(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.

(101.) It were to do injustice to Aristotle, however, to judge of him

by _such_ a sample of his philosophy. He, at least, saw the necessity

of having recourse to nature for something like principles of physical

science; and, as an observer, a collector and recorder of facts and

phenomena, stood without an equal in his age. It was the fault of that

age, and of the perverse and flimsy style of verbal disputation which

had infected all learning, rather than his own, that he allowed himself

to be contented with vague and loose notions drawn from general and

vulgar observation, in place of seeking carefully, in well arranged

and thoroughly considered instances, for the true laws of nature. His

voluminous works, on every department of human knowledge existing in

his time, have nearly all perished. From his work on animals, which

has descended to us, we are, however, enabled to appreciate his powers

of observation; and a parallel drawn by an eminent Oxford professor

between his classifications and those of the most illustrious of

living naturalists, shows him to have attained a view of animated

nature in a remarkable degree comprehensive, and which contrasts

strikingly with the confusion, vagueness, and assumption of his

physical opinions and dogmas. In these it is easy to recognize a mind

not at home, and an impression of the necessity of saying something

learned and systematic, without knowing what to say. Thus he divides

motions into natural and unnatural; the natural motion of fire and

light bodies being upwards, those of heavy downwards, each seeking its

kindred nature in the heavens and the earth. Thus, too, the immediate

impressions made on us by external objects, such as hardness, colour,

heat, &c. are referred at once, in the Aristotelian philosophy, to

occult qualities, in virtue of which they are as they are, and beyond

which it is useless to enquire.[30] Of course there will occur a limit

beyond which it _is_ useless for merely human faculties to enquire; but

where that limit is placed, experience alone can teach us; and at least

to assert that we _have_ attained it, is now universally recognized as

the sure criterion of dogmatism.

(102.) In the early ages of the church the writings of Aristotle were

condemned, as allowing too much to reason and sense; and even so late

as the twelfth century they were sought out and burned, and their

readers excommunicated. By degrees, however, the extreme injustice

of this impeachment of their character was acknowledged: they became

the favourite study of the schoolmen, and furnished the keenest

weapons of their controversy, being appealed to in all disputes as of

sovereign authority; so that the slightest dissent from any opinion

of the “great master,” however absurd or unintelligible, was at once

drowned by clamour, or silenced by the still more effectual argument of

bitter persecution. If the logic of that gloomy period could be justly

described as “the art of talking unintelligibly on matters of which we

are ignorant,” its physics might, with equal truth, be summed up in a

deliberate preference of ignorance to knowledge, in matters of every

day’s experience and use.

(103.) In “this opake of nature and of soul,” the perverse activity of

the alchemists from time to time struck out a doubtful spark[31]; and

our illustrious countryman, Roger Bacon, shone out at the obscurest

moment, like an early star predicting dawn. It was not, however, till

the sixteenth century that the light of nature began to break forth

with a regular and progressive increase. The vaunts of Paracelsus

of the power of his chemical remedies and elixirs, and his open

condemnation of the ancient pharmacy, backed as they were by many

surprising cures, convinced all rational physicians that chemistry

could furnish many excellent remedies, unknown till that time[32], and

a number of valuable experiments began to be made by physicians and

chemists, desirous of discovering and describing new chemical remedies.

The chemical and metallurgic arts, exercised by persons empirically

acquainted with their secrets, began to be seriously studied with a

view to the acquisition of rational and useful knowledge, and regular

treatises on branches of natural science at length to appear. George

Agricola, in particular, devoted himself with ardour to the study

of mineralogy and metallurgy in the mining districts of Bohemia and

Schemnitz, and published copious and methodical accounts of all

the facts within his knowledge: and our countryman, Dr. Gilbert of

Colchester, in 1590, published a treatise on magnetism, full of

valuable facts and experiments, ingeniously reasoned on; and he

likewise extended his enquiries to a variety of other subjects, in

particular to electricity.

(104.) But, as the decisive mark of a great commencing change in the

direction of the human faculties, astronomy, the only science in which

the ancients had made any real progress, and ascended to any thing like

large and general conceptions, began once more to be studied in the

best spirit of a candid philosophy; and the Copernican or Pythagorean

system arose or revived, and rapidly gained advocates. Galileo at

length appeared, and openly attacked and refuted the Aristotelian

dogmas respecting motion, by direct appeal to the evidence of sense,

and by experiments of the most convincing kind. The persecutions

which such a step drew upon him, the record of his perseverance and

sufferings, and the ultimate triumph of his opinions and reasonings,

have been too lately and too well related[33] to require repetition

here.

(105.) By the discoveries of Copernicus, Kepler, and Galileo, the

errors of the Aristotelian philosophy were effectually overturned on a

plain appeal to the facts of nature; but it remained to show on broad

and general principles, how and why Aristotle was in the wrong; to set

in evidence the peculiar weakness of his method of philosophizing,

and to substitute in its place a stronger and better. This important

task was executed by Francis Bacon, Lord Verulam, who will, therefore,

justly be looked upon in all future ages as the great reformer of

philosophy, though his own actual contributions to the stock of

physical truths were small, and his ideas of particular points strongly

tinctured with mistakes and errors, which were the fault rather of the

general want of physical information of the age than of any narrowness

of view on his own part; and of this he was fully aware. It has been

attempted by some to lessen the merit of this great achievement, by

showing that the inductive method had been practised in many instances,

both ancient and modern, by the mere instinct of mankind; but it is not

the introduction of inductive reasoning, as a new and hitherto untried

process, which characterizes the Baconian philosophy, but his keen

perception, and his broad and spirit-stirring, almost enthusiastic,

announcement of its paramount importance, as the alpha and omega of

science, as the grand and only chain for the linking together of

physical truths, and the eventual key to every discovery and every

application. Those who would deny him his just glory on such grounds

would refuse to Jenner or to Howard their civic crowns, because a few

farmers in a remote province had, time out of mind, been acquainted

with vaccination, or philanthropists, in all ages, had occasionally

visited the prisoner in his dungeon.

(106.) An immense impulse was now given to science, and it seemed as

if the genius of mankind, long pent up, had at length rushed eagerly

upon Nature, and commenced, with one accord, the great work of

turning up her hitherto unbroken soil, and exposing the treasures

so long concealed. A general sense now prevailed of the poverty and

insufficiency of existing knowledge in _matters of fact_; and, as

information flowed fast in, an era of excitement and wonder commenced,

to which the annals of mankind had furnished nothing similar. It

seemed, too, as if Nature herself seconded the impulse; and, while

she supplied new and extraordinary aids to those senses which were

henceforth to be exercised in her investigation,--while the telescope

and the microscope laid open _the infinite_ in both directions,--as

if to call attention to her wonders, and signalize the epoch, she

displayed the rarest, the most splendid and mysterious, of all

astronomical phenomena, the appearance and subsequent total extinction

of a new and brilliant fixed star twice within the lifetime of Galileo

himself.[34]

(107.) The immediate followers of Bacon and Galileo ransacked all

nature for new and surprising facts, with something of that craving

for the marvellous, which might be regarded as a remnant of the age of

alchemy and natural magic, but which, under proper regulation, is a

most powerful and useful stimulus to experimental enquiry. Boyle, in

particular, seemed animated by an enthusiasm of ardour, which hurried

him from subject to subject, and from experiment to experiment,

without a moment’s intermission, and with a sort of undistinguishing

appetite; while Hooke (the great contemporary, and almost the worthy

rival, of Newton) carried a keener eye of scrutinizing reason into a

range of research even yet more extensive. As facts multiplied, leading

phenomena became prominent, laws began to emerge, and generalizations

to commence; and so rapid was the career of discovery, so signal the

triumph of the inductive philosophy, that a single generation and the

efforts of a single mind sufficed for the establishment of the system

of the universe, on a basis never after to be shaken.

