Chapter I (1)

OF EXPERIENCE AS THE SOURCE OF OUR KNOWLEDGE.--OF THE DISMISSAL OF
PREJUDICES.--OF THE EVIDENCE OF OUR SENSES.

(66.) Into abstract science, as we have before observed, the notion of cause does not enter. The truths it is conversant with are _necessary_ ones, and exist independent of cause. There may be no such real _thing_ as a right-lined triangle marked out in space; but the moment we conceive one in our minds, we cannot refuse to admit the sum of its three angles to be equal to two right angles; and if in addition we conceive one of its angles to be a right angle, we cannot thenceforth refuse to admit that the sum of the squares on the two sides, including the right angle, is equal to the square on the side subtending it. To maintain the contrary, would be, in effect, to deny its being right angled. No one _causes_ or _makes_ all the diameters of an ellipse to be bisected in its centre. To assert the contrary, would not be to rebel against a power, but to deny our own words. But in natural science _cause_ and _effect_ are the ultimate relations we contemplate; and _laws_, whether imposed or maintained, which, for aught we can perceive, might have been other than they are. This distinction is very important. A clever man, shut up alone and allowed unlimited time, might reason out for himself all the truths of mathematics, by proceeding from those simple notions of space and number of which he cannot divest himself without ceasing to think. But he could never tell, by any effort of reasoning, what would become of a lump of sugar if immersed in water, or what impression would be produced on his eye by mixing the colours yellow and blue.

(67.) We have thus pointed out to us, as the great, and indeed only ultimate source of our knowledge of nature and its laws, EXPERIENCE; by which we mean, not the experience of one man only, or of one generation, but the accumulated experience of all mankind in all ages, registered in books or recorded by tradition. But experience may be acquired in two ways: either, first, by noticing facts as they occur, without any attempt to influence the frequency of their occurrence, or to vary the circumstances under which they occur; this is OBSERVATION: or, secondly, by putting in action causes and agents over which we have control, and purposely varying their combinations, and noticing what effects take place; this is EXPERIMENT. To these two sources we must look as the fountains of all natural science. It is not intended, however, by thus distinguishing observation from experiment, to place them in any kind of contrast. Essentially they are much alike, and differ rather in degree than in kind; so that, perhaps, the terms _passive_ and _active observation_ might better express their distinction; but it is, nevertheless, highly important to mark the different states of mind in inquiries carried on by their respective aids, as well as their different effects in promoting the progress of science. In the former, we sit still and listen to a tale, told us, perhaps obscurely, piecemeal, and at long intervals of time, with our attention more or less awake. It is only by after-rumination that we gather its full import; and often, when the opportunity is gone by, we have to regret that our attention was not more particularly directed to some point which, at the time, appeared of little moment, but of which we at length appretiate the importance. In the latter, on the other hand, we cross-examine our witness, and by comparing one part of his evidence with the other, while he is yet before us, and reasoning upon it in his presence, are enabled to put pointed and searching questions, the answer to which may at once enable us to make up our minds. Accordingly it has been found invariably, that in those departments of physics where the phenomena are beyond our control, or into which experimental enquiry, from other causes, has not been carried, the progress of knowledge has been slow, uncertain, and irregular; while in such as admit of experiment, and in which mankind have agreed to its adoption, it has been rapid, sure, and steady. For example, in our knowledge of the nature and causes of volcanoes, earthquakes, the fall of stones from the sky, the appearance of new stars and disappearance of old ones, and other of those great phenomena of nature which are altogether beyond our command, and at the same time are of too rare occurrence to permit any one to repeat and rectify his impressions respecting them, we know little more now than in the earliest times. Here our tale is told us slowly, and in broken sentences. In astronomy, again, we have at least an uninterrupted narrative; the opportunity of observation is constantly present, and makes up in some measure for the impossibility of varying our point of view, and calling for information at the precise moment it is wanted. Accordingly, astronomy, regarded as a science of mere observation, arrived, though by very slow degrees, to a state of considerable maturity. But the moment that it became a branch of mechanics, a science essentially experimental, (that is to say, one in which any principle laid down can be subjected to immediate and decisive _trial_, and where experience does not require to be waited for,) its progress suddenly acquired a tenfold acceleration; nay, to such a degree, that it has been asserted, and we believe with truth, that were the records of all observations from the earliest ages annihilated, leaving only those made in a single observatory[27], during a single lifetime[28], the whole of this most perfect of sciences might, from those data, and as to the objects included in them, be at once reconstructed, and appear precisely as it stood at their conclusion. To take another instance: mineralogy, till modern times, could hardly be said to exist. The description of even the precious stones in Theophrastus and Pliny are, in most cases, hardly sufficient to identify them, and in many fall short even of that humble object; more recent observers, by attending more carefully to the obvious characters of minerals, had formed a pretty extensive catalogue of them, and made various attempts to arrange and methodize the knowledge thus acquired, and even to deduce some general conclusions respecting the forms they habitually assume: but from the moment that chemical analysis was applied to resolve them into their constituent elements, and that, led by a happy accident, the genius of Bergmann discovered the general fact, that they could be _cloven_ or split in such directions as to lay bare their peculiar primitive or fundamental forms, (which lay concealed within them, as the statue might be conceived encrusted in its marble envelope,)--from that moment, mineralogy ceased to be an unmeaning list of names, a mere laborious cataloguing of stones and rubbish, and became, what it now is, a regular, methodical, and most important science, in which every year is bringing to light new relations, new laws, and new practical applications.

