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The song of knocker and of bell was over ;
Upon the steps two chimney-sweeps repos'd;
And hope, and such cold unsubstantial dishes;
None knew. The curious reader, if he wishes,
From their own lips the world will never know,
Beyond all other mysteries here below,
'Tis proper and polite her name should end it;
Or moral can be trac'd, 'twas not intended;
I'm sorry for it—so is my bookseller.' Fanny, whether real or unreal, is quite indulgent to our poet's taste for episode, and permits him to ramble almost at will over our bustling city of Gotham, in pursuit of such flying vanities as may be shot at consistently with good nature.
With one or two exceptions, he has used the license with discretion, and has for the present left the tribe of graver phantoms undisturbed by the touch of his satirical wand. We shall leave them too, and conclude this article with the author's beautiful apostrophe to Weehawken-a picture that exhibits powers of description, an ease and sweetness of versification, and a poetic sensibility, which, if spread over a larger work, and applied to subjects less fleeting than the local and eyanescent follies of the day, would secure to their possessor that enviable reputation of taste and genius, which receives its stamp in the temple of the muses.
Weehawken ! In thy mountain scenery yet,
All we adore of nature in her wild
And never has a summer's morning smild
O'er crags, that proudly tower above the deep,
The breathless moment—when his daring step
And clings to the green turf with desperate corce,
As the heart clings to life ; and when resume
The currents in his veins their wonted course,
Ocean, and earth, and heaven, burst before him ;
Of Summer's sky, in beauty bending o'er him-
And banners floating in the sunny air ;
Green isle, and circling shore, are blended there,
Whose infant breath was drawn, or boyhood's days
That in his manhood's prime can calmly gaze
Art. I. Base du Systéme Mètrique Décimal, ou Mesure de l'Arc du Méridian entre les parallales de Dunkerque and Barcelone.
Exécutée par MM. Mechain et Delambre. Tome Premier. Paris. 4to. 1806.
[Edinburgh Review-Jan. 1807.]
It is remarkable that some of the clearest of our ideas are incapable of being accurately expressed by means of language, or of any arbitrary symbols whatsoever. This happens with respect to certain ideas of quantity, while with respect to others, not more clear or definite, the contrary takes place. Of the magnitude of a line, for instance, no precise notion can be conveyed in words from one man to another, except by comparing it with a line already known to them both; and if such a standard of comparison is wanting, the ordinary means of information fail entirely, and there is no resource but in the actual exhibition of the line itself. It is quite otherwise again, where either the ratio or the angular position of magnitudes are concerned : these can be fully explained by verbal communication, and never require the production of the objects themselves. We know what
a Greek geometer meant by a right angle, or by an angle of one degrée, just as well as if we had before our eyes a circle divided by some artist of Athens or Alexandria. We understand, too, what he means when he speaks of the ratio of two to one, or of the ratio of the diagonal of a square to its side; but if he specifies some individual length, of a foot, for example, a spithame, or a stadium, we comprehend nothing of the matter, unless he has made a reference to some common standard, that is, to some magnitude which remains the same now as when he wrote.
So also when Eratasthenes tells us that the distance between Alexandria and Syene subtends, at the earth's centre, an angle, which is the fiftieth part of four right angles, we are at no loss to comprehend what is meant; but when he says that the distance between the two places is 5000 stad we receive no accurate information; and much critical discussion has been required to extract even a very uncertain meaning from his words.
