-multiples of each kind of measure, whether of weight, capacity, surface, or length, should be always taken in the decimal progression, as being the most simple, the most natural, and the most easy for calculation, according to the system of numeration, which all Europe has employed for centuries. Such are the fundamental and essential points of the new metrical system, which the academy has proposed; which has been adopted by the constituent assembly; and which, under names different indeed from those chosen by the academy, have been confirmed by the law of 18th Germinal, in the third year of the republic.

But as the basis of the new metric system depends on the fourth part of the terrestrial meridian, it is necessary that the magnitude of this arc should be known, if not with an extreme precision, yet, at least, with a degree of precision sufficient for practice. Various operations had been already made in France, about the end of the last century, to determine the magnitude of several arcs of the meridian, which crosses this vast empire; and though there might remain some doubts with regard to the perfect accuracy of these operations, notwithstanding the verifications which have from time to time been made, there were good reasons to conclude, after the researches of the celebrated La Caille, that the mean degree would not differ much from 57027 toises; and consequently that the fourth part of the meridian would contain 5,123,420, and that the ten millionth part of this arc would be 443.443 lines. In the just impatience to enjoy the great benefit of exact, uniform, and universal measures, the length of the metre was provisionally settled at 443.44 under the well-formed persuasion that the more precise determinations, which were to be expected, would produce but a slight change in this magnitude.

Nevertheless, the academy, which considered this subject in its true point of view, as well in its general as in its particular relation, with regard to the public utility, its intimate connexion with the most important points of physical astronomy, with the national reputation, to which it was of consequence that the foundations of a new metrical system, proposed to a great people, and presented to the whole world for their adoption, should be determined with the greatest precision, conceived the great project of obtaining a new measure of the meridian which crosses France, by extending it beyond the frontiers, as far as Barcelona, and to apply this great arc to determine the fourth part of the earth. The constituent assembly adopted this vast project, and entrusted the execution to the academy, which nominated, without delay, several of its members to employ themselves on the different parts which composed the totality of the metrical system; and lastly, they charged the Citizens Mechain and Delambre, so worthy, in every respect, of this honourable, though laborious mission, with the task of measuring the meridianal arc. The Institute afterwards nominated Cit. Lefevre Gineau to make the experiments relative to the determination of the unity of weight; and he has proved, by the beauty and accuracy of his work, how truly deserving he was of being associated with his illustrious brethren of the academy.

This great and important operation; projected by the academy of sciences for the establishment of a new metrical system, began by their orders, and happily terminated under the auspices of the institute, after seven years' labour and care, is in many respects deserving of remark. It is singular for the extent of the terrestrial arc, which being more than nine degrees and two thirds, surpasses all those which have been measured; —for the extreme exactness with which all the parts have been executed; the terrestrial survey for determining the length of the arc; the astronomical observations; the operations for fixing the unity of weight; the experiments on the length of the pendulum; all these have proceeded together, and each has been treated with the same precision; and lastly, it is remarkable, and perhaps without parallel for the degree of authenticity with which it is sanctioned. In fact, the Institute has desired not only that commissioners chosen from its own body should examine every thing that is done, but likewise that learned foreigners should join, and make it a common work. The government has seconded this wish, by inviting the allied or neutral powers to send deputies for this object. Several have accepted this invitation; and these deputies, joined to the French commissioners, composed the commission of weights and measures6, which has met, for some months past, in this palace under your auspices, to fix decisively the magnitude of the basis of the new metrical system. This commission made the most minute enquiries into all the details of every observation, and each individual experiment. They weighed all the circumstances jointly with the observers themselves; deduced from the observations those results which were to serve as grounds for calculation; and they determined the unities of measure and weight, which are the definitive results of the whole undertaking. Never did an operation of this kind undergo so strict an examination; and the commission, as well from duty, as to express the satisfaction they have received, have thought fit to acquaint the Institute, that the Citizens Mechain, Delambre, and Lefevre Ginneau, were, in every case desirous of submitting their original documents to their inspection; that they readily gave every possible explanation, as well with regard to the instruments as the methods they employed; and in a word, that they anticipated the desires of the commissioners in every point with the attention, of brothers and friends, and with that respectable openness of character which distinguishes the accurate observer, who far from fearing a severe examination, is, on the contrary, desirous that the minutest detail, and the most scrupulous enquiries, should be entered into, in order that the truth may appear in all its lustre.