(108.) We shall now endeavour to enumerate and explain in detail the

principal steps by which legitimate and extensive inductions are

arrived at, and the processes by which the mind, in the investigation

of natural laws, purges itself by successive degrees of the

superfluities and incumbrances which hang about particulars, and

obscure the perception of their points of resemblance and connection.

We shall state the helps which may be afforded us, in a work of so

much thought and labour, by a methodical course of proceeding, and

by a careful notice of those means which have at any time been found

successful, with a view to their better understanding and adaptation

to other cases: a species of mental induction of no mean utility and

extent in itself; inasmuch as by pursuing it alone we can attain a more

intimate knowledge than we actually possess of the laws which regulate

our discovery of truth, and of the rules, so far as they extend, to

which invention is reducible. In doing this, we shall commence at the

beginning, with experience itself, considered as the accumulation of

the knowledge of individual objects and facts.

CHAP. IV.

OF THE OBSERVATION OF FACTS AND THE COLLECTION OF INSTANCES.

(109.) Nature offers us two sorts of subjects of contemplation in the

external world,--objects, and their mutual actions. But, after what

has been said on the subject of sensation, the reader will be at no

loss to perceive that we know nothing of the objects themselves which

compose the universe, except through the medium of the impressions they

excite in us, which impressions are the results of certain actions and

processes in which sensible objects and the material parts of ourselves

are directly concerned. Thus, our observation of external nature is

limited to the mutual action of material objects on one another; and

to facts, that is, the associations of phenomena or appearances. We

gain no information by perceiving merely that an object is black; but

if we also perceive it to be fluid, we at least acquire the knowledge

that blackness is not incompatible with fluidity, and have thus made

a step, however trifling, to a knowledge of the more intimate nature

of these two qualities. Whenever, therefore, we would either analyse

a phenomenon into simpler ones, or ascertain what is the course or

law of nature under any proposed general contingency, the first step

is to accumulate a sufficient quantity of well ascertained facts or

recorded instances, bearing on the point in question. Common sense

dictates this, as affording us the means of examining the same subject

in several points of view; and it would also dictate, that the more

different these collected facts are in all other circumstances but that

which forms the subject of enquiry, the better; because they are then

in some sort brought into contrast with one another in their points of

disagreement, and thus tend to render those in which they agree more

prominent and striking.

(110.) The only facts which can ever become useful as grounds of

physical enquiry are those which happen uniformly and invariably

under the same circumstances. This is evident: for if they have

not this character they cannot be included in laws; they want that

universality which fits them to enter as elementary particles into the

constitution of those universal axioms which we aim at discovering.

If one and the same result does not constantly happen under a given

combination of circumstances, apparently the same, one of two things

must be supposed,--caprice (_i. e._ the arbitrary intervention of

mental agency), or differences in the circumstances themselves,

really existing, but unobserved by us. In either case, though we may

record such facts as curiosities, or as awaiting explanation when

the difference of circumstances shall be understood, we can make

no use of them in scientific enquiry. Hence, whenever we notice a

remarkable effect of any kind, our first question ought to be, Can it

be reproduced? What are the circumstances under which it has happened?

And will it _always_ happen again if those circumstances, so far as we

have been able to collect them, co-exist?

(111.) The circumstances, then, which accompany any observed fact, are

main features in its observation, at least until it is ascertained

by sufficient experience what circumstances have nothing to do with

it, and might therefore have been left unobserved without sacrificing

_the fact_. In observing and recording a fact, therefore, altogether

new, we ought not to omit any circumstance capable of being noted,

lest some one of the omitted circumstances should be essentially

connected with the fact, and its omission should, therefore, reduce

the implied statement of a _law of nature_ to the mere record of an

_historical event_. For instance, in the fall of meteoric stones,

flashes of fire are seen proceeding from a cloud, and a loud rattling

noise like thunder is heard. These circumstances, and the sudden stroke

and destruction ensuing, long caused them to be confounded with an

effect of lightning, and called thunderbolts. But one circumstance is

enough to mark the difference: the flash and sound have been perceived

occasionally to emanate from a _very small cloud_ insulated in _a clear

sky_; a combination of circumstances which never happens in a thunder

storm, but which is undoubtedly intimately connected with their real

origin.

(112.) Recorded observation consists of two distinct parts: 1st, an

exact notice of the thing observed, and of all the particulars which

may be supposed to have any natural connection with it; and, 2dly, a

true and faithful record of them. As our senses are the only inlets

by which we receive impressions of facts, we must take care, in

observing, to have them all in activity, and to let nothing escape

notice which affects any one of them. Thus, if lightning were to

strike the house we inhabit, we ought to notice what kind of light we

saw--whether a sheet of flame, a darting spark, or a broken zig-zag;

in what direction moving, to what objects adhering, its colour, its

duration, &c.; what sounds were heard--explosive, crashing, rattling,

momentary, or gradually increasing and fading, &c.; whether any smell

of fire was perceptible, and if sulphureous, metallic, or such as

would arise merely from substances scorched by the flash, &c.; whether

we felt any shock, stroke, or peculiar sensation, or experienced any

strange taste in our mouths. Then, besides detailing the effects of the

stroke, all the circumstances which might in any degree seem likely to

attract, produce, or modify it, such as the presence of conductors,

neighbouring objects, the state of the atmosphere, the barometer,

thermometer, &c., and the disposition of the clouds, should be noted;

and after all this particularity, the question _how_ the house _came

to be struck?_ might ultimately depend on the fact that a flash of

lightning twenty miles off passed at that particular moment _from

the ground to the clouds_, by an effect of what has been termed the

returning stroke.

(113.) A writer in the Edinburgh Philosophical Journal[35] states

himself to have been led into a series of investigations on the

chemical nature of a peculiar acid, by noticing, accidentally, a bitter

taste in a liquid about to be thrown away. Chemistry is full of such

incidents.

(114.) In transient phenomena, if the number of particulars be

great, and the time to observe them short, we must consult our

memory before they have had time to fade, or refresh it by placing

ourselves as nearly as possible in the same circumstances again; go

back to the spot, for instance, and try the words of our statement

by appeal to all remaining indications, &c. This is most especially

necessary where we have not observed ourselves, but only collect and

record the observations of others, particularly of illiterate or

prejudiced persons, on any rare phenomenon, such as the passing of

a great meteor,--the fall of a stone from the sky,--the shock of an

earthquake,--an extraordinary hailstorm, &c.

(115.) In all cases which admit of numeration or measurement, it is of

the utmost consequence to obtain precise numerical statements, whether

in the measure of time, space, or quantity of any kind. To omit this,

is, in the first place, to expose ourselves to illusions of sense which

may lead to the grossest errors. Thus, in alpine countries, we are

constantly deceived in heights and distances; and when we have overcome

the first impression which leads us to under-estimate them, we are then

hardly less apt to run into the opposite extreme. But it is not merely

in preserving us from exaggerated impressions that numerical precision

is desirable. It is the very soul of science; and its attainment

affords the only criterion, or at least the best, of the truth of

theories, and the correctness of experiments. Thus, it was entirely

to the omission of exact numerical determinations of quantity that the

mistakes and confusion of the Stahlian chemistry were attributable,--a

confusion which dissipated like a morning mist as soon as precision,

in this respect, came to be regarded as essential. Chemistry is in the

most pre-eminent degree a science of quantity; and to enumerate the

discoveries which have arisen in it, from the mere determination of

weights and measures, would be nearly to give a synopsis of this branch

of knowledge. We need only mention the law of definite proportions,

which fixes the composition of every body in nature in determinate

proportional weights of its ingredients.

