"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.