[Note 41\3: B. vii. c. i.]

When it had been proved by Newton that the planets were

really retained in their elliptical orbits by a central

force, his calculations also showed that the above-stated

_law_ of the force must be at least very approximately

correct, since otherwise the aphelia of the orbits could not

be so nearly at rest as they were. Yet when it seemed as if

the motion of the moon's apogee could not be accounted for

without some new supposition, the _à priori_ argument in

favour of the inverse square did not prevent Clairaut from

trying the hypothesis of a small term added to that which

expressed the ancient law: but when, in order to test the

accuracy of this hypothesis, the calculation of the motion

of the moon's apogee was pushed to a greater degree of

exactness than had been obtained before, it was found that

the new term vanished of itself; and that the inverse square

now accounted for the whole of the motion. And thus, as in

the case of the second law of motion, the most scrupulous

examination terminated in showing the simplest rule to be

rigorously true.

3. Similar events occurred in the history of another part of

the law of gravitation: namely, that the attraction is

proportional to the quantity of matter attracted. This part

of the law may also be thus stated, That the weight of

bodies arising from gravity is proportional to their

inertia; and thus, that the _accelerating force_ on all

bodies under the same circumstances is the same. Newton made

experiments which proved this with regard to terrestrial

bodies; for he found that, at the end of equal strings,

balls of all substances, gold, silver, lead, glass, wood,

&c., oscillated in equal times[42\3]. But a few years ago,

doubts {274} arose among the German astronomers whether this

law was rigorously true with regard to the planetary bodies.

Some calculations appeared to prove, that the attraction of

Jupiter as shown by the perturbations which he produces in

the small planets Juno, Vesta, and Pallas, was different

from the attraction which he exerts on his own satellites.

Nor did there appear to these philosophers anything

inconceivable in the supposition that the attraction of a

planet might be thus _elective_. But when Mr. Airy obtained

a more exact determination of the mass of Jupiter, as

indicated by his effect on his satellites, it was found that

this suspicion was unfounded; and that there was, in this

case, no exception to the universality of the rule, that

this cosmical attraction is in the proportion of the

attracted mass.

[Note 42\3: _Prin._ lib. iii. prop. 6.]

4. Again: when it had thus been shown that a mutual

attraction of parts, according to the law above mentioned,

prevailed throughout the extent of the solar system, it

might still be doubted whether the same law extended to

other regions of the universe. It might have been perhaps

imagined that each fixed star had its peculiar law of force.

But the examination of the motions of double stars about

each other, by the two Herschels and others, appears to show

that these bodies describe ellipses as the planets do; and

thus extends the law of the inverse squares to parts of the

universe immeasurably distant from the whole solar system.

5. Since every doubt which has been raised with regard to

the universality and accuracy of the law of gravitation, has

thus ended in confirming the rule, it is not surprizing that

men's minds should have returned with additional force to

those views which had at first represented the law as a

necessary truth, capable of being established by reason

alone. When it had been proved by Newton that gravity is

really a _universal_ attribute of matter as far as we can

learn, his pupils were not content without maintaining it to

be an _essential_ quality. This is the doctrine held by

Cotes in the preface to the second edition of the

_Principia_ (1712): {275} 'Gravity,' he says, 'is a primary

quality of bodies, as extension, mobility, and

impenetrability are.' But Newton himself by no means went so

far. In his second Letter to Bentley (1693), he says, 'You

sometimes speak of gravity as essential and inherent to

matter; pray do not ascribe that notion to me. The cause of

gravity,' he adds, 'I do not pretend to know, and would take

more time to consider of it.'

Cotes maintains his opinion by urging, that we learn by

_experience_ that all bodies possess gravity, and that we do

not learn in any other way that they are extended, moveable,

or solid. But we have already seen, that the ideas of space,

time, and reaction, on which depend extension, mobility, and

solidity, are not results, but conditions, of experience. We

cannot conceive a body except as extended; we cannot

conceive it to exert mechanical action except with some kind

of solidity. But so far as our conceptions of body have

hitherto been developed, we find no difficulty in conceiving

two bodies which do not attract each other.

6. Newton lays down, in the second edition of the

_Principia_, this 'Rule of Philosophizing' (book iii.); that

'The qualities of bodies which cannot be made more or less

intense, and which belong to all bodies on which we are able

to make experiments, are to be held to be qualities of all

bodies in general.' And this Rule is cited in the sixth

Proposition of the Third Book of the _Principia_, (Cor. 2,)

in order to prove that gravity, proportional to the quantity

of matter, may be asserted to be a quality of all bodies

universally. But we may remark that a Rule of

Philosophizing, itself of precarious authority, cannot

authorize us in ascribing universality to an empirical

result. Geometrical and statical properties are seen to be

necessary, and _therefore_ universal: but Newton appears

disposed to assert a like universality of gravity, quite

unconnected with any necessity. It would be a very

inadequate statement, indeed a false representation, of

statical truth, if we were to say, that because every body

which has hitherto been tried _has been found_ to have a

center of gravity, we venture to assert that all bodies

whatever {276} have a center of gravity. And if we are ever

able to assert the absolute universality of the law of

gravitation, we shall have to rest this truth upon the

clearer development of our ideas of matter and force; not

upon a Rule of Philosophizing, which, till otherwise proved,

must be a mere rule of prudence, and which the opponent may

refuse to admit.

7. Other persons, instead of asserting gravity to be in its

own nature essential to matter, have made hypotheses

concerning some mechanism or other, by which this mutual

attraction of bodies is produced[43\3]. Thus the Cartesians

ascribed to a vortex the tendency of bodies to a center;

Newton himself seems to have been disposed to refer this

tendency to the elasticity of an ether; Le Sage propounded a

curious hypothesis, in which this attraction is accounted

for by the impulse of infinite streams of particles flowing

constantly through the universe in all directions. In these

speculations, the force of gravity is resolved into the

pressure or impulse of solids or fluids. On the other hand,

hypotheses have been propounded, in which the solidity, and

other physical qualities of bodies, have been explained by

representing the bodies as a collection of points, from

which points, repulsive, as well as attractive, forces

emanate. This view of the constitution of bodies was

maintained and developed by Boscovich, and is hence termed

'Boscovich's Theory:' and the discussion of it will more

properly come under our review at a future period, when we

speak of the question whether bodies are made up of atoms.

But we may observe, that Newton himself appears to have

inclined, as his followers certainly did, to this mode of

contemplating the physical properties of bodies. In his

Preface to the _Principia_, after speaking of the central

forces which are exhibited in cosmical phenomena, he says:

'Would that we could derive the other phenomena of Nature

from mechanical principles by the same mode of reasoning.

For many things move me {277} so that I suspect all these

phenomena may depend upon certain forces, by which the

particles of bodies, through causes not yet known, are

either impelled to each other and cohere according to

regular figures, or are repelled and recede from each other:

which forces being unknown, philosophers have hitherto made

their attempts upon nature in vain.'

[Note 43\3: See Vince, _Observations on the Hypothesis

respecting Gravitation_, and the Critique of that work,

_Edinb. Rev._ vol. xiii.]

8. But both these hypotheses;--that by which cohesion and

solidity are reduced to attractive and repulsive forces, and

that by which attraction is reduced to the impulse and

pressure of media;--are hitherto merely modes of

representing mechanical laws of nature; and cannot, either

of them, be asserted as possessing any evident truth or

peremptory authority to the exclusion of the other. This

consideration may enable us to estimate the real weight of

the difficulty felt in assenting to the mutual attraction of

bodies not in contact with each other; for it is often urged

that this attraction of bodies at a distance is an absurd

supposition.

The doctrine is often thus stigmatized, both by popular and

by learned writers. It was long received as a maxim in

philosophy (as Monboddo informs us[44\3]), that a body

cannot act _where_ it is not, any more than _when_ it is

not. But to this we reply, that time is a necessary

condition of our conception of causation, in a different

manner from space. The action of force can only be conceived

as taking place in a succession of moments, in each of which

cause and effect immediately succeed each other: and thus

the interval of time between a cause and its remote effect

is filled up by a continuous succession of events connected

by the same chain of causation. But in space, there is no

such visible necessity of continuity; the action and

reaction may take place at a distance from each other; all

that is necessary being that they be equal and opposite.

[Note 44\3: _Ancient Metaphysics_, vol. ii. p. 175.]

Undoubtedly the existence of attraction is rendered more

acceptable to common apprehension by supposing {278} some

intermediate machinery,--a cord, or rod, or fluid,--by which

the forces may be conveyed from one point to another. But

such images are rather fitted to satisfy those prejudices

which arise from the earlier application of our ideas of

force, than to exhibit the real nature of those ideas. If we

suppose two bodies to pull each other by means of a rod or

cord, we only suppose, in addition to those equal and

opposite forces acting upon the two bodies, (which forces

are alone essential to mutual attraction) a certain power of

resisting transverse pressure at every point of the

intermediate line: which additional supposition is entirely

useless, and quite unconnected with the essential conditions

of the case. When the Newtonians were accused of introducing

into philosophy an unknown cause which they termed

_attraction_, they justly replied that they knew as much

respecting attraction as their opponents did about impulse.

In each case we have a knowledge of the conception in

question so far as we clearly apprehend it under the

conditions of those axioms of mechanical causation which

form the basis of our science on such subjects.

Having thus examined the degree of certainty and generality

to which our knowledge of the law of universal gravitation

has been carried, by the progress of mechanical discovery

and speculation up to the present time, we might proceed to

the other branches of science, and examine in like manner

their grounds and conditions. But before we do this, it will

be worth our while to attend for a moment to the effect

which the progress of mechanical ideas among mathematicians

and mechanical philosophers has produced upon the minds of

other persons, who share only in an indirect and derivative

manner in the influence of science.

{{279}}

CHAPTER X.

OF THE GENERAL DIFFUSION OF CLEAR MECHANICAL IDEAS.

1. WE have seen how the progress of knowledge upon the

subject of motion and force has produced, in the course of

the world's history, a great change in the minds of acute

and speculative men; so that such persons can now reason

with perfect steadiness and precision upon subjects on

which, at first, their thoughts were vague and confused; and

can apprehend, as truths of complete certainty and evidence,

laws which it required great labour and time to discover.

This _complete_ development and clear manifestation of

mechanical ideas has taken place only among mathematicians

and philosophers. But yet a progress of thought upon such

subjects,--an advance from the obscure to the clear, and

from errour to truth,--may be traced in the world at large,

and among those who have not directly cultivated the exact

sciences. This diffused and collateral influence of science

manifests itself, although in a wavering and fluctuating

manner, by various indications, at various periods of

literary history. The opinions and reasonings which are put

forth upon mechanical subjects, and above all, the adoption,

into common language, of terms and phrases belonging to the

prevalent mechanical systems, exhibit to us the most

profound discoveries and speculations of philosophers in

their effect upon more common and familiar trains of

thought. This effect is by no means unimportant, and we

shall point out some examples of such indications as we have

mentioned.

