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Page:Popular Science Monthly Volume 49.djvu/214

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Nombre complexe (or compound number). Littré gives the following definition of it under "Complexe": "Complexe; Terme d'arithmétique. Nombre complexe, nombre composé d'unités différentes, comme nos anciennes mesures: 1 toise, 5 pieds, 9 pouces; 25 livres, 13 sous, 6 deniers, sont des nombres complexes." {Translation: "Arithmetical term, compound number; a number composed of different kinds of units, like our old measures: 1 toise, 5 feet, and 9 inches; 25 livres, 13 sous, and 6 deniers are compound numbers."


Memoranda for use in a History of France under Napoleon, written at St. Helena by General Comte de Montholon, "Volume IV, pp. 213-218:

The need of uniformity in weights and measures has been felt in all ages; the States-General have pointed it out many times. This good gift was expected from the Revolution. A sufficient simple law to assure it might have been drawn up in twenty-four hours, adopted, and put in operation in all France in less than a year. All that was needed was to make the unit of weights and measures of the city of Paris common to all the provinces. The Government and the artists have used them for many centuries; by sending the standards into all the communes, and enjoining the administrative officers and the courts from admitting any others, the benefit would have been operative without effort, without restriction, and without coercive laws. Instead, geometricians and algebraists were consulted upon a question which was of administrative jurisdiction. They thought that the unit of weights and measures should be deduced from a natural constant, so that it might be adopted by all nations. They thought it was not enough to provide for the advantage of forty million men; they wanted the whole universe to participate in it. They found that the metre was an aliquot part of the meridian; they made the demonstration of it and proclaimed it in an assembly composed of French, Italian, Spanish, and Dutch geometricians.

From that time a new unit of weights and measures was decreed, which did not square with the rules of the public administration, or with the tables of dimensions of all the arts, or with those of any existing machines.

There was no advantage in extending this system to the whole universe. That was, besides, impossible. The national spirit of the English and Germans was opposed to it. That Gregory VII, in reforming the calendar, made it common to all Europe, was because the reform pertained to religious ideas, and was not made by a nation, but by the power of the Church.

Meanwhile the good of present generations was sacrificed to abstractions and vain hopes, for to make an old nation adopt a new unit of weights and measures it is necessary to make over again all the rules of public administration, all the calculations of the arts—a task to frighten reason. The new unit of weights and measures, whatever it may be, has an ascending and descending-scale which does not accord in simple numbers with the scale of the unit of weights and measures which has been used for centuries by the Government, men of science, and artists.

No transfer can be made from one nomenclature to the other, because what is expressed by the simplest number in the old system will have to take a composite number in the new. It will be necessary, then, to increase or diminish the amount by some fraction, so that the space or the