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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 a 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

* From the Edinburgh Review, Vol. IX. (1807.)—ED.

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themselves. We know what a Greek geometer meant by a right angle, or by an angle of one degree, 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


So also when Eratosthenes tells us that the distance between Alexandria and Syené 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 stadia, we receive no accurate information; and much critical discussion has been required to extract even a very uncertain meaning from his words.

This imperfection of language is founded in the nature of things, and is impossible to be removed. The inconveniences arising from it have been felt not only by the learned and scientific, but by all who have been concerned about measuring, weighing, or computing, even in the most imperfect state of the arts. In the measures of every country, we

may perceive attempts to obviate the difficulties which have just been mentioned, and must feel some interest in remarking the expedients adopted for that purpose by rude and unenlightened men. The foot which we recognize among the measures of almost all nations, was taken from the standard of the human foot, and varies, accordingly, within limits of no very considerable extent. Other standards, supposed more precise, were sometimes had recourse to. Among agricultural nations, the inch has been determined by the length of three barley corns; and to the equestrian tribes of Arabia, the breadth of a certain number of hairs from a horse's tail afforded a standard of the same kind. In weights, a drop of water appears to have been regarded as a unit, according to some methods of reckoning; and, according to others, a grain of wheat stood for the weight which still takes its name from that origin. Some authors would have us believe that the ancients, in their attempts to form a standard measure, had proceeded very far beyond these rude essays. Paucton, in his Métrologie, will have it, that the circumference, or the diameter of the earth, was the standard to which they referred in their measures of length. Bailly has supported the same opinion, with the ingenuity and learning displayed in all his speculations; and he endeavours to prove, that the stadium was always taken for an aliquot part of the earth's cir

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cumference, that part being different with different nations, and with different authors. No ingenuity, however, can render this supposition probable.

The ancients had no means of determining, with any tolerable precision, the magnitude of that great unit to which their measures are supposed to refer. Besides, if such a reference had been intended, it could not surely have been unknown to themselves; yet we are well assured, that neither Aristotle, nor Possidonius, nor Pliny, nor any other ancient author who lays down the dimensions of the globe, conceived that the difference between him and other writers was only apparent, or that he agreed with them about the magnitude of the earth, and differed only about the length of the measure in which he chose that its dimensions should be expressed. 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 ineasures 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 occurred to Mouton. 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

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