5. _Controversy of the Composition of Wa_History of scientific ideas

another controversy of our times to which we may with great

propriety apply the maxim now before us. After the glory of

having first given a true view of the composition of water

had long rested tranquilly upon the names of Cavendish and

Lavoisier, a claim was made in favour of James Watt as the

real author of this discovery by his son, (Mr J. Watt,) and

his eulogist, (M. Arago[34\6]). It is not to our purpose

here to discuss the various questions which have arisen on

this subject respecting priority of publication, and

respecting the translation of opinions published at one time

into the language of another period. But if we look at

Watt's own statement of his views, given soon after those of

Cavendish had been published, we shall perceive that it is

marked by a violation of this maxim: we shall find that he

does admit imponderable fluids {45} as chemical elements;

and thus shows a vagueness and confusion in his idea of

chemical composition. With such imperfection in his views,

it is not surprising that Watt, not only did not anticipate,

but did not apprehend quite precisely the discovery of

Cavendish and Lavoisier. Watt's statement of his views is as

follows[35\6]:--'Are we not authorized to conclude that

water is composed of dephlogisticated air and phlogiston

deprived of part of their latent or elementary heat; that

dephlogisticated or pure air is composed of water deprived

of its phlogiston and united to elementary heat and light;

and that the latter are contained in it in a latent state,

so as not to be sensible to the thermometer or to the eye;

and if light be only a modification of heat, or a

circumstance attending it, or a component part of the

inflammable air, then pure or dephlogisticated air is

composed of water deprived of its phlogiston and united to

elementary heat?'

[Note 34\6: Éloge de James Watt, _Annuaire du Bur. des

Long._ 1839.]

[Note 35\6: _Phil. Trans._ 1784, p. 332.]

When we compare this doubtful and hypothetical statement,

involving so much that is extraneous and heterogeneous, with

the conclusion of Cavendish, in which there is nothing

hypothetical or superfluous, we may confidently assent to

the decision which has been pronounced by one[36\6] of our

own time in favour of Cavendish. And we may with pleasure

recognize, in this enlightened umpire, a due appreciation of

the value of the maxim on which we are now insisting.

'Cavendish,' says Mr. Vernon Harcourt, 'pared off {46} from

the hypotheses their theories of combustion, and _affinities

of imponderable for ponderable matter_, as complicating

chemical with physical considerations.'

[Note 36\6: The Rev. W. Vernon Harcourt, Address to the

British Association, 1839.--Since the first edition of this

work was published, and also since the second edition of the

_History of the Inductive Sciences_, Mr. Watt's

correspondence bearing upon the question of the Composition

of Water has been published by Mr. Muirhead. I do not find,

in this publication, any reason for withdrawing what I have

stated in the text above: but with reference to the

statement in the _History_, it appears that Mr. Cavendish's

claim to the discovery was not uncontested in his own time.

Mr. Watt had looked at the composition of water, as a

problem to be solved, perhaps more distinctly than Mr.

Cavendish had done; and he conceived himself wronged by Mr.

Cavendish's putting forwards his experiment as the first

solution of this problem.]

6. _Relation of Heat to Chemistry._--But while we thus

condemn the attempts to explain the thermotical phenomena of

chemical processes by means of chemical considerations, it

may be asked if we are altogether to renounce the hope of

understanding such phenomena? It is plain, it may be said,

that heat generated in chemical changes is always a very

important circumstance, and can sometimes be measured, and

perhaps reduced to laws; are we prohibited from speculating

concerning the causes of such circumstances and such laws?

And to this we reply, that we may properly attempt to

connect chemical with thermotical processes, _so far as_ we

have obtained a clear and probable view of the nature of the

thermotical processes. When our theory of Thermotics is

tolerably complete and certain, we may with propriety

undertake to connect it with our theory of Chemistry. But at

present we are not far enough advanced in our knowledge of

heat to make this attempt with any hope of success. We can

hardly expect to understand the part which heat plays in the

union of two bodies, when we cannot as yet comprehend in

what manner it produces the liquefaction or vaporization of

one body. We cannot look to account for Gay Lussac and

Dalton's Law, that all gases expand equally by heat, till we

learn how heat causes a gas to expand. We cannot hope to see

the grounds of Dulong and Petit's Law, that the specific

heat of all atoms is the same, till we know much more, not

only about atoms, but about specific heat. We have as yet no

thermotical theory which even professes to account for all

the prominent facts of the subject[37\6]: and the theories

which have been proposed are of the most diverse kind.

Laplace assumes particles of bodies surrounded by

atmospheres of caloric[38\6]; Cauchy makes heat consist in

longitudinal vibrations of the ether of which transverse

vibrations {47} produce light: in Ampère's theory[39\6],

heat consists in the vibrations of the particles of bodies.

And so long as we have nothing more certain in our

conceptions of heat than the alternative of these and other

precarious hypotheses, how can we expect to arrive at any

real knowledge, by connecting the results of such hypotheses

with the speculations of Chemistry, of which science the

theory is at least equally obscure?

[Note 37\6: _Hist. Ind. Sci._ b. x. c. 4.]

[Note 38\6: _Ib._]

[Note 39\6: _Hist. Ind. Sci._ b. x. c. 4.]

The largest attempts at chemical theory have been made in

the form of the Atomic Theory, to which I have just had

occasion to allude. I must, therefore, before quitting the

subject, say a few words respecting this theory.

CHAPTER V.

THE ATOMIC THEORY.

1. _The Atomic Theory considered on Chemical Grounds._--WE

have already seen that the combinations which result from

chemical affinity are definite, a certain quantity of one

ingredient uniting, not with an uncertain, but with a

certain quantity of another ingredient. But it was found, in

addition to this principle, that one ingredient would often

unite with another in different proportions, and that, in

such cases, these proportions are multiples one of another.

In the three salts formed by potassa with oxalic acid, the

quantities of acid which combine with the same quantity of

alkali are exactly in the proportion of the numbers 1, 2, 4.

And the same rule of the existence of multiple proportions

is found to obtain in other cases.

It is obvious that such results will be accounted for, if we

suppose that the base and the acid consist each of numerous

definite equal particles, and that the formation of the

salts above mentioned consists in the combination of one

particle of the base with one particle of acid, with two

particles of acid, and with four particles of acid,

respectively. But further; as we have already stated,

chemical affinity is not only definite, but reciprocal. The

proportions of potassa and soda which form neutral salts

being 590 and 391 in one case, they are so in all cases.

These numbers represent _proportions_ of weight in which the

two bases, potassa and soda, enter into analogous

combinations; 590 of potassa is _equivalent_ to 391 of soda.

These facts with regard to combination are still expressed

by the above supposition of equal particles, assuming that

the weights of a {49} particle of potassa and of soda are in

the proportion of 590 to 391.

But we pursue our analysis further. We find that potassa is

a compound of a metallic base, potassium, and of oxygen, in

the proportion of 490 to 100; we suppose, then, that the

particle of potassa consists of a particle of potassium and

a particle of oxygen; and these latter particles, since we

see no present need to suppose them divided, potassium and

oxygen being simple bodies, we may call _atoms_, and assume to

be indivisible. And by supposing all simple bodies to

consist of such atoms, and compounds to be formed by the

union of two, or three, or more of such atoms, we explain

the occurrence of definite and multiple proportions, and we

construct the Atomic Theory.

