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 not strictly proved) was yet such as to leave no doubt that it had some foundation in nature.
Analogy the Ground of antecedent Probability.
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 pro
bably 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 our presumed generalization with already established laws. One induction must be the guide to another. We must seek to interpret nature in agreement 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 another collection of facts, which leads to the belief that the cases are parallel. 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
Now 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, that is, the amount of the deviation. 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 which 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 magnetism. 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.