ment of our stores of information from wider observation of physical facts, soon begins to induce the habit of extending our persuasion of the uniformity of natural causes, beyond the mere bounds of familiar phenomena, to those which are placed out of our immediate examination, but which we come naturally to imagine must be regulated by a like constancy.

Founded, then, on the natural constitution of the human mind, confirmed by daily experience, and verified by every advance in the accurate study both of mental and material phenomena, the belief in the existence of this uniformity becomes, in fact, the basis of all acquisition of knowledge, and enables us, without hesitation, to advance in our conclusions from the known to the unknown, from truths actually before us and within our reach, to those which may be hidden from us, or utterly beyond the limits of sensible experience.

The belief in the uniformity and permanence of natural order, combined with, and perhaps dependent on, the tendency of the human mind to generalize its observations, unite to supply, as it were, the rude materials of philosophic investigation. But it is further necessary that they should be skilfully wrought and fashioned before they can be of any use. We have then further to inquire how this is to be done; and we shall find that the models by which we must work, are to be found in the careful and extended study of already established natural relations.

The rules by which we are to be guided in advancing to these generalizations of observed physical relations, must be those derived from the careful study and comparison of such generalizations previously confirmed in other corresponding instances.

It will be to little purpose that we are persuaded of the existence of some uniformity in natural laws, unless we have this guide to assist in tracing what the principle of uniformity is in any particular case. Without such assistance, we may go on collecting and observing a vast number of facts, and yet arrive at no conclusions, or only at such as are altogether empty and visionary.

As we have already remarked, that merely to affirm what we observe in common of a number of individuals, all of whom are before us, is hardly worthy the name of an induction, so it is a violation of all just induction to infer a general property from too limited a number of instances. But what constitutes the sufficient number of instances must depend on the nature of the case, and the experience and power of judgment possessed by the inquirer.

And if we fall into the error of too small an induction, the usual cause of such error is rather that the induction is wanting in a just principle of probability in our first conjecture, or that we have proceeded on the supposition of a wrong sort of relation. It is this which has commonly much more to do with the justness of our conclusion than the mere number of instances collected. And, on the other hand, it often happens that a very few instances, or even almost a single instance, have been admitted without question as a sufficient verification: but this has depended entirely on the justness of the assumed relation.

We will illustrate these remarks by a few examples, both of suc

cessful and unsuccessful inductions, taken from different departments of science.

1. As we descend in mines, it has been found that the temperature uniformly increases. Hence it has been inferred as an inductive conclusion, that the earth is universally hotter, the lower we descend into its interior, and that there exists a source of central heat of great intensity.

This conclusion is objected to by some philosophers; and it is a fair question, Why we should infer that the temperature goes on perpetually increasing to the centre, because it may do so within a limited depth?

The regular increase of temperature with the depth has been carefully ascertained in various parts of the globe; the presumption that it increases in all parts as we descend, is, therefore, not altogether without foundation. But the question cannot be considered as positively decided. It clearly depends on whether the number of places in which observations have been made, be as yet sufficient to justify the universality of the conclusion: and whether there may not be local sources of heat at comparatively small depths, such as those which produce volcanoes, which may be sufficient to account for the effects. There is a want of any fair ground of antecedent probability in favour of the hypothesis to guide us.

2. Newton, on passing a ray of light through a prism of glass, found it separated into coloured rays; and measuring the proportion in which it is thus spread out, or "dispersed," announced that proportion as the general law of prismatic dispersion.

Dr. Lucas repeated the experiment; but assigned a much less proportion as the law. Both parties positively maintained the correctness of their respective conclusions. But they had both argued on a faulty ground of induction: they had each taken for granted that their prisms ought to act equally on light. The fact was, they had used different sorts

of glass, which vary considerably in dispersive power.

This is remarkable as one of the very few instances in which Newton failed in an induction; but such failures are instructive; for we learn to observe the reason of the error. It was manifestly from neglecting to consider, in this case, what probability there would be, previous to trial, that different sorts of glass should possess the same dispersive power.