2. _Hypothesis of Atoms._--So far as the assumption of such

atoms as we have spoken of serves to express those laws of

chemical composition which we have referred to, it is a

clear and useful generalization. But if the Atomic Theory be

put forwards (and its author, Dr. Dalton, appears to have

put it forwards with such an intention,) as asserting that

chemical elements are really composed of _atoms_, that is,

of such particles not further divisible, we cannot avoid

remarking, that for such a conclusion, chemical research has

not afforded, nor can afford, any satisfactory evidence

whatever. The smallest observable quantities of ingredients,

as well as the largest, combine according to the laws of

proportions and equivalence which have been cited above. How

are we to deduce from such facts any inference with regard

to the existence of certain smallest possible particles? The

Theory, when dogmatically taught as a physical truth,

asserts that all observable quantities of elements _are_

composed of proportional numbers of particles which can no

further be subdivided; but all which observation teaches us

is, that if there be such particles, they are smaller than

the smallest observable quantities. In chemical experiment,

at least, there is not the slightest positive evidence for

the existence of such atoms. The assumption of _indivisible_

particles, smaller than the smallest {50} observable, which

combine, particle with particle, will explain the phenomena;

but the assumption of particles bearing this proportion, but

_not_ possessing the property of indivisibility, will explain

the phenomena at least equally well. The decision of the

question, therefore, whether the Atomic Hypothesis be the

proper way of conceiving the chemical combinations of

substances, must depend, not upon chemical facts, but upon

our conception of Substance. In this sense the question is

an ancient and curious controversy, and we shall hereafter

have to make some remarks upon it.

3. _Chemical Difficulties of the Hypothesis._--But before

doing this, we may observe that there is no small difficulty

in reconciling this hypothesis with the facts of chemistry.

According to the theory, all salts, compounded of an acid

and a base, are analogous in their atomic constitution; and

the number of atoms in one such compound being known or

assumed, the number of atoms in other salts may be

determined. But when we proceed in this course of reasoning

to other bodies, as metals, we find ourselves involved in

difficulties. The protoxide of iron is a base which,

according to all analogy, must consist of one atom of iron

and one of oxygen: but the peroxide of iron is also a base,

and it appears by the analysis of this substance that it

must consist of _two-thirds_ of an atom of iron and one atom

of oxygen. Here, then, our indivisible atoms must be

divisible, even upon chemical grounds. And if we attempt to

evade this difficulty by making the peroxide of iron consist

of two atoms of iron and three of oxygen, we have to make a

corresponding alteration in the theoretical constitution of

all bodies analogous to the protoxide; and thus we overturn

the very foundation of the theory. Chemical facts,

therefore, not only do not prove the Atomic Theory as a

physical truth, but they are not, according to any

modification yet devised of the theory, reconcileable with

its scheme.

Nearly the same conclusions result from the attempts to

employ the Atomic Hypothesis in expressing another important

chemical law;--the law of the {51} combinations of gases

according to definite proportions of their volumes,

experimentally established by Gay Lussac[40\6]. In order to

account for this law, it has been very plausibly suggested

that all gases, under the same pressure, contain an equal

number of atoms in the same space; and that when they

combine, they unite atom to atom. Thus one volume of

chlorine unites with one volume of hydrogen, and forms

hydrochloric acid[41\6]. But then this hydrochloric acid

occupies the space of the two volumes; and therefore the

proper number of particles cannot be supplied, and the

uniform distribution of atoms in all gases maintained,

without dividing into two each of the compound particles,

constituted of an atom of chlorine and an atom of hydrogen.

And thus in this case, also, the Atomic Theory becomes

untenable if it be understood to imply the indivisibility of

the atoms.

[Note 40\6: _Hist. Ind. Sc._ b. xiv. c. 8.]

[Note 41\6: Dumas, _Phil. Chim._ 263.]

In all these attempts to obtain distinct physical conception

of chemical union by the aid of the Atomic Hypothesis, the

atoms are conceived to be associated by certain forces of

the nature of mechanical attractions. But we have already

seen[42\6] that no such mode of conception can at all

explain or express the facts of chemical combination; and

therefore it is not wonderful that when the Atomic Theory

attempts to give an account of chemical relations by

contemplating them under such an aspect, the facts on which

it grounds itself should be found not to authorize its

positive doctrines; and that when these doctrines are tried

upon the general range of chemical observation, they should

prove incapable of even expressing, without

self-contradiction, the laws of phenomena.

[Note 42\6: See Chapter I. of this book.]

4. _Grounds of the Atomic Doctrine._--Yet the doctrine of

atoms, or of substance as composed of indivisible particles,

has in all ages had great hold upon the minds of physical

speculators; nor would this doctrine ever have suggested

itself so readily, or have been maintained so tenaciously,

as the true mode of {52} conceiving chemical combinations,

if it had not been already familiar to the minds of those

who endeavour to obtain a general view of the constitution

of nature. The grounds of the assumption of the atomic

structure of substance are to be found rather in the idea of

substance itself, than in the experimental laws of chemical

affinity. And the question of the existence of atoms, thus

depending upon an idea which has been the subject of

contemplation from the very infancy of philosophy, has been

discussed in all ages with interest and ingenuity. On this

very account it is unlikely that the question, so far as it

bears upon chemistry, should admit of any clear and final

solution. Still it will be instructive to look back at some

of the opinions which have been delivered respecting this

doctrine.

5. _Ancient Prevalence of the Atomic Doctrine._--The

doctrine that matter consists of minute, simple,

indivisible, indestructible particles as its ultimate

elements, has been current in all ages and countries,

whenever the tendency of man to wide and subtle speculations

has been active. I need not attempt to trace the history of

this opinion in the schools of Greece and Italy. It was the

leading feature in the physical tenets of the Epicureans,

and was adopted by their Roman disciples, as the poem of

Lucretius copiously shows us. The same tenet had been held

at still earlier periods, in forms more or less definite, by

other philosophers. It is ascribed to Democritus, and is

said to have been by him derived from Leucippus. But this

doctrine is found also, we are told[43\6], among the

speculations of another intellectual and acute race, the

Hindoos. According to some of their philosophical writers,

the ultimate elements of matter are atoms, of which it is

proved by certain reasonings, that they are each one-sixth

of one of the motes that float in the sunbeam.

[Note 43\6: By Mr. Colebrook. _Asiatic Res._ 1824.]

This early prevalence of controversies of the widest and

deepest kind, which even in our day remain undecided, has in

it nothing which need surprize us; or, at least, it has in

it nothing which is not in conformity {53} with the general

course of the history of philosophy. As soon as any ideas

are clearly possessed by the human mind, its activity and

acuteness in reasoning upon them are such, that the

fundamental antitheses and ultimate difficulties which

belong to them are soon brought into view. The Greek and

Indian philosophers had mastered completely the Idea of

Space, and possessed the Idea of Substance in tolerable

distinctness. They were, therefore, quite ready, with their

lively and subtle minds, to discuss the question of the

finite and infinite divisibility of matter, so far as it

involved only the ideas of space and of substance, and this

accordingly they did with great ingenuity and perseverance.