In the performance of my charge of rendering this account of the work of these excellent observers, and of the operations of the commission of weights and measures, to fix the unities which serve as the base of the new metrical system, let me be allowed, for the sake of order among the multiplicity of objects I am to submit to your judgment, to speak first of that which relates to the measure of the arc of the meridian, and the determination of the metre, or unity of linear measures thence resulting; after which, I shall offer to your consideration, the experiments which it was necessary to make to fix the unity of weight; and lastly, while I present to you the standards of these two unities, may I offer some reflexions on their nature, their use, and the method of restoring them with the greatest exactness, supposing even that every standard was destroyed, and the name only to remain; an invaluable advantage of these new measures, which gives them a right to the title of invariable.

Let us begin with what concerns the measure of the meridian. Citizens Mechain and Delambre shared this immense work. The northern part from Dunkirk to Rhodes was performed by the first, and Citizen Mechain performed all the rest from Rhodes to Barcelona. He greatly regretted that circumstances did not permit him to carry his operations, as far as the island Carbera. He had even made all the preparations for that enterprize, had undertaken the necessary excursions to examine the place, and settle the stations; and he even laid down on paper the triangles necessary to be measured; so that the whole of this part is sketched out, and by the activity and care he has bestowed upon it, it will be easy to add that arc to what has already been measured, and by that means to prolong the meridian two degrees. Let us hope that more favourable circumstances may hereafter permit that to be carried into effect which hitherto has been impracticable7.

The observers made use, for the measurement of every kind of angles, of the entire circle of Borda, which is justly called the repeating circle, from the valuable advantage which it affords of repeating the angle to be observed any number of times, and consequently diminishing the errors in the same proportion. This circle, which was constructed by the celebrated Lenoir, under the inspection of Borda himself, was fully tried by the observations made in the year 1787 by Cassini, Mechain, and Legendre, in the operations for the junction of the observatories of Paris and Greenwich.

More than one series of observations was made at each station, and the observers formed each series out of such a number of observations as they thought necessary to produce a constant and sufficiently accurate result. They noted in their register the numbers indicated by each observation as well as the particular circumstances which took place, such as the state of the atmosphere, the direction of the light, and, in a word, every thing which could serve to determine the intrinsic value of an observation. The members of the commission nominated for the arrangement of these observations were, therefore, capable of judging of this value, not only from the facts so recorded, but also from the information they received from the observers themselves.

From such an attention to the agreement or variations between the different series of observations, the commissioners were enabled to determine the value of each angle abstractedly, without paying any attention to the others, nor to the sum of the three angles of each triangle. They have thought it their duty to take the angles, such as they were, without making the least correction, or proceeding in any other manner than by taking the means of the observations, according to the authority which the register appeared to give to each. These careful discussions for the most part related to the determination of tenth parts of seconds, and very seldom to whole seconds. The commissioners in this manner formed tables of all the triangles, which have served for the determination of the medium. They have presented this to the general commission, together with a detail of the method they have employed, and the reasons of their determinations. The commission has received these tables, and passed their resolutions, by which they are deposited in the Institute as authentic, as including all the principles applicable to the computation of the triangles and the parts of the meridian; and, in fact, the calculations were afterwards made from them.

The precision with which the angles were observed is such, that out of ninety triangles, which connect the extremities of the meridian, there are thirty-six in which the sum of the three angles differs from its proper quantity by less than one second; that is to say, in which the error of the three angles taken together is less than one second: there are 27 triangles in which this error is less than two seconds; in 18 others it does not amount to three seconds. and there are four triangles in which it falls between three and four seconds, and three triangles only in which it is more than four, but less than five seconds. It may be doubted whether a greater degree of accuracy be obtainable, particularly in the country where the operations were performed; and accordingly it may be supposed by those who consider these tables without being informed of the manner in which they were made, that this appearance of precision may have been given by management and subsequent correction; but the original registers of the observers, the results which they themselves sent to Paris, long before the bases were measured, and at a time when they were still busied with their operations, and the labours of the commissioners themselves, prove the contrary in the most authentic manner. No arbitrary or conjectural correction, however slight, has in any case been made; and all the angles have been determined from considerations derived from the observations themselves.