(116.) Indeed, it is a character of all the higher laws of nature to

assume the form of precise _quantitative_ statement. Thus, the law of

gravitation, the most universal truth at which human reason has yet

arrived, expresses not merely the general fact of the mutual attraction

of all matter; not merely the vague statement that its influence

decreases as the distance increases, but the exact numerical rate at

which that decrease takes place; so that when its amount is known at

any one distance it may be calculated exactly for any other. Thus, too,

the laws of crystallography, which limit the forms assumed by natural

substances, when left to their own inherent powers of aggregation, to

precise geometrical figures, with fixed angles and proportions, have

the same essential character of strict mathematical expression, without

which no exact particular conclusions could ever be drawn from them.

(117.) But, to arrive at laws of this description, it is evident that

every step of our enquiry must be perfectly free from the slightest

degree of looseness and indecision, and carry with it the full force of

strict numerical announcement; and that, therefore, the observations

themselves on which all laws ultimately rest ought to have the same

property. None of our senses, however, gives us direct information

for the exact comparison of quantity. Number, indeed, that is to

say, integer number, is an object of sense, because we can count;

but we can neither weigh, measure, nor form any precise estimate of

fractional parts by the unassisted senses. Scarcely any man could tell

the difference between twenty pounds and the same weight increased or

diminished by a few ounces; still less could he judge of the proportion

between an ounce of gold and a hundred grains of cotton by balancing

them in his hands. To take another instance: the eye is no judge of the

proportion of different degrees of illumination, even when seen side

by side; and if an interval elapses, and circumstances change, nothing

can be more vague than its judgments. When we gaze with admiration

at the gorgeous spectacle of the golden clouds at sunset, which seem

drenched in light and glowing like flames of real fire, it is hardly

by any effort we can persuade ourselves to regard them as the very

same objects which at noonday pass unnoticed as mere white clouds

basking in the sun, only participating, from their great horizontal

distance, in the ruddy tint which luminaries acquire by shining through

a great extent of the vapours of the atmosphere, and thereby even

losing something of their light. So it is with our estimates of time,

velocity, and all other matters of quantity; they are absolutely vague,

and inadequate to form a foundation for any exact conclusion.

(118.) In this emergency we are obliged to have recourse to

instrumental aids, that is, to contrivances which shall substitute for

the vague impressions of sense the precise one of number, and reduce

all measurement to counting. As a first preliminary towards effecting

this, we fix on convenient _standards_ of weight, dimension, time,

&c., and invent contrivances for readily and correctly repeating them

as often as we please, and counting how often such a standard unit is

contained in the thing, be it weight, space, time, or angle, we wish to

measure; and if there be a fractional part over, we measure this as a

new quantity by aliquot parts of the former standard.

(119.) If every scientific enquirer observed only for his own

satisfaction, and reasoned only on his own observations, it would be

of little importance what standards he used, or what contrivances (if

only just ones) he employed for this purpose; but if it be intended

(as it is most important they should) that observations once made

should remain as records to all mankind, and to all posterity, it is

evidently of the highest consequence that all enquirers should agree on

the use of a common standard, and that this should be one not liable

to change by lapse of time. The selection and verification of such

standards, however, will easily be understood to be a matter of extreme

difficulty, if only from the mere circumstance that, to verify the

permanence of one standard, we must compare it with others, which it

is possible may be themselves inaccurate, or, at least, stand in need

of verification.

(120.) Here we can only call to our assistance the presumed permanence

of the great laws of Nature, with all experience in its favour, and the

strong impression we have of the general composure and steadiness of

every thing relating to the gigantic mass we inhabit--“the great globe

itself.” In its uniform rotation on its axis, accordingly, we find a

standard of time, which nothing has ever given us reason to regard

as subject to change, and which, compared with other periods which

the revolutions of the planets about the sun afford, has demonstrably

undergone none since the earliest history. In the dimensions of the

earth we find a natural unit of the measure of space, which possesses

in perfection every quality that can be desired; and in its attraction

combined with its rotation the researches of dynamical science have

enabled us, through the medium of the pendulum, to obtain another

invariable standard, more refined and less obvious, it is true, in

its origin, but possessing a great advantage in its capability of

ready verification, and therefore easily made to serve as a check on

the other. The former, viz. direct measurement of the dimensions of

the earth, is the origin of the _mètre_, the French unit of linear

measure; the latter, of the British yard. Theoretically speaking,

they are equally eligible; but when we consider that the _quantity

directly measured_, in the case of the mètre, is a length a great many

thousand times the final unit, and in the pendulum or yard very nearly

the unit itself, there can be no hesitation in giving the preference

as an original measure to the former, because any error committed in

the process by which that is determined becomes subdivided in the

final result; while, on the other hand, any minute error committed

in determining the length of the pendulum becomes multiplied by the

repetition of the unit in all measurements of considerable lengths

performed in yards.

(121.) The same admirable invention of the pendulum affords a means of

subdividing time to an almost unlimited nicety. A clock is nothing more

than a piece of mechanism for counting the oscillations of a pendulum;

and by that peculiar property of the pendulum, that one vibration

commences exactly where the last terminates, no part of time is lost

or gained in the juxta-position of the units so counted, so that the

precise fractional part of a day can be ascertained which each such

unit measures.

(122.) It is owing to this peculiar property by which the

_juxta-position_ of units of time and weight can be performed _without

error_, that the whole of the accuracy with which time and weight can

be multiplied and subdivided is owing.[36] The same thing cannot be

accomplished in _space_, by any method we are yet acquainted with, so

that our means of subdividing space are much inferior in precision.

The beautiful principle of repetition, invented by Borda, offers the

nearest approach to it, but cannot be said to be absolutely free from

the source of error in question. The method of “double weighing,” which

we owe to the same distinguished observer, affords an instance of the

direct comparison of two equal weights independent of almost every

source of error which can affect the comparison of one object with

another. It has been remarked by Biot, that previous to the invention

of this elegant method, instruments afforded no perfect means of

ascertaining the weight of a body.

(123.) But it is not enough to possess a standard of this abstract

kind: a real material measure must be constructed, and exact copies of

it taken. This, however, is not very difficult; the great difficulty

is to preserve it unaltered from age to age; for unless we transmit to

posterity the units of our measurements, _such as we have ourselves

used them_, we, in fact, only half bequeath to them our observations.

This is a point too much lost sight of, and it were much to be wished

that some direct provision for so important an object were made.[37]

(124.) But, it may be asked, if our measurement of quantity is thus

unavoidably liable to error, how is it possible that our observations

can possess that quality of numerical veracity which is requisite to

render them the foundation of laws, whose distinguishing perfection

consists in their strict mathematical expression? To this the reply is

twofold. 1st, that though we admit the necessary existence of numerical

error in every observation, we can always assign a limit which such

error cannot possibly exceed; and the extent of this _latitude of

error of observation_ is less in proportion to the perfection of

the instrumental means we possess, and the care bestowed on their

employment. In the greater part of modern measurements it is, in point

of fact, extremely minute, and may be still further diminished, almost

to any required extent, by repeating the measurements a great number of

times, and under a great variety of circumstances, and taking a mean of

the results, when errors of opposite kinds will, at length, compensate

each other. But, 2dly, there exists a much more fundamental reply to

this objection. In reasoning upon our observations, the existence and

possible amount of quantitative error is always to be allowed for; and

the extent to which theories may be affected by it is never to be lost

sight of. In reasoning upwards, from observations confessedly imperfect

to general laws, we must take care always to regard our conclusions

as conditional, so far as they may be affected by such unavoidable

imperfections; and when at length we shall have arrived at our highest

point, and attained to axioms which admit of general and deductive

reasoning, the question, whether they _are_ vitiated by the errors of

observation or not, will still remain to be decided, and must become

the object of subsequent verification. This point will be made the

subject of more distinct consideration hereafter, when we come to speak

of the verification of theories and the laws of probability.

