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.
Or better, one might, for convenience, use the formula of squares to serve for a law of mind. Any other formula would do as well, either of chemical explosion, or electrolysis, or vegetable growth, or of expansion or contraction in innumerable forms; but this happens to be simple and convenient. Its force increases in the direct ratio of its squares. As the human meteoroid approached the sun or centre of attractive force, the attraction of one century squared itself to give the measure of attraction in the next.
Behind the year 1400, the process certainly went on, but the progress became so slight as to be hardly measurable. What was gained in the east or elsewhere, cannot be known; but forces, called loosely Greek fire and gunpowder, came into use in the west in the thirteenth century, as well as instruments like the compass, the blow-pipe, clocks and spectacles, and materials like paper; Arabic notation and algebra were introduced, while metaphysics and theology acted as violent stimulants to mind. An architect might detect a sequence between the Church of St. Peter's at Rome, the Amiens Cathedral, the Duomo at Pisa, San Marco at Venice, Sancta Sofia at Constantinople and the churches at Ravenna. All the historian dares affirm is that a sequence is manifestly there, and he has a right to carry back his ratio, to represent the fact, without assuming its numerical correctness. On the human mind as a moving body, the break in acceleration in the Middle Ages is only apparent; the attraction worked through shifting forms of force, as the sun works by light or heat, electricity, gravitation, or what not, on different organs with different sensibilities, but with invariable law.
The science of prehistoric man has no value except to prove that the law went back into indefinite antiquity. A stone arrowhead is as convincing as a steam-engine. The values were as clear a hundred thousand years ago as now, and extended equally over the whole world. The motion at last became infinitely slight, but cannot be proved to have stopped. The motion of Newton's comet at aphelion may be equally slight. To evolutionists may be left the processes of evolution; to historians the single interest is the law of reaction between force and force -- between mind and nature -- the law of progress.
The great division of history into phases by Turgot and Comte first affirmed this law in its outlines by asserting the unity of progress, for a mere phase interrupts no growth, and nature shows innumerable such phases.
The development of coal-power in the nineteenth century furnished the first means of assigning closer values to the elements; and the appearance of supersensual forces towards 1900 made this calculation a pressing necessity; since the next step became infinitely serious.
A law of acceleration, definite and constant as any law of mechanics, cannot be supposed to relax its energy to suit the convenience of man.
No one is likely to suggest a theory that man's convenience had been consulted by Nature at any time, or that Nature has consulted the convenience of any of her creations, except perhaps the Terebratula . In every age man has bitterly and justly complained that Nature hurried and hustled him, for inertia almost invariably has ended in tragedy. Resistance is its law, and resistance to superior mass is futile and fatal.
Fifty years ago, science took for granted that the rate of acceleration could not last. The world forgets quickly, but even today the habit remains of founding statistics on the faith that consumption will continue nearly stationary. Two generations, with John Stuart Mill, talked of this stationary period, which was to follow the explosion of new power. All the men who were elderly in the forties died in this faith, and other men grew old nursing the same conviction, and happy in it; while science, for fifty years, permitted, or encouraged, society to think that force would prove to be limited in supply. This mental inertia of science lasted through the eighties before showing signs of breaking up; and nothing short of radium fairly wakened men to the fact, long since evident, that force was inexhaustible. Even then the scientific authorities vehemently resisted.
Nothing so revolutionary had happened since the year 300. Thought had more than once been upset, but never caught and whirled about in the vortex of infinite forces. Power leaped from every atom, and enough of it to supply the stellar universe showed itself running to waste at every pore of matter.
Man could no longer hold it off. Forces grasped his wrists and flung him about as though he had hold of a live wire or a runaway automobile; which was very nearly the exact truth for the purposes of an elderly and timid single gentleman in Paris, who never drove down the Champs Élysées without expecting an accident, and commonly witnessing one; or found himself in the neighborhood of an official without calculating the chances of a bomb. So long as the rates of progress held good, these bombs would double in force and number every ten years.