(68.) Experience once recognized as the fountain of all our knowledge of nature, it follows that, in the study of nature and its laws, we ought at once to make up our minds to dismiss as idle prejudices, or at least suspend as premature, any preconceived notion of what might or what ought to be the order of nature in any proposed case, and content ourselves with observing, as a plain matter of fact, what _is_. To experience we refer, as the only ground of all physical enquiry. But before experience itself can be used with advantage, there is one preliminary step to make, which depends wholly on ourselves: it is the absolute dismissal and clearing the mind of all prejudice, from whatever source arising, and the determination to stand and fall by the result of a direct appeal to facts in the first instance, and of strict logical deduction from them afterwards. Now, it is necessary to distinguish between two kinds of prejudices, which exercise very different dominion over the mind, and, moreover, differ extremely in the difficulty of dispossessing them, and the process to be gone through for that purpose. These are,--

1. Prejudices of opinion.
2. Prejudices of sense.

(69.) By prejudices of opinion, we mean opinions hastily taken up, either from the assertion of others, from our own superficial views, or from vulgar observation, and which, from being constantly admitted without dispute, have obtained the strong hold of habit on our minds. Such were the opinions once maintained that the earth is the greatest body in the universe, and placed immovable in its centre, and all the rest of the universe created for its sole use; that it is the nature of fire and of sounds to ascend; that the moonlight is cold; that dews _fall_ from the air, &c.

(70.) To combat and destroy such prejudices we may proceed in two ways, either by demonstrating the falsehood of the facts alleged in their support, or by showing how the appearances, which seem to countenance them, are more satisfactorily accounted for without their admission. But it is unfortunately the nature of prejudices of opinion to adhere, in a certain degree, to every mind, and to some with pertinacious obstinacy, _pigris radicibus_, after all ground for their reasonable entertainment is destroyed. Against such a disposition the student of natural science must contend with all his power. Not that we are so unreasonable as to demand of him an instant and peremptory dismission of all his former opinions and judgments; all we require is, that he will hold them without bigotry, retain till he shall see reason to question them, and be ready to resign them when fairly proved untenable, and to doubt them when the weight of probability is shown to lie against them. If he refuse this, he is incapable of science.

(71.) Our resistance against the destruction of the other class of prejudices, those of sense, is commonly more violent at first, but less persistent, than in the case of those of opinion. Not to trust the evidence of our senses, seems, indeed, a hard condition, and one which, if proposed, none would comply with. But it is not the direct evidence of our senses that we are in any case called upon to reject, but only the erroneous judgments we unconsciously form from them, and this only when they can be shown to be so _by counter evidence of the same sort_; when one sense is brought to testify against another, for instance; or the same sense against itself, and the obvious conclusions in the two cases disagree, so as to compel us to acknowledge that one or other must be wrong. For example, nothing at first can seem a more rational, obvious, and incontrovertible conclusion, than that the _colour_ of an object is an inherent quality, like its weight, hardness, &c. and that to _see_ the object, and see it _of its own colour_, when nothing intervenes between our eyes and it, are one and the same thing. Yet this is only a prejudice; and that it is so, is shown by bringing forward the same sense of vision which led to its adoption, as evidence on the other side; for, when the differently coloured prismatic rays are thrown, in a dark room, in succession upon any object, whatever be the colour we are in the habit of calling its own, it will appear of the particular hue of the light which falls upon it: a yellow paper, for instance, will appear scarlet when illuminated by red rays, yellow when by yellow, green by green, and blue by blue rays; its own (so called) proper colour _not in the least degree mixing with that it so exhibits_.

(72.) To give one or two more examples of the kind of illusion which the senses practise on us, or rather which we practise on ourselves, by a misinterpretation of their evidence: the moon at its rising and setting appears much larger than when high up in the sky. This is, however, a mere erroneous judgment; for when we come to measure its diameter, so far from finding our conclusion borne out by fact, we actually find it to measure materially less. Here is eyesight opposed to eyesight, with the advantage of deliberate measurement. In ventriloquism we have the hearing at variance with all the other senses, and especially with the sight, which is sometimes contradicted by it in a very extraordinary and surprising manner, as when the voice is made to seem to issue from an inanimate and motionless object. If we plunge our hands, one into ice-cold water, and the other into water as hot as can be borne, and, after letting them stay awhile, suddenly transfer them both to a vessel full of water at a blood heat, the one will feel a sensation of heat, the other of cold. And if we cross the two first fingers of one hand, and place a pea in the fork between them, moving and rolling it about on a table, we shall (especially if we close our eyes) be fully persuaded we have two peas. If the nose be held while we are eating cinnamon, we shall perceive no difference between its flavour and that of a deal shaving.