But the ideas of Space and of Substance are far from being

sufficient to enable men to form a complete general view of

the constitution of matter. We must add to these ideas, that

of mechanical Force with its antagonist Resistance, and that

of the Affinity of one kind of matter for another. Now the

former of these ideas the ancients possessed in a very

obscure and confused manner; and of the latter they had no

apprehension whatever. They made vague assumptions

respecting the impact and pressure of atoms on each other;

but of their mutual attraction and repulsion they never had

any conception, except of the most dim and wavering kind;

and of an affinity different from mere local union they did

not even dream. Their speculations concerning atoms,

therefore, can have no value for us, except as a part of the

history of science. If their doctrines appear to us to

approach near to the conclusions of our modern philosophy,

it must be because our modern philosophy is that philosophy

which has not fully profited by the additional light which

the experiments and meditations of later times have thrown

upon the constitution of matter.

6. _Bacon._--Still, when modern philosophers look upon the

Atomic Theory of the ancients in a general point of view

merely, without considering the special conditions which

such a theory must fulfil, in order to represent the

discoveries of modern times, they are {54} disposed to

regard it with admiration. Accordingly we find Francis Bacon

strongly expressing such a feeling. The Atomic Theory is

selected and dwelt upon by him as the chain which connects

the best parts of the physical philosophy of the ancient and

the modern world. Among his works is a remarkable

dissertation _On the Philosophy of Democritus, Parmenides,

and Telesius_: the last mentioned of whom was one of the

revivers of physical science in modern times. In this work

he speaks of the atomic doctrine of Democritus as a

favourable example of the exertions of the undisciplined

intellect. 'Hæc ipsa placita, quamvis paulo emendatiora,

talia sunt qualia esse possunt illa quæ ab intellectu sibi

permisso, nec continenter et gradatim sublevato, profecta

videntur.'--'These doctrines, thus [in an ancient fable]

presented in a better form, are such glimpses of truth as

can be obtained by the intellect left to its own natural

impulses, and not ascending by successive and connected

steps,' [as the Baconian philosophy directs]. 'Accordingly,'

he adds, 'the doctrine of Atoms, from its going a step

beyond the period in which it was advanced, was ridiculed by

the vulgar, and severely handled in the disputations of the

learned, notwithstanding the profound acquaintance with

physical science by which its author was allowed to be

distinguished, and from which he acquired the character of a

magician.'

'However,' he continues, 'neither the hostility of

Aristotle, with all his skill and vigour in disputation,

(though, like the Ottoman sultans, he laboured to destroy

all his brother philosophers that he might rest undisputed

master of the throne of science,) nor the majestic and lofty

authority of Plato, could effect the subversion of the

doctrine of Democritus. And while the opinions of Plato and

Aristotle were rehearsed with loud declamation and

professorial pomp in the schools, this of Democritus was

always held in high honour by those of a deeper wisdom, who

followed in silence a severer path of contemplation. In the

days of Roman speculation it kept its ground and its favour;

Cicero everywhere speaks of its author with the {55}

greatest praise; and Juvenal, who, like poets in general,

probably expressed the prevailing judgment of his time,

proclaims his merit as a noble exception to the general

stupidity of his countrymen.

. . . . Cujus prudentia monstrat

Magnos posse viros et magna exempla daturos

Vervecum in patriâ crassoque sub aere nasci.

'The destruction of this philosophy was not effected by

Aristotle and Plato, but by Genseric and Attila, and their

barbarians. For then, when human knowledge had suffered

shipwreck, those fragments of the Aristotelian and Platonic

philosophy floated on the surface like things of some

lighter and emptier sort, and so were preserved; while more

solid matters went to the bottom, and were almost lost in

oblivion.'

7. _Modern Prevalence of the Atomic Doctrine._--It is our

business here to consider the doctrine of Atoms only in its

bearing upon existing physical sciences, and I must

therefore abstain from tracing the various manifestations of

it in the schemes of hypothetical cosmologists;--its place

among the _vortices_ of Descartes, its exhibition in the

_monads_ of Leibnitz. I will, however, quote a passage from

Newton to show the hold it had upon his mind.

At the close of his _Opticks_ he says, 'All these things

being considered, it seems probable to me that God, in the

beginning, formed matter in solid, massy, hard,

impenetrable, moveable particles, of such sizes and figures,

and with such other properties, and in such proportions to

space, as most conduced to the end for which He formed them;

and that the primitive particles, being solids, are

incomparably harder than any porous bodies compounded of

them, even so very hard as never to wear or break in pieces;

no ordinary power being able to divide what God had made one

in the first creation. While the particles continue entire,

they may compose bodies of one and the same nature and

texture in all ages: but should they wear away or break in

pieces, the nature of things depending on them would be

changed. Water and earth composed {56} of old worn particles

and fragments of particles would not be of the same nature

and texture now with water and earth composed of entire

particles in the beginning. And therefore that nature may be

lasting, the changes of corporeal things are to be placed

only in the various separations and new associations and

motions of these permanent particles; compounded bodies

being apt to break, not in the midst of solid particles, but

where those particles are laid together and only touch in a

few points.'

We shall hereafter see how extensively the atomic doctrine

has prevailed among still more recent philosophers. Not only

have the chemists assumed it as the fittest form for

exhibiting the principles of multiple proportions; but the

physical mathematicians, as Laplace and Poisson, have made

it the basis of their theories of heat, electricity,

capillary action; and the crystallographers have been

supposed to have established both the existence and the

arrangement of such ultimate molecules.

In the way in which it has been employed by such writers,

the hypothesis of ultimate particles has been of great use,

and is undoubtedly permissible. But when we would assert

this theory, not as a convenient hypothesis for the

expression or calculation of the laws of nature, but as a

philosophical truth respecting the constitution of the

universe, we find ourselves checked by difficulties of

reasoning which we cannot overcome, as well as by

conflicting phenomena which we cannot reconcile. I will

attempt to state briefly the opposing arguments on this

question.

8. _Arguments for and against Atoms._--The leading arguments

on the two sides of the question, in their most general

form, may be stated as follows:

_For_ the Atomic Doctrine.--The appearances which nature

presents are compounded of many parts, but if we go on

resolving the larger parts into smaller, and so on

successively, we must at last come to something simple. For

that which is compound can be so no otherwise than by

composition of what is simple; and if we suppose all

composition to be removed, which {57} hypothetically we may

do, there can remain nothing but a number of simple

substances, capable of composition, but themselves not

compounded. That is, matter being dissolved, resolves itself

into atoms.

_Against_ the Atomic Doctrine.--Space is divisible without

limit, as may be proved by Geometry; and matter occupies

space, therefore matter is divisible without limit, and no

portion of matter is indivisible, or an _atom_.

And to the argument on the other side just stated, it is

replied that we cannot even hypothetically divest a body of

composition, if by composition we mean the relation of point

to point in space. However small be a particle, it is

compounded of parts having relation in space.

