all those habits and usages of men which have reference to numbers. Every thing was to be numbered by tens, hundreds, thousands, &c. Lengths, areas, moneys, weights, periods of times, arcs of circles, every thing that was numerable, was to be numbered by tens. We may here remark by the way, as has been remarked before in substance by Professor Playfair, that if they had carried their spirit of reform a step farther, and had abandoned the decimal notation altogether, and adopted in its stead the duodecimal, they would probably have succeeded in gaining a footing for the innovation much better than they have actually succeeded. We know no reason why we should count by tens, except that we have been endowed by our Creator with ten fingers; and although this might be a very good reason for the original adoption of the decimal notation when men used their fingers as account books, it seems a very insufficient reason for retaining it in these times, when every man and woman is in every civilized country taught the elements of accounts. But there is a very obvious reason why a duodecimal notation should be preferred to the decimal. It is simply this, that the number twelve is divisible without a remainder by no less than four other numbers, whereas ten is so divisible only by two. It is somewhat remarkable that this consideration did not weigh with the revolutionary philosophers to adopt the duodecimal notation and division: and we are afraid we must conclude, though the conclusion be little to the credit of science, that they were led to decline this system by the very consideration that ought to have induced them to adopt it-to wit that its preferableness had led the common sense of mankind to adopt it in a great number of instances in the division of their standards, (as among the English the shilling consists of 12 pence, the pound of 12 ounces, the year of 12 months, and the circle of the Zodiac of 12 signs, the average day and night of 12 hours each,) notwithstanding the obstacles that were thrown in the way by the decimal scale of numbers. But be this as it may, it formed part of the meditated reform to introduce a new standard of measure, whose basis should be some grand unalterable line, and which should be divided and multiplied according to the powers and reciprocal powers of 10. The question then came to be, what should be adopted as the basis of this standard, which was designed not only for France, but for the world. "The fixing on a national and universal standard of measure, (says Professor Playfair,) and the abolition of the present diversity of weights and measures, was an object that very early drew the attention of the Constituent Assembly. It was proposed in that assembly by M. de Talleyrand, and decreed accordingly, that the

They

King should be entreated to write to his Britannic Majesty, to engage the Parliament of England to concur with the National Assembly in fixing a natural unit of weights and measures; that under the auspices of the two nations, an equal number of Commissioners from the Academy of Sciences and the Royal Society of London might unite in order to determine the length of the pendulum in the latitude of 45°, or in any other latitude that might be thought preferable, and to deduce from them an invariable standard of measures and of weights. This decree passed in August 1790. The Academy named a Commission, composed of Borda, Lagrange, Laplace, Monge and Condorcet; and their report is printed in the Memoirs of the Academy for 1788, (Published 1791). Three different units fell under the consideration of these Philosophers; to wit, the length of the pendulum, the quadrant of the Meridian, and the quadrant of the Equator. If the first of these was to be adopted, the Commissioners were of opinion that the pendulum vibrating seconds in the parallel of 45°, deserved the preference, because it is the arithmetical mean between the like pendulums in all other latitudes. observed however that the pendulum involves an element which is heterogeneous, to wit time, and another which is arbitrary, to wit, the division of the day into 86,400 seconds. It seemed to be better that the unit of length should not depend on a quantity, of a kind different from itself, nor on any thing that was arbitrarily assumed."* These reasons for rejecting the length of the pendulum, and preferring the length of a quadrant of the meridian, are certainly quite insufficient. It must have been a matter of utter indifference to the man who bought a metre of tape for shoe-ties, whether the length with which he was served were equal to that of a pendulum that at a certain place would vibrate 3,600 times in an hour, or whether it were a 40millionth part of a line that would stretch all round the earth, passing through both poles! For the purpose in view, the pendulum would questionably have been a far better standard; it could have been verified at any time, with a moderate amount of labor; and a verification could even have been made at any place, the length of the seconds pendulum in any latitude being easily deduced from its ascertained length in any other latitude. It is impossible that these and many other considerations should not have occurred to the French mathematicians as favoring the adoption of the pendulum for the standard, rather than the quadrant of the meridian; we are therefore very