(125.) With respect to our record of observations, it should be not

only circumstantial but _faithful_; by which we mean, that it should

contain all we did _observe_, and nothing else. Without any intention

of falsifying our record, we may do so unperceived by ourselves, owing

to a mixture of the views and language of an erroneous theory with

that of simple fact. Thus, for example, if, in describing the effect

of lightning, we should say, “The thunderbolt struck with violence

against the side of the house, and beat in the wall,” a fact would be

stated which we did not see, and would lead our hearers to believe that

a solid or ponderable projectile was concerned. The “strong smell of

sulphur,” which is sometimes said to accompany lightning, is a remnant

of the theory which made thunder and lightning the explosion of a kind

of aërial gunpowder, composed of sulphureous and nitrous exhalations.

There are some subjects particularly infested with this mixture of

theory in the statement of observed fact. The older chemistry was

so overborne by this mischief, as quite to confound and nullify the

descriptions of innumerable curious and laborious experiments. And in

geology, till a very recent period, it was often extremely difficult,

from this circumstance, to know what _were_ the facts observed. Thus,

Faujas de St. Fond, in his work on the volcanoes of central France,

describes with every appearance of minute precision craters existing

no where but in his own imagination. There is no greater fault (direct

falsification of fact excepted) which can be committed by an observer.

(126.) When particular branches of science have acquired that degree

of consistency and generality, which admits of an abstract statement

of laws, and legitimate deductive reasoning, the principle of the

division of labour tends to separate the province of the observer from

that of the theorist. There is no accounting for the difference of

minds or inclinations, which leads one man to observe with interest

the developements of phenomena, another to speculate on their causes;

but were it not for this happy disagreement, it may be doubted whether

the higher sciences could ever have attained even their present degree

of perfection. As laws acquire generality, the influence of individual

observations becomes less, and a higher and higher degree of

refinement in their performance, as well as a great multiplication in

their number, becomes necessary to give them importance. In astronomy,

for instance, the superior departments of theory are completely

disjoined from the routine of practical observation.

(127.) To make a perfect observer, however, either in astronomy

or in any other department of science, an extensive acquaintance

is requisite, not only with the particular science to which his

observations relate, but with every branch of knowledge which may

enable him to appretiate and neutralize the effect of extraneous

disturbing causes. Thus furnished, he will be prepared to seize on any

of those minute indications, which (such is the subtlety of nature)

often connect phenomena which seem quite remote from each other. He

will have his eyes as it were opened, that they may be struck at once

with any occurrence which, according to received theories, ought

not to happen; for these are the facts which serve as clews to new

discoveries. The deviation of the magnetic needle, by the influence

of an electrified wire, must have happened a thousand times to a

perceptible amount, under the eyes of persons engaged in galvanic

experiments, with philosophical apparatus of all kinds standing around

them; but it required the eye of a philosopher such as Oërsted to

seize the indication, refer it to its origin, and thereby connect

two great branches of science. The grand discovery of Malus of the

polarization of light by reflection originated in his casual remark of

the disappearance of one of the images of a window in the Luxembourg

palace, one evening, when strongly illuminated by the setting sun,

viewed through a doubly refracting prism.

(128.) To avail ourselves as far as possible of the advantages which

a division of labour may afford for the collection of facts, by the

industry and activity which the general diffusion of information,

in the present age, brings into exercise, is an object of great

importance. There is scarcely any well-informed person, who, if he

has but the will, has not also the power to add something essential

to the general stock of knowledge, if he will only observe regularly

and methodically some particular class of facts which may most excite

his attention, or which his situation may best enable him to study

with effect. To instance one or two subjects, which can only be

effectually improved by the united observations of great numbers widely

dispersed:--Meteorology, one of the most complicated but important

branches of science, is at the same time one in which any person

who will attend to plain rules, and bestow the necessary degree of

attention, may do effectual service. What benefits has not Geology

reaped from the activity of industrious individuals, who, setting

aside all theoretical views, have been content to exercise the useful

and highly entertaining occupation of collecting specimens from the

countries which they visit? In short, there is no branch of science

whatever in which, at least, if useful and sensible queries were

distinctly proposed, an immense mass of valuable information might not

be collected from those who, in their various lines of life, at home

or abroad, stationary or in travel, would gladly avail themselves of

opportunities of being useful. Nothing would tend better to attain

this end than the circulation of printed skeleton forms, on various

subjects, which should be so formed as, 1st, to ask distinct and

pertinent questions, admitting of short and definite answers; 2dly, To

call for exact numerical statement on all principal points; 3dly, To

point out the attendant circumstances most likely to prove influential,

and which ought to be observed; 4thly, To call for their transmission

to a common centre.

CHAP. V.

OF THE CLASSIFICATION OF NATURAL OBJECTS AND PHENOMENA, AND OF

NOMENCLATURE.

(129.) The number and variety of objects and relations which the

observation of nature brings before us are so great as to distract

the attention, unless assisted and methodized by such judicious

distribution of them in classes as shall limit our view to a few at

a time, or to groups so bound together by general resemblances that,

for the immediate purpose for which we consider them, they may be

regarded as individuals. Before we can enter into any thing which

deserves to be called a general and systematic view of nature, it is

necessary that we should possess an enumeration, if not complete, at

least of considerable extent, of her materials and combinations; and

that those which appear in any degree important should be distinguished

by names which may not only tend to fix them in our recollection,

but may constitute, as it were, nuclei or centres, about which

information may collect into masses. The imposition of a name on any

subject of contemplation, be it a material object, a phenomenon of

nature, or a group of facts and relations, looked upon in a peculiar

point of view, is an epoch in its history of great importance. It not

only enables us readily to refer to it in conversation or writing,

without circumlocution, but, what is of more consequence, it gives

it a recognized existence in our own minds, as a matter for separate

and peculiar consideration; places it on a list for examination;

and renders it a head or title, under which information of various

descriptions may be arranged; and, in consequence, fits it to perform

the office of a connecting link between all the subjects to which such

information may refer.

(130.) For these purposes, however, a temporary or provisional name,

or one adapted for common parlance, may suffice. But when a very great

multitude of objects come to be referred to one class, especially of

such as do not offer very obvious and remarkable distinctions, a more

systematic and regular nomenclature becomes necessary, in which the

names shall recall the differences as well as the resemblances between

the individuals of a class, and in which the direct relation between

the name and the object shall materially assist the solution of the

problem, “_given the one, to determine the other_.” How necessary

this may become, will be at once seen, when we consider the immense

number of individual objects, or rather species, presented by almost

every branch of science of any extent; which absolutely require to be

distinguished by names. Thus, the botanist is conversant with from

80,000 to 100,000 species of plants; the entomologist with, perhaps,

as many, of insects: the chemist has to register the properties of

combinations, by twos, threes, fours, and upwards, in various doses

of upwards of fifty different elements, all distinguished from each

other by essential differences; and of which though a great many

thousands are known, by far the greater part have never yet been

formed, although hundreds of new ones are coming to light, in perpetual

succession, as the science advances; all of which are to be named as

they arise. The objects of astronomy are, literally, as numerous as the

stars of heaven; and although not more than one or two thousand require

to be expressed by distinct names, yet the number, respecting which

particular information is required, is not less than a hundred times

that amount; and all these must be registered in lists, (so as to be

at once referred to, and so that none shall escape,) if not by actual

names, at least by some equivalent means.

(131.) Nomenclature, then, is, in itself, undoubtedly an important

part of science, as it prevents our being lost in a wilderness of

particulars, and involved in inextricable confusion. Happily, in those

great branches of science where the objects of classification are most

numerous, and the necessity for a clear and convenient nomenclature

most pressing, no very great difficulty in its establishment is felt.

The very multitude of the objects themselves affords the power of

grouping them in subordinate classes, sufficiently well defined to

admit of names, and these again into others, whose names may become

attached to, or compounded with, the former, till at length the

particular species is identified. The facility with which the botanist,

the entomologist, or the chemist, refers by name to any individual

object in his science shows what may be accomplished in this way

when characters are themselves distinct. In other branches, however,

considerable difficulty is experienced. This arises mostly where the

species to be distinguished are separated from each other chiefly by

difference in degree, of certain qualities common to all, and where the

degrees shade into each other insensibly. Perhaps such subjects can

hardly be considered ripe for systematic nomenclature; and that the

attempt to apply it ought only to be partial, embracing such groups

and parcels of individuals as agree in characters evidently natural

and generic, and leaving the remainder under trivial or provisional

denominations, till they shall be better known, and capable of being

scientifically grouped.

