what is true of one case will be true of similar cases, and probably true of what are probably similar. Whenever we find that a law or similarity is rigorously fulfilled up to a certain point in time or space, we expect with a very high degree of probability that it will continue to be fulfilled at least a little longer. If we see part of a circle, we naturally expect that the form of the line will be maintained in the part hidden from us. If a body has moved uniformly over a certain space, we expect that it will continue to move uniformly. The ground of such inference is doubtless identical with that of all other inductive inferences. In continuous motion every infinitely small space passed over constitutes a separate constituent fact, and had we perfect powers of observation the smallest finite motion would include an infinity of information, which, by the principles of the inverse method of probabilities, would enable us to infer with actual certainty to the next infinitely small portion of the path. But when we attempt to infer from one finite portion of a path to another finite part, the inference will be only more or less probable, according to the comparative lengths of the parts and the accuracy of the observations; the longer our experience is, the more probable our inferences will be; the greater the length of time or space over which the inference extends, the less probable.

This principle of continuity presents itself in nature in a great variety of forms and cases. It is familiarly expressed in the dictum Natura non agit per saltum, in other words, no change in a natural phenomenon comes on with perfect suddenness or abruptness. There is always some notice some forewarning of every phenomenon, and every change begins by insensible degrees, could we observe it with perfect accuracy. The cannon ball, indeed, is forced from the cannon in an inappreciable portion of time; the trigger is pulled, the fuze fired, the powder inflamed, the

longer in movement. A delicately suspended pendulum is almost free from friction against its supports, but it is gradually stopped by the resistance of the air; place it in the vacuous receiver of an air-pump and we find the motion immensely prolonged. A large planet like Jupiter experiences almost infinitely less friction, in comparison to its vast momentum, than we can produce experimentally, and we find through centuries that there is not the least evidence of the falsity of the law. Experience, then, informs us that we may approximate indefinitely to a uniform motion by sufficiently decreasing the disturbing forces. It is a pure act of inference which enables us to travel on beyond experience, and assert that, in the total absence of any extraneous force, motion would be absolutely uniform. The state of rest, again, is but a singular case in which motion is infinitely small or zero, to which we may attain, on the principle of continuity, by considering successively cases of slower and slower motion.

There are many interesting cases of physical phenomena, in which, by gradually passing from the apparent to the obscure, we can assure ourselves of the nature of phenomena which would otherwise be a matter of great doubt. Thus we can sufficiently prove, in the manner of Galileo, that a musical sound consists of rapid uniform pulses, by causing strokes to be made at intervals which we gradually diminish until the separate strokes coalesce into a uniform hum or note. With great advantage we approach, as Tyndall says, the sonorous through the grossly mechanical. In listening to a great organ we cannot fail to perceive that the longest pipes, or their partial tones, produce a tremor and fluttering of the building. At the other extremity of the scale, there is no fixed limit to the acuteness of sounds which we can hear some individuals can hear sounds too shrill for other ears, and as there is nothing in the nature of the

atmosphere to prevent the existence of undulations incomparably more rapid than any of which we are conscious, we may infer, by the principle of continuity, that such undulations probably exist.

There are many habitual actions which we perform we know not how. So rapidly are many acts of mind accomplished that analysis seems impossible. We can only investigate them when in process of formation, observing that the best formed habit or instinct is slowly and continuously acquired, and it is in the early stages that we can perceive the rationale of the process.

Let it be observed that this principle of continuity must be held of much weight only in exact physical laws, those which doubtless repose ultimately upon the simple laws of motion. If we fearlessly apply the principle to all kinds of phenomena, we may often be right in our inference, but also often wrong. Thus, before the development of spectrum analysis, astronomers had observed that the more they increased the powers of their telescopes the more nebule they could resolve into distinct stars. This result had been so often found true that they almost irresistibly assumed that all the nebule would be ultimately resolved by telescopes of sufficient ewer; yet Mr. Huggins has in recent years proved by The spectroscope, that certain nebulæ are actually gaseous, na truly nebulous state. Even one such observation al exception sufficient to invalidate previous in* as to the constitution of the universe.

nciple of continuity must have been continually in the inquiries of Galileo, Newton, and other

philosophers, but it appears to have been elated for the first time by Leibnitz. He em to have first spoken of the law of conrer to Bayle, printed in the Nouvelles de des Lettres,' an extract from which is

given in Erdmann's edition of Leibnitz' works, p. 104, under the title Sur un Principe Général utile à l'explication des Lois de la Natureb.' It has indeed been asserted that the doctrine of the latens processus of Francis Bacon involves the principle of continuity, but I think that this doctrine, like that of the natures of substances is merely a vague statement of the principle of causation.

Failure of the Law of Continuity.

There are certain requisite cautions which must be given as to the application of the principle of continuity. In the first place, where this principle really holds true, it may seem to fail owing to our imperfect means of observation. Though a physical law may never admit of perfectly abrupt change, there is no limit to the approach which it may make to abruptness. When we warm a piece of very cold ice, the absorption of heat, the temperature, and the dilatation of the ice vary according to apparently simple laws until we come to the zero of the Centigrade scale. Everything is then changed; an enormous absorption of heat takes place without any rise of temperature, and the volume of the ice decreases as it changes into water. Unless most carefully investigated, this change appears perfectly abrupt; but accurate observation seems to show that there is a certain forewarning; the ice does not turn into water all at once, but through a small fraction of a degree the change is gradual. All the phenomena concerned, if measured very exactly, would be represented not by angular lines, but continuous curves, undergoing rapid flexures; and we may

b 'Life of Sir W. Hamilton,' p. 439.

c Powell's History of Natural Philosophy,' p. 201. 'Novum Organum,' bk. II. Aphorisms 5−7.

VOL. II.

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