The Atomists urge again, that if matter be infinitely

divisible, a finite body consists of an infinite number of

parts, which is a contradiction. To this it is replied, that

the finite body consists of an infinite number of parts in

the same sense in which the parts are infinitely small,

which is no contradiction.

But the opponents of the Atomists not only rebut, but retort

this argument drawn from the notion of infinity. Your atoms,

they say, are indivisible by any finite force; therefore

they are infinitely hard; and thus your finite particles

possess infinite properties. To this the Atomists are wont

to reply, that they do not mean the hardness of their

particles to be infinite, but only so great as to resist all

usual natural forces. But here it is plain that their

position becomes untenable; for, in the first place, their

assumption of this precise degree of hardness in the

particles is altogether gratuitous; and in the next place,

if it were granted, such particles are not atoms, since in

the next moment the forces of nature may be augmented so as

to divide the particle, though hitherto undivided.

Such are the arguments for and against the Atomic Theory in

its original form. But when these atoms are conceived, as

they have been by Newton, and commonly by his followers, to

be solid, hard particles exerting attractive and repulsive

forces, a new set of {58} arguments come into play. Of

these, the principal one may be thus stated: According to

the Atomic Theory thus modified, the properties of bodies

depend upon the attractions and repulsions of the particles.

Therefore, among other properties of bodies, their hardness

depends upon such forces. But if the hardness _of the

bodies_ depends upon the forces, the repulsion, for

instance, of the particles, upon what does the hardness _of

the particles_ depend? what progress do we make in

explaining the properties of bodies, when we assume the same

properties in our explanation? and to what purpose do we

assume that the particles are hard?

9. _Transition to Boscovich's Theory._--To this difficulty

it does not appear easy to offer any reply. But if the

hardness and solidity of the particles be given up as an

incongruous and untenable appendage to the Newtonian view of

the Atomic Theory, we are led to the theory of Boscovich,

according to which matter consists not of solid particles,

but of mere mathematical centers of force. According to this

theory, each body is composed of a number of geometrical

points from which emanate forces, following certain

mathematical laws in virtue of which the forces become, at

certain small distances attractive, at certain other

distances repulsive, and at greater distances attractive

again. From these forces of the points arise the cohesion of

the parts of the same body, the resistance which it exerts

against the pressure of another body, and finally the

attraction of gravitation which it exerts upon bodies at a

distance.

This theory is at least a homogeneous and consistent theory,

and it is probable that it may be used as an instrument for

investigating and expressing true laws of nature; although,

as we have already said, the attempt to identify the forces

by which the particles of bodies are bound together with

mechanical attraction, appears to be a confusion of two

separate ideas[44\6].

[Note 44\6: 'Boscovich's Theory,' that all bodies may be

considered as consisting of a mere collection of centers of

forces, may be so conceived as possibly to involve an

explanation of all the powers which their parts exert, (such

powers, namely, as those which produce optical, thermotical

and chemical phenomena;) but this theory cannot supply an

explanation of the mechanical properties of a body as a

whole, especially of its _inertia_. A collection of mere

centers of force can have no inertia. If two bodies are

considered as two collections of centers of force, the one

attracting the other, there is in this view nothing to limit

or determine the velocity with which the one body will

approach the other. A world composed of such bodies is not a

_material_ world: for matter (as we have already seen in

book iii. chapter v.) implies not only force, but something

which resists the action of force.]

{59} 10. _Use of the Molecular Hypothesis._--In this form,

representing matter as a collection of molecules or centers

of force, the Atomic Theory has been abundantly employed in

modern times as an hypothesis on which calculations

respecting the elementary forces of bodies might be

conducted. When thus employed it is to be considered as

expressing the principle that the properties of bodies

depend upon forces emanating from immovable points of their

mass. This view of the way in which the properties of bodies

are to be treated by the mechanical philosopher was

introduced by Newton, and was a natural sequel to the

success which he had obtained by reasoning concerning

central forces on a large scale. I have already quoted his

Preface to the _Principia_, in which he says, 'Many things

induce me to believe that the rest of the phenomena of

nature, as well as those of astronomy, may depend upon

certain forces by which the particles of bodies, in virtue

of causes not yet known, are urged towards each other and

cohere in regular figures, or are mutually repelled and

recede; and philosophers, knowing nothing of these forces,

have hitherto failed in their examination of nature.' Since

the time of Newton, this line of speculation has been

followed with great assiduity, and by some mathematicians

with great success. In particular Laplace has shown that the

hypothesis may, in many instances, be made a much closer

representation of nature, if we suppose the forces exerted

by the particles to decrease so rapidly with the increasing

distance from them, that {60} the force is finite only at

distances imperceptible to our senses, and vanishes at all

remoter points. He has taught the method of expressing and

calculating such forces, and he and other mathematicians of

his school have applied this method to many of the most

important questions of physics; as capillary action, the

elasticity of solids, the conduction and radiation of heat.

The explanation of many apparently unconnected and curious

observed facts by these mathematical theories gives a strong

assurance that its essential principles are true. But it

must be observed that the actual constitution of bodies as

composed of distinct and separate particles is by no means

proved by these coincidences. The assumption, in the

reasoning, of certain centers of force acting at a distance,

is to be considered as nothing more than a method of

reducing to calculation that view of the constitution of

bodies which supposes that they exert force at _every_

point. It is a mathematical artifice of the same kind as the

hypothetical division of a body into infinitesimal parts, in

order to find its center of gravity; and no more implies a

physical reality than that hypothesis does.

11. _Poisson's Inference._--When, therefore, M. Poisson, in

his views of Capillary Action, treats this hypothetical

distribution of centers of force as if it were a physical

fact, and blames Laplace for not taking account of their

different distribution at the surface of the fluid and below

it[45\6], he appears to push the claims of the molecular

hypothesis too far. The only ground for the assumption of

separate centers, is that we can thus explain the action of

the whole mass. The intervals between the centers nowhere

enter into this explanation: and therefore we can have no

reason for assuming these intervals different in one part of

the fluid and in the other. M. Poisson asserts that the

density of the fluid diminishes when we approach very near

the surface; but he allows that this diminution is not

detected by experiment, and that the formulæ on {61} his

supposition, so far as the results go, are identical with

those of Laplace. It is clear, then, that his doctrine

consists merely in the assertion of the necessary truth of a

part of the hypothesis which cannot be put to the test of

experiment. It is true, that so long as we have before us

the hypothesis of separate centers, the particles very near

the surface are not in a condition symmetrical with that of

the others: but it is also true that this hypothesis is only

a step of calculation. There results, at one period of the

process of deduction, a stratum of smaller density at the

surface of the fluid; but at a succeeding point of the

reasoning the thickness of this stratum vanishes; it has no

physical existence.

[Note 45\6: Poisson, _Théorie de l'Action Capillaire_.]

Thus the _molecular_ hypothesis, as used in such cases, does

not differ from the doctrine of forces acting at _every

point_ of the mass; and this principle, which is common to

both the opposite views, is the true part of each.