(132.) Indeed, nomenclature, in a systematic point of view, is as

much, perhaps more, a consequence than a cause of extended knowledge.

Any one may give an arbitrary name to a thing, merely to be able to

talk of it; but, to give a name which shall at once refer it to a

place in a system, we must know its properties; and we must _have_ a

system, large enough, and regular enough, to receive it in a place

which belongs to it, and to no other. It appears, therefore, doubtful

whether it is desirable, for the essential purposes of science, that

extreme refinement in systematic nomenclature should be insisted on.

Were science perfect, indeed, systems of classification might be

agreed on, which should assign to every object in nature a place in

some class, to which it more remarkably and pre-eminently belonged

than to any other, and under which it might acquire a name, never

afterwards subject to change. But, so long as this is not the case,

and new relations are daily discovered, we must be very cautious how

we insist strongly on the establishment and extension of classes

which have in them any thing artificial, as a basis of a rigid

nomenclature; and especially how we mistake the means for the end, and

sacrifice convenience and distinctness to a rage for arrangement. Every

nomenclature dependent on artificial classifications is necessarily

subject to fluctuations; and hardly any thing can counterbalance the

evil of disturbing well-established names, which have once acquired a

general circulation. In nature, one and the same object makes a part of

an infinite number of different systems,--an individual in an infinite

number of groups, some of greater, some of less importance, according

to the different points of view in which they may be considered. Hence,

as many different systems of nomenclature may be imagined as there can

be discovered different heads of classification, while yet it is highly

desirable that each object should be universally spoken of under one

name, _if possible_. Consequently, in all subjects where comprehensive

heads of classification do not prominently offer themselves, all

nomenclature must be a balance of difficulties, and a good, short,

_unmeaning_ name, which has once obtained a footing in usage, is

preferable to almost any other.

(133.) There is no science in which the evils resulting from a rage for

nomenclature have been felt to such an extent as in mineralogy. The

number of simple minerals actually recognised by mineralogists does not

exceed a few hundreds, yet there is scarcely one which has not four or

five names in different books. The consequence is most unhappy. No name

is suffered to endure long enough to take root; and every new writer

on this interesting science begins, as a matter of course, by making a

_tabula rasa_ of all former nomenclature, and proposing a new one in

its place. The climax has at length been put to this most inconvenient

and bewildering state of things by the appearance of a system supported

by extraordinary merit in other respects, and therefore carrying

the highest authority, in which names which had acquired universal

circulation, and had hitherto maintained their ground in the midst of

the general confusion, and even worked their way into common language,

as denotive of _species_ too definite to admit of mistake, are actually

rendered _generic_, and extended to whole groups, comprising objects

agreeing in nothing but the arbitrary heads of a classification

from which the most important natural relations are professedly and

purposely rejected.[38]

(134.) The classifications by which science is advanced, however, are

widely different from those which serve as bases for artificial systems

of nomenclature. They cross and intersect one another, as it were, in

every possible way, and have for their very aim to interweave all the

objects of nature in a close and compact web of mutual relations and

dependence. As soon, then, as any resemblance or analogy, any point of

agreement whatever, is perceived between any two or more things,--be

they what they will, whether objects, or phenomena, or laws,--they

immediately and _ipso facto_ constitute themselves into a group or

class, which may become enlarged to any extent by the accession of

such new objects, phenomena, or laws, agreeing in the same point, as

may come to be subsequently ascertained. It is thus that the materials

of the world become grouped in natural families, such as chemistry

furnishes examples of, in its various groups of acids, alkalies,

sulphurets, &c.; or botany, in its euphorbiaceæ, umbelliferæ, &c. It is

thus, too, that phenomena assume their places under general points of

resemblance; as, in optics, those which refer themselves to the class

of periodic colours, double refraction, &c.; and that resemblances

themselves become traced, which it is the business of induction to

generalize and include in abstract propositions.

(135.) But every class formed on a positive resemblance of characters,

or on a distinct analogy, draws with it the consideration of a negative

class, in which that resemblance either does not subsist at all, or the

contrary takes place; and again, there are classes in which a given

quality is possessed by the different individuals in a descending scale

of intensity. Now, it is of consequence to distinguish between cases

in which there is a real opposition of quality, or a mere diminution

of intensity, in some quality susceptible of degrees, till it becomes

imperceptible. For example, between transparency and opacity there

would at first sight appear a direct opposition; but, on nearer

consideration, when we consider the gradations by which transparency

diminishes in natural substances, we shall see reason to admit that

the latter quality, instead of being the _opposite_ of the former,

is only its _extreme lowest degree_. Again, in the arrangement of

natural objects under the head of weight or specific gravity, the scale

extends through all nature, and we know of no natural body in which the

opposite of gravity, or positive _levity_, subsists. On the other hand,

the opposite electricities; the north and south magnetic polarities;

the alkaline and acid qualities of chemical agents; the positive and

negative rotations impressed by plates of rock crystal on the planes

of polarization of the rays of light, and many other cases, exemplify

not merely a negation, but an active opposition of quality. Both these

modes of classification have their peculiar importance in the inductive

process: the one, as affording an opportunity of tracing a relation

between phenomena by the observation of a correspondence in their

scales of intensity; the other, by that of contrast, as we shall show

more at large in the next section.

(136.) There is a very wide distinction, too, to be taken between such

classes as turn upon a single head of resemblance among individuals

otherwise very different, and such as bind together in natural groups,

by a great variety of analogies, objects which yet differ in many

remarkable particulars. For example: if we make colourless transparency

a head of classification, the list of the class will comprise objects

differing most widely in their nature, such as water, air, diamond,

spirit of wine, glass, &c. On the other hand, the chemical families of

alkalies, metals, &c. are instances of groups of the other kind; which,

with properties in many respects different, still agree in a general

resemblance of several others, which at once decides us in considering

them as having a natural relation. In the former cases, our ingenuity

is exercised to determine what can be the cause of their resemblance,

in the latter, of their difference; the former belong to the province

of inductive generalization, and afford the most instructive cases for

the investigation of causes; the latter appertain to the more secret

recesses of nature; the very existence of such families being in itself

one of the great and complicated phenomena of the universe, which we

cannot hope to unriddle without an intimate and extensive acquaintance

with the highest laws.[39]

CHAP. VI.

OF THE FIRST STAGE OF INDUCTION.--THE DISCOVERY OF PROXIMATE

CAUSES, AND LAWS OF THE LOWEST DEGREE OF GENERALITY, AND THEIR

VERIFICATION.

(137.) The first thing that a philosophic mind considers, when any

new phenomenon presents itself, is its _explanation_, or reference

to an immediate producing cause. If that cannot be ascertained, the

next is to _generalize_ the phenomenon, and include it, with others

analogous to it, in the expression of some law, in the hope that its

consideration, in a more advanced state of knowledge, may lead to the

discovery of an adequate proximate cause.

