diversity enable the mind to lop off these circumstances, and to discover the pair of phenomena distinctly. In short, we can only perform induction by discovering pairs of phenomena; we form these only by isolation; we isolate only by means of comparisons.

Section VIII.-Applications of the Theory of Induction

These are the rules; an example will make them clearer. We will show you the methods in exercise; here is an example which combines nearly the whole of them, namely, Dr. Well's theory of dew. I will give it to you in Mill's own words, which are so clear that you must have the pleasure of pondering over them: "We must separate dew from rain and the moisture of fogs, and limit the application of the term to what is really meant, which is, the spontaneous appearance of moisture on substances exposed in the open air when no rain or visible wet is falling." What is the cause of the phenomena we have thus defined, and how was that cause discovered?

"Now, here we have analogous phenomena, in the moisture which bedews a cold metal or stone when we breathe upon it; that which appears on a glass of water fresh from the well in hot weather; that which appears on the inside of windows when sudden rain or hail chills the external air; that which runs down our walls when, after a long frost, a warm moist thaw comes on.' Comparing these cases, we find that they all contain the phenomenon which was proposed as the subject of investigation. Now all these instances agree in one point: the coldness of the object dewed, in comparison with the air in contact with it.' But there still remains the most important case of all, that of nocturnal dew: does the same circumstance exist in this case? 'Is it a fact that the object dewed is colder than the air? Certainly not, one would at first be inclined to say; for what is to make it so? But ... the experiment is easy; we have only to lay a thermometer in contact with the dewed substance, and hang one at a little distance above it, out of reach of its influence. The experiment has been therefore made; the question has been asked, and the answer has been invariably in the affirmative. Whenever an object contracts dew, it is colder than the air.'

"Here then is a complete application of the Method of Agreement, establishing the fact of an invariable connection between the deposition of dew on a surface, and the coldness of that surface, compared with

1 This quotation, and all the others in this paragraph, are taken from Mill's Logic," i. 451-9. Mr. Mill quotes from

Sir John Herschel's "Discourse on the Study of Natural Philosophy."

the external air. But which of these is cause, and which effect? or are they both effects of something else? On this subject the Method of Agreement can afford us no light: we must call in a more potent method. We must collect more facts, or, which comes to the same thing, vary the circumstances; since every instance in which the circumstances differ is a fresh fact: and especially, we must note the contrary or negative cases, i.e., where no dew is produced': for a comparison between instances of dew and instances of no dew, is the condition necessary to bring the Method of Difference into play.

"Now, first, no dew is produced on the surface of polished metals, but it is very copiously on glass, both exposed with their faces upwards, and in some cases the under side of a horizontal plate of glass is also dewed.' Here is an instance in which the effect is produced, and another instance in which it is not produced; but we cannot yet pronounce, as the canon of the Method of Difference requires, that the latter instance agrees with the former in all its circumstances except one: for the differences between glass and polished metals are manifold, and the only thing we can as yet be sure of is, that the cause of dew will be found among the circumstances by which the former substance is distinguished from the latter."

To detect this particular circumstance of difference, we have but one practicable method, that of Concomitant Variations:

"In the cases of polished metal and polished glass, the contrast shows evidently that the substance has much to do with the phenomenon; therefore let the substance alone be diversified as much as possible, by exposing polished surfaces of various kinds. This done, a scale of intensity becomes obvious. Those polished substances are found to be most strongly dewed which conduct heat worst, while those which conduct well resist dew most effectually. . . .'

"The conclusion obtained is, that cæteris paribus the deposition of dew is in some proportion to the power which the body possesses of resisting the passage of heat; and that this, therefore (or something connected with this), must be at least one of the causes which assist in producing the deposition of dew on the surface.

"But if we expose rough surfaces instead of polished, we sometimes find this law interfered with. Thus, roughened iron, especially if painted over or blackened, becomes dewed sooner than varnished paper: the kind of surface, therefore, has a great influence. Expose, then, the same material in very diversified states as to surface' (that is, employ the Method of Difference to ascertain concomitance of variations), ‘and another scale of intensity becomes at once apparent; those surfaces which part with their heat most readily by radiation, are found to contract dew most copiously. . . .'

"The conclusion obtained by this new application of the method is, that cæteris paribus the deposition of dew is also in some proportion to the power of radiating heat; and that the quality of doing this

abundantly (or some cause on which that quality depends) is another of the causes which promote the deposition of dew on the substance. "Again, the influence ascertained to exist of substance and surface, leads us to consider that of texture; and here, again, we are presented on trial with remarkable differences, and with a third scale of intensity, pointing out substances of a close firm texture, such as stones, metals, etc., as unfavourable, but those of a loose one, as cloth, velvet, wool, eiderdown, cotton, etc., as eminently favourable to the contraction of dew.' The Method of Concomitant Variations is here, for the third time, had recourse to; and, as before, from necessity, since the texture of no substance is absolutely firm or absolutely loose. Looseness of texture, therefore, or something which is the cause of that quality, is another circumstance which promotes the deposition of dew; but this third cause resolves itself into the first, viz., the quality of resisting the passage of heat: for substances of loose texture are precisely those which are best adapted for clothing, or for impeding the free passage of heat from the skin into the air, so as to allow their outer surfaces to be very cold, while they remain warm within. . . . "It thus appears that the instances in which much dew is deposited, which are very various, agree in this, and, so far as we are able to observe, in this only, that they either radiate heat rapidly or conduct it slowly qualities between which there is no other circumstance of agreement than that by virtue of either, the body tends to lose heat from the surface more rapidly than it can be restored from within. The instances, on the contrary, in which no dew, or but a small quantity of it, is formed, and which are also extremely various, agree (so far as we can observe) in nothing except in not having this same property.