Two bases were measured by Cit. Delambre; one between Melun and Lieusaint, the other near Perpignan, between Vernet and Salces. The care and precaution with which these operations were performed, and the means adopted for that purpose, are detailed at full length by Cit. Delambre, in his Memoir already mentioned. The instruments were four rods of platina, constructed with great care by Citizen Lenfire, from the instructions, and under the inspection of Citizen Borda. Each of these rules is covered to within four inches of its anterior extremity with a similar plate of brass, movable in the direction of the length of the rule of platina, and fixed to it by the extremity which is most remote from the uncovered part. This plate of brass forms, by the different dilatations which the same variation of temperature produces in the brass and the platina, a very sensible metallic thermometer, the dimensions of which are engraved upon the anterior extremity, which carries a vernier and a microscope to ascertain the subdivisions. Before these rules were used a number of experiments were made to ascertain their dilatation; the state and motion of the metallic thermometers, and their comparison with the ordinary thermometers. The lengths of the rules, Nos. 2, 3 and 4, were compared with that of No. 1, to which all the measures were reduced, which for that reason was called the original (le module); which comparisons were made with such accuracy as to have no doubt of the two hundred thousandth part. Citizen Borda has delivered to the commission a memoir containing a detail of all his experiments, which will form an essential and interesting part of the collection to be published respecting this great operation.

These rules were placed in proper cases, to secure them for every external action or flexure without checking their expansion or contraction, as well as to defend them from the rays of the sun &c.

Every care was taken to support and dispose them properly in measuring the bases themselves. Their extremities were never brought into contact; but an interval was left, which was measured by a tongue of Platina, sliding from the end of one of the rules, and carrying a vernier and microscope. The corrections or allowances for differences of temperature; for obliquities of the line actually measured, and for the elevation above the level of the sea, were also of necessity to be attended to and allowed for.

As the length of the bases are expressed in modules, all the other results are denoted by the same unity. But to give a proper notion of the comparative value of this unity, with regard to the standards employed in other great operations, it became necessary to ascertain the length of No. 1, or the module from the toise of the academy called the toise of Peru; which was done before the commencement of the measuring the base. This comparison was made with a degree of precision sufficient to ascertain the hundred thousandth part of a toise. The details of these experiments are given in the Memoir of Cit. Borda, already mentioned. After his return Cit. Delambre did not fail to compare the rules which had been used for the measurement of the bases, and did not find the slightest change in their length. Lastly, the commission charged several of its members to repeat the same comparison of the module with that of the toise of Peru, that of the North, and that of Mairan, all three of which have become celebrated or important; the two first by the great operations to which they have been applied, and the third, because it was in parts of that toise that Mairan has expressed the results of his valuable experiments on the length of the pendulum, and because it is the standard of the toises which were used to measure the two terrestrial degrees in the neighbourhood of Rome, by the celebrated Boscovich and Lemaire. This new comparison of the module to the toise of Peru again afforded the same result, namely, that the scales had undergone no changes, and proved, moreover, that the module is exactly twice the length of the toise of Peru, and consequently 12 feet in length, when the centigrade thermometer is at 12½ degrees: whence it is deducible, as well by a calculation from the dilatation of the metals as from the direct experiments of Borda, that at the temperature of 16¼ degrees, which answers to 13 degrees of Reaumur's thermometer, the module is shorter than the double toise by two hundred parts of a line; that is to say, about the eighty-fifth thousandth part of the whole.