2. The discoveries of the ancients in speculative mechanics

were, as we have seen, very scanty; and {280} hardly

extended their influence to the unmathematical world. Yet

the familiar use of the term 'center of gravity' preserved

and suggested the most important part of what the Greeks had

to teach. The other phrases which they employed, as

_momentum_, _energy_, _virtue_, _force_, and the like, never

had any exact meaning, even among mathematicians; and

therefore never, in the ancient world, became the means of

suggesting just habits of thought. I have pointed out, in

the History of Science, several circumstances which appear

to denote the general confusion of ideas which prevailed

upon mechanical subjects during the times of the Roman

empire. I have there taken as one of the examples of this

confusion, the fable narrated by Pliny and others concerning

the echineïs, a small fish, which was said to stop a ship

merely by sticking to it[45\3]. This story was adduced as

betraying the absence of any steady apprehension of the

equality of action and reaction; since the fish, except it

had some immoveable obstacle to hold by, must be pulled

forward by the ship, as much as it pulled the ship backward.

If the writers who speak of this wonder had shown any

perception of the necessity of a reaction, either produced

by the rapid motion of the fish's fins in the water, or in

any other way, they would not be chargeable with this

confusion of thought; but from their expressions it is, I

think, evident that they saw no such necessity[46\3]. Their

idea of mechanical action was not sufficiently distinct to

enable them to see the absurdity of {281} supposing an

intense pressure with no obstacle for it to exert itself

against.

[Note 45\3: _Hist. Ind. Sc._ b. iv. c. i. sect. 2.]

[Note 46\3: See Prof. Powell, _On the Nature and Evidence of

the Laws of Motion_. _Reports of the Ashmolean Society_.

Oxford. 1837. Professor Powell has made an objection to my

use of this instance of confusion of thought; the remark in

the text seems to me to justify what I said in the History.

As an evidence that the fish was not supposed to produce its

effect by its muscular power acting on the water, we may

take what Pliny says, _Nat. Hist._ xxxii. 1, 'Domat mundi

rabiem, nullo suo labore; non retinendo, aut alio modo quam

adhærendo:' and also what he states in another place (ix.

41), that when it is preserved in pickle, it may be used in

recovering gold which has fallen into a deep well. All this

implies adhesion alone, with no conception of reaction.]

3. We may trace, in more modern times also, indications of a

general ignorance of mechanical truths. Thus the phrase of

shooting at an object 'point-blank,' implies the belief that

a cannon-ball describes a path of which the first portion is

a straight line. This errour was corrected by the true

mechanical principles which Galileo and his followers

brought to light; but these principles made their way to

popular notice, principally in consequence of their

application to the motions of the solar system, and to the

controversies which took place respecting those motions.

Thus by far the most powerful argument against the reception

of the Copernican system of the universe, was that of those

who asked, Why a stone dropt from a tower was not left

behind by the motion of the earth? The answer to this

question, now universally familiar, involves a reference to

the true doctrine of the composition of motions. Again;

Kepler's persevering and strenuous attempts[47\3] to frame a

physical theory of the universe were frustrated by his

ignorance of the first law of motion, which informs us that

a body will retain its velocity without any maintaining

force. He proceeded upon the supposition that the sun's

force was requisite to _keep up_ the motion of the planets,

as well as to deflect and modify it; and he was thus led to

a system which represented the sun as carrying round the

planets in their orbits by means of a _vortex_, produced by

his revolution. The same neglect of the laws of motion

presided in the formation of Descartes' system of vortices.

Although Descartes had enunciated in words the laws of

motion, he and his followers showed that they had not the

practical habit of referring to these mechanical principles;

and dared not trust the planets to move in free space

without some surrounding machinery to support them[48\3].

[Note 47\3: _Hist. Ind. Sc._ b. v. c. iv. and b. vii. c. i.]

[Note 48\3: I have, in the History, applied to Descartes the

character which Bacon gives to Aristotle, 'Audax simul et

pavidus:' though he was bold enough to enunciate the laws of

motion without knowing them aright, he had not the courage

to leave the planets to describe their orbits by the agency

of those laws, without the machinery of contact.]

{282} 4. When at last mathematicians, following Newton, had

ventured to consider the motion of each planet as a

mechanical problem not different in its nature from the

motion of a stone cast from the hand; and when the solution

of this problem and its immense consequences had become

matters of general notoriety and interest; the new views

introduced, as is usual, new terms, which soon became

extensively current. We meet with such phrases as 'flying

off in the tangent,' and 'deflexion from the tangent;' with

antitheses between 'centripetal' and 'centrifugal force,' or

between 'projectile' and 'central force.' 'Centers of

force,' 'disturbing forces,' 'perturbations,' and

'perturbations of higher orders,' are not unfrequently

spoken of: and the expression 'to gravitate,' and the term

'universal gravitation,' acquired a permanent place in the

language.

Yet for a long time, and even up to the present day, we find

many indications that false and confused apprehensions on

such subjects are by no means extirpated. Arguments are

urged against the mechanical system of the universe,

implying in the opponents an absence of all clear mechanical

notions. Many of this class of writers retrograde to

Kepler's point of view. This is, for example, the case with

Lord Monboddo, who, arguing on the assumption that force is

requisite to maintain, as well as to deflect motion,

produced a series of attacks upon the Newtonian philosophy;

which he inserted in his _Ancient Metaphysics_, published in

1779 and the succeeding years. This writer (like Kepler),

measures force by the velocity which the body _has_[49\3],

not by that which it _gains_. Such a use of language would

prevent our obtaining any laws of motion at all.

Accordingly, the author, in the very next page to that which

I have just quoted, abandons this measure of force, and, in

curvilinear motion, measures {283} force by 'the fall from

the extremity of the arc.' Again; in his objections to the

received theory, he denies that curvilinear motion is

compounded, although his own mode of considering such motion

assumes this composition in the only way in which it was

ever intended by mathematicians. Many more instances might

be adduced to show that a want of cultivation of the

mechanical ideas rendered this philosopher incapable of

judging of a mechanical system.

[Note 49\3: _Anc. Met._ vol. ii. b. v. c. vi. p. 413.]

The following extract from the _Ancient Metaphysics_, may be

sufficient to show the value of the author's criticism on

the subjects of which we are now speaking. His object is to

prove that there do not exist a centripetal and a

centrifugal force in the case of elliptical motion. 'Let any

man move in a circular or elliptical line described to him;

and he will find no tendency in himself either to the center

or from it, much less both. If indeed he attempt to make the

motion with great velocity, or if he do it carelessly and

inattentively, he may go out of the line, either towards the

center or from it: but this is to be ascribed, not to the

nature of the motion, but to our infirmity; or perhaps to

the animal form, which is more fitted for progressive motion

in a right line than for any kind of curvilinear motion. But

this is not the case with a sphere or spheroid, which is

equally adapted to motion in all directions[50\3].' We need

hardly remind the reader that the manner in which a man

running round a small circle, finds it necessary to lean

inwards, in order that there may be a centripetal

inclination to counteract the centrifugal force, is a

standard example of our mechanical doctrines; and this fact

(quite familiar in practice as well as theory) is in direct

contradiction of Lord Monboddo's assertion.

[Note 50\3: _Anc. Met._ vol. i. b. ii. c. 19, p. 264.]

5. A similar absence of distinct mechanical thought appears

in some of the most celebrated metaphysicians of Germany. I

have elsewhere noted[51\3] the opinion expressed by Hegel,

that the glory which belongs to {284} Kepler has been

unjustly transferred to Newton; and I have suggested, as the

explanation of this mode of thinking, that Hegel himself, in

the knowledge of mechanical truth, had not advanced beyond

Kepler's point of view. Persons who possess conceptions of

space and number, but who have not learnt to deal with ideas

of force and causation, may see more value in the

discoveries of Kepler than in those of Newton. Another

exemplification of this state of mind may be found in

Professor Schelling's speculations; for instance, in his

_Lectures on the Method of Academical Study_. In the twelfth

Lecture, on the study of Physics and Chemistry, he says, (p.

266,) 'What the mathematical natural philosophy has done for

the knowledge of the laws of the universe since the time

that they were discovered by his (Kepler's) godlike genius,

is, as is well known, this: it has attempted a construction

of those laws which, according to its foundations, is

altogether empirical. We may assume it as a general rule,

that in any proposed construction, that which is not a pure

general form cannot have any scientific import or truth. The

foundation from which the centrifugal motion of the bodies

of the world is derived, is no necessary form, it is an

empirical fact. The Newtonian attractive force, even if it

be a necessary assumption for a merely reflective view of

the subject, is still of no significance for the Reason,

which recognizes only absolute relations. The grounds of the

Keplerian laws can be derived, without any empirical

appendage, purely from the doctrine of Ideas, and of the two

Unities, which are in themselves one Unity, and in virtue of

which each being, while it is absolute in itself, is at the

same time in the absolute, and reciprocally.'

[Note 51\3: _Hist. Ind. Sc._ b. vii. c. ii. sect. 5.]

It will be observed, that in this passage our mechanical

laws are objected to because they are not necessary results

of our ideas; which, however, as we have seen, according to

the opinion of some eminent mechanical philosophers, they

are. But to assume this evident necessity as a condition of

every advance in science, is to mistake the last, perhaps

unattainable step, for the first, which lies before our

feet. And, {285} without inquiring further about 'the

Doctrine of the two Unities,' or the manner in which from

that doctrine we may deduce the Keplerian laws, we may be

well convinced that such a doctrine cannot supply any

sufficient reason to induce us to quit the inductive path by

which all scientific truth up to the present time has been

acquired.

6. But without going to schools of philosophy opposed to the

Inductive School, we may find many loose and vague habits of

thinking on mechanical subjects among the common classes of

readers and reasoners. And there are some familiar modes of

employing the phraseology of mechanical science, which are,

in a certain degree, chargeable with inaccuracy, and may

produce or perpetuate confusion. Among such cases we may

mention the way in which the centripetal and centrifugal

forces, and also the projectile and central forces of the

planets, are often compared or opposed. Such antitheses

sometimes proceed upon the false notion that the two members

of these pairs of forces are of the same kind: whereas on

the contrary the _projectile_ force is a hypothetical

impulsive force which may, at some former period, have

caused the motion to begin; while the _central_ force is an

actual force, which must act continuously and during the

whole time of the motion, in order that the motion may go on

in the curve. In the same manner the _centrifugal_ force is

not a distinct force in a strict sense, but only a certain

result of the first law of motion, measured by the portion

of _centripetal_ force which counteracts it. Comparisons of

quantities so heterogeneous imply confusion of thought, and

often suggest baseless speculations and imagined reforms of

the received opinions.

7. I might point out other terms and maxims, in addition to

those already mentioned, which, though formerly employed in

a loose and vague manner, are now accurately understood and

employed by all just thinkers; and thus secure and diffuse a

right understanding of mechanical truths. Such are

_momentum_, _inertia_, _quantity of matter_, _quantity of

motion_; that _force is proportional to its effects_; that

_action and_ {286} _reaction are equal_; that _what is

gained in force by machinery is lost in time_; that _the

quantity of motion in the world cannot be either increased

or diminished_. When the expression of the truth thus

becomes easy and simple, clear and convincing, the meanings

given to words and phrases by discoverers glide into the

habitual texture of men's reasonings, and the effect of the

establishment of true mechanical principles is felt far from

the school of the mechanician. If these terms and maxims are

understood with tolerable clearness, they carry the

influence of truth to those who have no direct access to its

sources. Many an extravagant project in practical machinery,

and many a wild hypothesis in speculative physics, has been

repressed by the general currency of such maxims as we have

just quoted.