12. _Wollaston's Argument._--An attempt has been made in

another case, but depending on nearly the same arguments, to

bring the doctrine of ultimate atoms to the test of

observation. In the case of the air, we know that there _is_

a diminution of density in approaching the upper surface of

the atmosphere, if it have a surface: but it is held by some

that except we allow the doctrine of ultimate molecules, it

will not be bounded by any surface, but will extend to an

infinite distance. This is the reasoning of Wollaston[46\6].

'If air consists of any ultimate particles no longer

divisible, then must the expansion of the medium composed of

them cease at that distance where the force of gravity

downwards is equal to the resistance arising from the

repulsive force of the medium.' But if there be no such

ultimate particles, every stratum will require a stratum

beyond it to prevent by its weight a further expansion, and

thus the atmosphere {62} must extend to an infinite

distance. And Wollaston conceived that he could learn from

observation whether the atmosphere was thus diffused through

all space; for if so, it must, he argued, be accumulated

about the larger bodies of the system, as Jupiter and the

Sun, by the law of universal gravitation; and the existence

of an atmosphere about these bodies, might, he remarked, be

detected by its effects in producing refraction. His result

is, that 'all the phenomena accord entirely with the

supposition that the earth's atmosphere is of finite extent,

limited by the weight of ultimate atoms of definite

magnitude, no longer divisible by repulsion of their parts.'

[Note 46\6: _Phil. Trans._ 1822, p. 89.]

A very little reflection will show us that such a line of

reasoning cannot lead to any result. For we know nothing of

the law which connects the density with the compressing

force, in air so extremely rare as we must suppose it to be

near the boundary of the atmosphere. Now there are possible

laws of dependence of the density upon the compressing force

such that the atmosphere would terminate in virtue of the

law without any assumption of atoms. This may be proved by

mathematical reasoning. If we suppose the density of air to

be as the square root of the compressing force, it will

follow that at the very limits of the atmosphere, the strata

of equal thickness may observe in their densities such a law

of proportion as is expressed by the numbers 7, 5, 3,

1[47\6].

[Note 47\6: For the compressing force on each being as the

whole weight beyond it, it will be for the four highest

strata, 16, 9, 4 and 1, of which the square roots are as 4,

3, 2, 1, or, as 8, 6, 4, 2; and though these numbers are not

exactly as the densities 7, 5, 3, 1, those who are a little

acquainted with mathematical reasoning, will see that the

difference arises from taking so small a number of strata.

If we were to make the strata indefinitely thin, as to avoid

error we ought to do, the coincidence would be exact; and

thus, according to this law, the series of strata terminates

as we ascend, without any consideration of atoms.]

If it be asked how, on this hypothesis, the density of the

highest stratum can be as 1, since there is {63} nothing to

compress it, we answer that the upper part of the highest

stratum compresses the lower, and that the density

diminishes continually to the surface, so that the need of

compression and the compressing weight vanish together.

The fallacy of concluding that because the height of the

atmosphere is finite, the weight of the highest stratum must

be finite, is just the same as the fallacy of those who

conclude that when we project a body vertically upwards,

because it occupies only a finite time in ascending to the

highest point, the velocity at the last instant of the

ascent must be finite. For it might be said, if the last

velocity of ascent be not finite, how can the body describe

the last particle of space in a finite time? and the answer

is, that there is no last finite particle of space, and

therefore no last finite velocity.

13. _Permanence of Properties of Bodies._--We have already

seen that, in explaining the properties of matter as we find

them in nature, the assumption of solid, hard,

indestructible particles is of no use or value. But we may

remark, before quitting the subject, that Newton appears to

have had another reason for assuming such particles, and one

well worthy of notice. He wished to express, by means of

this hypothesis, the doctrine that the laws of nature do not

alter with the course of time. This we have already seen in

the quotation from Newton. 'The ultimate particles of matter

are indestructible, unalterable, impenetrable; for if they

could break or wear, the structure of material bodies now

would be different from that which it was when the particles

were new.' No philosopher will deny the truth which is thus

conveyed by the assertion of atoms; but it is obviously

equally easy for a person who rejects the atomic view, to

state this truth by saying that the forces which matter

exerts do not vary with time, but however modified by the

new modifications of its form, are always unimpaired in

quantity, and capable of being restored to their former mode

of action. {64}

We now proceed to speculations in which the fundamental

conceptions may, perhaps, be expressed, at least in some

cases, by means of the arrangement of atoms; but in which

the philosophy of the subject appears to require a reference

to a new Fundamental Idea.

BOOK VII.

THE

PHILOSOPHY

MORPHOLOGY,

INCLUDING

CRYSTALLOGRAPHY.

CRYSTALLIZATION exhibits to us the effects of the natural

arrangement of the ultimate particles of various compound

bodies; but we are scarcely yet sufficiently acquainted with

chemical synthesis and analysis to understand the rationale

of this process. The rhomboidal form may arise from the

proper position of 4, 6, 8 or 9 globular particles, the

cubic form from 8 particles, the triangular form from 3, 6

or 10 particles, the hexahedral prism from 7 particles, &c.

Perhaps, in due time we may be enabled to ascertain the

number and order of elementary particles, constituting any

given compound element, and from that determine the figure

which it will prefer on crystallization, and _vice versâ_.

JOHN DALTON, _Chemical Philosophy_ (1808), p. 210.

BOOK VII.

THE PHILOSOPHY OF MORPHOLOGY, INCLUDING CRYSTALLOGRAPHY.

CHAPTER I.

EXPLICATION OF THE IDEA OF SYMMETRY.

1. WE have seen in the History of the Sciences, that the

principle which I have there termed[1\7] the Principle of

Developed and Metamorphosed Symmetry, has been extensively

applied in botany and physiology, and has given rise to a

province of science termed Morphology. In order to

understand clearly this principle, it is necessary to obtain

a clear idea of the Symmetry of which we thus speak. But

this Idea of Symmetry is applicable in the inorganic, as

well as in the organic kingdoms of nature; it is presented

to our eyes in the forms of minerals, as well as of flowers

and animals; we must, therefore, take it under our

consideration here, in order that we may complete our view

of Mineralogy, which, as I have repeatedly said, is an

essential part of Chemical science. I shall accordingly

endeavour to unfold the Idea of Symmetry with which we here

have to do.

[Note 1\7: _Hist. Ind. Sc._ b. xvii. c. vi.]

It will of course be understood that by the term _Symmetry_

I here intend, not that more indefinite attribute of form

which belongs to the domain of the fine arts, as when we

speak of the 'symmetry' of an edifice {68} or of a

sculptured figure, but a certain definite relation or

property, no less rigorous and precise than other relations

of number and position, which is thus one of the sure guides

of the scientific faculty, and one of the bases of our exact

science.