The observations of Azimuth were made on the sun, and on the pole star at Watten, at Bourges, at Carcassonne, and at Mountjouy; that is to say, at the two extremities of the meridian, and two intermediate places. The observations of latitude, which were made with the circle of Borda. From the great number of the observations, and their agreements with each other, it is considered as a certainly that the error cannot amount to any thing near half a second in any of the latitudes observed.

These observations were made at Dunkirk and at Evaux by Citizen Delambre; at Carcassonne and Montjouy by Citizen Mechain; and at Paris by Citizen Mechain, at the national observatory, and by Citizen Delambre at his own private observatory.

Four commissioners were specially charged with the computation of the triangles, which they performed separately, by different methods, in order to leave nothing doubtful as to the certainty of the results. They have also calculated, and in every case by different methods, the four portions of the meridian comprehended between the places at which the latitude was observed; namely, the terrestrial arc comprehended between Dunkirk and the Pantheon at Paris; the Pantheon and Evaux; Evaux and Carcassonne; Carcassonne and Montjouy. The details of these calculations, and the principles on which they are founded, are contained in a memoir deposited in the archives of the Institute88.

Among other conclusions which present themselves in these calculations, there are two, to which the attention of the Institute is directed: the first, that the mean degrees concluded for the four intervals, of which mention is made, all decrease as they approach the equator; and, consequently, that this operation alone would prove the oblate figure of the earth, if this article required any proof: the second, which was far from being suspected, and exhibits a very remarkable phenomenon, worthy of the enquiries of the most profound mathematicians, that these same degrees do not follow a gradual diminution, but decrease at first very slowly, between Paris and Evaux, only two modules for a degree of latitude; afterwards very rapidly, namely, sixteen modules for the degree of latitude between Evaux and Carcassonne, and that this rapid diminution becomes less between the last-mentioned town and Montjouy, being no more than seven modules.9

This remarkable fall is intimately connected with another, namely, that there are differences between the azimuths calculated for Bourges, Carcassonne, and Montjouy, from that of Dunkirk taken as a base and the azimuths actually observed at these three stations. These two facts eventually confirm and support each other; and when combined, they indicate, either an irregularity in the terrestrial meridian, or an elliptic form in the equator and its parallels, or an irregularity in the internal structure of the earth, or an effect of the attraction of mountains, or a powerful action of all these causes, or a certain number of them united. It is a task worthy of the most celebrated mathematicians to fix their attention upon these facts, and endeavour to develope their elements, in order to obtain a more perfect theory of the earth than we have hitherto possessed.

The commissioners, whose object it was to determine the length of the fourth part of the meridian, and thence the unity of measure, directed their whole attention towards that object. They employed the whole arc comprized between Dunkirk and Montjouy in their calculations, which were strictly made, according to the elliptical hypothesis. To make this calculation, it was requisite to know the difference between the equatorial and polar diameters. This was obtained by comparing the newly-measured arc with the largest and best situated of the arcs already measured; namely, that in Peru. The computations carefully made, and by different formulae, gave one three hundred and thirty-fourth part for the flattening of the earth, which is the same as results from the combination of a great number of experiments at different places on the earth, on the length of the simple pendulum, as well as conformable to the theory of the nutation of the earth's axis, and precession of the equinoctial points. It is, moreover, observed, that as the middle of the entire arc, terminated by Dunkirk and Montjouy, passes near the forty-fifth, or mean degree, of latitude, a slight error would have the less influence on the final determination.

By various methods of computation, employing the arc between Dunkirk and Montjouy, of two hundred and seventy-five thousand seven hundred and ninety-two modules, and thirty-six hundredth parts; and the quantity, three hundred and thirty-four for the oblate figure; it was found that the fourth part of the terrestrial meridian is two million five hundred and sixty-five thousand three hundred and seventy modules; and consequently, that its ten millioneth part, or the metre, or unity of measure, is 256537 millioneth parts of the module.