8. Indeed so familiar and evident are the elementary truths

of mechanics when expressed in this simple form, that they

are received as truisms; and men are disposed to look back

with surprise and scorn at the speculations which were

carried on in neglect of them. The most superficial reasoner

of modern times thinks himself entitled to speak with

contempt and ridicule of Kepler's hypothesis concerning the

physical causes of the celestial motions: and gives himself

credit for intellectual superiority, because he sees, as

self-evident, what such a man could not discover at all. It

is well for such a person to recollect, that the real cause

of his superior insight is not the pre-eminence of his

faculties, but the successful labours of those who have

preceded him. The language which he has learnt to use

unconsciously, has been adapted to, and moulded on,

ascertained truths. When he talks familiarly of

"accelerating forces" and "deflexions from the tangent," he

is assuming that which Kepler did not know, and which it

cost Galileo and his disciples so much labour and thought to

establish. Language is often called an instrument of

thought; but it is also the nutriment of thought; or rather,

it is the atmosphere in which thought lives: a medium

essential to the activity of our speculative power, although

invisible {287} and imperceptible in its operation; and an

element modifying, by its qualities and changes, the growth

and complexion of the faculties which it feeds. In this way

the influence of preceding discoveries upon subsequent ones,

of the past upon the present, is most penetrating and

universal, though most subtle and difficult to trace. The

most familiar words and phrases are connected by

imperceptible ties with the reasonings and discoveries of

former men and distant times. Their knowledge is an

inseparable part of ours; the present generation inherits

and uses the scientific wealth of all the past. And this is

the fortune, not only of the great and rich in the

intellectual world: of those who have the key to the ancient

storehouses, and who have accumulated treasures of their

own;--but the humblest inquirer, while he puts his

reasonings into words, benefits by the labours of the

greatest discoverers. When he counts his little wealth, he

finds that he has in his hands coins which bear the image

and superscription of ancient and modern intellectual

dynasties; and that in virtue of this possession,

acquisitions are in his power, solid knowledge within his

reach, which none could ever have attained to, if it were

not that the gold of truth, once dug out of the mine,

circulates more and more widely among mankind.

9. Having so fully examined, in the preceding instances, the

nature of the progress of thought which science implies,

both among the peculiar cultivators of science, and in that

wider world of general culture which receives only an

indirect influence from scientific discoveries, we shall not

find it necessary to go into the same extent of detail with

regard to the other provinces of human knowledge. In the

case of the Mechanical Sciences, we have endeavoured to

show, not only that Ideas are requisite in order to form

into a science the Facts which nature offers to us, but that

we can advance, almost or quite, to a complete

identification of the Facts with the Ideas. In the sciences

to which we now proceed, we shall not seek to fill up the

chasm by which Facts and Ideas are separated; but we shall

endeavour to detect the Ideas which our {288} knowledge

involves, to show how essential these are; and in some

respects to trace the mode in which they have been gradually

developed among men.

10. The motions of the heavenly bodies, their laws, their

causes, are among the subjects of the first division of the

Mechanical Sciences; and of these sciences we formerly

sketched the history, and have now endeavoured to exhibit

the philosophy. If we were to take any other class of

motions, _their_ laws and causes might give rise to sciences

which would be mechanical sciences in exactly the same sense

in which Physical Astronomy is so. The phenomena of magnets,

of electrical bodies, of galvanical apparatus, seem to form

obvious materials for such sciences; and if they were so

treated, the philosophy of such branches of knowledge would

naturally come under our consideration at this point of our

progress.

But on looking more attentively at the sciences of

Electricity, Magnetism, and Galvanism, we discover cogent

reasons for transferring them to another part of our

arrangement; we find it advisable to associate them with

Chemistry, and to discuss their principles when we can

connect them with the principles of chemical science. For

though the first steps and narrower generalizations of these

sciences depend upon mechanical ideas, the highest laws and

widest generalizations which we can reach respecting them,

involve chemical relations. The progress of these portions

of knowledge is in some respects opposite to the progress of

Physical Astronomy. In this, we begin with phenomena which

appear to indicate peculiar and various qualities in the

bodies which we consider, (namely, the heavenly bodies,) and

we find in the end that all these qualities resolve

themselves into one common mechanical property, which exists

alike in all bodies and parts of bodies. On the contrary, in

studying magnetical and electrical laws, we appear at first

to have a single extensive phenomenon, attraction and

repulsion: but in our attempts to generalize this

phenomenon, we find that it is governed by conditions

depending upon something quite separate from the bodies

themselves, upon {289} the presence and distribution of

peculiar and transitory agencies; and, so far as we can

discover, the general laws of these agencies are of a

_chemical_ nature, and are brought into action by peculiar

properties of special substances. In cosmical phenomena,

everything, in proportion as it is referred to mechanical

principles, tends to simplicity,--to permanent uniform

forces,--to one common, positive, property. In magnetical

and electrical appearances, on the contrary, the application

of mechanical principles leads only to a new complexity,

which requires a new explanation; and this explanation

involves changeable and various forces,--gradations and

oppositions of qualities. The doctrine of the universal

gravitation of matter is a simple and ultimate truth, in

which the mind can acquiesce and repose. We rank gravity

among the mechanical attributes of matter, and we see no

necessity to derive it from any ulterior properties. Gravity

belongs to matter, independent of any conditions. But the

_conditions_ of magnetic or electrical activity require

investigation as much as the _laws_ of their action. Of

these conditions no mere mechanical explanation can be

given; we are compelled to take along with us chemical

properties and relations also: and thus magnetism,

electricity, galvanism, are _mechanico-chemical sciences_.

11. Before considering these, therefore, I shall treat of

what I shall call _Secondary Mechanical Sciences_; by which

expression I mean the sciences depending upon certain

qualities which our senses discover to us in

bodies;--_Optics_, which has visible phenomena for its

subject; _Acoustics_, the science of hearing; the doctrine

of _Heat_, a quality which our touch recognizes: to this

last science I shall take the liberty of sometimes giving

the name _Thermotics_, analogous to the names of the other

two. If our knowledge of the phenomena of Smell and Taste

had been successfully cultivated and systematized, the

present part of our work would be the place for the

philosophical discussion of those sensations as the subjects

of science.

The branches of knowledge thus grouped in one class involve

common Fundamental Ideas, from which {290} their principles

are derived in a mode analogous, at least in a certain

degree, to the mode in which the principles of the

mechanical sciences are derived from the fundamental ideas

of causation and reaction. We proceed now to consider these

Fundamental Ideas, their nature, development, and

consequences.

{{291}}

BOOK IV.

THE

PHILOSOPHY

OF THE

SECONDARY

MECHANICAL SCIENCES.

Πάσχοντος γάρ τι τοῦ αἰσθητικοῦ γίνεται τὸ ὁρᾶν· ὑπ' αὐτοῦ

μὲν οὖν τοῦ ὁρωμένου χρώματος ἀδύνατον· λείπεται δὴ ὑπὸ _τοῦ

μεταξύ_, ὥστ' ἀναγκαῖόν τι εἶναι _μεταξύ_· κενοῦ δὲ

γενομένου οὐχ ὅτι ἀκριβῶς, ἀλλ' ὅλως οὐθὲν ὀφθήσεται. δι' ἣν

μὲν οὖν αἰτίαν τὸ χρῶμα ἀναγκαῖον ἐν φωτὶ ὁρᾶσθαι, εἴρηται.

πῦρ δὲ ἐν ἀμφοῖν ὁρᾶται, καὶ ἐν σκότει καὶ ἐν φωτί, καὶ

τοῦτο _ἐξ ἀνάγκης_· τὸ γὰρ διαφανὲς ὑπὸ τούτου γίνεται

διαφανές. ὁ δ' αὐτὸς λόγος καὶ περὶ ψόφου καὶ ὀσμῆς ἐστιν·

οὐθὲν γὰρ αὐτῶν ἁπτόμενον τοῦ αἰσθητηρίου ποιεῖ τὴν

αἴσθησιν, ἀλλ' ὑπὸ μὲν ὀσμῆς καὶ ψόφου _τὸ μεταξὺ_ κινεῖται,

ὑπὸ δὲ τούτου τῶν αἰσθητηρίων ἑκάτερον· ὅταν δ' ἐπ' αὐτό τις

ἐπιθῇ τὸ αἰσθητήριον τὸ ψοφοῦν ἢ τὸ ὄζον, οὐδεμίαν αἴσθησιν

ποιήσει.

ARISTOT. _De Anima_, II. 7.

{{293}} BOOK IV.

THE PHILOSOPHY OF THE SECONDARY MECHANICAL SCIENCES.

CHAPTER I.

OF THE IDEA OF A MEDIUM AS COMMONLY EMPLOYED.

1. _Of Primary and Secondary Qualities._--IN the same way in

which the mechanical sciences depend upon the Idea of Cause,

and have their principles regulated by the development of

that Idea, it will be found that the sciences which have for

their subject Sound, Light, and Heat, depend for _their_

principles upon the Fundamental Idea of Media by means of

which we perceive those qualities. Like the idea of cause,

this idea of a medium is unavoidably employed, more or less

distinctly, in the common, unscientific operations of the

understanding; and is recognized as an express principle in

the earliest speculative essays of man. But here also, as in

the case of the mechanical sciences, the development of the

idea, and the establishment of the scientific truths which

depend upon it, was the business of a succeeding period, and

was only executed by means of long and laborious researches,

conducted with a constant reference to experiment and

observation.

Among the most prominent manifestations of the influence of

the idea of a medium of which we have now to speak, is the

distinction of the qualities of bodies into _primary_, and

_secondary_ qualities. This distinction has {294} been

constantly spoken of in modern times: yet it has often been

a subject of discussion among metaphysicians whether there

be really such a distinction, and what the true difference

is. Locke states it thus[1\4]: Original or Primary qualities

of bodies are 'such as are utterly inseparable from the body

in what estate soever it may be,--such as sense constantly

finds in every particle of matter which has bulk enough to

be perceived, and the mind finds inseparable from every

particle of matter, though less than to make itself singly

perceived by our senses:' and he enumerates them as

solidity, extension, figure, motion or rest, and number.

Secondary qualities, on the other hand, are such 'which in

truth are nothing in the objects themselves, but powers to

produce various sensations in us by their primary qualities,

_i.e._ by the bulk, figure, texture, and motion of their

insensible parts, as colours, sounds, tastes, &c.'

[Note 1\4: _Essay_, b. ii. ch. viii. s. 9, 10.]

