_Superstitious Belief of the Ancients._--The tendency of men to believe in the universal permanence of nature, and, on that ground, to generalize from insufficient data, is illustrated in the superstitious and widely prevalent idea among the ancients, and some of the moderns also, of grand cycles of events extending both to the natural and the _moral_ world. According to this idea, the changes of the atmosphere, and all other natural phenomena, as observed at any time, would, after a period, return again in the same order of succession as before; storms, and seasons, and times, being subject to some regular law. It was supposed, in fact, "that all the events"--to use the language of one of these theorists--"within the immeasurable circuit of the universe, are the successive evolutions of an extended series, which, at the return of some vast period, repeats its eternal round during the endless flux of time." This is a sufficiently grand induction, startling in its sweep and range of thought, but requiring for its data a somewhat wider observation of facts than can fall to the lot of short-lived and short-sighted man, during the few years of his narrow sojourn, and pilgrimage, in a world like this. 3. _Reasoning from Analogy._ _Meaning of the term Analogy._--This word, analogy, is used with great variety of meaning, and with much vagueness, therefore. It properly denotes any sort of resemblance, whether of relation or otherwise; and the argument from analogy is an argument from resemblance, an argument of an inductive nature, but not amounting to complete induction. A resembles B in certain respects; therefore it probably resembles it, also, in a certain other respect: such is the argument from _analogy_. A resembles B in such and such properties, but these are always found connected with a certain other property; therefore A resembles B also in regard to that property: such is the argument from _induction_. Every resemblance which can be pointed out between A and B creates a further and increased probability that the resemblance holds also in respect to the property which is the object of inquiry. If the two resembled each other in all their properties, there would be no longer any doubt as to this one, but a positive certainty, and the more resemblances in other respects so much the nearer we come to certainty respecting the one that happens to be in question. _Illustration of this Principle._--It was observed by Newton, that the diamond possessed a very high refractive power compared with its density. The same thing he knew to be true of combustible substances. Hence, he conjectured that the diamond was combustible. He conjectured the same thing, and for the same reason, of water, _i. e._, that it contains a combustible ingredient. In both instances, he guessed right--reasoning from analogy.