(73.) These, and innumerable instances we might cite, will convince us, that though we are never deceived in the _sensible impression_ made by external objects on us, yet in forming our judgments of them we are greatly at the mercy of circumstances, which either modify the impressions actually received, or combine them with adjuncts which have become habitually associated with different judgments; and, therefore, that, in estimating the degree of confidence we are to place in our conclusions, we must, of necessity, take into account these modifying or accompanying circumstances, whatever they may be. We do not, of course, here speak of deranged organization; such as, for instance, a distortion of the eye, producing double vision, and still less of mental delusion, which absolutely perverts the meaning of sensible impressions.

(74.) As the mind exists not in the place of sensible objects, and is not brought into immediate relation with them, we can only regard sensible impressions as signals conveyed from them by a wonderful, and, to us, inexplicable mechanism, to our minds, which receives and reviews them, and, by habit and association, connects them with corresponding qualities or affections in the objects; just as a person writing down and comparing the signals of a telegraph might interpret their meaning. As, for instance, if he had constantly observed that the exhibition of a certain signal was sure to be followed next day by the announcement of the arrival of a ship at Portsmouth, he would connect the two facts by a link of the very same nature with that which connects the notion of a large wooden building, filled with sailors, with the impression of her outline on the retina of a spectator on the beach.

(75.) In captain Head’s amusing and vivid description of his journey across the Pampas of South America occurs an anecdote quite in point. His guide one day suddenly stopped him, and, pointing high into the air, cried out, “A lion!” Surprised at such an exclamation, accompanied with such an act, he turned up his eyes, and with difficulty perceived, at an immeasurable height, a flight of condors soaring in circles in a particular spot. Beneath that spot, far out of sight of himself or guide, lay the carcass of a horse, and over that carcass stood (as the guide well knew) the lion, whom the condors were eyeing with envy from their airy height. The signal of the birds was to him what the sight of the lion alone could have been to the traveller, a full assurance of its existence.

CHAP. II.

OF THE ANALYSIS OF PHENOMENA

(76.) _Phenomena_, then, or appearances, as the word is literally rendered, are the sensible results of processes and operations carried on among external objects, or their constituent principles, of which they are only signals, conveyed to our minds as aforesaid. Now, these processes themselves may be in many instances rendered _sensible_; that is to say, analysed, and shown to consist in the motions or other affections of sensible objects themselves. For instance, the phenomenon of the sound produced by a musical string, or a bell, when struck, may be shown to be the result of a process consisting in the rapid vibratory motion of its parts communicated to the air, and thence to our ears; though the immediate effect on our organs of hearing does not excite the least idea of such a motion. On the other hand, there are innumerable instances of sensible impressions which (at least at present) we are incapable of tracing beyond the mere sensation; for example, in the sensations of bitterness, sweetness, &c. These, accordingly, if we were inclined to form hasty decisions, might be regarded as ultimate qualities; but the instance of sounds, just adduced, alone would teach us caution in such decisions, and incline us to believe them mere results of some secret process going on in our organs of taste, which is too subtle for us to trace. A simple experiment will serve to set this in a clearer light. A solution of the salt called by chemists _nitrate of silver_, and another of the _hyposulphite of soda_, have each of them separately, when taken into the mouth, a disgustingly bitter taste; but if they be mixed, or if one be tasted before the mouth is thoroughly cleared of the other, the sensible impression is that of intense sweetness. Again, the salt called _tungstate of soda_ when first tasted is sweet, but speedily changes to an intense and pure bitter, like quassia.[29]

(77.) How far we may ever be enabled to attain a knowledge of the ultimate and inward processes of nature in the production of phenomena, we have no means of knowing; but, to judge from the degree of obscurity which hangs about the only case in which we feel within ourselves a _direct_ power to produce any one, there seems no great hope of penetrating so far. The case alluded to is the production of motion by the exertion of force. We are conscious of a power to move our limbs, and by their intervention other bodies; and that this effect is the result of a certain inexplicable process which we are aware of, but can no way describe in words, by which we exert _force_. And even when such exertion produces no visible effect, (as when we press our two hands violently together, so as just to oppose each other’s effort,) we still perceive, by the fatigue and exhaustion, and by the impossibility of maintaining the effort long, that something is going on within us, of which the mind is the agent, and the will the determining cause. This impression which we receive of the nature of force, from our own effort and our sense of fatigue, is quite different from that which we obtain of it from seeing the effect of force exerted by others in producing _motion_. Were there no such thing as motion, had we been from infancy shut up in a dark dungeon, and every limb encrusted with plaster, this internal consciousness would give us a complete idea of _force_; but when set at liberty, habit alone would enable us to recognize its exertion by its _signal_, motion, and _that_ only by finding that the same action of the mind which in our confined state enables us to fatigue and exhaust ourselves by the tension of our muscles, puts it in our power, when at liberty, to move ourselves and other bodies. But how obscure is our knowledge of the process going on within us in the exercise of this important privilege, in virtue of which alone we act as direct _causes_, we may judge from this, that when we put any limb in motion, the seat of the exertion seems to us to be _in_ the limb, whereas it is demonstrably no such thing, but either in the brain or in the spinal marrow; the proof of which is, that if a little fibre, called a nerve, which forms a communication between the limb and the brain, or spine, be divided in any part of its course, however we may make the effort, the limb will not move.