Dr. Reid[2\4], reconsidering this subject, puts the

difference in another way. There is, he says, a real

foundation for the distinction of Primary and Secondary

qualities, and it is this: 'That our senses give us a direct

and distinct notion of the primary qualities, and inform us

what they are in themselves; but of the secondary qualities,

our senses give us only a relative and obscure notion. They

inform us only that they are qualities that affect us in a

certain manner, that is, produce in us a certain sensation;

but as to what they are in themselves, our senses leave us

in the dark.'

[Note 2\4: _Essays_, b. ii. c. xvii.]

Dr. Brown[3\4] states the distinction somewhat otherwise. We

give the name of Matter, he observes, to that which has

extension and resistance: these, therefore, are Primary

qualities of matter, because they compose our definition of

it. All other qualities are Secondary, since they are

ascribed to bodies only because we find them associated with

the primary qualities which form our notion of those bodies.

[Note 3\4: _Lectures_, ii. 12.]

{295} It is not necessary to criticize very strictly these

various distinctions. If it were, it would be easy to find

objections to them. Thus Locke, it may be observed, does not

point out any _reason_ for believing that his secondary

qualities are produced by the primary. How are we to learn

that the colour of a rose arises from the bulk, figure,

texture, and motion of its particles? Certainly our senses

do not teach us this; and in what other way, on Locke's

principles, can we learn it? Reid's statement is not more

free from the same objection. How does it appear that our

notion of Warmth is relative to our own sensations more than

our notion of Solidity? And if we take Brown's account, we

may still ask whether our selection of certain qualities to

form our idea and definition of Matter be arbitrary and

without reason? If it be, how can it make a real

distinction? if it be not, what is the reason?

I do not press these objections, because I believe that any

of the above accounts of the distinction of Primary and

Secondary qualities is right in the main, however imperfect

it may be. The difference between such qualities as

Extension and Solidity on the one hand, and Colour or

Fragrance on the other, is assented to by all, with a

conviction so firm and indestructible, that there must be

some fundamental principle at the bottom of the belief,

however difficult it may be to clothe the principle in

words. That successive efforts to express the real nature of

the difference were made by men so clear-sighted and acute

as those whom I have quoted, even if none of them are

satisfactory, shows how strong and how deeply-seated is the

perception of truth which impels us to such attempts.

The most obvious mode of stating the difference of Primary

and Secondary qualities, as it naturally offers itself to

speculative minds, appears to be that employed by Locke,

slightly modified. Certain of the qualities of bodies, as

their bulk, figure, and motion, are perceived immediately in

the bodies themselves. Certain other qualities as sound,

colour, heat, are {296} perceived by means of some medium.

Our conviction that this is the case is spontaneous and

irresistible; and this difference of qualities immediately

and mediately perceived is the distinction of Primary and

Secondary qualities. We proceed further to examine this

conviction.

2. _The Idea of Externality._--In reasoning concerning the

Secondary Qualities of bodies, we are led to assume the

bodies to be external to us, and to be perceived by means of

some Medium intermediate between us and them. These

assumptions are fundamental conditions of perception,

inseparable from perception even in thought.

That objects are _external_ to us, that they are _without_

us, that they have _outness_, is as clear as it is that

these words have any meaning at all. This conviction is,

indeed, involved in the exercise of that faculty by which we

perceive all things as existing in space; for by this

faculty we place ourselves and other objects in one common

space, and thus they are exterior to us. It may be remarked

that this apprehension of objects as external to us,

although it assumes the idea of space, is far from being

implied in the idea of space. The objects which we

contemplate are considered as existing in space, and by that

means become invested with certain mutual relations of

position; but when we consider them as existing without

_us_, we make the additional step of supposing _ourselves_

and the objects to exist in one common space. The question

respecting the Ideal Theory of Berkeley has been mixed up

with the recognition of this condition of the externality of

objects. That philosopher maintained, as is well known, that

the perceptible qualities of bodies have no existence except

in a perceiving mind. This system has often been understood

as if he had imagined the world to be a kind of optical

illusion, like the images which we see when we shut our

eyes, appearing to be without us, though they are only in

our organs; and thus this Ideal System has been opposed to a

belief in an external world. In truth, however, no such

opposition exists. The Ideal System is an attempt to explain

the {297} mental process of perception, and to get over the

difficulty of mind being affected by matter. But the author

of that system did not deny that objects were perceived

under the conditions of space and mechanical

causation;--that they were _external_ and _material_ so far

as those words describe perceptible qualities. Berkeley's

system, however visionary or erroneous, did not prevent his

entertaining views as just, concerning optics or acoustics,

as if he had held any other doctrine of the nature of

perception.

But when Berkeley's theory was understood as a denial of the

existence of objects without us, how was it answered? If we

examine the answers which are given by Reid and other

philosophers to this hypothesis, it will be found that they

amount to this: that objects _are_ without us, since we

_perceive_ that they are so; that we perceive them to be

external, by the same act by which we perceive them to be

objects. And thus, in this stage of philosophical inquiry,

the externality of objects is recognized as one of the

inevitable conditions of our perception of them; and hence

the Idea of Externality is adopted as one of the necessary

foundations of all reasoning concerning all objects

whatever.

3. _Sensation by a Medium._--Objects, as we have just seen,

are necessarily apprehended as _without_ us; and in general,

as removed from us by a great or small distance. Yet they

affect our bodily senses; and this leads us irresistibly to

the conviction that they are perceived by means of something

intermediate. Vision, or hearing, or smell, or the warmth of

a fire, must be communicated to us by some Medium of

Sensation. This unavoidable belief appears in all attempts,

the earliest and the latest alike, to speculate upon such

subjects. Thus, for instance, Aristotle says[4\4], 'Seeing

takes place in virtue of some action which the sentient

organ suffers: now it cannot suffer action from the colour

of the object directly: the only remaining possible case

then is, that it is acted upon by an {298} intervening

Medium; there must then be an intervening Medium.' 'And the

same may be said,' he adds, 'concerning sounding and odorous

bodies; for these do not produce sensation by touching the

sentient organ, but the intervening Medium is acted on by

the sound or the smell, and the proper organ, by the Medium

... In sound the Medium is air; in smell we have no name for

it.' In the sense of taste, the necessity of a Medium is not

at first so obviously seen, because the object tasted is

brought into contact with the organ; but a little attention

convinces us that the taste of a solid body can only be

perceived when it is conveyed in some liquid vehicle. Till

the fruit is crushed, and till its juices are pressed out,

we do not distinguish its flavour. In the case of heat, it

is still more clear that we are compelled to suppose some

invisible fluid, or other means of communication, between

the distant body which warms us and ourselves.

[Note 4\4: Περὶ Ψυχῆς. ii. 7. See the motto to this Book.]

It may appear to some persons that the assumption of an

intermedium between the object perceived and the sentient

organ results from the principles which form the basis of

our mechanical reasonings,--that every change must have a

cause, and that bodies can act upon each other only by

contact. It cannot be denied that this principle does offer

itself very naturally as the ground of our belief in media

of sensation; and it appears to be referred to for this

purpose by Aristotle in the passage quoted above. But yet we

cannot but ask, Does the principle, that matter produces its

effect by contact only, manifestly apply here? When we so

apply it, we include _sensation_ among the _effects_ which

material contact produces;--a case so different from any

merely mechanical effect, that the principle, so employed,

appears to acquire a new signification. May we not, then,

rather say that we have here a new axiom,--That sensation

implies a material cause immediately acting on the

organ,--than a new application of our former

proposition,--That all mechanical change implies contact?

The solution of this doubt is not of any material

consequence to our reasonings; for whatever be the {299}

ground of the assumption, it is certain that we do assume

the existence of media by which the sensations of sight,

hearing, and the like, are produced; and it will be seen

shortly that principles inseparably connected with this

assumption are the basis of the sciences now before us.

This assumption makes its appearance in the physical

doctrines of all the schools of philosophy. It is exhibited

perhaps most prominently in the tenets of the Epicureans,

who were materialists, and extended to all kinds of

causation the axiom of the existence of a corporeal

mechanism by which alone the effect is produced. Thus,

according to them, vision is produced by certain images or

material films which flow from the object, strike upon the

eyes, and so become sensible. This opinion is urged with

great detail and earnestness by Lucretius, the poetical

expositor of the Epicurean creed among the Romans. His

fundamental conviction of the necessity of a material medium

is obviously the basis of his reasoning, though he attempts

to show the existence of such a medium by facts. Thus he

argues[5\4], that by shouting loud we make the throat sore;

which shows, he says, that the voice must be material, so

that it can hurt the passage in coming out.

Haud igitur dubium est quin voces verbaque constent

Corporeis e principiis ut lædere possint.

[Note 5\4: _De Rerum Naturâ_, Lib. iv. 529.]

4. _The Process of Perception of Secondary Qualities._--The

likenesses or representatives of objects by which they

affect our senses were called by some writers _species_, or

_sensible species_, a term which continued in use till the

revival of science. It may be observed that the conception

of these _species_ as films cast off from the object, and

retaining its shape, was different, as we have seen, from

the view which Aristotle took, though it has sometimes been

called the Peripatetic doctrine[6\4]. We may add that the

expression was latterly applied to express the supposition

of an emanation of any kind, and implied little {300} more

than that supposition of a Medium of which we are now

speaking. Thus Bacon, after reviewing the phenomena of

sound, says[7\4], 'Videntur motus soni fieri per _species

spirituales_: ita enim loquendum donec certius quippiam

inveniatur.'

[Note 6\4: Brown, vol. ii. p. 98.]

[Note 7\4: _Hist. Son. et Aud._ vol. ix. p. 87.]

Though the fundamental principles of several sciences depend

upon the assumption of a Medium of Perception, these

principles do not at all depend upon any special view of the

Process of our perceptions. The mechanism of that process is

a curious subject of consideration; but it belongs to

physiology, more properly than either to metaphysics, or to

those branches of physics of which we are now speaking. The

general nature of the process is the same for all the

senses. The object affects the appropriate intermedium; the

medium, through the proper organ, the eye, the ear, the

nose, affects the nerves of the particular sense; and, by

these, in some way, the sensation is conveyed to the mind,

But to treat the _impression_ upon the nerves as the _act_

of sensation which we have to consider, would be to mistake

our object, which is not the constitution of the human body,

but of the human mind. It would be to mistake one link of

the chain for the power which holds the end of the chain. No

anatomical analysis of the corporeal conditions of vision,

or hearing, or feeling warm, is necessary to the sciences of

Optics, or Acoustics, or Thermotics.

Not only is this physiological research an extraneous part

of our subject, but a partial pursuit of such a research may

mislead the inquirer. We perceive objects _by means of_

certain media, and _by means of_ certain impressions on the

nerves: but we cannot with propriety say that we perceive

either the media or the impressions on the nerves. What

person in the act of seeing is conscious of the little

coloured spaces on the retina? or of the motions of the

bones of the auditory apparatus whilst he is hearing?

Surely, no one. This may appear obvious enough, and yet a

writer of no common acuteness, Dr. Brown, has put forth

several {301} very strange opinions, all resting upon the

doctrine that the coloured spaces on the retina are the

_objects_ which we perceive; and there are some supposed

difficulties and paradoxes on the same subject which have

become quite celebrated (as upright vision with inverted

images), arising from the same confusion of thought.