(138.) Experience having shown us the manner in which one phenomenon

depends on another in a great variety of cases, we find ourselves

provided, as science extends, with a continually increasing stock

of such antecedent phenomena, or causes (meaning at present merely

proximate causes), competent, under different modifications, to the

production of a great multitude of effects, besides those which

originally led to a knowledge of them. To such causes Newton has

applied the term _veræ causæ_; that is, causes recognized as having a

real existence in nature, and not being mere hypotheses or figments

of the mind. To exemplify the distinction:--The phenomenon of shells

found in rocks, at a great height above the sea, has been attributed

to several causes. By some it has been ascribed to a plastic virtue in

the soil; by some, to fermentation; by some, to the influence of the

celestial bodies; by some, to the casual passage of pilgrims with their

scallops; by some, to birds feeding on shell-fish; and by all modern

geologists, with one consent, to the life and death of real mollusca

at the bottom of the sea, and a subsequent alteration of the relative

level of the land and sea. Of these, the plastic virtue and celestial

influence belong to the class of figments of fancy. Casual transport

by pilgrims is a real cause, and might account for a few shells here

and there dropped on frequented passes, but is not extensive enough for

the purpose of explanation. Fermentation, generally, is a real cause,

so far as that there _is such a thing_; but it is not a real cause

of the production of a shell in a rock, since no such thing was ever

witnessed as one of its effects, and rocks and stones do not ferment.

On the other hand, for a shell-fish dying at the bottom of the sea to

leave his shell in the mud, where it becomes silted over and imbedded,

happens daily; and the elevation of the bottom of the sea to become dry

land has really been witnessed so often, and on such a scale, as to

qualify it for a _vera causa_ available in sound philosophy.

(139.) To take another instance, likewise drawn from the same

deservedly popular science:--The fact of a great change in the general

climate of large tracts of the globe, if not of the whole earth,

and of a diminution of general temperature, having been recognised

by geologists, from their examination of the remains of animals and

vegetables of former ages enclosed in the strata, various causes for

such diminution of temperature have been assigned. Some consider

the whole globe as having gradually cooled from absolute fusion;

some regard the immensely superior activity of former volcanoes, and

consequent more copious communication of internal heat to the surface,

in former ages, as the cause. Neither of these can be regarded as

real causes in the sense here intended; for we do not _know_ that the

globe has so cooled from fusion, nor are we sure that such supposed

greater activity of former than of present volcanoes really did exist.

A cause, possessing the essential requisites of a _vera causa_, has,

however, been brought forward[40] in the varying influence of the

distribution of land and sea over the surface of the globe: a change

of such distribution, in the lapse of ages, by the degradation of the

old continents, and the elevation of new, being a demonstrated fact;

and the influence of such a change on the climates of particular

regions, if not of the whole globe, being a perfectly fair conclusion,

from what we know of continental, insular, and oceanic climates by

actual observation. Here, then, we have, at least, a cause on which a

philosopher may consent to reason; though, whether the changes actually

going on are such as to warrant the whole extent of the conclusion,

or are even taking place in the right direction, may be considered as

undecided till the matter has been more thoroughly examined.

(140.) To this we may add another, which has likewise the essential

characters of a _vera causa_, in the astronomical _fact_ of the actual

slow diminution of the eccentricity of the earth’s orbit round the

sun; and which, as a general one, affecting the _mean temperature of

the whole globe_, and as one of which the effect is both inevitable,

and susceptible, to a certain degree, of exact estimation, deserves

consideration. It is evident that the _mean_ temperature of the

whole surface of the globe, in so far as it is maintained by the

action of the sun at a higher degree than it would have were the sun

extinguished, must depend on the mean quantity of the sun’s rays which

it receives, or, which comes to the same thing, on the _total_ quantity

received in a given invariable time: and the length of the year

being unchangeable in all the fluctuations of the planetary system,

it follows, that the total _annual_ amount of solar radiation will

determine, _cæteris paribus_, the general climate of the earth. Now,

it is not difficult to show that this amount is inversely proportional

to the minor axis of the ellipse described by the earth about the

sun, regarded as slowly variable; and that, therefore, the major axis

remaining, as we know it to be, constant, and the orbit being actually

in a state of approach to a circle, and, consequently, the minor axis

being on the _increase_, the mean annual amount of solar radiation

received by the whole earth must be actually on the _decrease_. We have

here, therefore, an evident real cause, of sufficient universality, and

acting _in the right direction_, to account for the phenomenon. Its

adequacy is another consideration.[41]

(141.) Whenever, therefore, any phenomenon presents itself for

explanation, we naturally seek, in the first instance, to refer it to

some one or other of those real causes which experience has shown to

exist, and to be efficacious in producing similar phenomena. In this

attempt our probability of success will, of course, mainly depend,

1st, On the number and variety of causes experience has placed at our

disposal; 2dly, On our habit of applying them to the explanation of

natural phenomena; and, 3dly, On the number of analogous phenomena

we can collect, which have either been explained, or which admit of

explanation by some one or other of those causes, and the closeness of

their analogy with that in question.

(142.) Here, then, we see the great importance of possessing a stock

of analogous instances or phenomena which class themselves with that

under consideration, the explanation of one among which may naturally

be expected to lead to that of all the rest. If the analogy of two

phenomena be very close and striking, while, at the same time, the

cause of one is very obvious, it becomes scarcely possible to refuse

to admit the action of an analogous cause in the other, though not so

obvious in itself. For instance, when we see a stone whirled round in a

sling, describing a circular orbit round the hand, keeping the string

stretched, and flying away the moment it breaks, we never hesitate

to regard it as retained in its orbit by the tension of the string,

that is, by _a force_ directed to the centre; for we feel that we do

really exert such a force. We have here _the direct perception_ of the

cause. When, therefore, we see a great body like the moon circulating

round the earth and not flying off, we cannot help believing it to

be prevented from so doing, not indeed by a material tie, but by

that which operates in the other case through the intermedium of the

string,--a _force_ directed constantly to the centre. It is thus that

we are continually acquiring a knowledge of the existence of causes

acting under circumstances of such concealment as effectually to

prevent their direct discovery.

(143.) In general we must observe that motion, wherever produced or

changed, invariably points out the existence of _force_ as its cause;

and thus the forces of nature become known and measured by the

motions they produce. Thus, the _force_ of magnetism becomes known by

the deviation produced by iron in a compass needle, or by a needle

leaping up to a magnet held over it, as certainly as by that adhesion

to it, when in contact and at rest, which requires force to break the

connection; and thus the currents produced in the surface of a quantity

of quicksilver, electrified under a conducting fluid, have pointed out

the existence and direction of forces of enormous intensity developed

by the electric circuit, of which we should not otherwise have had the

least suspicion.[42]

(144.) But when the cause of a phenomenon neither presents itself

obviously on the consideration of the phenomenon itself, nor is as it

were forced on our attention by a case of strong analogy, such as above

described, we have then no resource but in a deliberate assemblage of

all the parallel instances we can muster; that is, to the formation

of a class of facts, having the phenomenon in question for a head of

classification; and to a search among the individuals of this class

for some other common points of agreement, among which the cause will

of necessity be found. But if more than one cause should appear, we

must then endeavour to find, or, if we cannot find, to _produce, new

facts_, in which each of these in succession shall be wanting, while

yet they agree in the general point in question. Here we find the use

of what Bacon terms “_crucial instances_,” which are phenomena brought

forward to decide between two causes, each having the same analogies in

its favour. And here, too, we perceive the utility of _experiment_ as

distinguished from mere passive observation. We make an experiment of

the crucial kind when we form combinations, and put in action causes

from which some particular one shall be deliberately excluded, and

some other purposely admitted; and by the agreement or disagreement of

the resulting phenomena with those of the class under examination, we

decide our judgment.

(145.) When we would lay down general rules for guiding and

facilitating our search, among a great mass of assembled facts, for

their common cause, we must have regard to the characters of that

relation which we intend by cause and effect. Now, these are,--

1st, Invariable connection, and, in particular, invariable

antecedence of the cause and consequence of the effect, unless

prevented by some counteracting cause. But it must be observed,

that, in a great number of natural phenomena, the effect is

produced gradually, while the cause often goes on increasing in

intensity; so that the antecedence of the one and consequence

of the other becomes difficult to trace, though it really

exists. On the other hand, the effect often follows the cause

so instantaneously, that the interval cannot be perceived. In

consequence of this, it is sometimes difficult to decide, of two

phenomena constantly accompanying one another, which is cause or

which effect.