"This doubt we are now able to resolve. We have found that in every such instance, the substance must be one which, by its own properties or laws, would, if exposed in the night, become colder than the surrounding air. The coldness, therefore, being accounted for independently of the dew, while it is proved that there is a connection between the two, it must be the dew which depends on the coldness; or, in other words, the coldness is the cause of the dew.

"This law of causation, already so amply established, admits, however, of efficient additional corroboration in no less than three ways. First, by deduction from the known laws of aqueous vapour when diffused through air or any other gas, and though we have not yet come to the Deductive Method, we will not omit what is necessary to render this speculation complete. It is known, by direct experiment, that only a limited quantity of water can remain suspended in the state of vapour at each degree of temperature, and that this maximum grows less and less, as the temperature diminishes. From this it follows deductively, that if there is already as much vapour suspended as the air will contain at its existing temperature, any lowering of that temperature will cause a portion of the vapour to be condensed, and become water. But, again, we know deductively, from the laws of heat, that the contact of VOL. III.-25

the air with a body colder than itself, will necessarily lower the temperature of the stratum of air immediately applied to its surface; and will therefore cause it to part with a portion of its water, which accordingly will, by the ordinary laws of gravitation or cohesion, attach itself to the surface of the body, thereby constituting dew. This deductive proof, it will have been seen, has the advantage of proving at once causation as well as coexistence; and it has the additional advantage that it also accounts for the exceptions to the occurrence of the phenomenon, the cases in which, although the body is colder than the air, yet no dew is deposited, by showing that this will necessarily be the case when the air is so under-supplied with aqueous vapour, comparatively to its temperature, that even when somewhat cooled by the contact of the colder body, it can still continue to hold in suspension all the vapour which was previously suspended in it: thus, in a very dry summer there are no dews, in a very dry winter no hoar frost.

"The second corroboration of the theory is by direct experiment, according to the canon of the Method of Difference. We can, by cooling the surface of any body, find in all cases some temperature (more or less inferior to that of the surrounding air, according to its hygrometric condition) at which dew will begin to be deposited. Here, too, therefore, the causation is directly proved. We can, it is true, accomplish this only on a small scale; but we have ample reason to conclude that the same operation, if conducted in Nature's great laboratory, would equally produce the effect.

And, finally, even on that great scale we are able to verify the result. The case is one of those rare cases, as we have shown them to be, in which nature works the experiment for us in the same manner in which we ourselves perform it; introducing into the previous state of things a single and perfectly definite new circumstance, and manifesting the effect so rapidly that there is not time for any other material change in the pre-existing circumstances. It is observed that dew is never copiously deposited in situations much screened from the open sky, and not at all in a cloudy night; but if the clouds withdraw even for a few minutes, and leave a clear opening, a deposition of dew presently begins, and goes on increasing. Dew formed in clear intervals will often even evaporate again when the sky becomes thickly overcast.' The proof, therefore, is complete, that the presence or absence of an uninterrupted communication with the sky causes the deposition or non-deposition of dew. Now, since a clear sky is nothing but the absence of clouds, and it is a known property of clouds, as of all other bodies between which and any given object nothing intervenes but an elastic fluid, that they tend to raise or keep up the superficial temperature of the object by radiating heat to it, we see at once that the disappearance of clouds will cause the surface to cool; so that Nature, in this case, produces a change in the antecedent by definite and known means, and the consequent follows accordingly: a natural experiment which satisfies the requisitions of the Method of Difference."

Section IX.-The Province and Method of Deduction

These four are not all the scientific methods, but they lead up to the rest. They are all linked together, and no one has shown their connection better than Mill. In many cases these processes of isolation are powerless; namely, in those in which the effect, being produced by a concourse of causes, cannot be reduced into its elements. Methods of isolation are then impracticable. We cannot eliminate, and consequently we cannot perform induction. This serious difficulty presents itself in almost all cases of motion, for almost every movement is the effect of a concurrence of forces; and the respective effects of the various forces are found so mixed up in it that we cannot separate them without destroying it, so that it seems impossible to tell what part each force has in the production of the movement. Take a body acted upon by two forces whose directions form an angle: it moves along the diagonal; each part, each moment, each position, each element of its movement, is the combined effect of the two impelling forces. The two effects are so commingled that we cannot isolate either of them, and refer it to its source. In order to perceive each effect separately, we should have to consider the movements apart, that is, to suppress the actual movement, and to replace it by others. Neither the Method of Agreement, nor of Difference, nor of Residues, nor of Concomitant Variations, which are all decomposing and eliminative, can avail against a phenomenon which by its nature excludes all elimination and decomposition. We must, therefore, evade the obstacle; and it is here that the last key of nature appears, the Method of Deduction. We quit the study of the actual phenomenon to observe other and simpler cases; we establish their laws, and we connect each with its cause by the ordinary methods of induction. Then, assuming the concurrence of two or of several of these causes, we conclude from their known laws what will be their total effect. We next satisfy ourselves as to whether the actual movement exactly coincides with the movement foretold; and if this is so, we attribute it to the causes from which we have deduced it. Thus, in order to discover the causes of the planetary motions, we seek by simple induc