3. On the other hand, Newton's capital result that "to the same ray ever belongs the same refrangibility" (the media being the same), is a conclusion, indeed, of a most general nature, and which universal experience has amply confirmed, but it was founded on a very limited induction derived from prismatic experiments with, at most, three or four different media.

4. The early history of Astronomy is full of examples of the compatibility of accumulated observation with the want of satisfactory induction. The ancient astronomers were indefatigable in the diligence with which they amassed observations. But they constructed out of them no theory which could attain a real permanence. The system of Ptolemy sufficed to a certain extent to represent the observed motions of the planets. The advance in accuracy of observations, however, soon required corresponding improvements in the system; which was obliged to be modified to accord with them: but, at length, the immense complexity

introduced by the cycles and epicycles which were necessary to account for the apparent motions, began to induce a persuasion that such complication could not be the real law of nature: juster principles were therefore to be sought. No astronomer ever laboured more sedulously in making and recording observations, than Tycho Brahe. But though persuaded of the insufficiency of the Ptolemaic hypothesis, he did not succeed in constructing a better: not from deficiency of facts, but from his strangely-erroneous assumption of a guiding theoretical principle.

Kepler worked upon Tycho's materials. The labour which he bestowed on calculation was absolutely incredible. But theory after theory was adopted and rejected, because he had not any other guide than random conjecture, and nothing but the accurate calculation of every detail could suffice to put those conjectures to the test. He had not lighted on any happy ground of antecedent probability. When, however, at last, he did seize upon the true law of nature, the numerical verification was perfect and decisive; and when thus established in the single instance of the planet Mars, it is extremely instructive to observe the rapidity and facility with which the inference was extended to the whole solar system.

When the laws of the motion of one planet were established, a single conjecture sufficed to point out, with the highest degree of probability, the laws of all the other planetary orbits: and a single calculation to verify it. The difference was, that there was now a ground of antecedent probability. A presumption of a guiding resemblance, which (though perhaps no precise reason could be assigned for it) was yet such as to leave no doubt that it had some foundation in nature.

Thus, then, it is manifest, that to possess some reasonable ground of antecedent probability, as a guide to our conclusion, is absolutely essential to physical induction. And we cannot employ the term correctly in its higher sense, (as referring to anything above a mere collection of instances,) without meaning to include specially the notion of a fair presumption of some relation, in virtue of which we can argue from the known to the unknown; and infer that those cases which we do not see, are probably connected with those which we do. This constitutes one most essential characteristic of the inductive process; and without it, assuredly we can never advance to a substantial conclusion. We must

always, then, consider the inductive method as referring, not merely to the accumulation of instances, but as involving the idea of some presiding conception, some guiding principle, of presumed connexion and probable relation between the facts on which we are reasoning.

In replying, then, to the inquiry, What constitutes the ground of antecedent probability, so essential to a good induction? it will be almost apparent, from the examples already cited, that the main ground is that afforded by the comparison of one class of phenomena with another: the perception of a parallelism in their respective conditions: the existence of an ANALOGY between them.

The success, then, with which induction may be carried on, depends on the just appreciation of such trains of analogy. This can only be attained by a habit of cautiously comparing one presumed generalization with already established laws. One induction must be the guide to

another. We must seek to interpret nature in accordance with her own principles already displayed. Every real natural truth, we may be assured, will be in harmony with other parts of the great series and scale of natural truth. With this our hypothesis must be in accordance; to ascertain and verify such accordance is the aim of the true philosopher; and it is entirely on the justness with which it is preserved that the whole truth and success of induction depends.

Observation exhibits a certain law or relation among a particular class of facts. This suggests to the mind of the philosopher the probability of the same relation in some parallel class of facts. The relation being firmly established in one set of instances, he feels satisfied with even a slight indication of it in the other. The conviction of its probability once formed, a very few cases adduced serve to verify it. The experience of instances actually tried, leads to the expectation of analogous results in cases untried. But the essential point is the real parallelism of the cases. The hypothesis will be philosophical or not, according to the extent and justness of the comparison which has suggested it.