As the consideration of the difficulties which have arisen

respecting the Philosophy of Perception may serve still

further to illustrate the principles on which we necessarily

reason respecting the secondary qualities of bodies, I shall

here devote a few pages to that subject.

{{302}}

CHAPTER II.

ON PECULIARITIES IN THE PERCEPTIONS OF THE DIFFERENT SENSES.

1. WE cannot doubt that we perceive all secondary qualities

by means of immediate impressions made, through the proper

medium of sensation, upon our organs. Hence all the senses

are sometimes vaguely spoken of as modifications of the

sense of feeling. It will, however, be seen, on reflection,

that this mode of speaking identifies in words things which

in our conceptions have nothing in common. No impression on

the organs of touch can be conceived as having any

resemblance to colour or smell. No effort, no ingenuity, can

enable us to describe the impressions of one sense in terms

borrowed from another.

The senses have, however, each its peculiar powers, and

these powers may be in some respects compared, so as to show

their leading resemblances and differences, and the

characteristic privileges and laws of each. This is what we

shall do as briefly as possible.

SECT. I.--_Prerogatives of Sight._

THE sight distinguishes colours, as the hearing

distinguishes tones; the sight estimates degrees of

brightness, the ear, degrees of loudness; but with several

resemblances, there are most remarkable differences between

these two senses.

2. _Position._--The sight has this peculiar prerogative,

that it apprehends the _place_ of its objects directly and

primarily. We see _where_ an object is at the same instant

that we see what it is. If we see two objects, we see their

relative position. We cannot help {303} perceiving that one

is above or below, to the right or to the left of the other,

if we perceive them at all.

There is nothing corresponding to this in sound. When we

hear a noise, we do not necessarily assign a place to it. It

may easily happen that we cannot tell from which side a

thunder-clap comes. And though we often can judge in what

direction a voice is heard, this is a matter of secondary

impression, and of inference from concomitant circumstances,

not a primary fact of sensation. The judgments which we form

concerning the position of sounding bodies are obtained by

the conscious or unconscious comparison of the impressions

made on the two ears, and on the bones of the head in

general; they are not inseparable conditions of hearing. We

may hear sounds, and be uncertain whether they are 'above,

around, or underneath!' but the moment anything visible

appears, however unexpected, we can say, 'see _where_ it

comes!'

Since we can see the relative position of things, we can see

_figure_, which is but the relative position of the

different parts of the boundary of the object. And thus the

whole visible world exhibits to us a scene of various

shapes, coloured and shaded according to their form and

position, but each having relations of position to all the

rest; and altogether, entirely filling up the whole range

which the eye can command.

3. _Distance._--The distance of objects from us is no matter

of immediate perception, but is a judgment and inference

formed from our sensations, in something of the same way as

our judgment of position by the ear, though more precise.

That this is so, was most distinctly shown by Berkeley, in

his _New Theory of Vision_. The elements on which we form

our judgment are, the effort by which we fix both eyes on

the same object, the effort by which we adjust each eye to

distinct vision, and the known forms, colours, and parts of

objects, as compared with their appearance. The right

interpretation of the information which these circumstances

give us respecting the true distances and forms of things,

is gradually learnt by experience, the lesson being begun in

our earliest infancy, and inculcated upon us every hour

during which we {304} use our eyes. The completeness with

which the lesson is learnt is truly admirable; for we forget

that our conclusion is obtained indirectly, and mistake a

judgment on evidence for an intuitive perception. This,

however, is not more surprizing than the rapidity and

unconsciousness of effort with which we understand the

meaning of the speech that we hear, or the book that we

read. In both cases, the habit of interpretation is become

as familiar as the act of perception. And this is the case

with regard to vision. We see the breadth of the street as

clearly and readily as we see the house on the other side of

it. We see the house to be square, however obliquely it be

presented to us. Indeed the difficulty is, to recover the

consciousness of our real and original sensations;--to

discover what is the _apparent_ relation of the lines which

appear before us. As we have already said, (book ii. chap.

6) in the common process of vision we suppose ourselves to

see that which cannot be seen; and when we would make a

picture of an object, the difficulty is to represent what is

visible and no more.

But perfect as is our habit of interpreting what we

perceive, we could not interpret if we did not perceive. If

the eye did not apprehend visible position, it could not

infer actual position, which is collected from visible

position as a consequence: if we did not see apparent

figure, we could not arrive at any opinion concerning real

form. The perception of place, which is the prerogative of

the eye, is the basis of all its other superiority.

The precision with which the eye can judge of apparent

position is remarkable. If we had before us two stars

distant from each other by one-twentieth of the moon's

diameter, we could easily decide the apparent direction of

the one from the other, as above or below, to the right or

left. Yet eight millions of stars might be placed in the

visible hemisphere of the sky at such distances from each

other; and thus the eye would recognize the relative

position in a portion of its range not greater than one

eight-millionth of the whole. Such is the accuracy of the

sense of vision in this {305} respect; and, indeed, we might

with truth have stated it much higher. Our judgment of the

position of distant objects in a landscape depends upon

features far more minute than the magnitude we have here

described.

As our object is to point out principally the differences of

the senses, we do not dwell upon the delicacy with which we

distinguish tints and shades, but proceed to another sense.

SECT. II.--_Prerogatives of Hearing._

THE sense of hearing has two remarkable prerogatives; it can

perceive a definite and peculiar relation between certain

tones, and it can clearly perceive two tones together; in

both these circumstances it is distinguished from vision,

and from the other senses.

4. _Musical intervals._--We perceive that two tones have, or

have not, certain definite relations to each other, which we

call _Concords_: one sound is a _Fifth_, an _Octave_, &c.,

above the other. And when this is the case, our perception

of the relation is extremely precise. It is easy to perceive

when a fifth is out of tune by one-twentieth of a tone; that

is, by one-seventieth of itself. To this there is nothing

analogous in vision. Colours have certain vague relations to

one another; they look well together, by contrast or by

resemblance; but this is an indefinite, and in most cases a

casual and variable feeling. The relation of _complementary_

colours to one another, as of red to green, is somewhat more

definite; but still, has nothing of the exactness and

peculiarity which belongs to a musical concord. In the case

of the two sounds, there is an exact point at which the

relation obtains; when by altering one note we pass this

point, the concord does not gradually fade away, but

instantly becomes a discord; and if we go further still, we

obtain another concord of quite a different character.

We learn from the theory of sound that concords occur when

the times of vibration of the notes have exact simple

ratios; an octave has these times as 1 to {306} 2; a fifth,

as 2 to 3. According to the undulatory theory of light, such

ratios occur in colours, yet the eye is not affected by them

in any peculiar way. The times of the undulations of certain

red and certain violet rays are as 2 to 3, but we do not

perceive any peculiar harmony or connexion between those

colours.

5. _Chords._--Again, the ear has this prerogative, that it

can apprehend two notes together, yet distinct. If two

notes, distant by a fifth from each other, are sounded on

two wind instruments, both they and their musical relation

are clearly perceived. There is not a mixture, but a

concord, a musical interval. In colours, the case is

otherwise. If blue and yellow fall on the same spot, they

form green; the colour is simple to the eye; it can no more

be decomposed by the vision than if it were the simple green

of the prismatic spectrum: it is impossible for us, by

sight, to tell whether it is so or not.

These are very remarkable differences of the two senses: two

colours can be compounded into an apparently simple one; two

sounds cannot: colours pass into each other by gradations

and intermediate tints; sounds pass from one concord to

another by no gradations: the most intolerable discord is

that which is near a concord. We shall hereafter see how

these differences affect the _scales_ of sound and of

colour.

6. _Rhythm._--We might remark, that as we see objects in

_space_, we hear sounds in _time_; and that we thus

introduce an arrangement among sounds which has several

analogies with the arrangement of objects in space. But the

conception of time does not seem to be peculiarly connected

with the sense of hearing; a faculty of apprehending tone

and time, or in musical phraseology _tune_ and _rhythm_, are

certainly very distinct. I shall not, therefore, here dwell

upon such analogies.

The other Senses have not any peculiar prerogatives, at

least none which bear on the formation of science. I may,

however, notice, in the feeling of heat, this circumstance;

that it presents us with two opposites, heat and cold, which

graduate into each other. This {307} is not quite peculiar,

for vision also exhibits to us white and black, which are

clearly opposites, and which pass into each other by the

shades of gray.

SECT. III.--_The Paradoxes of Vision._

7. _First Paradox of Vision. Upright Vision._--All our

senses appear to have this in common; That they act by means

of organs, in which a bundle of nerves receives the

impression of the appropriate medium of the sense. In the

construction of these organs there are great differences and

peculiarities, corresponding, in part at least, to the

differences in the information given. Moreover, in some

cases, as we have noted in the case of audible position and

visible distance, that which seems to be a perception is

really a judgment founded on perceptions of which we are not

directly aware. It will be seen, therefore, that with

respect to the peculiar powers of each sense, it may be

asked;--whether they can be explained by the construction of

the peculiar organ;--whether they are acquired judgments and

not direct perceptions;--or whether they are inexplicable in

either of these ways, and cannot, at present at least, be

resolved into anything but conditions of the intellectual

act of perception.

Two of these questions with regard to vision, have been much

discussed by psychological writers: the cause of our seeing

objects upright by inverted images on the retina; and of our

seeing single with two such images.

Physiologists have very completely explained the exquisitely

beautiful mechanism of the eye, considered as analogous to

an optical instrument; and it is indisputable that by means

of certain transparent lenses and humours, an inverted image

of the objects which are looked at is formed upon the

_retina_, or fine net-work of nerve, with which the back of

the eye is lined. We cannot doubt that the impression thus

produced on these nerves is essential to the act of vision;

and so far as we consider the nerves {308} themselves to

feel or perceive by contact, we may say that they perceive

this image, or the affections of light which it indicates.

But we cannot with any propriety say that _we_ perceive, or

that our mind perceives, this image; for we are not

conscious of it, and none but anatomists are aware of its

existence: we perceive _by means_ of it.

A difficulty has been raised, and dwelt upon in a most

unaccountable manner, arising from the neglect of this

obvious distinction. It has been asked, how is it that we

see an object, a man for instance, upright, when the

immediate object of our sensation, the image of the man on

our retina, is inverted? To this we must answer, that we see

him upright _because_ the image is inverted; that the

inverted image is the necessary means of seeing an upright

object. This is granted, and where then is the difficulty?