To reduce this length to the ancient measures, it is observed that if the module and the toise of Peru were supposed to be each at the temperature of the latter when employed by the academicians, which answers to the thirteenth degree of the thermometer of Mercury, divided into 80 parts, or sixteen and a quarter of the centigrade thermometer, the metre would be equal to 443.291 lines of that toise; but by reducing the module to the temperature (as it ought to be) to which it was reduced in the expression of the length of the bases which was used to calculate the triangles, and the length of the portion of the terrestrial meridian, the true and definitive metre is four hundred and forty-three lines, and two hundred and ninety-six thousandth parts of a line of the toise of Peru, this last being constantly supposed to have the temperature of sixteen degrees and a quarter. This last correction became necessary, on account of the difference of expansion in the two metals.

MEASURES of surface are easily deduced from the determination of the length of the metre, which is the basis of the whole system. But this is not the case with measures of weight. The delicate and laborious task of determining the unity of weight was entrusted by the National Institute to Lefevre Gineau, together with Fabroni of Florence; and a special commission was afterwards employed in examining all the registers of observation and experiment, and verifying all the computations. The unity of weight must necessarily consist of some solid, the magnitude of which shall be determined from the lineal measures of the system, and the material of which shall be such as can at all times be procured of one and the same uniform density. The magnitude of the solid adopted for this purpose was the cube of the decimeter, and the substance itself distilled water. Hence the experiment was reduced to determining the relation between the new unity of weight and those of the ancient system, by an actual experiment with such a solid of water. Experimental philosophers are aware that there are two methods of doing this; that is to say, by actually weighing the water contained in a vessel of known dimensions, or otherwise by finding the weight of the quantity of water displaced by a solid, of which the dimensions must also be known. The latter method was preferred, and with justice, on the present occasion.

A hollow cylinder of brass, internally supported by edge-bar-work, was constructed by C. Fortin, together with a guage capable of ascertaining longitudinal measures, to the precision of the four thousandth part of a line of the ancient measure. On the bases of this cylinder were drawn twelve diameters, intersecting each other at equal angles, and each diameter lying in the same plane with a correspondent diameter upon the opposite base. Three concentric circles were drawn on each base, also corresponding by pairs with each other. The points of intersection, including the centre itself, were consequently 37; and by measuring all the several differences between each of these points, and its correspondent point on the other base, the true figure of these boundaries, and the mean length, of the cylinder, were then deducible. Eight circles were also described on the convex surface, and twelve right lines were drawn joining the extreme points of the diameter that had been drawn on the bases. These lines and circles afforded ninety-fix intersections, to every pair of which the guage being duly applied, gave the measure of forty-eight diameters. From all these measures, suitably reduced, it was found that the volume of the cylinder at the temperature of 17.6 of the centigrade thermometer was 0.011290054 of the cubic metre, or more than eleven times the magnitude of the intended unity.

The balances used for weighing were extremely accurate. One of there, charged with rather more than two pounds poids de marc, in each bason, shews the millionth part of the weight; that is to say, one fiftieth of a grain, and it turns with one tenth of a grain when each arm is loaded with 23 pounds.

The weights were arbitrary, though nearly the intended standard; it being of more consequence that they should be adjusted to the most precise equality, than that they should agree with any definite weight. The sub-divisions were in the decimal order.

The cylinder was made hollow, in order that it might load the balance as little as possible, under a given magnitude, but it was necessary that it should be heavy enough to sink in water.

There was a communication between the external air and the inside of the cylinder, by means of a tube, which served to suspend it; and the weights being of the same material, the result in air was the same as it would have been in vacuo.

In order to avoid all dependence upon the relative lengths of the arms of the beam, the weighing was always performed in one and the same scale, the thing itself being first counterpoised, and afterwards taken out, in order to admit the equivalent weight in the same scale. By 53 experiments, the weight of the cylinder proved to be at a mean 11.4660055 of the arbitrary unities, and the extreme difference among these experiments did not amount to 45 millionth parts of the unity. The more difficult operation of weighing the cylinder in water was repeated thirty-six times, and the mean apparent residual weight, proved 0,2094190 unities with no greater absolute difference between the extremes than before.