(78.) This one instance of the obscurity which hangs about the only act of direct _causation_ of which we have an immediate consciousness, will suffice to show how little prospect there is that, in our investigation of nature, we shall ever be able to arrive at a knowledge of ultimate causes, and will teach us to limit our views to that of _laws_, and to the analysis of complex phenomena by which they are resolved into simpler ones, which, appearing to us incapable of further analysis, we must consent to regard as causes. Nor let any one complain of this as a limitation of his faculties. We have here “ample room and verge enough” for the full exercise of all the powers we possess; and, besides, it does so happen, that we are actually able to trace up a very large portion of the phenomena of the universe to this one _cause_, viz. the exertion of mechanical _force_; indeed, so large a portion, that it has been made a matter of speculation whether this is not the only one that is capable of acting on material beings.

(79.) What we mean by the analysis of complex phenomena into simpler ones, will best be understood by an instance. Let us, therefore, take the phenomenon of sound, and, by considering the various cases in which sounds of all kinds are produced, we shall find that they all agree in these points:--1st, The excitement of a motion in the sounding body. 2dly, The communication of this motion to the air or other intermedium which is interposed between the sounding body and our ears. 3dly, The propagation of such motion from particle to particle of such intermedium in due succession. 4thly, Its communication, from the particles of the intermedium adjacent to the ear, to the ear itself. 5thly, Its conveyance in the ear, by a certain mechanism, to the auditory nerves. 6thly, The excitement of sensation. Now, in this analysis, we perceive that two principal matters must be understood, before we can have a true and complete knowledge of sound:--1st, The excitement and propagation of motion. 2dly, The production of sensation. These, then, are two other phenomena, of a simpler, or, it would be more correct to say, of a more general or elementary order, into which the complex phenomenon of sound resolves itself. But again, if we consider the communication of motion from body to body, or from one part to another of the same, we shall perceive that it is again resolvable into several other phenomena. 1st, The original setting in motion of a material body, or any part of one. 2dly, The behaviour of a particle set in motion, when it meets another lying in its way, or is otherwise impeded or influenced by its connection with surrounding particles. 3dly, The behaviour of the particles so impeding or influencing it under such circumstances; besides which, the last two point out another phenomenon, which it is necessary also to consider, viz. the phenomenon of the connection of the parts of material bodies in masses, by which they form aggregates, and are enabled to influence each other’s motions.

(80.) Thus, then, we see that an analysis of the phenomenon of sound leads to the enquiry, 1st, of two _causes_, viz. the cause of motion, and the cause of sensation, these being phenomena which (at least as human knowledge stands at present) we are unable to analyse further; and, therefore, we set them down as simple, elementary, and referable, for any thing we can see to the contrary, to the immediate action of their causes. 2dly, Of several questions relating to the connection between the motion of material bodies and its cause, such as, _What will happen_ when a moving body is surrounded on all sides by others not in motion? _What will happen_ when a body not in motion is advanced upon by a moving one? It is evident that the answers to such questions as these can be no other than _laws of motion_, in the sense we have above attributed to laws of nature, viz. a statement in words of what will happen in such and such proposed general contingencies. Lastly, we are led, by pursuing the analysis, and considering the phenomenon of the aggregation of the parts of material bodies, and the way in which they influence each other, to two other general phenomena, viz., the cohesion and elasticity of matter; and these we have no means of analysing further, and must, therefore, regard them (till we see reasons to the contrary) as _ultimate phenomena_, and referable to the direct action of causes, viz. an attractive and a repulsive _force_.

(81.) Of force, as counterbalanced by opposing force, we have, as already said, an internal consciousness; and though it may seem strange to us that matter should be capable of exerting on matter the same kind of effort, which, judging alone from this consciousness, we might be led to regard as a mental one; yet we cannot refuse the direct evidence of our senses, which shows us that when we keep a spring stretched with one hand, we feel our effort opposed exactly in the same way as if we had ourselves opposed it with the other hand, or as it would be by that of another person. The enquiry, therefore, into the aggregation of matter resolves itself into the general question, What will be the behaviour of material particles under the mutual action of opposing forces capable of counterbalancing each other? and the answer to this question can be no other than the announcement of the _law_ of equilibrium, whatever law that may be.

(82.) With regard to the cause of sensation, it must be regarded as much more obscure than that of motion, inasmuch as we have no conscious knowledge of it, _i. e._ we have no power, by any act of our minds and will, to call up a sensation. It is true, we are not destitute of an approach to it, since, by an effort of memory and imagination, we can produce in our minds an impression, or idea, of a sensation which, in peculiar cases, may even approach in vividness to actual reality. In dreams, too, and, in some cases of disordered nerves, we have sensations without objects. But if force, as a cause of motion, is obscure to us, even while we are in the act of exercising it, how much more so is this other cause, whose exercise we can only imitate imperfectly by any voluntary act, and of whose purely internal action we are only fully conscious when in a state that incapacitates us from reasoning, and almost from observation!