Perhaps it may be put thus: How is it that we do not judge

the man to be inverted, since the sensible image is so? To

this we may reply, that we have no notion of _upright_ or

inverted, except that which is founded on experience, and

that all our experience, without exception, must have taught

us that such a sensible image belongs to a man who is in an

upright position. Indeed, the contrary judgment is not

conceivable; a man is upright whose head is upwards and his

feet downwards. But what are the sensible images of

_upwards_ and _downwards_? Whatever be our standard of up

and down, the sensible representation of _up_ will be an

image moving on the retina towards the lower side, and the

sensible representation of _down_ will be a motion towards

the upper side. The head of the man's image is towards the

image of the sky, its feet are towards the image of the

ground; how then should it appear otherwise than upright? Do

we expect that the whole world should appear inverted? Be it

so: but if the whole be inverted, how is the relation of the

parts altered? Do we expect that we should think our own

persons in particular? This cannot be, for we look at them

as we do at other objects. Do we expect that things should

appear to fall {309} upwards? Surely not. For what do we

know of upwards, except that it is the direction in which

bodies do _not_ fall? In short, the whole of this

difficulty, though it has in no small degree embarrassed

metaphysicians, appears to result from a very palpable

confusion of ideas; from an attempt at comparison of what

_we_ see, with that which the retina feels, as if they were

separately presentable. It is a sufficient explanation to

say, that we do not see the image on the retina, but see by

_means_ of it. The perplexity does not require much more

skill to disentangle, than it does to see that a word

written in _black_ ink, may signify _white_[8\4].

[Note 8\4: The explanation of our seeing objects erect when

the image is inverted has been put very simply, by saying,

'We _call_ that the _lower_ end of an object which is next

the ground.' The observer cannot look into his own eye; he

knows _by experience_ what kind of image corresponds to a

man in an upright position. The anatomist tells him that

this image is _inverted_: but this does not disturb the

process of judging by experience. It does not appear why any

one should be perplexed at the notion of seeing objects

erect by means of inverted images, rather than at the notion

of seeing objects large by means of small images; or cubical

and pyramidal, by means of images on a spherical surface; or

green and red, by means of images on a black surface. Indeed

some persons have contrived to perplex themselves with these

latter questions, as well as the first.

The above explanation is not at all affected, as to its

substance, if we adopt Sir David Brewster's expression, and

say that the _line of visible direction_ is a line passing

through the center of the spherical surface of the retina,

and therefore of course perpendicular to the surface. In

speaking of 'the inverted image,' it has always been

supposed to be determined by such lines; and though the

point where they intersect may not have been ascertained

with exactness by previous physiologists, the philosophical

view of the matter was not in any degree vitiated by this

imperfection.]

8. _Second Paradox of Vision. Single Vision._--(1.) _Small

or Distant Objects._--The other difficulty, why with two

images on the retina we see only one object, is of a much

more real and important kind. This effect is manifestly

limited by certain circumstances of a very precise nature;

for if we direct our eyes at an object which is very near

the eye, we see {310} all other objects double. The fact is

not, therefore, that we are incapable of receiving two

impressions from the two images, but that, under certain

conditions, the two impressions form one. A little attention

shows us that these conditions are, that with both eyes we

should look at the same object; and again, we find that to

look at an object with either eye, is to direct the eye so

that the image falls on or near a particular point about the

middle of the retina. Thus these middle points in the two

retinas correspond, and we see an image single when the two

images fall on the corresponding points.

Again, as each eye judges of position, and as the two eyes

judge similarly, an object will be seen in the same place by

one eye and by the other, when the two images which it

produces are _similarly situated_ with regard to the

_corresponding points_ of the retina[9\4].

[Note 9\4: The explanation of single vision with two eyes

may be put in another form. Each eye judges immediately of

the relative position of all objects within the field of its

direct vision. Therefore when we look with both eyes at a

_distant_ prospect (so distant that the distance between the

eyes is small in comparison) the two prospects, being

similar collections of forms, will coincide altogether, if a

corresponding point in one and in the other coincide. If

this be the case, the two images of every object will fall

upon corresponding points of the retina, and will appear

single.

If the two prospects seen by the two eyes do not exactly

coincide, in consequence of nearness of the objects, or

distortion of the eyes, but if they nearly coincide, the

stronger image of an object absorbs the weaker, and the

object is seen single; yet modified by the combination, as

will be seen when we speak of the single vision of near

objects. When the two images of an object are considerably

apart, we see it double.

This explanation is not different in substance from the one

given in the text; but perhaps it is better to avoid the

assertion that the law of corresponding points is 'a

distinct and original principle of our constitution,' as I

had stated in the first edition. The simpler mode of stating

the law of our constitution appears to be to say, that each

eye determines similarly the position of objects; and that

when the positions of an object, as seen by the two eyes,

coincide (or nearly coincide) the object is seen single.]

This is the Law of Single Vision, at least so far as regards

small objects; namely, objects so small that in

contemplating them we consider their position only, {311}

and not their solid dimensions. Single vision in such cases

is a result of the law of vision simply: and it is a mistake

to call in, as some have done, the influence of habit and of

acquired judgments, in order to determine the result in such

cases.

To ascribe the apparent singleness of objects to the

impressions of vision corrected by the experience of

touch[10\4], would be to assert that a person who had not

been in the habit of handling what he saw, would see all

objects double; and also, to assert that a person beginning

with the double world which vision thus offers to him,

would, by the continued habit of handling objects, gradually

and at last learn to see them single. But all the facts of

the case show such suppositions to be utterly fantastical.

No one can, in this case, go back from the habitual judgment

of the singleness of objects, to the original and direct

perception of their doubleness, as the draughtsman goes back

from judgments to perception, in representing solid

distances and forms by means of perspective pictures. No one

can point out any case in which the habit is imperfectly

formed; even children of the most tender age look at an

object with both eyes, and see it as one.

[Note 10\4: See Brown, vol. ii. p. 81.]

In cases when the eyes are distorted (in squinting), one eye

only is used, or if both are employed, there is double

vision; and thus any derangement of the correspondence of

motion in the two eyes will produce double-sightedness.

Brown is one of those[11\4] who assert that two images

suggest a single object because we have _always found_ two

images to belong to a single object. He urges as an

illustration, that the _two_ words 'he conquered,' by custom

excite exactly the same notion as the _one_ Latin word

'vicit;' and thus that two visual images, by the effect of

habit, produce the same belief of a single object as one

tactual impression. But in order to make this pretended

illustration of any value, it ought to be true that when a

person has thoroughly learnt the Latin language, he can no

longer distinguish {312} any separate meaning in 'he' and in

'conquered.' We can by no effort perceive the double

sensation, when we look _at_ the object with the two eyes.

Those who squint, learn by habit to see objects single: but

the habit which they acquire is that of attending to the

impressions of one eye only at once, not of combining the

two impressions. It is obvious, that if each eye spreads

before us the same visible scene, with the same objects and

the same relations of place, then, if one object in each

scene coincide, the whole of the two visible impressions

will be coincident. And here the remarkable circumstance is,

that not only each eye judges for itself of the relations of

position which come within its field of view; but that there

is a superior and more comprehensive faculty which combines

and compares the two fields of view; which asserts or denies

their coincidence; which contemplates, as in a relative

position to one another, these two visible worlds, in which

all other relative position is given. This power of

confronting two sets of visible images and figured spaces

before a purely intellectual tribunal, is one of the most

remarkable circumstances in the sense of vision.

[Note 11\4: _Lectures_, vol. ii. p. 81.]

9. (2.) _Near Objects._--We have hitherto spoken of the

singleness of objects whose images occupy corresponding

positions on the retina of the two eyes. But here occurs a

difficulty. If an object of moderate size, a small thick

book for example, be held at a little distance from the

eyes, it produces an image on the retina of each eye; and

these two images are perspective representations of the book

from different points of view, (the positions of the two

eyes,) and are therefore of different forms. Hence the two

images cannot occupy corresponding points of the retina

throughout their whole extent. If the central parts of the

two images occupy corresponding points, the boundaries of

the two wall not correspond. How is it then consistent with

the law above stated that in this case the object appears

single?

It may be observed, that the two images in such a case will

differ most widely when the object is not a {313} mere

surface, but a solid. If a book, for example, be held with

one of its upright edges towards the face, the right eye

will see one side more directly than the left eye, and the

left eye will see another side more directly, and the

outline of the two images upon the two retinas will exhibit

this difference. And it may be further observed, that this

difference in the images received by the two eyes, is a

plain and demonstrative evidence of the solidity of the

object seen; since nothing but a solid object could (without

some special contrivance) produce these different forms of

the images in the two eyes.

Hence the absence of exact coincidence in the two images on

the retina is the necessary condition of the solidity of the

object seen, and must be one of the indications by means of

which our vision apprehends an object as solid. And that

this is so, Mr. Wheatstone has proved experimentally, by

means of some most ingenious and striking contrivances. He

has devised[12\4] an instrument (the _stereoscope_) by which

two images (drawn in outline) differing exactly as much as

the two images of a solid body seen near the face would

differ, are conveyed, one to one eye, and the other to the

other. And it is found that when this is effected, the

object which the images represent is not only seen single,

but is apprehended as solid with a clearness and reality of

conviction quite distinct from any impression which a mere

perspective representation can give.

[Note 12\4: _Phil. Trans._ 1839.]

At the same time it is found that the object is then only

apprehended as single when the two images are such as are

capable of being excited by one single object placed in

solid space, and seen by the two eyes. If the images differ

more or otherwise than this condition allows, the result is,

that both are seen, their lines crossing and interfering

with one another.

It may be observed, too, that if an object be of such large

size as not to be taken in by a single glance of the eyes,

it is no longer apprehended as single by a direct act of

perception; but its parts are looked at {314} separately and

successively, and the impressions thus obtained are put

together by a succeeding act of the mind. Hence the objects

which are directly seen as solid, will be of moderate size;

in which case it is not difficult to show that the outlines

of the two images will differ from each other only slightly.

Hence we are led to the following, as the Law of Single

Vision for _near_ objects:--When the two images in the two

eyes are situated (part for part) nearly, but not exactly,

upon corresponding points, the object is apprehended as

single, if the two images are such as are or would be given

by a single solid object seen by the two eyes separately:

and in this case the object is necessarily apprehended as solid.

This law of vision does not contradict that stated above for

distant objects: for when an object is removed to a

considerable distance, the images in the two eyes coincide

exactly, and the object is seen as single, though without

any direct apprehension of its solidity. The first law is a

special case of the second. Under the condition of _exactly_

corresponding points, we have the perception of singleness,

but no evidence of solidity. Under the condition of _nearly_

corresponding points, we may have the perception of

singleness, and with it, of solidity.

We have before noted it as an important feature in our

visual perception, that while we have two distinct

impressions upon the sense, which we can contemplate

separately and alternately, (the impressions on the two

eyes,) we have a higher perceptive faculty which can

recognize these two impressions, exactly similar to each

other, as only two images of one and the same assemblage of

objects. But we now see that the faculty by which we

perceive visible objects can do much more than this:--it can

not only unite two impressions, and recognize them as

belonging to one object in virtue of their coincidence, but

it can also unite and identify them, even when they do not

exactly coincide. It can correct and adjust their small

difference, so that they are both apprehended as

representations of the same figure. It can infer from them a

real form, not {315} agreeing with either of them; and a

solid space, which they are quite incapable of exemplifying.

The visual faculty decides whether or not the two ocular

images can be pictures of the same solid object, and if they

can, it undoubtingly and necessarily accepts them as being

so. This faculty operates as if it had the power of calling

before it all possible solid figures, and of ascertaining by

trial whether any of those will, at the same time, fit both

the outlines which are given by the sense. It assumes the

reality of solid space, and, if it be possible, reconciles

the appearances with that reality. And thus an activity of

the mind of a very remarkable and peculiar kind is exercised

in the most common act of seeing.

