200 POPULAR SCIENCE MONTHLY. 



Nombre complexe (or compound number). Littre gives the following 

 definition of it under "Complexe": "Complexe; Terme d'arithmetique. 

 Nombre complexe, nombre compose d'unites differentes, comme nos an- 

 ciennes mesures : 1 toise, 5 pieds, 9 pouces ; 25 livres, 13 sous, 6 deniers, 

 sont des nombres complexes." (Translation: "Arithmetical term, com- 

 pound 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." 



(Translation.) 



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 con- 

 sulted 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 Ger- 

 mans 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 adminis- 

 tration, 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 in- 

 crease or diminish the amount by some fraction, so that the space or the 



