Thus, taking the year 1900 as the starting point for carrying back the series, nothing was easier than to assume a ten-year period of retardation as far back as 1800, but beyond that point the statistician failed, and only the mathematician could help. La Place would have found it child's-play to fix a ratio of progression in mathematical science between Descartes, Leibnitz, Newton and himself. Watt could have given in pounds the increase of power between Newcomen's engines and his own. Volta and Benjamin Franklin would have stated their progress as absolute creation of power. Dalton could have measured minutely his advance on Boerhave. Napoleon I must have had a distinct notion of his own numerical relation to Louis XIV. No one in 1789 doubted the progress of force, least of all those who were to lose their heads by it.
Pending agreement between these authorities, theory may assume what it likes, say a twenty-five year period of reduplication for the eighteenth century, for the period matters little until the acceleration itself is admitted. The subject is even more amusing in the seventeenth than in the eighteenth century, because Galileo and Kepler, Descartes, Huyghens and Isaac Newton took vast pains to fix the laws of acceleration for moving bodies, while Lord Bacon and William Harvey were content with showing experimentally the fact of acceleration in knowledge; but from their combined results a historian might be tempted to maintain the same rate of movement back to 1600, subject to correction from the historians of mathematics.
The mathematicians might carry their calculations back as far as the fourteenth century when algebra seems to have become for the first time, the standard measure of mechanical progress in western Europe; for not only Copernicus and Tycho Brahe, but even artists like Leonardo, Michael Angelo and Albert Dürer worked by mathematical processes, and their testimony would probably give results more exact than that of Montaigne or Shakespeare; but, to save trouble, one might tentatively carry back the same ratio of acceleration, or retardation, to the year 1400, with the help of Columbus and Gutenberg, so taking a uniform rate during the whole four centuries (1400-1800), and leaving to statisticians the task of correcting it.
In other words, one might, for convenience, use the formula of terrestrial gravitation to serve for a law of mind. Any other formula