10. It may be said that this doctrine, of such a visual

faculty as has been described, is very vague and obscure,

since we are not told what are its limits. It adjusts and

corrects figures which _nearly_ coincide, so as to identify

them. But _how_ nearly, it may be asked, must the figures

approach each other, in order that this adjustment may be

possible? What discrepance renders impossible the

reconcilement of which we speak? Is it not impossible to

give a definite answer to these questions, and therefore

impossible to lay down definitely such laws of vision as we

have stated? To this I reply, that the indefiniteness thus

objected to us, is no new difficulty, but one with which

philosophers are familiar, and to which they are already

reconciled. It is, in fact, no other than the indefiniteness

of the limits of distinct vision. How near to the face must

an object be brought, so that we shall cease to see it

distinctly? The distance, it will be answered, is

indefinite: it is different for different persons; and for

the same person, it varies with the degree of effort,

attention, and habit. But this indefiniteness is only the

indefiniteness, in another form, of the deviation of the two

ocular images from one another: and in reply to the question

concerning them we must still say, as before, that in

doubtful cases, the power of apprehending an object as

single, when this _can_ be done, will vary with effort,

attention, and habit. The assumption {316} that the apparent

object exists as a real figure, in real space, is to be

verified, if possible; but, in extreme cases, from the

unfitness of the point of view, or from any other cause of

visual confusion or deception, the existence of a real

object corresponding to the appearance may be doubtful; as

in any other kind of perception it may be doubtful whether

our senses, under disadvantageous circumstances, give us

true information. The vagueness of the limits, then, within

which this visual faculty can be successfully exercised, is

no valid argument against the existence of the faculty, or

the truth of the law which we have stated concerning its

action.

SECT. IV.--_The Perception of Visible Figure._

11. _Visible Figure._--There is one tenet on the subject of

vision which appears to me so extravagant and

unphilosophical, that I should not have thought it necessary

to notice it, if it had not been recently promulgated by a

writer of great acuteness in a book which has obtained, for

a metaphysical work, considerable circulation. I speak of

Brown's opinion[13\4] that we have no immediate perception

of visible figure. I confess myself unable to comprehend

fully the doctrine which he would substitute in the place of

the one commonly received. He states it thus[14\4]: 'When

the simple affection of sight is blended with the ideas of

suggestion [those arising from touch, &c.] in what are

termed the acquired perceptions of vision, as, for example,

in the perception of a sphere, it is colour only which is

blended with the large convexity, and not a small coloured

plane.' The doctrine which Brown asserts in this and similar

passages, appears to be, that we do not by vision perceive

_both_ colour and _figure_; but that the colour which we see

is blended with the figure which we learn the existence of

by other means, as by touch. But if this were possible when

we can call in other perceptions, how is it possible when we

cannot or do not touch the object? {317} Why does the moon

appear round, gibbous, or horned? What sense besides vision

suggests to us the idea of her figure? And even in objects

which we can reach, what is that circumstance in the sense

of vision which suggests to us that the colour belongs to

the sphere, except that we see the colour where we see the

sphere? If we do not see figure, we do not see position; for

figure is the relative position of the parts of a boundary.

If we do not see position, why do we ascribe the yellow

colour to the sphere on our left, rather than to the cube on

our right? We _associate_ the colour with the object, says

Dr. Brown; but if his opinion were true, we could not

associate two colours with two objects, for we could not

apprehend the colours as occupying two different places.

[Note 13\4: _Lectures_, vol. ii. p. 82.]

[Note 14\4: _Ib._ vol. ii. p. 90.]

The whole of Brown's reasoning on this subject is so

irreconcilable with the first facts of vision, that it is

difficult to conceive how it could proceed from a person who

has reasoned with great acuteness concerning touch. In order

to prove his assertion, he undertakes to examine the only

reasons which, he says[15\4], he can imagine for believing

the immediate perception of visible figure: (1) That it is

absolutely impossible, in our present sensations of sight,

to separate colour from extension; and (2) That there are,

in fact, figures on the retina corresponding to the apparent

figures of objects.

[Note 15\4: _Lectures_, vol. ii. p. 83.]

On the subject of the first reason, he says, that the figure

which we perceive as associated with colour, is the real,

and not the apparent figure. 'Is there,' he asks, 'the

slightest consciousness of a perception of visible figure,

corresponding to the affected portion of the retina?' To

which, though he seems to think an affirmative answer

impossible, we cannot hesitate to reply, that there is

undoubtedly such a consciousness; that though obscured by

being made the ground of habitual inference as to the real

figure, this consciousness is constantly referred to by the

draughtsman, and easily recalled by any one. We may separate

colour, he says {318} again[16\4], from the figures on the

retina, as we may separate it from length, breadth, and

thickness, which we do not see. But this is altogether

false: we cannot separate colour from length, breadth, and

thickness, _in any other way_, than by transferring it to

the visible figure which we do see. He cannot, he allows,

separate the colour from the visible form of the trunk of a

large oak; but just as little, he thinks, can he separate it

from the convex mass of the trunk, which (it is allowed on

all hands) he does not immediately see. But in this he is

mistaken: for if he were to make a _picture_ of the oak, he

would separate the colour from the convex shape, which he

does not imitate, but he could not separate it from the

visible figure, which he does imitate; and he would then

perceive that the fact that he _has not_ an immediate

perception of the convex form, is necessarily connected with

the fact that he _has_ an immediate perception of the

apparent figure; so far is the rejection of immediate

perception in the former case from being a reason for

rejecting it in the latter.

[Note 16\4: _Lectures_, vol. ii. p. 84.]

Again, with regard to the second argument. It does not, he

says, follow, that because a certain figured portion of the

retina is affected by light, we should see such a figure;

for if a certain figured portion of the olfactory organ were

affected by odours, we should not acquire by smell any

perception of such figure[17\4]. This is merely to say, that

because we do not perceive position and figure by one sense,

we cannot do so by another sense. But this again is

altogether erroneous. It is an office of our sight to inform

us of position, and consequently of figure; for this

purpose, the organ is so constructed that the position of

the object determines the position of the point of the

retina affected. There is nothing of this kind in the organ

of smell; objects in different positions and of different

forms do not affect different parts of the olfactory nerve,

or portions of different shape. Different objects, remote

from each other, if perceived by smell, affect the same

{319} part of the olfactory organs. This is all quite

intelligible; for it is not the office of smell to inform us

of position. Of what use or meaning would be the curious and

complex structure of the eye, if it gave us only such vague

and wandering notions of the colours and forms of the

flowers in a garden, as we receive from their odours when we

walk among them blindfold? It is, as we have said, the

_prerogative_ of vision to apprehend position: the places of

objects on the retina give this information. We do not

suppose that the affection of a certain shape of nervous

expanse will necessarily and in all cases give us the

impression of figure; but we know that in vision it does;

and it is clear that if we did not acquire our acquaintance

with visible figure in this way, we could not acquire it in

any way[18\4].

[Note 17\4: _Ib._ p. 87.]

[Note 18\4: When Brown says further (p. 87), that we can

indeed show the image in the dissected eye; but that 'it is

not in the dissected eye that vision takes place;' it is

difficult to see what his drift is. Does he doubt that there

is an image formed in the living as completely as in the

dissected eye?]

The whole of this strange mistake of Brown's appears to

arise from the fault already noticed;--that of considering

the image on the retina as the _object_ instead of the

_means_ of vision. This indeed is what he says: 'the true

object of vision is not the distant body itself, but the

light that has reached the expansive termination of the

optic nerve[19\4].' Even if this were so, we do not see why

we should not perceive the position of the impression on

this expanded nerve. But as we have already said, the

impression on the nerve is the means of vision, and enables

us to assign a place, or at least a direction, to the object

from which the light proceeds, and thus makes vision

possible. Brown, indeed, pursues his own peculiar view till

he involves the subject in utter confusion. Thus he

says[20\4], 'According to the common theory [that figure can

be perceived by the eye,] a visible sphere is at once to my

perception convex and plane; and if the sphere be a one, it

is perceived at once to be a sphere of {320} many feet in

diameter, and a plane circular surface of the diameter of a

quarter of an inch.' It is easy to deduce these and greater

absurdities, if we proceed on his strange and baseless

supposition that the object and the image on the retina are

_both_ perceived. But who is conscious of the image on the

retina in any other way than as he sees the object by means

of it?

[Note 19\4: _Lectures_, vol. ii. p. 57.]

[Note 20\4: _Ib._ vol. ii. p. 89.]

Brown seems to have imagined that he was analysing the

perception of figure 'in the same manner in which Berkeley

had analyzed the perception of distance. He ought to have

recollected that such an undertaking, to be successful,

required him to show _what_ elements he analyzed it _into_.

Berkeley analyzed the perception of real figure into the

interpretation of visible figure according to certain rules

which he distinctly stated. Brown analyzes the perception of

visible figure into no elements. Berkeley says, that we do

not directly perceive distance, but that we perceive

something else, from which we infer distance, namely,

visible figure and colour, and our own efforts in seeing;

Brown says, that we do not see figure, but infer it; what

then do we see, which we infer it from? To this he offers no

answer. He asserts the seeming perception of visible figure

to be a result of 'association;'--of 'suggestion.' But what

meaning can we attach to this? Suggestion requires something

which suggests; and not a hint is given what it is which

suggests position. Association implies two things

associated; what is the sensation which we associate with

form? What is that visual perception which is not figure,

and which we mistake for figure? What perception is it that

suggests a square to the eye? What impressions are those

which have been associated with a visible triangle, so that

the revival of the impressions revives the notion of the

triangle? Brown has nowhere pointed out such perceptions and

impressions; nor indeed was it possible for him to do so;

for the only visual perceptions which he allows to remain,

those of colour, most assuredly do not suggest visible

figures by their differences; red is not associated with

square rather than with round, or with round rather than

square. On the contrary, the {321} eye, constructed in a

very complex and wonderful manner in order that it may give

to us directly the perception of position as well as of

colour, has it for one of its prerogatives to give us this

information; and the perception of the relative position of

each part of the visible boundary of an object constitutes

the perception of its apparent figure; which faculty we

cannot deny to the eye without rejecting the plain and

constant evidence of our senses, making the mechanism of the

eye unmeaning, confounding the object with the means of

vision, and rendering the mental process of vision utterly

unintelligible.

Having sufficiently discussed the processes of perception, I

now return to the consideration of the Ideas which these

processes assume.

{{322}}

CHAPTER III.

SUCCESSIVE ATTEMPTS AT THE SCIENTIFIC APPLICATION OF THE

IDEA OF A MEDIUM.

1. IN what precedes, we have shown by various considerations

that we necessarily and universally assume the perception of

secondary qualities to take place by means of a medium

interjacent between the object and the person perceiving.

Perception is affected by various peculiarities, according

to the nature of the quality perceived: but in all cases a

medium is equally essential to the process.