* Edinburgh Review, vol. IX., and Playfair's Works, vol. IV.

strongly inclined to suspect that they made this ascertainment of a metrical standard a mere pretext for procuring the means of accomplishing a most desirable object, the measurement of an arc of the meridian. If they had told the people that this measurement would enable them to determine with greater accuracy the size and figure of the earth, and to ascertain with greater precision the latitudes and longitudes of places on its surface, they would probably have been met with the question, cui bono? But when they gave out that they were to regulate the length of a yard of ribbon, and the size of a pint of wine, every man saw that the object was a good one, and gave it his hearty suffrage. If we be right in this conjecture, it is certainly very humiliating to think that one of the most important admeasurements of a great arc of the Meridian should have been achieved by means of what might have been called in the dark ages "a pious fraud;" humiliating that the projectors of it should have been willing to resort to such an expedient, and humiliating that such an expedient should have been necessary in order to attain the object desired.

Be these things as they may, the French Commissioners proceeded with vigour to the execution of their task, which, though laborious, was to them doubtless a labour of love. The arc selected was more than nine and a half degrees in length, extending from Dunkirk to Barcelona. The measurement of this arc was committed to MM. Mechain and De Lambre. They began their labours in 1792, and prosecuted them with the greatest assiduity and success, notwithstanding that they met with much opposition from the ignorant and excited peasantry, who, like all uncivilized men, put the worst possible construction on what they could not understand. It was indeed a "pursuit of knowledge under difficulties," and De Lambre was many times in imminent danger of his life.

It is not consistent with our plan, or with the exclusive orientalism prescribed for all the articles that appear in these pages, to give any detailed account of this Survey. We only note a few of the particulars in which the mode of operation, and some of the results deduced from the measurement, differed from those of the great Indian Survey, which is the main object of our present dissertation.

We may state, however, that the instruments employed, both for measuring the altitudes of stars for the purpose of ascertaining the positions of the stations, and for measuring the angles of the terrestrial triangles, were four Borda's repeating circles, made by Lenoir, an instrument-maker of great celebrity, and whose work seems to have done full justice to his reputation.

L

Two bases were measured, one at Melun by De Lambre, and the other at Perpigan by Mechain. They were each about 7 miles long, and it is one proof of the accuracy of the whole survey, that though they were 436 miles apart, yet the lengths of each, as estimated by triangulation from the other, did not differ from its measured length by more than 10 or 12 feet.

The result of the measurement gave the compression of the earth's poles part, or in other words, the earth's polar diameter was found to be to the equatoreal as 333 334.

It is, after all, the determination of the figure and size of the earth that is the great object to be attained by the measurement of an arc of the meridian, which always forms the main part of a Trigonometrical Survey. If the earth were a sphere, or a spheroid, or any regular figure, it would be sufficient to measure one long arc, and to ascertain the latitudes of various stations throughout its length; but it is found that the earth, though nearly an oblate spheroid, is not accurately so. Its figure is not regular; and therefore, in order to get a knowledge of its size and figure, it is necessary to know the lengths of degrees of latitude in all parts of its surface. The more such arcs are measured therefore, and the further they are distant from one another, the more nearly will our knowledge of this important geographical element approach to accuracy. Accordingly, ever since the perfect accuracy of geographical knowledge began to be appreciated, it has been a grand object with scientific geographers to have as many arcs measured, and in as distant places, as possible. A clear summary of all that has been done in this matter is presented by Professor Airy, in his report on astronomy presented to the British Association in 1832. This gives such a clear statement of the whole matter that we shall take the liberty to lay it entire before our readers:

"The materials upon which a knowledge of the earth's figure was grounded, at the beginning of the century, were the following: The arc measured in Peru by Bouguer, Lacondamine, &c.; that measured in Lapland by Clairaut, Maupertuis, &c.; that in America by Mason and Dixon, &c.; that, from Rome to Rimini by Boscovich; and that from Barcelona to Dunkirk measured by Delambre and Mechain. Besides these there were some others, as one in Piedmont by Beccaria, one in Austria by Liesganig, and one in India by Reuben Burrows, to which little credit was given; and there was Lacaille's measure at the Cape of Good Hope, which could not be reconciled with the others. One arc of parallel had also been measured in France and one of much greater value in England. The pendulum experiments (serving, with the help of Clairaut's theorem, to determine the proportion of the earth's axes,) were principally scattered observations by De la Croyêre, Campbell, Mairan, Bouguer, Godin, Maupertuis, Lacaille, Legentil, Phipps, Malaspina, and Borda. The last of these (confined to Paris,) were the only ones from which great accuracy could be expected; of the others, the only set in which a series of considerable geographical extent.

were observed by the same persons and with the same instrument, was Malaspina's. The observations of the attraction of Schehallien, and Cavendish's experiments with leaden balls, had given a pretty good knowledge of the earth's mean density.

In the years 1801, 1802, 1803, the arc measured in Lapland (which, according to the calculations of Clairaut and Maupertuis, seemed to present a strange anomaly,) was remeasured and extended by Ofverbom, Svanberg, and others, so as to embrace an amplitude exceeding 13 degree. For the geodesic part, as well as for the astronomical determinations, the new repeating-circle was used. The conclusions at which they arrived differed from those of Maupertuis, and are more in accordance with those given by other measures. But they did not succeed in pointing out the cause of their difference; and, as far as their measures admitted of comparison, they confirmed greatly the accurary of the former measure. The former measure has lately been much discussed, especially by M. Rosenberger in various numbers of the Ast. Nachr.; and the general opinion I think is now, that the first measure was the best, and that its anomaly depended only on the ruggedness of the country. In the Phil. Trans. 1803, is an account of the English measure of an arc from the south-eastern part of the Isle of Wight to Clifton in Yorkshire. The bases were measured with Ramsden's steel chain, and the horizontal angles with a large theodolite: the astronomical observations were made with Ramsden's zenith-sector. There is no doubt that, for its length, this was the most accurate arc that had been measured. Yet a point near the middle of this arc presented an anomaly in regard to the direction of gravity. The measure was afterwards extended to Burleigh Moor: and it thus comprehends an arc of nearly four degrees. Two arcs (of which the details are to be found in the Asiatic Researches,) were measured by Colonel Lambton in India. The first of these, near Madras, was of 1 degree: the other, beginning near Cape Comorin, nearly 10 degrees. The latter has lately been extended by Captain Everest, to nearly 16 degrees. The methods adopted in these measures differ in no respect from those of the English measure: and this arc is undoubtedly the best that has ever been surveyed. The French arc from Dunkirk to Barcelona has been extended by Biot and Arago to the little island Formentera in the Mediterranean (near Iviza), and its whole length is now nearly 12 degrees. Of the excellence of the geodetic part of this there is no doubt; but there seems some reason to doubt the goodness of the astronomical determinations, though no labour was spared by the observers. The account of this forms a conclusion to the Base du Systéme Métrique. The Piedmontese arc of Beccaria has been remeasured with much care by Plana and Carlini: and the account is published in the Operations Géodésiques et Astronomiques en Piémont et Savoie. It is clearly proved that the astronomical part of Beccaria's measure was erroneous: but the result of MM. Plana and Carlini's measure is still anomalous; perhaps not more so than the form of the country would lead us to expect. I may mention here that Zach, in the Monatliche Correspondenz and in the Correspondence Astronomique, has shown clearly that Leisganig's measure is worth nothing. An arc has been measured by Gauss from Gottingen to Altona, of 2 degrees; the astronomical observations being made with Ramsden's zenith-sector; some accounts of it will be found in the Ast. Nachr., and in a small work entitled Bestimmung des Breitenunterscheides, &c. An arc of 3 degrees has been measured by Struve, the northern extremity being on an island in the Gulf of Finland. In many parts of this operation, new instruments and new methods have been used: in particular, for the determination of the latitudes, great reliance was placed on the method of observing stars with a transit instrument whose motion is confined to the