(83.) Dismissing, then, as beyond our reach, the enquiry into causes, we must be content at present to concentrate our attention on the laws which prevail among phenomena, and which seem to be their immediate results. From the instance we have just given, we may perceive that every enquiry into the intimate nature of a complex phenomenon branches out into as many different and distinct enquiries as there are simple or elementary phenomena into which it may be analysed; and that, therefore, it would greatly assist us in our study of nature, if we could, by any means, ascertain what _are_ the ultimate phenomena into which all the composite ones presented by it may be resolved. There is, however, clearly no way by which this can be ascertained _à priori_. We must go to nature itself, and be guided by the same kind of rule as the chemist in his analysis, who accounts every ingredient an _element_ till it can be decompounded and resolved into others. So, in natural philosophy, we must account every phenomenon an elementary or simple one till we can analyse it, and show that it is the result of others, which in their turn become elementary. Thus, in a modified and relative sense, we may still continue to speak of causes, not intending thereby those ultimate principles of action on whose exertion the whole frame of nature depends, but of those proximate links which connect phenomena with others of a simpler, higher, and more general or elementary kind. For example: we may regard the vibration of a musical string as the proximate cause of the sound it yields, receiving it, so far, as an ultimate fact, and waving or deferring enquiry into the cause of vibrations, which is of a higher and more general nature.

(84.) Moreover, as in chemistry we are sometimes compelled to acknowledge the existence of elements different from those already identified and known, though we cannot insulate them, and to perceive that substances have the characters of compounds, and must therefore be susceptible of analysis, though we do not see how it is to be set about; so, in physics, we may perceive the complexity of a phenomenon, without being able to perform its analysis. For example: in magnetism, the agency of electricity is clearly made out, and they are shown to stand to one another in the relation of effect and cause. But the analysis of magnetism, in its relation to particular metals, is not yet quite satisfactorily performed; and we are compelled to admit the existence of some cause, whether proximate or ultimate, whose presence in different metals, or in different states of the same metal, determines that peculiar electric condition which constitutes permanent magnetism. Cases like these, of all which science presents, offer the highest interest. They excite enquiry, like the near approach to the solution of an enigma; they show us that there is light, could only a certain veil be drawn aside.

(85.) In pursuing the analysis of any phenomenon, the moment we find ourselves stopped by one of which we perceive no analysis, and which, therefore, we are forced to refer (at least provisionally) to the class of ultimate facts, and to regard as elementary, the study of that phenomenon and of its laws becomes a separate branch of science. If we encounter the same elementary phenomenon in the analysis of several composite ones, it becomes still more interesting, and assumes additional importance; while at the same time we acquire information respecting the phenomenon itself, by observing those with which it is habitually associated, that may help us at length to its analysis. It is thus that sciences increase, and acquire a mutual relation and dependency. It is thus, too, that we are at length enabled to trace parallels and analogies between great branches of science themselves, which at length terminate in a perception of their dependence on some common phenomenon of a more general and elementary nature than that which form the subject of either separately. It was thus, for example, that, previous to Oërsted’s great discovery of electro-magnetism, a general resemblance between the two sciences of electricity and magnetism was recognised, and many of the chief phenomena in each were ascertained to have their parallels, _mutatis mutandis_, in the other. It was thus, too, that an analogy subsisting between sound and light has been gradually traced into a closeness of agreement, which can hardly leave any reasonable doubt of their ultimate coincidence in one common phenomenon, the vibratory motion of an elastic medium. If it be allowed to pursue our illustration from chemistry, and to ground its application not on what has been, but on what may one day be, done, it is thus that the general family resemblance between certain groups of bodies, now regarded as elementary, (as nickel and cobalt, for instance, chlorine, iode, and brome,) will, perhaps, lead us hereafter to perceive relations between them of a more intimate kind than we can at present trace.

(86.) On those phenomena which are most frequently encountered in an analysis of nature and which most decidedly resist further decomposition, it is evident that the greatest pains and attention ought to be bestowed, not only because they furnish a key to the greatest number of enquiries, and serve to group and classify together the greatest range of phenomena, but by reason of their higher nature, and because it is in these that we must look for the direct action of causes, and the most extensive and general enunciation of the laws of nature. These, once discovered, place in our power the explanation of all particular facts, and become grounds of reasoning, independent of particular trial: thus playing the same part in natural philosophy that axioms do in geometry; containing, in a refined and condensed state, and as it were in a quintessence, all that our reason has occasion to draw from experience to enable it to follow out the truths of physics by the mere application of logical argument. Indeed, the axioms of geometry themselves may be regarded as in some sort an appeal to experience, not corporeal, but mental. When we say, the whole is greater than its part, we announce a general fact, which rests, it is true, on our ideas of whole and part; but, in abstracting these notions, we begin by considering them as subsisting in space, and time, and body, and again, in linear, and superficial, and solid space. Again, when we say, the equals of equals are equal, we mentally make comparisons, in equal spaces, equal times, &c.; so that these axioms, however self-evident, are still general propositions so far of the inductive kind, that, independently of experience, they would not present themselves to the mind.

