Dynamics
The world had to wait for eighteen hundred years till the Greek mathematical physicists found successors. In the sixteenth and seventeenth centuries of our era great Italians, in particular Leonardo da Vinci, the artist
(born 1452, died 1519), and Galileo (born 1564, died 1642), rediscovered the secret, known to Archimedes, of relating abstract mathematical ideas with the experimental investigation of natural phenomena. Meanwhile the slow advance of mathematics and the accumulation of accurate astronomical knowledge had placed natural philosophers in a much more advantageous position for research. Also the very egoistic self-assertion of that age, its greediness for personal experience, led its thinkers to want to see for themselves what happened; and the secret of the relation of mathematical theory and experiment in inductive reasoning was practically discovered. It was an act eminently characteristic of the age that Galileo, a philosopher, should have
dropped the weights from the leaning tower of Pisa. There are always men of thought and men of action; mathematical physics is the product of an age which combined in the same men impulses to thought with impulses to action.
This matter of the dropping of weights from
the tower marks picturesquely an essential step in knowledge, no less a step than the first attainment of correct ideas on the science of dynamics, the basal science of the whole subject. The particular point in dispute was as to whether bodies of different weights would fall from the same height in the same time. According to a dictum of Aristotle, universally followed up to that epoch, the heavier weight would fall the quicker. Galileo affirmed that they would fall in the same time, and proved his point by dropping weights from the top of the leaning tower. The apparent exceptions to the rule all arise when, for some reason, such as extreme lightness or great speed, the air resistance is important. But neglecting the air the law is exact.
Galileo's successful experiment was not the
result of a mere lucky guess. It arose from his correct ideas in connection with inertia and mass. The first law of motion, as following Newton we now enunciate it, is–-Every
body continues in its state of rest or of uniform
motion in a straight line, except so far as it is compelled by impressed force to change that state. This law is more than a dry formula: it is also a pæan of triumph over defeated heretics. The point at issue can be understood by deleting from the law the phrase "or of uniform motion in a straight line." We there obtain what might be taken as the Aristotelian opposition formula: "Every body continues in its state of rest except so far as it is compelled by impressed force to change that state."
In this last false formula it is asserted that, apart from force, a body continues in a state of rest; and accordingly that, if a body is moving, a force is required to sustain the motion; so that when the force ceases,