Land; and intestine broils and inter-state conflicts, as well as these greater social movements, withdrew the minds of men once more from the arts of peace and the pursuits of scholars. It is not, then, until the beginning of the seventeenth century-the time of Galileo and of Newton-that we find the nations of Europe sufficiently quiet and secure to permit general attention to intellectual vocations, although it was a half-century earlier (1543) that Copernicus left to the world that legacy which revolutionized the theories of the astronomers and established as correct the hypothesis which made the sun the centre of the solar system. Galileo now began to overturn the speculations of the deductive philosophers, and to proclaim the still disputed principle that the book of Nature is a trustworthy commentary in the study of theological and revealed truths, so far as they affect or are affected by science; he suffered martyrdom when he proclaimed the fact that God's laws, as they now stand, had been instituted without deference to the preconceived notions of the most ignorant of men. Bruno had a few years earlier (1600) been burned at the stake for a similar offense. Galileo was perhaps the first, too, to combine invariably in application the idea of Plato, the philosophy of Aristotle, and the methods of modern experimentation, to form the now universal scientific method of experimental philosophy. He showed plainly how the grouping of ascertained facts, in natural sequence, leads to the revelation of the law of that sequence, and indicated the existence of a principle which is now known as the law of continuity-the law that in all the operations of Nature there is to be seen an un broken chain of effect leading from the present back into a known or an unknown past, toward a cause which may or may not be determinable by science or known to history. Galileo, the Italian, was worthily matched by Newton, the prince of English philosophers. The science of theoretical mechanics was hardly beginning to assume the posi tion which it was afterward given among the sciences; and the grand work of collating facts already ascertained, and of definitely stating principles which had previously been vaguely recognized, was splendidly done by Newton. The needs of physical astronomy urged this work upon him. Da Vinci had, in the latter half of the fifteenth century, summarized as much of the statics of mechanical philosophy as had, up to his time, been given shape; he also rewrote and added very much to what was known on the subject of friction, and enunciated its laws. He had evidently a good idea of the principle of "virtual velocities," that simple case of equivalence of work, in a connected system, which has done such excellent service since; and with his mechanical philosophy this versatile engineer and artist curiously mingled much of physical science. Then Stevinus, the "brave engineer of Bruges," a hundred years later (1586), alternating office and field work, somewhat after the manner of the engineer of to-day, wrote a treatise on mechanics, which showed the value of practical experience and judgment in even scientific work. And thus the path had been cleared for Newton. Meantime, also, Kepler had hit upon the true relations of the distances of the planets and their periodic times, after spending half a generation in blindly groping for them, thus furnishing those great landmarks of fact in the mechanics of astronomy; and Galileo had enunciated the laws of motion. Thus the foundation of the science of dynamics, as distinguished from statics, was laid, and the beginning was made of that later science of energetics, of which the philosophy of the steam-engine is so largely constituted. Hooke, Huyghens, and others, had already seen some of the principal consequences of these laws; but it remained for Newton to enunciate them with the precision of a true mathematician, and to base upon them a system of dynamical laws, which, complemented by his announcement of the existence of the force of gravitation, and his statement of its laws, gave a firm basis for all that the astronomer has since done in those quantitative determinations of size, weight, and distance, and of the movements of the heavenly bodies, which compel the wonder and admiration of mankind. The Arabians and Greeks had noticed that the direction taken by a body falling under the action of gravitation was directly toward the centre of the earth, wherever its fall might occur; Galileo had shown, by his experiments at Pisa, that the velocity of fall, second after second, varied as the numbers 1, 3, 5, 7, 9, etc., and that the distances varied as the squares of the total periods of time during which the body was falling, and that it was, in British feet, very nearly sixteen times the square of that time in seconds. Kepler had proved that the movements of the heavenly bodies were just such as would occur under the action of central attractive forces and of centrifugal force. Putting all these things together, Newton was led to believe that there existed a "force of gravity," due to the attraction, by the great mass of the earth, of its own particles and of neighboring bodies, like the moon, of which force the influence extended as far, at least, as the latter. He calculated the motion of the earth's satellite, on the assumption that his theory and the then accepted measurements of the earth's dimensions were correct, and obtained a roughly approximate result. Later, in 1679, he revised his calculations, using Picard's more accurate determination of the dimensions of the earth, and obtained a result which precisely tallied with careful measurements, made by the astronomers, of the moon's motion. The science of mechanics had now, with the publication of Newton's "Principia," become thoroughly consistent and logically complete, so far as was possible without a knowledge of the principles of energetics; and Newton's enunciations of the laws of motion, concise and absolutely perfect as they still seem, were the basis of the whole science of dynamics, as applied to bodies moving freely under the action of applied forces, either constant or variable. They are as perfect a basis for that science as are the primary principles of geometry for the whole beautiful structure which is built up on them. The three perfect qualitative expressions of dynamica! law are: 1. Every free body continues in the state in which it may be, whether of rest or of rectilinear uniform motion, until compelled to deviate from that state by impressed forces. 2. Change of motion is proportional to the force impressed, and in the direction of the right line in which that force acts. 3. Action is always opposed by reaction; action and reaction are equal, and in directly contrary directions. We may add to these principles a definition of a force, which is equally and absolutely complete : Force is that which produces, or tends to produce, motion, or change of motion, in bodies. It is measured statically by the weight that will counterpoise it, or by the pressure which it will produce, and dynamically by the velocity which it will produce, acting in the unit of time on the unit of mass. The quantitative determinations of dynamic effects of forces are always readily made when it is remembered that the effect of a force equal to its own weight, when the body is free to move, is to produce in one second a velocity of 32.2 feet per second, which quantity is the unit of dynamic measurement. Work is the product of the resistance met in any instance of the exertion of a force, into the distance through which that force overcomes the resistance. Energy is the work which a body is capable of doing, by its weight or inertia, under given conditions. The energy of a falling body, or of a flying shot, is about weight multiplied by the square of its velocity, or, which its is the same thing, the product of its weight into the height of fall or height due its velocity. These principles and definitions, with the long-settled definitions of the primary ideas of space and time, were all that were needed to lead the way to that grandest of all physical generalizations the doctrine of the persistence or conservation of all energy, and to its corollary declaring the equivalence of all forms of energy, and also to the experimental demonstration of the transformability of energy from one mode of existence to another, and its universal existence in the various modes of motion of bodies and of their molecules. Experimental physical science had hardly become acknowledged as the only and the proper method of acquiring knowledge of natural phenomena at the time of Newton; but it soon became a generally accepted principle. In physics, Gilbert had made valuable investigations before Newton, and Galileo's experiments at Pisa had been examples of similarly useful research. In chemistry, it was only when, a century later, Lavoisier showed by his splendid example what could be done by the skillful and intelligent use of quantitative measurements, and made the balance the chemist's most important tool, that a science was formed comprehending all the facts and laws of chemical change and molecular combination. We have already seen how astronomy and mathematics together led philosophers to the creation and the study of what finally became the science of mechanics, when experiment and observation were finally brought to their aid. We can now see how, in all these physical sciences, four primitive ideas are comprehended: matter, force, motion, and space-which latter two terms include all relations of position. Based on these notions, the science of mechanics comprehends four sections, which are of general application in the study of all physical phenomena. These are: Statics, which treats of the action and effect of forces. |