weight expressed in the new nomenclature shall be in simple numbers. Thus, for example, the ration of the soldier is expressed in the old nomenclature as twenty-four ounces; this is a very simple number. Translated into the new nomenclature, it gives seven hundred and thirty-four grammes and two hundred and fifty-nine thousandths. It is, then, evident that it is necessary to increase or diminish the weight so as to make seven hundred and thirty-four or seven hundred and thirty-five grammes.
All the component pieces or lines of architecture; all the pieces and tools used in watch-making, jewelry, book-selling, and all the arts; all instruments and machines, have been devised and calculated in the old nomenclature, and are expressed in simple numbers, which can be translated in the new system only into numbers composed of five or six figures. It will be necessary, therefore, to do everything over again.
The scientific men also conceived another idea wholly foreign to the benefit of unity of weights and measures: they adopted the decimal numeration, taking the metre for the unit; they suppressed all complex numbers. Nothing is more contrary to the organization of the mind, the memory, and the imagination. A toise, a foot, an inch, a line, a point, are fixed portions of extension, which the imagination conceives independently of their relations to one another; if, then, we ask for the third of an inch, the mind goes into instant operation. The length called an inch is divided into three parts. By the new system, on the contrary, the mind has, not to divide an inch into thirds, but a metre into a hundred and eleven parts. The experience of all ages had made the difficulty of dividing a space or a weight by more than twelve so evident that a new name was created for each of the divisions. If the twelfth of an inch was asked for—the operation was already performed—we had the measure called the line.
The decimal numeration was applied to all the complex numbers as a unit; and if we wanted a hundredth of a point, a hundredth of a line, a hundredth was written. By the new system, if we want to express a hundredth of a line, we have to consider its relation to the metre, and this involves us in an infinite calculation.
The divisor 12 was preferred to the divisor 10, because 10 has only two factors, 2 and 5, while 12 has four factors, 2, 3, 4, and 6.
It is true that the decimal system; generalized and adapted to the metre as the unit, gives facilities to astronomers and calculators; but these advantages are far from compensating for the inconvenience of rendering thought more difficult. The prime characteristic of eveiy method should be that of aiding the conception and the imagination, of facilitating the memory, of giving more force to the thought.
The compound numbers are as old as man, because they are in the nature of his organization, quite as it is in the nature of the decimal numeration to adapt itself to every unit, to every complex-number, and not exclusively to one unit.
Finally, they use Greek roots, and that augments the difficulties; the denominations, which may be useful for men of science, were not good for the people. The system of weights and measures was one of the greatest achievements of the Directory. Instead of letting time do its work, and being satisfied to encourage the new system by means of example and fashion, it made coercive laws and executed them vigorously.
The merchants and the citizens were vexed by affairs indifferent in