Motion is the ultimate object of science, and measures of motion are many; but with thought as with matter, the true measure is mass,—the sum of attractive forces. Science has quite enough trouble in measuring its material motions without volunteering help to the historian, but the historian needs not much help to measure some kinds of social movement; and especially in the nineteenth century, society by common accord agreed in measuring its progress by the coal-output. The ratio of increase in the volume of coal-power may serve as dynamometer.
The coal-output of the world, speaking roughly, doubled every ten years between 1800 and 1900, in the form of utilized power, for the ton of coal yielded three or four times as much power in 1900 as in 1840. Rapid as this rate of acceleration in volume seems, it may be tested in a thousand ways without greatly reducing it. Perhaps the ocean steamer is nearest unity and easiest to measure, for anyone might hire, in 1905, for a small sum of money, the use of 30,000 steam-horse-power to cross the ocean, and by halving this figure every ten years, he got back to 234 horse power for 1835, which was accuracy enough for his purposes. In truth, his chief trouble came not from the ratio in volume of heat, but from the intensity, since he could get no basis for a ratio there. All ages of history have known high intensities, like the iron-furnace, the burning-glass, the blow-pipe; but no society has ever used high-intensities on any large scale till now, nor can a mere bystander decide what range of temperature is now in common use. Loosely guessing that science controls habitually the whole range from absolute zero to 3000 Centigrade, one might assume, for convenience, that the ten year ratio for volume could be used temporarily for intensity; and still there remained a ratio to be guessed for other forces than heat. Since 1800 scores of new forces had been discovered; old forces had been raised to higher powers, as could be measured in the navy-gun; great regions of chemistry had been opened up, and connected with other regions of physics. Within ten years a new universe of force had been revealed in radiation. Complexity had extended itself on immense horizons, and arithmetical ratios were useless for any attempt at accuracy. The force evolved seemed more like explosion than gravitation; but, at all events, the ten-year ratio seemed carefully conservative. Unless the calculator was prepared to be instantly overwhelmed by physical force and mental complexity, he must stop there.
