Without this decimalisation, at least in the popular series of measures, there was a geodesic basis—for this was resolved as necessary—already at hand in the Olympic system, and the Olympic foot cubed would have given a unit of capacity and the Olympic talent one of weight, all the more suitable inasmuch as 1/1000 of it would have been an ounce = 453·6 grains, closely approximating to the Cologne ounce and therefore likely to be acceptable in other countries. But the real object was to make a clean sweep of the past; and the formation of a Republican system of measures was entrusted to mathematicians and other scientists who did not consider that a system convenient to them might be very inconvenient to unscientific people. The division of all measures must be on an obligatory decimal system convenient to mathematicians and most inconvenient to nearly everyone else. The basis of the new system was a measure considered to be one ten-millionth of the quarter-meridian, of the distance from the equator to the pole. This unit was neither original in conception nor exact in measurement. When Aristotle divided the circumference of the globe into 400,000 stadia, instead of the 240,000 stadia of 1000 Olympic fathoms, his stadion, 1/100,000 of the quarter-meridian, was equal to 100 metres. But there was no practical advantage in it, and navigators continued to use the nautical mile of 10 Olympic stadia, as they do to this day. At least Aristotle did not seek to upset all the weights and measures of the Macedonian empire; and his stadion disappeared. It is doubtful if absolute exactness will ever be attained in the measurement of the surface of our globe, irregularly spherical in form and of very uneven surface; but there is no doubt that the ancient Chaldæans and Egyptians measured it sixty centuries ago quite as accurately as the astronomers of the first Republic; and the Olympic standard of the meridian mile, not the kilometre, is the unit used to this day by the navigators of France as by those of every other maritime nation. Having determined with little exactitude the metric decimal fraction of the quarter-meridian, the astronomers and mathematicians of the Republic, _les idéologues_ as Napoleon called them, proceeded to evolve from it the most inconvenient possible units of length, surface, capacity, and weight. All that could be said for these units is that they were exactly and decimally derived from the metre. The metre was unacceptable to the people, as no metric unit of length corresponds even approximately to the universal limb-units of fathom, cubit, foot, span, palm, finger or thumb-breadth. The different series admit only the factors, 1, 2, 5; so each decimal unit has a half (0·5) and a double, but no quarter or third. The prefixes—in Latin for divisions, _deci_, _centi_, _milli_; in Greek for multiples, _deca_, _hecto_, _kilo_, _myria_—give the only names allowed. _Length_