The first attempt at fixing such a standard of measure as should be accurate, and universal, both as to place and time, is due to the inventive genius of the celebrated Huygens. That philosopher demonstrated that the times of vibrations of pendulums depend on their length only; and, whatever be their structure, that a certain point may be found, which in pendulums that vibrate in the same time, is constantly at the same distance from the centre of suspension. Hence he conceived that the pendulum might afford a standard, or unit, for measures of length ; and though a correction would be necessary, because the intensity of gravitation was not the same in all latitudes, he believed that science furnished the means of determining this correction with sufficient accuracy. Picard laid hold of the same notion, and Cassini, in his book de la Grandeur de la Terre, proposed another unit, taken also from Nature, though not so easily obtained, viz. the six thousandth part of a minute of a degree of a great circle of the earth. A similar idea had even earlier occured to Mouton. No attempt, however, was made to raise, upon any of these standards, a regular system of measures, adapted either to the purposes of science or of ordinary life. Among the measures and weights that actually prevailed throughout Europe, the utmost confusion and perplexity continued to take place. In each sort of measure units of different magnitudes were admitted. These were inaccurately divided, and variously reckoned, to the disgrace of the economical arrangements of every country where they were found. The inconveniences which arose from thence, were generally felt and complained of. Remedies were every where proposed, but no serious attempt was made to apply them. France was, in these respects, in the same condition with other nations. A system, however, that had nothing to support it but
the authority of the past time, and the inactivity of the present, was not likely to maintain itself long against the spirit of reform which became so general in that country at the commencement of the Revolution. This system, too, beside the other objections to it, had the misfortune to appear connected with all the abominations of the feudal times. The abolition of it, therefore, was resolved on; and it would have been happy for France and for Europe, if every thing which was then destroyed had been replaced by as solid and useful a structure as that which we are going to describe. In the reformation proposed, two principal objects were kept in view. The first was the establishment of a natural standard for the measures of linear extension, and of course for the measures of all other quantities. The second was, to render the computation of those measures subject to the same arithmetical system that is used in other calculations. For this purpose, the unit of measure was to be divided decimally, and to be multiplied decimally, in order to constitute the other measures which it might be necessary to employ. No fractions but decimal were to be used in expressing quantities of any sort; and the great improvement of having but one arithmetical scale for reckoning integers and fractions of every kind, was in this way to be introduced ;-an improvement so obvious, and, withal, so little difficult, that it is matter of surprise that it should not have been attempted till near a thousand years after decimal arithmetic itself was first introduced into Europe.
The fixing a natural and universal standard of measure, 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 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 thence 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. 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 pen
dulum vibrating seconds in the parallel of 45° deserved the preference, because it is the arithmetical mean between the like pendulums in all other latitudes. They observed, however, that the pendulum involves one 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 them 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.
The commissioners, therefore, were brought to deliberate between the quadrant of the equator, and the quadrant of the meridian ; and they were determined to fix on the latter, because it is most accessible, and because it can be ascertained with most precision. The quadrant of the meridian then was to be taken as the real unit; and the ten-millionth part of it, being thought of a convenient length, was to be taken, in practice, for the unit of linear extension. At the same time, the ordinary division of the circle into 360° was to be abandoned, and the decimal division introduced ; the fourth part of the circumference being divided, not into 90, but into 100 equal parts; these parts into ten, and so on. With regard to the above determination, we must be permitted to remark, that the reasons for rejecting the pendulum are by no means completely satisfactory. The consideration, that time is a heterogeneous element, is too abstract and metaphysical to influence one's choice in a matter that is merely practical. The arbitrary element introduced by the division of the day into seconds, is perhaps an objection of more weight, were it not balanced by an equal objection in the case of the standard which has been actually adopted. That standard, in effect, is not the quadrant of the meridian, but the ten-millionth part of that quadrant; and ten million is, without doubt, a number just as arbitrary, and as far from being suggested by any natural appearance, as 86,400, the number of seconds into which the day is divided. It is impossible, indeed, whatever standard be adopted, to proceed without the use of some arbitrary division that must be determined by our conveniency, and not at all by the nature of the thing itself. Whether we take the quadrant of the meridian or the radius of the globe, as Cassini long ago proposed, for the unit with which all measures are to be compared, the portion of that standard which we can convert into a rod of brass or platina, to be preserved in our museums, or to be employed in. actual mensuration, must be a matter of arbitrary determination. The real unit or standard that is used in practice must always involve in it a similar assumption; and its doing so can never · afford a good reason for rejecting one standard and preferring another. Vol. II.