2. In order to explain what Symmetry is in this sense, let

the reader recollect that the bodies of animals consist of

_two_ equal and similar sets of members, the right and the

left side;--that some flowers consist of three or of five

equal sets of organs, similarly and regularly disposed, as

the iris has _three_ straight petals, and three reflexed

ones, alternately disposed, the rose has _five_ equal and

similar sepals of the calyx, and alternate with these, as

many petals of the corolla. This orderly and exactly similar

distribution of two, or three, or five, or any other number

of parts, is Symmetry; and according to its various

modifications, the forms thus determined are said to be

_symmetrical_ with various numbers of members. The

classification of these different kinds of symmetry has been

most attended to in Crystallography, in which science it is

the highest and most general principle by which the classes

of forms are governed. Without entering far into the

technicalities of the subject, we may point out some of the

features of such classes.

[Illustration] The first of the figures (1) in the margin

may represent the summit of a crystal as it appears to an

eye looking directly down upon it; the center of the figure

represents the summit of a pyramid, and the spaces of

various forms which diverge from this point represent

sloping sides of the pyramid. Now it will be observed that

the figure consists of three portions exactly similar to one

another, and that each part or member is repeated in each of

these portions. The faces, or pairs of faces, are repeated

in _threes_, with exactly similar forms and angles. This

figure is said to be _three-membered_, or to have

_triangular_ symmetry. The same kind of {69} symmetry may

exist in a flower, as presented in the accompanying figure,

and does, in fact, occur in a large class of flowers, as for

example, all the lily tribe. The next pair of figures (2)

have four equal and similar portions, and have their members

or pairs of members four times repeated. Such figures are

termed _four-membered_, and are said to have _square_ or

_tetragonal_ symmetry. The _pentagonal_ symmetry, formed by

_five_ similar _members_, is represented in the next figures

(3). It occurs abundantly in the vegetable world, but never

among crystals; for the pentagonal figures which crystals

sometimes assume, are never exactly regular. But there is

still another kind of symmetry (4) in which the opposite

ends are exactly similar to each other and also the opposite

sides; this is _oblong_, or _two-and-two-membered_ symmetry.

And finally, we have the case of _simple_ symmetry (5) in

which the two sides of the object are exactly alike (in

opposite positions) without any further repetition.

[Illustration]

3. These different kinds of symmetry occur in various ways

in the animal, vegetable, and mineral kingdom. Vertebrate

animals have a right and a {70} left side exactly alike, and

thus possess _simple_ symmetry. The same kind of symmetry

(simple symmetry) occurs very largely in the forms of

vegetables, as in most leaves, in _papilionaceous_,

_personate_, and _labiate_ flowers. Among minerals, crystals

which possess this symmetry are called _oblique-prismatic_,

and are of very frequent occurrence. The _oblong_, or

_two-and-two-membered_ symmetry belongs to _right-prismatic_

crystals; and may be seen in _cruciferous_ flowers, for

though these are cross-shaped, the cross has two longer and

two shorter arms, or pairs of arms. The _square_ or

_tetragonal_ symmetry occurs in crystals abundantly; to the

vegetable world it appears to be less congenial; for though

there are flowers with four exactly similar and

regularly-disposed petals, as the herb Paris (_Paris

quadrifolia_), these flowers appear, from various

circumstances, to be deviations from the usual type of

vegetable forms. The _trigonal_, or _three-membered_

symmetry is found abundantly both in plants and in crystals,

while the _pentagonal_ symmetry, on the other hand, though

by far the most common among flowers, nowhere occurs in

minerals, and does not appear to be a possible form of

crystals. This pentagonal form further occurs in the animal

kingdom, which the oblong, triangular, and square forms do

not. Many of Cuvier's _radiate_ animals appear in this

pentagonal form, as _echini_ and _pentacrinites_, which

latter have hence their name.

4. The regular, or as they may be called, the _normal_ types

of the vegetable world appear to be the forms which possess

triangular and pentagonal symmetry; from these the others

may be conceived to be derived, by transformations resulting

from the expansion of one or more parts. Thus it is manifest

that if in a three-membered or five-membered flower, one of

the petals be expanded more than the other, it is

immediately reduced from pentagonal or trigonal, to simple

symmetry. And the oblong or two-and-two-membered symmetry of

the flowers of cruciferous plants, (in which the stamens are

four large and two small ones, arranged in regular

opposition,) is held by botanists to result {71} from a

normal form with ten stamens; Meinecke explaining this by

adhesion, and Sprengel by the metamorphosis of the stamens

into petals[2\7].

[Note 2\7: Sprengel, _Gesch. d. Bot._ ii. 304.]

It is easy to see that these various kinds of symmetry

include relations both of form and of number, but more

especially of the latter kind; and as this symmetry is often

an important character in various classes of natural

objects, such classes have often curious numerical

properties. One of the most remarkable and extensive of

these is the distinction which prevails between

monocotyledonous and dicotyledonous plants; the number

_three_ being the ground of the symmetry of the former, and

the number _five_, of the latter. Thus liliaceous and

bulbous plants, and the like, have flowers of three or six

petals, and the other organs follow the same numbers: while

the vast majority of plants are pentandrous, and with their

five stamens have also their other parts in fives. This

great numerical distinction corresponding to a leading

difference of physiological structure cannot but be

considered as a highly curious fact in phytology. Such

properties of numbers, thus connected in an incomprehensible

manner with fundamental and extensive laws of nature, give

to numbers an appearance of mysterious importance and

efficacy. We learn from history how strongly the study of

such properties, as they are exhibited by the phenomena of

the heavens, took possession of the mind of Kepler; perhaps

it was this which, at an earlier period, contributed in no

small degree to the numerical mysticism of the Pythagoreans

in antiquity, and of the Arabians and others in the middle

ages. In crystallography, numbers are the primary characters

in which the properties of substances are expressed;--they

appear, first, in that classification of forms which depends

on the degree of symmetry, that is, upon the number of

correspondencies; and next, in the laws of derivation,

which, for the most part, appear to be common in their

occurrence in proportion to the numerical simplicity of

their expression. But the manifestation {72} of a governing

numerical relation in the organic world strikes us as more

unexpected; and the selection of the number _five_ as the

index of the symmetry of dicotyledonous plants and radiated

animals, (a number which is nowhere symmetrically produced

in inorganic bodies,) makes this a new and remarkable

illustration of the constancy of numerical relations. We may

observe, however, that the moment one of these radiate

animals has one of its five members expanded, or in any way

peculiarly modified, (as happens among the echini), it is

reduced to the common type of animals simply symmetrical,

with a right and left side.

5. It is not necessary to attempt to enumerate all the kinds

of Symmetry, since our object is only to explain what

Symmetry is, and for this purpose enough has probably been

said already. It will be seen, as soon as the notion of

Symmetry in general is well apprehended, that it is or

includes a peculiar Fundamental Idea, not capable of being

resolved into any of the ideas hitherto examined. It may be

said, perhaps, that the Idea of Symmetry is a modification

or derivative of our ideas of space and number;--that a

symmetrical shape is one which consists of parts exactly

similar, repeated a certain number of times, and placed so

as to correspond with each other. But on further reflection

it will be seen that this repetition and correspondence of

parts in symmetrical figures are something peculiar; for it

is not _any_ repetition or any correspondence of parts to

which we should give the name of symmetry, in the manner in

which we are now using the term. Symmetrical arrangements

may, no doubt, be concerned with space and position, time

and number; but there appears to be implied in them a

Fundamental Idea of regularity, of completeness, of complex

simplicity, which is not a mere modification of other ideas.

