ordinary power of animal charcoal for attracting organic matter, or of spongy platinum for condensing hydrogen, which can only be considered as exalted cases of a more general power of attraction. The number of substances which are decomposed by light in a striking manner is very limited; but many other substances, such as vegetable colours, are affected by long exposure; on the principle of continuity we might expect to find that all kinds of matter are more or less susceptible of change by the incidence of light rays. It is the opinion of Grove that wherever an electric current passes there is a tendency to decomposition, a strain on the molecules, which when sufficiently intense leads to disruption. Even a metallic conducting wire may be regarded as tending to decomposition. Davy was probably correct in describing electricity as chemical affinity acting on masses, or rather, as Grove suggests, creating a disturbance through a chain of particles.2 Laplace went so far as to suggest that all chemical phenomena may be results of the Newtonian law of attraction, applied to atoms of various mass and position; but the time is probably far distant when the progress of molecular philosophy and of mathematical methods will enable such a generalisation to be verified or refuted.

The Law of Continuity.

Under the title of the Law of Continuity we may place many applications of the general principle of reasoning, that 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 high degree of probability that it will continue to be fulfilled at least a little further. If we see part only of a circle, we naturally expect that the circular form will be continued 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 inferences is doubtless identical with that of other inductive inferences.

1 Grove, Correlation of Physical Forces, 3rd edit. p. 118.
? Ibid. pp. 166, 199, &c.

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 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 portion, inference will be only more or less probable, according to the comparative lengths of the portions and the accuracy of observation; the longer our experience is, the more probable our inference 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. As Graham expressed the maxim, there are in nature no abrupt transitions, and the distinctions of class are never absolute.' 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 ball expelled, all simultaneously to our senses. But there is no doubt that time is occupied by every part of the process, and that the ball begins to move at first with infinite slowness. Captain Noble is able to measure by his chronoscope the progress of the shot in a 300-pounder gun, and finds that the whole motion within the barrel takes place in something less than one 200th part of a second. It is certain that no finite force can produce motion, except in a finite space of time. The amount of momentum communicated to a body is proportional to the accelerating force multiplied by the time during which it acts uniformly. Thus a slight force produces a great velocity only by long-continued action. In a powerful shock, like that of a railway collision, the stroke of a hammer on an anvil, or the discharge of a gun, the

1 Philosophical Transactions, 1861. Chemical and Physical Researches, p. 598.

time is very short, and therefore the accelerating forces brought into play are exceedingly great, but never infinite. In the case of a large gun the powder in exploding is said to exert for a moment a force equivalent to at least 2,800,000 horses.

Our belief in some of the fundamental laws of nature rests upon the principle of continuity. Galileo is held to be the first philosopher who consciously employed this principle in his arguments concerning the nature of motion, and it is certain that we can never by mere experience assure ourselves of the truth even of the first law of motion. A material particle, we are told, when not acted on by extraneous forces will continue in the same state of rest or motion. This may be true, but as we can find no body which is free from the action of extraneous causes, how are we to prove it? Only by observing that the less the amount of those forces the more nearly is the law found to be true. A ball rolled along rough ground is soon stopped; along a smooth pavement it continues 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 much 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 in such a case 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 an 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 a limiting case in which motion is infinitely small or zero, to which we may attain, on the principle of continuity, by successively considering cases of slower and slower motion. There are many classes of 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 far 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 acts of minds accomplished that analysis seems impossible. We can only investigate them when in process of formation, observing that the best formed habit 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 inferences, 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 nebulæ they could resolve into distinct stars. This result had been so often found true that they almost irresistibly assumed that all nebula would be ultimately resolved by telescopes of sufficient power; yet Huggins has in recent years proved by the spectroscope, that certain nebulæ are actually gaseous, and in a truly nebulous state.

The principle of continuity must have been continually employed in the inquiries of Galileo, Newton, and other experimental philosophers, but it appears to have been distinctly formulated for the first time by Leibnitz. He at least claims to have first spoken of "the law of continuity' in a letter to Bayle, printed in the Nouvelles de la République des Lettres, an extract from which is given in Erdmann's edition of Leibnitz's works, p. 104, under the

title "Sur un Principe Général utile à l'explication des Lois de la Nature." 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 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 not 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 carefully investigated, this change appears to be 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 probably assert with safety that between whatever points of temperature we examine ice, there would be found some indication, though almost infinitesimally small, of the apparently abrupt change which was to occur at a higher temperature. It might also be pointed out that the important and apparently simple physical laws, such as those of Boyle and Marriotte, Dalton and Gay-Lussac, &c., are only approximately true, and the divergences from the simple laws are forewarnings of abrupt changes, which would otherwise break the law of continuity.

1 Life of Sir W. Hamilton, p. 439.

2 Powell's History of Natural Philosophy, p. 201. Novum Organum, bk. ii. Aphorisms 5-7.