The only difference between these and axioms obtained from extensive induction is this, that, in raising the axioms of geometry, the instances offer themselves spontaneously, and without the trouble of search, and are few and simple; in raising those of nature, they are infinitely numerous, complicated, and remote; so that the most diligent research and the utmost acuteness are required to unravel their web, and place their meaning in evidence.

(87.) By far the most general phenomenon with which we are acquainted, and that which occurs most constantly, in every enquiry into which we enter, is motion, and its communication. Dynamics, then, or the science of force and motion, is thus placed at the head of all the sciences; and, happily for human knowledge, it is one in which the highest certainty is attainable, a certainty no way inferior to mathematical demonstration. As its axioms are few, simple, and in the highest degree distinct and definite, so they have at the same time an immediate relation to geometrical quantity, space, time, and direction, and thus accommodate themselves with remarkable facility to geometrical reasoning. Accordingly, their consequences may be pursued, by arguments purely mathematical, to any extent, insomuch that the limit of our knowledge of dynamics is determined only by that of pure mathematics, which is the case in no other branch of physical science.

(88.) But, it will now be asked, how we are to proceed to analyse a composite phenomenon into simpler ones, and whether any general rules can be given for this important process? We answer, None; any more than (to pursue the illustration we have already had recourse to) general rules can be laid down by the chemist for the analysis of substances of which all the ingredients are unknown. Such rules, could they be discovered, would include the whole of natural science; but we are very far, indeed, from being able to propound them. However, we are to recollect that the analysis of phenomena, philosophically speaking, is principally useful, as it enables us to recognize, and mark for special investigation, those which appear to us simple; to set methodically about determining their laws, and thus to facilitate the work of raising up general axioms, or forms of words, which shall include the whole of them; which shall, as it were, transplant them out of the external into the intellectual world, render them creatures of pure thought, and enable us to reason them out _à priori_. And what renders the power of doing this so eminently desirable is, that, in thus reasoning back from generals to particulars, the propositions at which we arrive apply to an immense multitude of combinations and cases, which were never individually contemplated in the mental process by which our axioms were first discovered; and that, consequently, when our reasonings are pushed to the utmost limit of particularity, their results appear in the form of _individual facts_, of which we might have had no knowledge from immediate experience; and thus we are not only furnished with the explanation of all known facts, but with the actual discovery of such as were before unknown. A remarkable example of this has already been mentioned in Fresnel’s _à priori_ discovery of the extraordinary refraction of both rays in a doubly refracting medium. To give another example:--The law of gravitation is a physical axiom of a very high and universal kind, and has been raised by a succession of inductions and abstractions drawn from the observation of numerous facts and subordinate laws in the planetary system. When this law is taken for granted, and laid down as a basis of reasoning, and applied to the actual condition of our own planet, one of the consequences to which it leads is, that the earth, instead of being an exact sphere, must be compressed or flattened in the direction of its polar diameter, the one diameter being about thirty miles shorter than the other; and this conclusion, deduced at first by mere reasoning, has been since found to be true in fact. All astronomical predictions are examples of the same thing.

(89.) In the important business of raising these axioms of nature, we are not, as in the analysis of phenomena, left wholly without a guide. The nature of abstract or general reasoning points out in a great measure the course we must pursue. A law of nature, being the statement of what will happen in certain general contingencies, may be regarded as the announcement, in the same words, of a whole group or class of phenomena. Whenever, therefore, we perceive that two or more phenomena agree in so many or so remarkable points, as to lead us to regard them as forming a class or group, if we lay out of consideration, or _abstract_, all the circumstances in which they disagree, and retain in our minds those only in which they agree, and then, under this kind of mental convention, frame a definition or statement of one of them, in such words that it shall apply equally to them all, such statement will appear in the form of a general proposition, having so far at least the character of a law of nature.

(90.) For example: a great number of transparent substances, when exposed, in a certain particular manner, to a beam of light which has been prepared by undergoing certain reflexions or refractions, (and has thereby acquired peculiar properties, and is said to be “_polarized_,”) exhibit very vivid and beautiful colours, disposed in streaks, bands, &c. of great regularity, which seem to arise within the substance, and which, from a certain regular succession observed in their appearance, are called “periodical colours.” Among the substances which exhibit these periodical colours occur a great variety of transparent solids, but no fluids and no opake solids. Here, then, there seems to be sufficient community of nature to enable us to use a general term, and to state the proposition as a law, viz. _transparent solids_ exhibit periodical colours by exposure to polarized light. However, this, though true of many, does not apply to _all_ transparent solids, and therefore we cannot state it as a general truth or law of nature in this form; although the reverse proposition, that all solids which exhibit such colours in such circumstances are _transparent_, would be correct and general. It becomes necessary, then, to make a list of those to which it does apply; and thus a great number of substances of all kinds become grouped together, in a class linked by this common property. If we examine the individuals of this group, we find among them the utmost variety of colour, texture, weight, hardness, form and composition; so that, in these respects, we seem to have fallen upon an assemblage of contraries. But when we come to examine them closely, in all their properties, we find they have all one point of agreement, in the property of double refraction, (see page 30.) and therefore we may describe them all truly as _doubly refracting substances_. We may, therefore, state the fact in the form, “Doubly refracting substances exhibit periodical colours by exposure to polarized light;” and in this form it is found, on further examination, to be true, not only for those particular instances which we had in view when we first propounded it, but in all cases which have since occurred on further enquiry, without a single exception; so that the proposition is general, and entitled to be regarded as a law of nature.