6. It is, however, not necessary, in this and in similar

cases, to determine whether the idea which we have before us

be a peculiar and independent Fundamental Idea or a

modification of other ideas, provided we clearly perceive

the evidence of those Axioms by {73} means of which the Idea

is applied in scientific reasonings. Now in the application

of the Idea of Symmetry to crystallography, phytology and

zoology, we must have this idea embodied in some principle

which asserts more than a mere geometrical or numerical

accordance of members. We must have it involved in some

vital or productive action, in order that it may connect and

explain the facts of the organic world. Nor is it difficult

to enunciate such a principle. We may state it in this

manner. _All the symmetrical members of a natural product

are, under like circumstances, alike affected by the natural

formative power._ The parts which we have termed

_symmetrical_, resemble each other, not only in their form

and position, but also in the manner in which they are

produced and modified by natural causes. And this principle

we assume to be necessarily true, however unknown and

inconceivable may be the causes which determine the

phenomena. Thus it has not yet been found possible to

discover or represent to ourselves, in any intelligible

manner, the forces by which the various faces of a crystal

are consequent upon its primary form: for the hypothesis of

their being built up of integrant molecules, as Haüy held,

cannot be made satisfactory. But though the mechanism of

crystals is still obscure, there is no doubt as to the

principle which regulates their modifications. The whole of

crystallography rests upon this principle, that if one of

the primary planes or axes be modified in any manner, all

the symmetrical planes and axes must be modified in the same

manner. And though accidental mechanical or other causes may

interfere with the actual exhibition of such faces, we do

not the less assume their crystallographical reality, as

inevitably implied in the law of symmetry of the

crystal[3\7]. And we apply similar considerations to

organized beings. We assume that in a regular flower, each

of the similar {74} members has the same organization and

similar powers of developement; and hence if among these

similar parts some are much less developed than others, we

consider them as _abortive_; and if we wish to remove doubts

as to what are symmetrical members in such a case, we make

the inquiry by tracing the anatomy of these members, or by

following them in their earlier states of developement, or

in cases where their capabilities are magnified by

monstrosity or otherwise. The power of developement may be

modified by external causes, and thus we may pass from one

kind of symmetry to another; as we have already remarked.

Thus a regular flower with pentagonal symmetry, growing on a

lateral branch, has one petal nearest to the axis of the

plant: if this petal be more or less expanded than the

others, the pentagonal symmetry is interfered with, and the

flower may change to a symmetry of another kind. But it is

easy to see that all such conceptions of expansion,

abortion, and any other kind of metamorphosis, go upon the

supposition of identical faculties and tendencies in each

similar member, in so far as such tendencies have any

relation to the symmetry. And thus the principle we have

stated above is the basis of that which, in the History, we

termed the Principle of Developed and Metamorphosed

Symmetry.

[Note 3\7: Some crystalline forms, instead of being

_holohedral_ (provided with their whole number of faces),

are _hemihedral_ (provided with only half their number of

faces). But in these hemihedral forms the half of the faces

are still _symmetrically_ suppressed.]

We shall not at present pursue the other applications of

this Idea of Symmetry, but we shall consider some of the

results of its introduction into Crystallography.

CHAPTER II.

APPLICATION OF THE IDEA OF SYMMETRY TO CRYSTALS.

1. MINERALS and other bodies of definite chemical

composition often exhibit that marked regularity of form and

structure which we designate by terming them _Crystals_; and

in such crystals, when we duly study them, we perceive the

various kinds of symmetry of which we have spoken in the

previous chapter. And the different kinds of symmetry which

we have there described are now usually distinguished from

each other, by writers on crystallography. Indeed it is

mainly to such writers that we are indebted for a sound and

consistent classification of the kinds and degrees of

symmetry of which forms are capable. But this classification

was by no means invented as soon as mineralogists applied

themselves to the study of crystals. These first attempts to

arrange crystalline forms were very imperfect; those, for

example, of Linnæus, Werner, Romé de Lisle, and Haüy. The

essays of these writers implied a classification at once

defective and superfluous. They reduced all crystals to one

or other of certain _fundamental forms_; and this procedure

might have been a perfectly good method of dividing

crystalline forms into classes, if the fundamental forms had

been selected so as to exemplify the different kinds of

symmetry. But this was not the case. Haüy's fundamental or

'primitive' forms, were, for instance, the following: the

_parallelepiped_, the _octahedron_, the _tetrahedron_, the

_regular hexagonal prism_, the _rhombic dodecahedron_, and

the _double hexagonal pyramid_. Of these, the _octahedron_,

the _tetrahedron_, the _rhombic dodecahedron_, all belong to

the {76} same kind of symmetry (the TESSULAR systems); also

the _hexagonal prism_ and the _hexagonal pyramid_ both

belong to the RHOMBIC system; while the _parallelepiped_ is

so employed as to include all kinds of symmetry.

It is, however, to be recollected that Haüy, in his

selection of primitive forms, not only had an eye to the

external form of the crystal and to its degree and kind of

regularity, but also made his classification with an

especial reference to the _cleavage_ of the mineral, which

he considered as a primary element in crystalline analysis.

There can be no doubt that the cleavage of a crystal is one

of its most important characters: it is a relation of form

belonging to the interior, which is to be attended to no

less than the form of the exterior. But still, the cleavage

is to be regarded only as determining the degree of

geometrical symmetry of the body, and not as defining a

special geometrical figure to which the body _must_ be

referred. To have looked upon it in the latter light, was a

mistake of the earlier crystallographic speculators, on

which we shall shortly have to remark.

2. I have said that the reference of crystals to Primitive

Forms might have been well employed as a mode of expressing

a just classification of them. This follows as a consequence

from the application of the Principle stated in the last

chapter, that _all symmetrical members are alike affected_.

Thus we may take an upright triangular prism as the

representative of the rhombic system, and if we then suppose

one of the upper edges to be cut off, or truncated, we must,

by the Principle of Symmetry, suppose the other two upper

edges to be truncated in precisely the same manner. By this

truncation we may obtain the upper part of a rhombohedron;

and by truncations of the same kind, symmetrically affecting

all the analogous parts of the figure, we may obtain any

other form possessing three-membered symmetry. And the same

is true of any of the other kinds of symmetry, provided we

make a proper selection of a fundamental form. And this was

really the method employed by Demeste, Werner, and Romé de

Lisle. They {77} assumed a Primitive Form, and then

conceived other forms, such as they found in nature, to be

derived from the Primitive Form by truncation of the edges,

acumination of the corners, and the like processes. This

mode of conception was a perfectly just and legitimate

expression of the general Idea of Symmetry.

3. The true view of the degrees of symmetry was, as I have

already said, impeded by the attempts which Haüy and others

made to arrive at primitive forms by the light which

cleavage was supposed to throw upon the structure of

minerals. At last, however, in Germany, as I have narrated

in the History of Mineralogy[4\7], Weiss and Mohs introduced

a classification of forms implying a more philosophical

principle, dividing the forms into Systems; which, employing

the terms of the latter writer, we shall call the

_tessular_, the _pyramidal_ or _square pyramidal_, the

_prismatic_ or _oblong_, and the _rhombohedral_ systems.