This principle, which, as we have seen, is accepted as

evident by the common understanding of mankind, is confirmed

by all additional reflection and discipline of the mind, and

is the foundation of all the theories which have been

proposed concerning the processes by which the perception

takes place, and concerning the modifications of the

qualities thus perceived. The medium, and the mode in which

the impression is conveyed through the medium, seem to be

different for different qualities; but the existence of the

medium leads to certain necessary conditions or

alternatives, which have successively made their appearance

in science, in the course of the attempts of men to theorize

concerning the principal secondary qualities, sound, light,

and heat. We must now point out some of the ways, at first

imperfect and erroneous, in which the consequences of the

fundamental assumption were traced.

2. _Sound._--In all cases the medium of sensation, whatever

it is, is supposed to produce the effect of conveying

secondary qualities to our perception by means of its

primary qualities. It was conceived to operate {323} by the

size, form, and motion of its parts. This is a fundamental

principle of the class of sciences of which we have at

present to speak.

It was assumed from the first, as we have seen in the

passage lately quoted from Aristotle[21\4], that in the

conveyance of _sound_, the medium of communication was the

air. But although the first theorists were right so far,

that circumstance did not prevent their going entirely wrong

when they had further to determine the nature of the

process. It was conceived by Aristotle that the air acted

after the manner of a rigid body;--like a staff, which,

receiving an impulse at one end, transmits it to the other.

Now this is altogether an erroneous view of the manner in

which the air conveys the impulse by which sound is

perceived. An approach was made to the true view of this

process, by assimilating it to the diffusion of the little

circular waves which are produced on the surface of still

water when a stone is dropt into it. These little waves

begin from the point thus disturbed, and run outwards,

expanding on every side, in concentric circles, till they

are lost. The propagation of sound through the air from the

point where it is produced, was compared by Vitruvius to

this diffusion of circular waves in water; and thus the

notion of a propagation of impulse by the _waves_ of a fluid

was introduced, in the place of the former notion of the

impulse of an unyielding body.

[Note 21\4: _Supr._ p. 297.]

But though, taking an enlarged view of the nature of the

progress of a wave, this is a just representation of the

motion of air in conveying sound, we cannot suppose that the

process was, at the period of which we speak, rightly

understood. For the waves of water were contemplated only as

affecting the surface of the water; and as the air has no

surface, the communication must take place by means of an

internal motion, which can bear only a remote and obscure

resemblance to the waves which we see. And even with regard

to the waves of water, the mechanism by which they are {324}

produced and transferred was not at all understood; so that

the comparison employed by Vitruvius must be considered

rather as a loose analogy than as an exact scientific

explanation.

No correct account of such motions was given, till the

formation of the science of Mechanics in modern times had

enabled philosophers to understand more distinctly the mode

in which motion is propagated through a fluid, and to

discern the forces which the process calls into play, so as

to continue the motion once begun. Newton introduced into

this subject the exact and rigorous conception of an

_Undulation_, which is the true key to the explanation of

impulses conveyed through a fluid.

Even at the present day, the right apprehension of the

nature of an Undulation transmitted through a fluid is found

to be very difficult for all persons except those whose

minds have been duly disciplined by mathematical studies.

When we see a wave run along the surface of water, we are

apt to imagine at first that a portion of the fluid is

transferred bodily from one place to another. But with a

little consideration we may easily satisfy ourselves that

this is not so: for if we look at a field of standing corn,

when a breeze blows over it, we see waves like those of

water run along its surface. Yet it is clear that in this

case the separate stalks of corn only bend backwards and

forwards, and no portion of the grain is really conveyed

from one part of the field to the other. This is obvious

even to popular apprehension. The poet speaks of

. . . . The rye,

That stoops its head when whirlwinds rave

And springs again in eddying wave

As each wild gust sweeps by.

Each particle of the mass in succession has a small motion

backwards and forwards; and by this means a large ridge made

by many such particles runs along the mass to any distance.

This is the true conception of an undulation in general.

Thus, when an Undulation is propagated in a fluid, it is not

_matter_, but _form_, which is transmitted from {325} one

place to another. The particles along the line of each wave

assume a certain arrangement, and this arrangement passes

from one part to another, the particles changing their

places only within narrow limits, so as to lend themselves

successively to the arrangements by which the successive

waves, and the intervals between the waves, are formed.

When such an Undulation is propagated through air, the wave

is composed, not, as in water, of particles which are higher

than the rest, but of particles which are closer to each

other than the rest. The wave is not a ridge of elevation,

but a line of condensation; and as in water we have

alternately elevated and depressed lines, we have in air

lines alternately condensed and rarefied. And the motion of

the particles is not, as in water, up and down, in a

direction transverse to that of the wave which runs

forwards; in the motion of an undulation through air the

motion of each particle is alternately forwards and

backwards, while the motion of the undulation is constantly

forwards.

This precise and detailed account of the Undulatory Motion

of air by which sound is transmitted was first given by

Newton. He further attempted to determine the motions of the

separate particles, and to point out the force by which each

particle affects the next, so as to continue the progress of

the undulation once begun. The motions of each particle must

be oscillatory; he assumed the oscillations to be governed

by the simplest law of oscillation which had come under the

notice of mathematicians, (that of small vibrations of a

pendulum;) and he proved that in this manner the forces

which are called into play by the contraction and expansion

of the parts of the elastic fluid are such as the

continuance of the motion requires.

Newton's proof of the exact law of Oscillatory Motion of the

aërial particles was not considered satisfactory by

succeeding mathematicians; for it was found that the same

result, the development of forces adequate to continue the

motion, would follow if any other law of the motion were

assumed. Cramer proved this by a sort of _parody_ on

Newton's proof, in which, by the {326} alteration of a few

phrases in this formula of demonstration, it was made to

establish an entirely different conclusion.

But the general conception of an Undulation as presented by

Newton was, as from its manifest mechanical truth it could

not fail to be, accepted by all mathematicians; and in

proportion as the methods of calculating the motions of

fluids were further improved, the necessary consequences of

this conception, in the communication of sound through air,

were traced by unexceptionable reasoning. This was

especially done by Euler and Lagrange, whose memoirs on such

motions of fluids are some of the most admirable examples

which exist, of refined mathematical methods applied to the

solution of difficult mechanical problems.

But the great step in the formation of the theory of sound

was undoubtedly that which we have noticed, the introduction

of the Conception of an Undulation such as we have attempted

to describe it:--a state, condition, or arrangement of the

particles of a fluid, which is transferred from one part of

space to another by means of small motions of the particles,

altogether distinct from the movement of the Undulation

itself. This is a conception which is not obvious to common

apprehension. It appears paradoxical at first sight to speak

of a large _wave_ (as the tide-wave) running up a river at

the rate of twenty miles an hour, while the _stream_ of the

river is all the while flowing downwards. Yet this is a very

common fact. And the conception of such a motion must be

fully mastered by all who would reason rightly concerning

the mechanical transmission of impressions through a medium.

We have described the motion of sound as produced by small

motions of the particle forwards and backwards, while the

waves, or condensed and rarefied lines, move constantly

forwards. It may be asked what right we have to suppose the

motion to be of this kind, since when sound is heard, no

such motions of the particles of air can be observed, even

by refined methods of observation. Thus Bacon declares

himself against the hypothesis of such a vibration, since,

as he remarks, it {327} cannot be perceived in any visible

impression upon the flame of a candle. And to this we reply,

that the supposition of this Vibration is made in virtue of

a principle which is involved in the original assumption of

a medium; namely, That _a Medium, in conveying Secondary

qualities, operates by means of its Primary qualities_, the

bulk, figure, motion, and other mechanical properties of its

parts. This is an Axiom belonging to the Idea of a Medium.

In virtue of this axiom it is demonstrable that the motion

of the air, when any how disturbed, must be such as is

supposed in our acoustical reasonings. For the elasticity of

the parts of the air, called into play by its expansion and

contraction, lead, by a mechanical necessity, to such a

motion as we have described. We may add that, by proper

contrivances, this motion may be made perceptible in its

visible effects. Thus the theory of sound, as an impression

conveyed through air, is established upon evident general

principles, although the mathematical calculations which are

requisite to investigate its consequences are, some of them,

of a very recondite kind.

3. _Light._--The early attempts to explain Vision

represented it as performed by means of material rays

proceeding _from_ the eye, by the help of which the eye felt

out the form and other visible qualities of an object, as a

blind man might do with his staff. But this opinion could

not keep its ground long: for it did not even explain the

fact that light is necessary to vision. Light, as a peculiar

medium, was next assumed as the machinery of vision; but the

mode in which the impression was conveyed through the medium

was left undetermined, and no advance was made towards sound

theory, on that subject, by the ancients.

In modern times, when the prevalent philosophy began to

assume a mechanical turn (as in the theories of Descartes),

light was conceived to be a material substance which is

emitted from luminous bodies, and which is also conveyed

from all bodies to the eye, so as to render them visible.

The various changes of direction by which the rays of light

are affected, (reflection, {328} refraction, &c.,) Descartes

explained, by considering the particles of light as small

globules, which change their direction when they impinge

upon other bodies, according to the laws of Mechanics.

Newton, with a much more profound knowledge of Mechanics

than Descartes possessed, adopted, in the most mature of his

speculations, nearly the same view of the nature of light;

and endeavoured to show that reflection, refraction, and

other properties of light, might be explained as the effects

which certain forces, emanating from the particles of

bodies, produce upon the luminiferous globules.

But though some of the properties of light could thus be

accounted for by the assumption of particles emitted from

luminous bodies, and reflected or refracted by forces, other

properties came into view which would not admit of the same

explanation. The phenomena of _diffraction_ (the fringes

which accompany shadows) could never be truly represented by

such an hypothesis, in spite of many attempts which were

made. And the _colours of thin plates_, which show the rays

of light to be affected by an alternation of two different

conditions at small intervals along their length, led Newton

himself to incline, often and strongly, to some hypothesis

of undulation. The _double refraction_ of Iceland spar, a

phenomenon in itself very complex, could, it was found by

Huyghens, be expressed with great simplicity by a certain

hypothesis of undulations.

Two hypotheses of the nature of the luminiferous medium were

thus brought under consideration; the one representing Light

as Matter emitted from the luminous object, the other, as

Undulations propagated through a fluid. These two hypotheses

remained in presence of each other during the whole of the

last century, neither of them gaining any material advantage

over the other, though the greater part of mathematicians,

following Newton, embraced the emission theory. But at the

beginning of the present century, an additional class of

phenomena, those of the _interference_ of two rays of light,

were brought under {329} consideration by Dr. Young; and

these phenomena were strongly in favour of the undulatory

theory, while they were irreconcilable with the hypothesis

of emission. If it had not been for the original bias of

Newton and his school to the other side, there can be little

doubt that from this period light as well as sound would

have been supposed to be propagated by undulations; although

in this case it was necessary to assume as the vehicle of

such undulations a special medium or _ether_. Several points

of the phenomena of vision no doubt remained unexplained by

the undulatory theory, as absorption, and the natural

colours of bodies; but such facts, though they did not

confirm, did not evidently contradict the theory of a

Luminiferous Ether; and the facts which such a theory did

explain, it explained with singular happiness and accuracy.