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was resolved on; and it would have been happy for France and for Europe, if every thing which was then destroyed had been replaced by as solid and useful a structure as that which we are going to describe.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. In treating of this reform, however, we cannot help remarking that the French academicians, though freed at the moment we now speak of, like the rest of their countrymen, from the dominion of that inertia which reigns so powerfully both in the natural and moral world, and gives the time that is past such influence over that which is to come; though delivered from the action of this force, in a degree that was perhaps never before exemplified, they may be accused, at least in one instance, of having innovated too little, and of having been too cautious about departing from an established practice, though reason was by no means on its side. What we allude to, is the system of arithmetical computation, in which they resolved to adhere to the decimal scale, instead of adopting the duodeci mal, which, from the nature of number, is so evidently preferable. This preference, we believe, is generally admitted in theory; and there can be no doubt, that a rational being, conversant with the nature of number, if called on to choose his own arithmetical system, and having no bias from custom, prejudice, or authority, would not hesitate a moment about adopting the duodecimal system in preference to the decimal, and, as we think, in preference to all other systems whatsoever. The property of the number twelve, which recommends it so strongly for the purpose we are now considering, is its divisibility into so many more aliquot parts than ten, or any other number that is not much greater than itself. Twelve is divisible by 2, by 3, by 4, and by 6; and this circumstance fits it so well for the purposes of arithmetical computation, that it has been resorted to, in all times, as the most convenient number into which any unit either of weight or of measure could be divided. The divisions of the As, the Libra, the Jugerum, the Foot, are all proofs of what is here asserted; and this advantage, which was perceived in rude and early times, would have been found of great value in the most improved state of mathematical science. Ten has indeed no advantage as the radix of numerical computation, and has been raised to the dignity which it now holds, merely by the circumstance of its expressing the number of a man's fingers. They who regard science as the creature of pure reason, must feel somewhat indignant, that a consideration so foreign and mechanical should have determined the form and order of one of the most intellectual and abstract of all the sciences. The duodecimal scale would no where have been found of greater use than when applied to the circle, the case in which the decimal division is liable to the strongest objections. The number by which the circumference of the circle is expressed, ought not only to be divisible into four integer parts, (as in the French system,) but also into six; for the sixth part of the circumference, having its chord equal to the radius, naturally falls, in the construction of instruments, and in the computations of trigonometry, to be expressed by an integer number. According to the decimal division of the quadrant, the sixth part of the circumference not only is without an integer expression, but the decimal fraction by which it is measured is one that runs on continually without any termination. This is at least a deformity that arises from the rigid adherence to the decimal division; and it is probably the main cause why that division has been found so difficult to introduce into trigonometrical and astronomical calculation. In astronomical tables, we believe it has never been adopted. * The adopting of twelve for the radix of the arithmetical scale would have obviated all these difficulties; it could have been extended with equal ease *Supposing the decimal division to be extended to the circle, instead of dividing the quadrant into 100, and the circumference into 400, as the French have done, it would have been better, perhaps, to have divided the sixth part of the circumference into 100, the quadrant of course into 150, and the whole circumference into 600. This would have given an easy expression for the three great natural divisions of the circumference into 6, 4, and 2; and would have denoted the whole by a number (600) which does not violate the strict rule of dividing by the powers of 10, any more than 400 does. The advantages of the decimal and sexagesimal systems would by this means have been in a great measure united. to quantities of every kind; and the introduction of it would not have been accompanied with any present inconvenience of such magnitude as should have deterred geometers from making the attempt. We have lately seen a manuscript containing the system of duodecimal arithmetic pursued into all its detail. Two new names are necessary for the numbers eleven and twelve; and the whole arithmetical language, for the numbers above ten, is consequently changed, but in a manner so analogical, as to remove all difficulty, whether in the contrivance or in the acquisition of this new vocabulary. The arithmetical characters must also undergo an entire change; the first eleven letters of the Greek alphabet are adopted in the scheme to which we refer; and by means of them and the cypher, which is still retained, the notation proceeds by rules that are easy, and well known. We regret, therefore, that the experiment of this new arithmetic was not attempted. Another opportunity of trying it is not likely to occur soon. In the ordinary course of human affairs, such improvements are not thought of; and the moment may never again present itself, when the wisdom or delirium of a nation shall come up to the level of this species of reform. But, to return to what respects the natural and universal standard of measure, we must remark, that the fixing on such a standard, and the abolition |