"It may be inquired, is the induction which supposes gravitation universal so complete as to be entirely beyond doubt? We reply that within the solar system it certainly is. The laws of motion as established by observation and experiment at the surface of the earth must be considered as mathematically certain. Now, it is an observed fact that the planets in their motion deviate from straight lines in a certain way. By the first law of motion, such deviation can be produced only by a force; and the direction and intensity of this force admit of being calculated once that the motion is determined. When thus calculated, it is found to be exactly represented by one great force constantly directed toward the sun, and smaller subsidiary forces directed toward the several planets. Therefore, no fact in nature is more firmly established than is that of universal gravitation, as laid down by Newton, at least within the solar system."

It will thus be observed that the theory of Universal Gravitation is not by scientific men claimed to have been mathematically demonstrated, but its proof is regarded as resting upon its conformity with known natural phenomena. The same thing is true of Conservation of Energy. Scientists and mathematicians do not claim proof of this doctrine other than by its universal coincidence with all natural manifestations, and, yet its proof rests upon such a solid structure of coincidence and conformity with all known things in nature, that now all scientific research begins with its assumption, and with the exclusion of the possibility of Perpetual Motion.

It is not within the purview of this work to give a history of the origin and establishment in science of the doctrine. While, as heretofore noted in this book, a number of scientists of the past few centuries are shown by their reflections to have had a measure of appreciation of its ultimate effect, and to have applied that effect in their scientific researches, there is no evidence that they ever dreamed of its establishment as a basic fact of science. The real establishment and acceptance of the doctrine dates not much over a half century back. Since that time many scientists have in their researches and writings contributed to its evolution and formation. The experiments of Joule, of England, and the generalizations of Helmholtz, of Germany, are entitled to special mention.

Scientists are naturally and necessarily conservative. So many startling pseudo-scientific facts are announced, that every startling scientific theory, before it is accepted, is submitted to the most careful and crucial tests. No modern scientist will announce a scientific fact as having been demonstrated until the demonstration is complete and fortified with repeated tests of mathematical rigidity, and as long as there remains a phenomenon that does not conform to the supposed theory, acceptance and promulgation will be withheld. It is, therefore, not surprising that the doctrine of Conservation of Energy has been thoroughly intrenched as an established indisputable and accepted fact of science, less than a single generation.

The student of natural science should be warned against the common error of supposing that the discovery of a scientific fact or theory, means demolition of the old theories. The rule is the other way. New theories are additional information to the world, and usually conform to, and are built upon what was known before. Conservation of Energy was generalized from previously known facts conformed to them and reflexively elucidated them, and left them standing clearer than before.

The proof that Conservation of Energy conforms to all other known phenomena of nature has been aided, and hastened by the refinement of scientific instruments by which forms of energy such as heat, electricity, and magnetism can be more delicately measured and determined than ever before, and if instruments for measuring and determining the amount of energy in its various forms were as crude as they were even a single century ago, it is probable Conservation of Energy would still be the undiscovered foundation of all natural phenomena.

Let us now consider a few well-known facts which it has been determined positively by the most delicate instruments, prove and illustrate the doctrine of Conservation of Energy.

Resistance to motion, or which is the same thing, motion against resistance, is always accompanied by heat. This developed heat is not always readily perceptible to our sense of touch. A stone, ball or other object thrown through the air has its motion gradually arrested by the air. Heat is developed, but the heat is distributed through so much air and the object thrown is heated so little that this development of heat was not known until scientifically discovered. Where the resistance is friction, the development of heat is quite perceptible, and has always been well known. Suppose a coin be rubbed on a cloth or blotter. Heat is developed both in the coin and the blotter—the more vigorous the rubbing—i. e., the more energy expended, the greater the heat. Science has determined that the developed heat is exactly proportional to the expended energy. Every machinist knows that in turning a tap on a bolt where the threads are rusty so that it turns only with the application of great force, a considerable amount of heat is readily developed. The heat developed is proportional to the energy expended in turning the tap.

A wheel revolving on a spindle will develop heat exactly proportional to the resistance the spindle offers to the wheel turning upon it. Thus, we often see smoke and a blaze rising from the spindles of the car wheels where oil is lacking, and they turn with difficulty.

Every farmer knows that if a buggy wheel turns with difficulty for want of lubrication, or for any other reason, the spindle will heat, expand and lock the wheel, so that it will often either grind out the boxing or slide on the ground. Whereas, if the parts be kept lubricated so that less energy is required to turn the wheel on the spindle, there is no perceptible heat developed, but in all cases heat is developed to some extent, and the heat developed is exactly proportional to the energy necessary to force the revolution.