2d, Invariable negation of the effect with absence of the cause,

unless some other cause be capable of producing the same effect.

3d, Increase or diminution of the effect, with the increased

or diminished intensity of the cause, in cases which admit of

increase and diminution.

4th, Proportionality of the effect to its cause in all cases of

_direct unimpeded_ action.

5th, Reversal of the effect with that of the cause.

(146.) From these characters we are led to the following observations,

which may be considered as so many propositions readily applicable to

particular cases, or rules of philosophizing: we conclude, 1st, That if

in our group of facts there be one in which any assigned peculiarity,

or attendant circumstance, is wanting or opposite, such peculiarity

cannot be the cause we seek.

(147.) 2d, That any circumstance in which all the facts without

exception agree, _may_ be the cause in question, or, if not, at least

a collateral effect of the same cause: if there be but one such point

of agreement, this possibility becomes a certainty; and, on the other

hand, if there be more than one, they may be concurrent causes.

(148.) 3d, That we are not to deny the existence of a cause in favour

of which we have a unanimous agreement of strong analogies, though

it may not be apparent how such a cause can produce the effect, or

even though it may be difficult to conceive its existence under the

circumstances of the case; in such cases we should rather appeal to

experience when possible, than decide _à priori_ against the cause, and

try whether it cannot be made apparent.

(149.) For instance: seeing the sun vividly luminous, every analogy

leads us to conclude it intensely hot. How heat can produce light,

we know not; and how such a heat can be maintained, we can form no

conception. Yet we are not, therefore, entitled to deny the inference.

(150.) 4th, That contrary or opposing facts are equally instructive for

the discovery of causes with favourable ones.

(151.) For instance: when air is confined with moistened iron filings

in a close vessel over water, its bulk is diminished, by a certain

portion of it being abstracted and combining with the iron, producing

_rust_. And, if the remainder be examined, it is found that it will

_not_ support flame or animal life. This contrary fact shows that the

cause of the support of flame and animal life is to be looked for in

that part of the air which the iron abstracts, and which rusts it.

(152.) 5th, That causes will very frequently become obvious, by a

mere arrangement of our facts in the order of intensity in which

some peculiar quality subsists; though not of necessity, because

counteracting or modifying causes may be at the same time in action.

(153.) For example: sound consists in impulses communicated to our ears

by the air. If a series of impulses of equal force be communicated

to it at equal intervals of time, at first in slow succession, and

by degrees more and more rapidly, we hear at first a rattling noise,

then a low murmur, and then a hum, which by degrees acquires the

character of a musical note, rising higher and higher in acuteness,

till its pitch becomes too high for the ear to follow. And from

this correspondence between the pitch of the note and the rapidity

of succession of the impulse, we conclude that our sensation of

the different pitches of musical notes originates in the different

rapidities with which their impulses are communicated to our ears.

(154.) 6th, That such counteracting or modifying causes may subsist

unperceived, and annul the effects of the cause we seek, in instances

which, but for their action, would have come into our class of

favourable facts; and that, therefore, exceptions may often be made

to disappear by removing or allowing for such counteracting causes.

This remark becomes of the greatest importance, when (as is often the

case) a single striking exception stands out, as it were, against an

otherwise unanimous array of facts in favour of a certain cause.

(155.) Thus, in chemistry, the _alkaline_ quality of the alkaline

and earthy bases is found to be due to the presence of oxygen

combined with one or other of a peculiar set of metals. Ammonia is,

however, a violent outstanding exception, such as here alluded to,

being a compound of azote and hydrogen: but there are almost certain

indications that this exception is not a real one, but assumes that

appearance in consequence of some modifying cause not understood.

(156.) 7th, If we can either find produced by nature, or produce

designedly for ourselves, two instances which agree _exactly_ in all

but one particular, and differ in that one, its influence in producing

the phenomenon, if it have any, _must_ thereby be rendered sensible.

If that particular be present in one instance and wanting altogether

in the other, the production or non-production of the phenomenon will

decide whether it be or be not the only cause: still more evidently,

if it be present _contrariwise_ in the two cases, and the effect be

thereby reversed. But if its total presence or absence only produces

a change in the _degree_ or intensity of the phenomenon, we can then

only conclude that it acts as a concurrent cause or condition with

some other to be sought elsewhere. In nature, it is comparatively

rare to find instances pointedly differing in one circumstance and

agreeing in every other; but when we call experiment to our aid, it

is easy to produce them; and this is, in fact, the grand application

of _experiments of enquiry_ in physical researches. They become more

valuable, and their results clearer, in proportion as they possess this

quality (of agreeing exactly in all their circumstances but one), since

the question put to nature becomes thereby more pointed, and its answer

more decisive.

(157.) 8th, If we cannot obtain a complete negative or opposition of

the circumstance whose influence we would ascertain, we must endeavour

to find cases where it varies considerably in degree. If _this_ cannot

be done, we may perhaps be able to weaken or exalt its influence by

the introduction of some fresh circumstance, which, abstractedly

considered, seems _likely_ to produce this effect, and thus obtain

indirect evidence of its influence. But then we are always to remember,

that the evidence so obtained _is_ indirect, and that the new

circumstance introduced _may_ have a direct influence of its own, or

may exercise a modifying one on some _other_ circumstance.

(158.) 9th, Complicated phenomena, in which several causes concurring,

opposing, or quite independent of each other, operate at once, so as to

produce a compound effect, may be simplified by subducting the effect

of all the known causes, as well as the nature of the case permits,

either by deductive reasoning or by appeal to experience, and thus

leaving, as it were, a _residual phenomenon_ to be explained. It is by

this process, in fact, that science, in its present advanced state, is

chiefly promoted. Most of the phenomena which nature presents are very

complicated; and when the effects of all known causes are estimated

with exactness, and subducted, the residual facts are constantly

appearing in the form of phenomena altogether new, and leading to the

most important conclusions.

(159.) For example: the return of the comet predicted by professor

Encke, a great many times in succession, and the general good agreement

of its calculated with its observed place during any one of its periods

of visibility, would lead us to say that its gravitation towards the

sun and planets is the sole and sufficient cause of all the phenomena

of its orbitual motion; but when the effect of this cause is strictly

calculated and subducted from the observed motion, there is found to

remain behind a _residual phenomenon_, which would never have been

otherwise ascertained to exist, which is a small anticipation of the

time of its reappearances or a diminution of its periodic time, which

cannot be accounted for by gravity, and whose cause is therefore to be

enquired into. Such an anticipation would be caused by the resistance

of a medium disseminated through the celestial regions; and as there

are other good reasons for believing this to be a _vera causa_, it has

therefore been ascribed to such a resistance.

(160.) This 9th observation is of such importance in science, that

we shall exemplify it by another instance or two. M. Arago, having

suspended a magnetic needle by a silk thread, and set it in vibration,

observed, that it came much sooner to a state of rest when suspended

over a plate of copper, than when no such plate was beneath it. Now, in

both cases there were two _veræ causæ_ why it _should_ come at length

to rest, viz. the resistance of the air, which opposes, and at length

destroys, all motions performed in it; and the want of perfect mobility

in the silk thread. But the effect of these causes being exactly known

by the observation made in the absence of the copper, and being thus

allowed for and subducted, a _residual_ phenomenon appeared, in the

fact that a retarding influence was exerted by the copper itself;

and this fact, once ascertained, speedily led to the knowledge of

an entirely new and unexpected class of relations. To add one more

instance. If it be true (as M. Fourrier considers it demonstrated to

be) that the celestial regions have a temperature independent of the

sun, not greatly inferior to that at which quicksilver congeals, and

much superior to some degrees of cold which have been artificially

produced, two causes suggest themselves: one is that assigned by the

author above mentioned; the radiation of the stars; another may be

proposed in the ether or elastic medium mentioned in the last section,

which the phenomena of light and the resistance of comets give us

reason to believe fills all space, and which, in analogy to all the

elastic media known, may be supposed to possess a temperature and a

specific heat of its own, which it is capable of communicating to

bodies surrounded by it. Now, if we consider that the heat radiated

by the sun follows the same proportion as its light, and regard it as

reasonable to admit with respect to stellar heat what holds good of

solar; the effect of stellar radiation in maintaining a temperature in

space should be as much inferior to that of the radiation of the sun

as the light of a moonless midnight is to that of an equatorial noon;

that is to say, almost inconceivably smaller. Allowing, then, the full

effect for this cause, there would still remain a great residuum due to

the presence of the ether.