The reporter enumerates the various corrections to which this apparent weight must be subjected. In the first place he observes, that the air supports the counterpoise; and does not support the body plunged in the water. Secondly, the apparent weight expresses not only that of the cylinder, but likewise of the air contained in its cavity. Thirdly, regard must be had to the density of the water, as governed by its temperature. The experiments were made by surrounding the vessel that contained the water with pounded ice, which kept the temperature of the water itself at three tenths of a degree of the centigrade thermometer above the freezing point; but the results were reduced to the maximum of density of water, which by another course of experiments was found to be at the fourth centigrade degree, conformably to the experiments of Deluc. Lastly, it was requisite to allow for the expansion or contraction of the brass cylinder, by the difference of temperature at the time of admeasurement, and the subsequent experiment.

After all reductions, it was found that 11.2796203 cubic decimetres of water at its maximum of density weighed 11.27, and that one single cubic decimetre of water at its maximum of density weighs 0.9992072 of the unity, which is the true kilogramme of the new metrical system.

It remained then to determine the relation between the arbitrary unity made use of, and the ancient French weights. For this purpose the ancient pile weighing fifty marcs, called the pile of Charlemagne, was examined. The whole pile repeatedly weighed was found to be equal to 12.2279475: whence it follows, that each unity is equal to 18842.9088 grains poids de marc, and that the true kilogramme, or weight, of one cubic decimetre of distilled water, taken at its maximum of density and weight in vacuo, that is to say, the unity of weight, is 18827.15 grains. The reporter adds in a note, that according to these experiments, the foot cubic (French) of distilled water, taken at its maximum of density, is 70 pounds 223 grains; and at the temperature of three tenths of a degree, it weighs 70 pounds 141 grains; and at the temperature of melting ice it weighs 70 pounds 136 grains.

The pile of Charlemaine, though very accurately made for the workmanship of the fourteenth century, at which time it is pretended that it was made, or renewed, is not accurately the same in all its parts. The mark taken as the fiftieth part of the whole pile proved to be 0.2445589 of the unity. The hollow mark was 0,2445127; and the solid mark, 0.2444675. Whence the differences are: between the mark deduced from the whole pile and a hollow mark 0.87 grains; between the same and the solid mark, 1.87 grains; and between the solid mark, and the hollow mark, 0.85 grains. The mark which the celebrated Tillet used in his experiments on the weights of different countries, made in 1767, and inserted in the Memoirs of the Paris Academy for that year10, was different from this pile, though the reporter does not say what was the difference.

The standards presented to the Institute by this commission, were the metre in platina, equal at the temperature of melting ice to 443.296 lines of the toise of Peru, this toise being supposed to have the temperature 16 and a quarter, as has been already observed.

Besides this extraordinary standard, other standards made of iron were also presented for use on common occasions. It is recommended that the operations of adjusting measures of different metals to these standards should be performed at or near the 15th degree of the centigrade thermometer, because the subsequent variations, either to freezing or to a considerable heat, would then produce a less difference between the different kinds of metal.

The standards of weight were a kilogramme of platina intended for the legislative body, and to be preserved with the most scrupulous attention for very important occasions, and several other kilogrammes of brass, made with the same exactness, and intended for civil use. These two kilogrammes of platina and of brass being truly adjusted, are not equal in air, but only in vacuo. The difference in air is, that the brass weight is about one grain and two thirds lighter, on account of buoyancy.

Such are the standards which have been produced with great labour, from a course of observations, experiments, and deductions, capable indeed of being repeated, though not likely to be again performed by a less power than that of a public government. What might be the limit of difference between these results and others which might be had by such a repetition, can therefore be only estimated from a sedulous examination of the particulars of this arduous enterprize. It will not, however, be necessary, for the preservation of the results of Cit. Mechain and Delambre, to recur to the actual standards which have been here presented; for, as the reporter points out, it will be sufficient to render the operation of renewal more easy if the length of the simple pendulum at a known place be expressed in parts of the metre. Cit. Borda, Mechain, and Cassini, have determined this for Paris at the national observatory,with an apparatus which will be described in a memoir of Borda hereafter to be printed. The length of the simple pendulum which beats seconds at Paris was found to be 0.2549919 of the module supposed to be at the temperature of melting ice: whence it is easy to conclude that this length is 0.993827 of the metre.