(91.) We may therefore regard a law of nature either, 1st, as a general proposition, announcing, in abstract terms, a whole group of particular facts relating to the behaviour of natural agents in proposed circumstances; or, 2dly, as a proposition announcing that a whole class of individuals agreeing in one character agree also in another. For example: in the case before us, the law arrived at includes, in its general announcement, among others, the particular facts, that rock crystal and saltpetre exhibit periodical colours; for these are both of them doubly refracting substances. Or, it may be regarded as announcing a relation between the two phenomena of double refraction, and the exhibition of periodical colours; which in the actual case is one of the most important, viz. the relation of _constant association_, inasmuch as it asserts that in whatever individual the one character is found, the other will invariably be found also.

(92.) These two lights, in which the announcement of a general law may be regarded, though at bottom they come to the same thing, yet differ widely in their influence on our minds. The former exhibits a law as little more than a kind of artificial memory; but in the latter it becomes a step in philosophical investigation, leading directly to the consideration of a proximate, if not an ultimate, cause; inasmuch as, whenever two phenomena are observed to be invariably connected together, we conclude them to be related to each other, either as cause and effect, or as common effects of a single cause.

(93.) There is still another light in which we may regard a law of the kind in question, viz. as a proposition asserting the mutual connection, or in some cases the entire identity, of two classes of individuals (whether individual objects or individual facts); and this is, perhaps, the simplest and most instructive way in which it can be conceived, and that which furnishes the readiest handle to further generalization in the raising of yet higher axioms. For example: in the case above mentioned, if observation had enabled us to establish the existence of a class of bodies possessing the property of double refraction, and observations of another kind had, independently of the former, led as to recognize a class possessing that of the exhibition of periodical colours in polarized light, a mere comparison of lists would at once demonstrate the identity of the two classes, or enable us to ascertain whether one was or was not included in the other.

(94.) It is thus we perceive the high importance in physical science of just and accurate classifications of particular facts, or individual objects, under general well considered heads or points of agreement (for which there are none better adapted than the simple phenomena themselves into which they can be analysed in the first instance); for by so doing each of such phenomena, or heads of classification, becomes not a particular but a general fact; and when we have amassed a great store of such _general facts_, they become the objects of another and higher species of classification, and are themselves included in laws which, as they dispose of groups, not individuals, have a far superior degree of generality, till at length, by continuing the process, we arrive at _axioms_ of the highest degree of generality of which science is capable.

(95.) This process is what we mean by induction; and, from what has been said, it appears that induction may be carried on in two different ways,--either by the simple juxta-position and comparison of ascertained classes, and marking their agreements and disagreements; or by considering the individuals of a class, and casting about, as it were to find in what particular they all agree, besides that which serves as their principle of classification. Either of these methods may be put in practice as one or the other may afford facilities in any case; but it will naturally happen that, where facts are numerous, well observed, and methodically arranged, the former will be more applicable than in the contrary case: the one is better adapted to the maturity, the other to the infancy, of science: the one employs, as an engine, the division of labour; the other mainly relies on individual penetration, and requires a union of many branches of knowledge in one person.

CHAP. III.

OF THE STATE OF PHYSICAL SCIENCE IN GENERAL, PREVIOUS TO THE AGE OF GALILEO AND BACON.

(96.) It is to our immortal countryman Bacon that we owe the broad announcement of this grand and fertile principle; and the developement of the idea, that the whole of natural philosophy consists entirely of a series of inductive generalizations, commencing with the most circumstantially stated particulars, and carried up to universal laws, or axioms, which comprehend in their statements every subordinate degree of generality, and of a corresponding series of inverted reasoning from generals to particulars, by which these axioms are traced back into their remotest consequences, and all particular propositions deduced from them; as well those by whose immediate consideration we rose to their discovery, as those of which we had no previous knowledge. In the course of this descent to particulars, we must of necessity encounter all those facts on which the arts and works that tend to the accommodation of human life depend, and acquire thereby the command of an unlimited practice, and a disposal of the powers of nature co-extensive with those powers themselves. A noble promise, indeed, and one which ought, surely, to animate us to the highest exertion of our faculties; especially since we have already such convincing proof that it is neither vain nor rash, but, on the contrary, has been, and continues to be, fulfilled, with a promptness and liberality which even its illustrious author in his most sanguine mood would have hardly ventured to anticipate.

