Induction (Lat. inductio, from inducere, "to infer") is the philosophical name for the. process of real inference in other words, the act or process of reasoning from the known to the unknown, or from the limited to the unlimited. "All things that we do not know by actual trial or ocular demonstration, we know by an inductive operation. Deduction is not real inference in this sense, since the general proposition covers the case that we apply it to; in a proper deduction, the conclusion is more limited than the premises. By the inductive method we obtain a conclusion much larger than the premises; we adventure into the sphere of the unknown, and pronounce upon what we have not yet seen.... Accordingly, it is now considered a part of logic to lay down the rules for the right performance of this great operation." One of the greatest problems of inductive inquiry is that peculiar succession denominated cause and effect. Mill, in his Logic, has consequently illustrated in detail the methods to be adopted to ascertain. definitely the true causative circumstance that, may precede a given effect. They resolve themselves mainly into two. "One is, by comparing together different instances in which the phenomenon occurs. The other is, by comparing instances in which the phenomenon does occur, with instances, in other respects similar, in which it does not. These two methods may be respectively denominated the method of agreement, and the method of difference." There are many problems growing out of the application of induction to the great variety of. natural phenomena. "Thus, the great induction of universal gravity was applied deductively to explain a great many facts besides those that enabled the induction to be made. Not merely the motions of the planets about the sun, and the satellites about the planets, but the remote and previously unexplained phenomena of the tides, the precession of the equinoxes, etc., were found to be inferences from the general principle. This mode of determining causes is called the deductive method. When several agents unite in a compound effect, there is required a process of calculation to find from the effects of the causes acting separately the combined effect due to their concurrent action, as when the path of a projectile is deduced from the laws of gravity and of force. It is. the deductive stage of science that enables mathematical calculation to be brought into play with such remarkable success as is seen in astronomy, mechanics, etc.
"The circumstance that phenomena may result from a concurrence of causes, leads to the distinction between ultimate laws and derivative or subordinate laws. Thus, gravity is an ultimate law; the movement of the planets in ellipses is but a subordinate law. These inferior laws may be perfectly true within their own limits, but not necessarily so beyond certain limits, of time, place, and circumstance. A different adjustment of the two forces that determine a planet's motion would cause a circular or a parabolic orbit; and therefore when phenomena result from a combination of ultimate laws acting under a certain arrangement, they are not to be generalized beyond the sphere where that arrangement holds. These inferior laws are sometimes mere inductions that have not been resolved into their constituent laws, and then they go under the name of 'Empirical Laws.' Thus, in the hands of Kepler, the elliptic orbit of the planets was only an empirical generalization, ascertained by the method of agreement; Newton converted it into a derivative law, when he showed that it resulted from the more general laws of gravity, etc. The earlier stages of induction present us with many of those empirical laws; in some subjects, as physiology, medicine, etc., the greater number of inductions are of this character. The cure of disease is especially an example of this: hardly any medicine can have its efficacy traced to ultimate laws of the human system. Hence the uncertainty attending the application of remedies to new cases, and also the want of success that often attends them in circumstances where we think they ought to succeed." Induction applies also to the laws of causation, to the laws of uniformities, and to those of coexistence. See Mill, Logic, especially book 4.