 

Footnotes

1. Two separate reports were read to the class of physical and mathematical sciences, in the name of the commission of weights and measures; one on the 5th Prairial, by Citizen Van Swinden, on the measure at the meridian, and the determination of the metre; the other, on the 11th of the same month, by Citizen Tralles; on the unity of weight. It was decided by the class, that these two reports should be united and digested into one, to be read at a general fitting of the Institute; and one of its members was accordingly charged with this office. It was performed by Citizen Van Swinden. - Note of the reporter. BACK

2. I have translated the above from the Journal de Physique, Thermidor, an. 7; and to avoid the probability of any error of the press in the numerical results, I have compared them with the same in the bulletin of the Philomathic Society, and the Decade Philosophique, with which I find they agree.—N[icholson]. BACK

3. Memoirs of the Academy for 1748. BACK

4. Decree of the 8th of May, 1790. BACK

5. Memoirs of the Academy of 1789. BACK

6. The following is an alphabetic list of the names of the members of the commission of weights., Æneæ, from the Batavian republic; Balbo, deputy from the king of Sardinia, afterwards replaced by Cit. Vassali; Borda, who died in Ventose last; Brisson, Bugge, deputies from the king of Denmark; Cisear, deputy from the king of Spain; Coulomb, Darcet, Delambre, Fabbroni, deputies from Tuscany; la Grange, la Place, Lefevre-Gineau, Legendre, Franchini, deputies from the Roman republic; Mascheroni, deputy from the Cisalpine republic; Mechain, Multedo, deputies from the Ligurian republic; Pederayes, deputy from the king of Spain; Promi, Tralles, deputies from the Helvetic republic; Van Swinden, deputy from the Batavian Republic; Vassali, deputy from the provisional government of Piedmont.—Note of the Reporter.

I have translated the above note as it stands in the original; but I suppose that Brisson, Coulomb, Darcet, Delambre, la Grange, la Place, Legendre, Mechain, and Proni, are not deputies from foreign powers.-N[icholson]. BACK

7. On account of the length of this report, I shall confine myself to such extracts as relate to the immediate operations and results, omitting his general remarks. Cit. Delambre has published an account of his researches, under the title of Méthodes analytiques pour las Determination d'un Arc du Meredien, in quarto. This work is preceded by a memoir of Legendre on the same subject. —N[icholson]. BACK

8. The meridian between Dunkirk and Montjouy, which subtends a celestial arc of 9,6738 degrees, and of which the middle point passes through 46° 11′ 5″ of latitude, is equal to 275792.36 modules.

That is to say;

  [degrees]   Modules
1. The distance between the parallels of Dunkirk and the Pantheon,
the middle point of which lies in lat. 49° 56' 30", subtends an arc of
2.18910 and measures 62472.59
2. The distance between the parallels of the Pantheon and Evaux,
the middle point of which lies in lat. 47° 30' 46", subtends an arc of
2.66868 and measures 76145.74
3. The distance between the parallels of Evaux and Carcassonne,
the middle point of which lies in lat. 44° 41' 48", subtends an arc of
2.96336 and measures 84424.55
4. The distance between the parallels of Carcassonne and Montjouy,
the middle point of which lies in lat. 42° 17' 20", subtends an arc of
1.85266 and measures 52749.48
Whole celestial arc 9.67380 Measure 275792.36

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9. If from the four intervals before given, we deduce the mean degree, which may be concluded from the spherical hypothesis, which is sufficient for a cursory view, we shall find the mean degree in round members:

  Modules. Difference. Difference
for one degree.
Between Dunkirk and the Pantheon, mean latitude. 49° 56' 30". 28538 5 2
Between the Pantheon and Evaux, mean latitude, 47° 3' 46". 28533 44 16
Between Evaux and Carcassonne, mean latitude, 44° 41' 48". 28489 12 7
Between Carcassonne and Montjouy, mean latitude, 42° 17' 20". 28472    

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10. See also the First Principles of Chemistry; and my Chemical Dictionary, art. Balance. BACK

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