(97.) Previous to the publication of the Novum Organum of Bacon, natural philosophy, in any legitimate and extensive sense of the word, could hardly be said to exist. Among the Greek philosophers, of whose attainments in science alone, in the earlier ages of the world, we have any positive knowledge, and that but a very limited one, we are struck with the remarkable contrast between their powers of acute and subtle disputation, their extraordinary success in abstract reasoning, and their intimate familiarity with subjects purely intellectual, on the one hand; and, on the other, with their loose and careless consideration of external nature, their grossly illogical deductions of principles of sweeping generality from few and ill-observed facts, in some cases; and their reckless assumption of abstract principles having no foundation but in their own imaginations, in others; mere forms of words, with nothing corresponding to them in nature, from which, as from mathematical definitions, postulates, and axioms, they imagined that all phenomena could be derived, all the laws of nature deduced. Thus, for instance, having settled it in their own minds, that a circle is the most perfect of figures, they concluded, of course, that the movements of the heavenly bodies must all be performed in exact circles, and with uniform motions; and when the plainest observation demonstrated the contrary, instead of doubting the principle, they saw no better way of getting out of the difficulty than by having recourse to endless combinations of circular motions to preserve their ideal perfection.

(98.) Undoubtedly among the Greek philosophers were many men of transcendent talents and virtues, the ornaments of their species, and justly entitled to the veneration of all posterity; but regarded as a body they can hardly be considered otherwise than as a knot of disputatious candidates for popular favour, too busy in maintaining their ascendency over their followers and admirers, by an ostentatious display of superior knowledge, to have the leisure (had they always the inclination) to base their pretensions on a deep and sure foundation, and yet too sensible of the disgrace and inconvenience of failure, not to defend their dogmas, however shallow, when once promulgated, against their keen and sagacious opponents, by every art of sophism or appeal to passion. Hence the crudities and chimerical views with which their systems of philosophy, both natural and moral, were overloaded; their endless disputes about verbal subtleties, and, last and worst, the proud assumption with which they sheltered ignorance and indolence under the screen of unintelligible jargon or dogmatical assertion. Perhaps, however, this character applies rather to the later than to the earlier of the Greek philosophers. The spirit of rational enquiry into nature seems, if we can judge from the uncertain and often contradictory notices handed down to us of their tenets, to have been far more alive, and less warped by this vain and arrogant turn, then than at a later period. We know not now what was the precise meaning attached by Thales to his opinion, that water was the origin of all things; but modern geologists will not be at a loss to conceive how an observant traveller might become impressed with this notion, without having recourse to the mystic records of Egypt or Chaldea. His ideas of eclipses and of the nature of the moon were sound; and his prediction of an eclipse of the sun, in particular, was attended with circumstances so remarkable as to have made it a matter of important investigation to modern astronomers. Anaxagoras, among a number of crude and imperfectly explained notions, speculated rationally enough on the cause of the winds and of the rainbow, and less absurdly on earthquakes than many modern geologists have done, and appears generally to have had his attention alive to nature, and his mind open to just reasoning on its phenomena; while Pythagoras, whether he reasoned it out for himself, or borrowed the notion from Egypt or India, had attained a just conception of the general disposition of the parts of the solar system, and the place held by the earth in it; nay, according to some accounts, had even raised his views so far as to speculate on the attraction of the sun as the bond of its union.

(99.) But the successors of these _bonâ fide_ enquirers into nature debased the standard of truth; and, taking advantage of the credit justly attached to their discoveries, renounced the modest character of learners, and erected themselves into teachers, and, to maintain their pretensions to this character, adopted the tone of men who had nothing further to learn. Unfortunately for true science, the national character gave every encouragement to pretensions of this kind. That restless craving after novelty, which distinguished the Greeks in their civil and political relations, pursued them into their philosophy. Whatever speculations were only ingenious and new had irresistible charms; and the teacher who could embody a clever thought in elegant language, or at once save his followers and himself the trouble of thinking or reasoning, by bold assertion, was too often induced to acquire cheaply the reputation of superior knowledge, snatch a few superficial notions from the most ordinary and obvious facts, envelope them in a parade of abstruse words, declare them the primary and ultimate principles of all things, and denounce as absurd and impious all opinions opposed to his own.

(100.) In this war of words the study of nature was neglected, and an humble and patient enquiry after facts altogether despised, as unworthy of the high _priori_ ground a true philosopher ought to take. It was the radical error of the Greek philosophy to imagine that the same method which proved so eminently successful in mathematical, would be equally so in physical, enquiries, and that, by setting out from a few simple and almost self-evident notions, or _axioms_, every thing could be reasoned out. Accordingly, we find them constantly straining their invention to discover these principles, which were to prove so pregnant. One makes _fire_ the essential matter and origin of the universe; another, _air_; a third, discovers the key to every difficulty, and the explanation of all phenomena, in the “το απειρον” or infinitude of things; a fourth, in the το ὁν and the το μη ὁν, that is to say, in entity and nonentity;--till at length an authority, which was destined to command opinions for nearly two thousand years, settled this important point, by deciding, that _matter_, _form_, and _privation_, were to be considered the principles of all things.