boiling water. Here is a sequence which we feel confident will be repeated if we repeat the antecedent. Now if there were but one lobster this certainty, being merely hypothetical, would not serve our purpose. Then come in the coexistences to help us. The lobster, being a 'natural kind', belongs to a class containing a plurality of members, and all of these furnish us with the repetitions of the previous sequence if we choose to avail ourselves of them. The lowest or narrowest such uniformity of coexistence which would fall under our description of them, must at least contain two members, and even thus we should secure one repetition and so put our sequence to proof. But since in practice there are mostly many specimens of each kind, the coexistences become the main opportunity afforded to us of converting our sequences from hypothesis to actuality.

A few remarks may be added here as to the licence open to us, in various cases, to omit determining or individualizing circumstances. It is only by such omission, as already remarked, that we can ever secure repetitions of what we regard as the same phenomenon or event. A simple example or two will serve to bring out the distinction.

For instance, I take pieces of copper and of zinc, connect them in a certain way, and plunge them in an acid: a galvanic current follows. Now we all admit that if exactly the same process be repeated the same consequence will follow. But can the same process be repeated? Obviously it can up to a certain standard of precision. As we are dealing with voluntary actions we have not here to sit down and wait for another occasion of the same kind to present itself: we can make, or rather aid in making, our repetition. We can select other pieces of metal, and more acid, of the same quality, and treat them as we did before. We are thus appealing even here to the repetitions which nature so freely affords us in the case of simple substances, and by their aid we secure the desired opportunity of testing or applying our sequence.

We cannot indeed do exactly the same thing over again, as we should soon find if some exceedingly delicate operation had to be performed which turned on the precise quality and strength of the electric current. But it is soon found that for practical purposes many circumstances may be omitted as trivial, the temperature of the room, the moisture of the air

and so forth. Our power of thus recognizing insignificant attributes, and the fact that we are dealing with voluntary actions about comparatively simple substances, secure us as many repetitions as we require.

Now take the following case. I drink a quantity of sherry one night, and wake with a headache next morning. As before, I feel no doubt that if exactly the same thing were done over again exactly the same result would follow. Here too, as before, there are a number of notoriously insignificant circumstances, such as the moisture of the air, its electric condition, the direction of the wind, and so forth. And again, as before, there is a group of circumstances which we can repeat with tolerable accuracy, such as the strength of the liquor, its quantity, and the time of its consumption. So far no difference of importance can be detected. But whereas in the former instance these important attributes admitted of exhaustive determination, and tolerably accurate reproduction, in this latter instance many of them, those, for example, which are included in what is called our state of health at the time,-do not admit of determination. We cannot therefore procure two cases sufficiently resembling each other to give the Law of Causation fair scope to show what help it can give us. The cases are sufficiently in agreement to raise a presumption, but not sufficiently so to produce confidence.

One more example. I take a box of dominoes, toss the contents to the ceiling and mark the faces and directions of the pieces as they fall. As before, none of us has any doubt that repetition of the antecedent will be followed by certain repetition of the consequent. As before, some of the antecedents can be repeated, for we may throw the same pieces in the same room; and some, as before, are notoriously ineffective, such as the hour of the day and the phase of the moon. What baffles us is the vast number and impossibility of determination of really effective elements. Few conditions in fact can be so remote that we can make sure that they have no influence: even our state of health, and the temperature of the room, have something to do with the result. Consequently we cannot obtain anything that will pass muster as a concrete repetition of the event in question. That event is, to all relevant intents and purposes, in the position of a unique one. The repetition is wanting

here which alone could render the uniformity of sequence available for us.

III. The next class of uniformities which deserves notice. here may be briefly described as those of a rhythmic character. As we are merely passing them in review here I will not stop to enquire whether they may not by a stretch be brought under the head of sequences and coexistences; but for practical purposes they are best put in a class by themselves.

What I refer to here are those broad cycles of recurring events which may be traced in almost every direction in nature. They deserve notice apart if only for the fact that their immemorial recognition, and their enormous importance, have gained for them a quite proverbial acceptance as the type of natural stability giving ground for human reliance.