(161.) Many of the new elements of chemistry have been detected in

the investigation of _residual phenomena_. Thus, Arfwedson discovered

lithia by perceiving an _excess of weight_ in the sulphate produced

from a small portion of what he considered as magnesia present in a

mineral he had analysed. It is on this principle, too, that the _small

concentrated residues of great operations_ in the arts are almost

sure to be the lurking places of new chemical ingredients: witness

iodine, brome, selenium, and the new metals accompanying platina in the

experiments of Wollaston and Tennant. It was a happy thought of Glauber

to examine what every body else threw away.

(162.) Finally, we have to observe, that the detection of a _possible_

cause, by the comparison of assembled cases, _must_ lead to one of

two things: either, 1st, The detection of a real cause, and of its

manner of acting, so as to furnish a complete explanation of the facts;

or, 2dly, The establishment of an abstract law of nature, pointing

out two phenomena of a general kind as invariably connected; and

asserting, that where one is, there the other will always be found.

Such invariable connection is itself a phenomenon of a higher order

than any particular fact; and when many such are discovered, we may

again proceed to classify, combine, and examine them, with a view to

the detection of _their_ causes, or the discovery of still more general

laws, and so on without end.

(163.) Let us now exemplify this inductive search for a cause by one

general example: suppose _dew_ were the phenomenon proposed, whose

cause we would know. In the first place, 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. 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: all these instances agree

in one point (Rule 2. § 147.), the coldness of the object dewed, in

comparison with the air in contact with it.

(164.) But, in the case of the night dew, is this a _real cause_--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 analogies are cogent and unanimous; and, therefore, (pursuant to

Rule 3. § 148.) we are not to discard their indications; and, besides,

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, we have _an invariable concomitant_ circumstance:

but is this chill an effect of dew, or its cause? That dews are

accompanied with a chill is a common remark; but vulgar prejudice would

make the cold the _effect_ rather than the cause. We must, therefore,

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 (Rule 4. § 150.), _i. e._ where no dew is produced.

(165.) Now, 1st, 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; which last circumstance (by Rule 1. § 146.)

excludes the _fall_ of moisture from the sky in an invisible form,

which would naturally suggest itself as a cause. 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 (Rule 5. § 152.). Those polished substances are found

to be most strongly dewed which conduct heat worst; while those which

conduct well resist dew most effectually. Here we encounter a _law_

of the first degree of generality. But, if we expose rough surfaces,

instead of polished, we sometimes find this law interfered with

(Rule 5. § 152.). 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 (Rule 7. § 156.), 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: and thus we have detected another law of

the same generality with the former, by a comparison of two classes of

facts, one relating to dew, the other to the radiation of heat from

surfaces. 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, &c. as unfavourable, but those of a loose one,

as cloth, wool, velvet, eiderdown, cotton, &c. as eminently favourable,

to the contraction of dew: and these 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.

(166.) Lastly, among the negative instances, (§ 150.) 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. Here,

then, a cause is distinctly pointed out by its antecedence to the

effect in question (§ 145.). A clear view of the cloudless sky, then,

is an essential condition, or, which comes to the same thing, clouds or

surrounding objects act as _opposing causes_. This is so much the case,

that dew formed in clear intervals will often even evaporate again when

the sky becomes thickly overcast (Rule 4. § 150.).

(167.) When we now come to assemble these partial inductions so as to

raise from them a general conclusion, we consider, 1st, That all the

conclusions we have come to have a reference to that first general

fact--the cooling of the exposed surface of the body dewed below

the temperature of the air. Those surfaces which part with their

heat outwards most readily, and have it supplied from within most

slowly, will, of course, become coldest if there be an opportunity

for their heat to escape, and not be restored to them from without.

Now, a clear sky affords such an opportunity. It is a law well known

to those who are conversant with the nature of heat, that heat is

constantly escaping from _all bodies_ in rays, or by _radiation_, but

is as constantly restored to them by the similar radiation of others

surrounding them. Clouds and surrounding objects therefore act as

opposing causes by replacing the whole or a great part of the heat so

radiated away, which can escape effectually, without being replaced,

only through openings into infinite space. Thus, at length, we arrive

at the general proximate cause of dew, in the cooling of the dewed

surface by radiation faster than its heat can be restored to it, by

communication with the ground, or by counter-radiation; so as to

become colder than the air, and thereby to cause a condensation of its

moisture.

(168.) We have purposely selected this theory of dew, first developed

by the late Dr. Wells, as one of the most beautiful specimens we can

call to mind of inductive experimental enquiry lying within a moderate

compass. It is not possible in so brief a space to do it justice; but

we earnestly recommend his work[43] (a short and very entertaining one)

for perusal to the student of natural philosophy, as a model with which

he will do well to become familiar.

(169.) In the analysis above given, the formation of dew is referred to

two more general phenomena; the radiation of heat, and the condensation

of invisible vapour by cold. The cause of the former is a much higher

enquiry, and may be said, indeed, to be totally unknown; that of the

latter actually forms a most important branch of physical enquiry. In

such a case, when we reason upwards till we reach an ultimate fact, we

regard a phenomenon as fully explained; as we consider the branch of

a tree to terminate when traced to its insertion in the trunk, or a

twig to its junction with the branch; or rather, as a rivulet retains

its importance and its name till lost in some larger tributary, or in

the main river which delivers it into the ocean. This, however, always

supposes that, on a reconsideration of the case, we see clearly how the

admission of such a fact, with all its attendant laws, will perfectly

account for _every particular_--as well those which, in the different

stages of the induction, have led us to a knowledge of it, as those

which we had neglected, or considered less minutely than the rest.

But, had we no previous knowledge of the radiation of heat, this same

induction would have made it known to us, and, duly considered, might

have led to the knowledge of many of its laws.

(170.) In the study of nature, we must not, therefore, be scrupulous

as to _how_ we reach to a knowledge of such general facts: provided

only we verify them carefully when once detected, we must be content

to seize them wherever they are to be found. And this brings us to

consider the _verification_ of inductions.

(171.) If, in our induction, every individual case has actually been

present to our minds, we are sure that it will find itself duly

_represented_ in our final conclusion: but this is impossible for

such cases as were _unknown_ to us, and hardly ever happens even

with all the known cases; for such is the tendency of the human mind

to speculation, that on the least idea of an analogy between a few

phenomena, it leaps forward, as it were, to a cause or law, to the

temporary neglect of all the rest; so that, in fact, almost all our

principal inductions must be regarded as a series of ascents and

descents, and of conclusions from a few cases, verified by trial on

many.

(172.) Whenever, therefore, we think we have been led by induction to

the knowledge of the proximate cause of a phenomenon or of a law of

nature, our next business is to examine deliberately and _seriatim_

all the cases we have collected of its occurrence, in order to satisfy

ourselves that they are explicable by our cause, or fairly included in

the expression of our law: and in case any exception occurs, it must

be carefully noted and set aside for re-examination at a more advanced

period, when, possibly, the cause of exception may appear, and the

exception itself, by allowing for the effect of that cause, be brought

over to the side of our induction; but should exceptions prove numerous

and various in their features, our faith in the conclusion will be

proportionally shaken, and at all events its importance lessened by the

destruction of its universality.