For example (1.) Experiment had shown that electricity in a high state of tension discharges itself with a flash and a report. Lightning and thunder exhibited an instance of a flash and a report. The atmosphere was known to be susceptible of electrical influence. All this had been ascertained, but no relation had been established between the cases. Other causes might possibly produce a flash and a report. But the analogy of electricity presented itself strongly to the philosophic mind of Franklin. By the string of a kite, as a conductor, he brought down the electricity of the clouds, which, on its arrival at the ground, was regularly discharged with sparks, and the analogy converted into an identity.

(2.) Every one had been accustomed for ages, before the time of Newton, to observe, that bodies fall to the ground as soon as support is withdrawn. They were equally familiar with the fact, that the moon circulates periodically about the earth. But no one ever perceived any relation or imaginable connexion between these two classes of facts. Nay, the peripatetics, maintaining that the heavenly motions were of an essentially different kind from the terrestrial, led men to the belief that these two cases could not possibly have any common relation.

The penetrating mind of Newton, however, instantly perceived a connexion between them. He considered that a body launched into space would continue to move off in a straight line, unless made to deviate from that path by the action of some other cause. The moon does not go off in a rectilinear path, but has her course continually bent from such direction into a curvilinear orbit round the earth, and the degree in which it is thus bent or the amount of deviation from the straight course, is in fact so much of a real fall towards the earth: the moon is actually falling like a stone and the amount of its fall can be measured; since astronomical observation has given the size and form of its orbit and the rapidity of its motion. Also the amount of the fall of a stone near the earth's surface is known. It becomes a matter of calculation to compare them. Newton made the comparison, and found the two effects precisely in the inverse proportion of the squares of the distances from the earth's centre. This was the precise proportion which would agree with the supposition of

that law of central force, which, on abstract mechanical principles, ought to give rise to elliptic orbits, and to certain relations expressed by numerical laws between the magnitudes of those orbits and the motions in them. These were the very same as those numerical relations had been found by Kepler long before to subsist in the planetary revolutions.

Thus the single circumstance of the analogy between the moon's motion and that of a stone falling to the ground, sufficed as a clue to the whole system of planetary motions, and the establishment of the principle of universal gravitation.

(3.) Physical philosophers had been long seeking to establish (what there was every reason to suspect,) the existence of at least a close connexion, if not absolute identity, between electricity, galvanism, and mag netism. There were many points of resemblance in what was known of the nature of those agents; experiments had been multiplied, and many curious facts, and results had been accumulated. But all this collection of facts had not afforded a real induction. And the reason was, that the inquirers had been guided either by no principle of analogy, or by such as was incorrect.

The most powerful electric forces had been resorted to; but no evolution of galvanic influence, no shock, however strong, would affect the magnetic needle. Experimenters were accustomed to witness the most intense electric action when the current was broken, or the accumulated power discharged; here, therefore, they expected to find the greatest effect of a magnetic kind.

But the modes of action with which philosophers had been previously acquainted, were, in fact, of a kind offering no analogy to those concerned in the cases in question. This, however, was not perceived, till Ersted discovered the real point of connexion of electricity and magnetism. He succeeded, by a very slight change in the arrangement from that with which his predecessors had been so long and so fruitlessly working. By using an unbroken galvanic circuit, he instantly found an influence on the magnetic needle: not by violent concentration of forces but by a peculiar diffusion of them. And the whole system of action by transverse currents was almost immediately developed and followed out into all its correlative trains of consequences.

(4.) Newton published his Principia before any instance of the periodical return of a comet had been established, or even imagined. Yet, on comparing the masses of these bodies and their distances with those of the planets, he caught an analogy, and did not hesitate to speak positively of their describing orbits about the sun, and to recommend to future astronomers to verify their returns by comparison of observations. It is superfluous to notice how completely this idea has been borne out by subsequent discoveries*.

(5.) In the extension of the law of gravitation from the fall of a stone on the earth to the motions of the most distant planet or the most erratic comet, we have a remarkable instance where a conclusion is made from effects which we observe near us, to those of the same kind which are produced in the remotest regions of space. Let us compare this with a

* For example, see our last Number, p. 250.