The cycle of recurring events constituting day and night, and the similar cycle constituting summer and winter, are as above suggested the most prominent and familiar of such instances. In several respects such groups as these correspond to 'species' of things, or the other natural kinds' described by Mill. That is, they furnish us with a large number of similar groups, agreeing in the bulk of their important elements, but differentiated by a number of comparatively insignificant details. They therefore furnish us with numerous and convenient opportunities of applying our sequences, and thus setting the Law of Causation to do our work. I sow seed, and it flowers and ripens that year. In order to do the same thing over again, and thus to be able to anticipate the same result, I must obtain a repetition of such a cycle. And thus a group of 'seasons' comes, for these logical purposes, to resemble the kinds of substances or living organisms which as we saw gave us many of our opportunities of similar repetitions. It would not be correct to speak of these cycles as 'coexistences', for the bulk of the elements which constitute them are distinctly not simultaneous but successive; but inasmuch as this group of elements does not display the causal characteristic of rigid regularity, distinctive of strict laws of sequence, they are best classed with the coexistences. An example will make this plain. The light of day, increasing from dawn to noon and then declining to twilight, gives us a succession of events one of which does not cause' the other, even in the merely sequence sense of that

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term; the group is therefore more in the nature of a simple aggregate such as constitutes the popular notion of a Kind, sanctioned by Mill, viz. an uncaused group of attributes. We cannot call them strictly a coexistence; but then, as we have already seen, there is a great deal of conventional assignment and interpretation involved in every case in which we speak of a coexistence.

The rhythmic character of natural phenomena illustrated by these cycles has received notice from Mr Herbert Spencer. He regards it as a necessary and universal characteristic of nature, and as one which admits of a sort of à priori proof. That these cycles are very widely spread is certain; but so far from regarding their existence as necessary it seems to me easy enough to conceive an alteration which should at once mar their character and eventually destroy them. Just such a change as we suppose our agent to carry out for the purpose of baffling our predictions would suffice to do the business. The known Laws of Motion in no way demand an elliptic orbit in a planet; they will be equally satisfied with a hyperbolic orbit. And then the rhythm of summer and winter begins to suffer, and slowly to tend towards the dull monotony of one unchanging temperature. So with the day and night. Let space be filled with a resisting medium (and we certainly do not know that it is not) and the familiar rhythm that we now experience would gradually begin to be affected, and finally to disappear into the same dull unchanging monotony.

I cannot therefore regard these cyclic arrangements of phenomena as in any sense necessary or ultimate. They have their conditions,-in the case of the seasons a certain velocity of translation of the earth is demanded, and if this be exceeded, the cycle no longer remains unimpaired,—and so long as these conditions prevail that characteristic will be found, but no longer. This does not however diminish their practical utility, and they therefore deserve distinct notice in any discussion of the foundations of Inductive Logic.

IV. The Conservation of Energy. This now well known physical principle certainly deserves a place amongst the uniformities which furnish a ground for inference, though in a logical treatise our discussion of it must be very brief. The main characteristics of it which claim notice here seem to me

to be the three following, in all of which it represents an immense advance beyond the mere sequence regularities which play so large a part in our older logical treatises.

(1) In the first place it embraces a whole field of inference which sequences cannot reach, or can reach only with a violent strain. Suppose for instance a ball rolling along the ground, which gradually slackens in speed and at last comes to a stop. We can calculate its speed throughout, and therefore make inferences about it; but we should find it hard to apply any reasonable modification of the common account of causation to

such a case. Of course if it were a repetition of a precisely similar performance that account would be most appropriate; but failing this, I can only see our way to some such futile interpretation as the merely hypothetical one that, if another ball were set rolling just as that one is rolling, it would follow the same course throughout.

Now what the doctrine of Energy does here is to supply a principle which requires no appeal to any other concrete example. The energy of motion with which the ball started must be retained: what the ball loses in motion the ground and air must gain, through friction, in warmth. We must appeal to experience to ascertain the friction, and we may be unable to work out the problem accurately, but we have the data for the purpose in our hands.

The fact is that the ordinary sequence formula, as given in the Brown-Mill Law of Causation, is only appropriate where we are dealing with concrete cases of distinct, almost abrupt, change. In the words of Mill himself, "it is events, that is to say changes, not substances, that are subject to the Law of Causation" (Exam. of Ham. p. 295). And the great advance indicated, in this respect, by the doctrine of Conservation of Energy is its perfect appropriateness to entire absence of change (where the Energy is preserved unchanged); and to those slow and continuous changes, as in the gradually stopping ball, where the energy is very slowly yielded up into another form.

(2) In the second place the doctrine bridges over the chasm between different classes of sequences which the old formula had to leave perfectly unfilled. We knew, for instance, that a certain chemical action would produce electricity, and we knew that friction would produce heat; but between heat and