[Note 4\7: _Hist. Ind. Sc._ b. xv. c. iv.]

Of these forms, the three latter may be at once referred to

those kinds of symmetry of which we have spoken in the last

chapter. The _rhombohedral_ system has _triangular_

symmetry, or is three-membered: the _pyramidal_ has _square_

symmetry, or is four-membered: the _prismatic_ has _oblong_

symmetry, and is two-and-two-membered. But the kinds of

symmetry which were spoken of in the former chapter, do not

exhaust the idea when applied to minerals. For the symmetry

which was there explained was such only as can be exhibited

on a surface, whereas the forms of crystals are solid. Not

only have the right and left parts of the upper surface of a

crystal relations to each other; but the upper surface and

the lateral faces of the crystal have also their relations;

they may be different, or they may be alike. If we take a

cube, and hold it so that four of its faces are vertical,

not only are all these four sides exactly similar, so as to

give square symmetry; but also we may turn the cube, so that

any one of these four sides shall become the top, and still

the four sides which are thus made vertical, though {78} not

the same which were vertical before, are still perfectly

symmetrical. Thus this cubical figure possesses more than

square symmetry. It possesses square symmetry in a vertical

as well as in a horizontal sense. It possesses a symmetry

which has the same relation to a _cube_ which four-membered

symmetry has to a _square_. And this kind of symmetry is

termed the _cubical_ or _tessular_ symmetry. All the other

kinds of symmetry have reference to an axis, about which the

corresponding parts are disposed; but in tessular symmetry

the horizontal and vertical axes are also symmetrical, or

interchangeable; and thus the figure may be said to have no

axis at all.

4. It has already been repeatedly stated that, by the very

idea of symmetry, all the incidents of form must affect

alike all the corresponding parts. Now in crystals we have,

among these incidents, not only external figure, but

_cleavage_, which may be considered as internal figure.

Cleavage, then, must conform to the degree of symmetry of

the figure. Accordingly cleavage, no less than form, is to

be attended to in determining to what system a mineral

belongs. If a crystal were to occur as a square prism or

pyramid, it would not on that account necessarily belong to

the square pyramidal system. If it were found that it was

cleavable parallel to one side of the prism, but not in the

transverse direction, it has only oblong symmetry; and the

equality of the sides which makes it square is only

accidental.

Thus no cleavage is admissible in any system of

crystallization which does not agree with the degree of

symmetry of the system. On the other hand, _any_ cleavage

which _is_ consistent with the symmetry of the system, is

(hypothetically at least) allowable. Thus in the oblong

prismatic system we may have a cleavage parallel to one side

only of the prism; or parallel to both, but of different

distinctness; or parallel to the two diagonals of the prism

but of the same distinctness; or we may have both these

cleavages together. In the rhombohedral system, the cleavage

may be parallel to the sides of the rhombohedron, as in Calc

{79} Spar: or, in the same system, the cleavage, instead of

being thus oblique to the axis, may be along the axis in

those directions which make equal angles with each other:

this cleavage easily gives either a triangular or a

hexagonal prism. Again, in the tessular system, the cleavage

may be parallel to the surface of the cube, which is thus

readily separable into other cubes, as in Galena; or the

cleavage may be such as to cut off the solid angle of the

cube, and since there are eight of these, such cleavage

gives us an octahedron, which, however, may be reduced to a

tetrahedron, by rejecting all parallel faces, as being mere

repetitions of the same cleavage; this is the case with

Fluor Spar: or the cube of the tessular system may be

cleavable in planes which truncate all the edges of the

cube; and as these are twelve, we thus obtain the

dodecahedron with rhombic faces: this occurs in Zinc Blende.

And thus we see the origin of Haüy's various primitive

forms, the tetrahedron, octahedron, and rhombic

dodecahedron, all belonging to the tessular system:--they

are, in fact, different cleavage forms of that system.

5. I do not dwell upon other incidents of crystals which

have reference to form, nor upon the lustre, smoothness, and

striation of the surfaces. To all such incidents the general

principle applies, that similar parts are similarly

affected; and hence, if any parts are found to be constantly

and definitely different from other parts of the same sort,

they are not similar parts; and the symmetry is to be

interpreted with reference to this difference.

We have now to consider the inferences which have been drawn

from these incidents of crystallization, with regard to the

intimate structure of bodies.

CHAPTER III.

SPECULATIONS FOUNDED UPON THE SYMMETRY OF CRYSTALS.

1. WHEN a crystal, as, for instance, a crystal of Galena,

(sulphuret of lead,) is readily divisible into smaller

cubes, and these into smaller ones, and so on without limit,

it is very natural to represent to ourselves the original

cube as really consisting of small cubical elements; and to

imagine that it is a philosophical account of the physical

structure of such a substance to say that it is made up of

cubical molecules. And when the Galena crystal has

externally the form of a cube, there is no difficulty in

such a conception; for the surface of the crystal is also

conceived as made up of the surfaces of its cubical

molecules. We conceive the crystal so constituted, as we

conceive a wall built of bricks.

But if, as often happens, the Galena crystal be an

octahedron, a further consideration is requisite in order to

understand its structure, pursuing still the same

hypothesis. The mineral is still, as in the other case,

readily cleavable into small cubes, having their corners

turned to the faces of the octahedron. Therefore these faces

can no longer be conceived as made up of the faces of

cubical elements of which the whole is constituted. If we

suppose a pile of such small cubes to be closely built

together, but with decreasing width above, so as to form a

pyramid, the face of such a pyramid will no longer be plane;

it will consist of a great number of the corners or edges of

the small elementary cubes. It would appear at first sight,

therefore, that such a face cannot represent the smooth

polished surface of a crystal. {81}

But when we come to look more closely, this difficulty

disappears. For how large are these elementary cubes? We

cannot tell, even supposing they really have any size. But

we know that they must be, at any rate, very small; so small

as to be inappreciable by our senses, for our senses find no

limit to the divisibility of minerals by cleavage. Hence the

surface of the pyramid above described would not consist of

visible corners or edges, but would be roughened by specks

of imperceptible size; or rather, by supposing these specks

to become still smaller, the roughness becomes smoothness.

And thus we may have a crystal with a smooth surface, made

up of small cubes in such a manner that their surfaces are

all oblique to the surface of the crystal.

Haüy, struck by some instances in which the supposition of

such a structure of crystals appeared to account happily for

several of their relations and properties, adopted and

propounded it as a general theory. The small elements, of

which he supposed crystals to be thus built up, he termed

_integrant molecules_. The form of these molecules might or

might not be the same as the _primitive form_ with which his

construction was supposed to begin; but there was, at any

rate, a close connexion between these forms, since both of

them were founded on the cleavage of the mineral. The tenet

that crystals are constituted in the manner which I have

been describing, I shall call the _Theory of Integrant

Molecules_, and I have now to make some remarks on the

grounds of this theory.

2. In the case of which I have spoken, the mineral used as

the example, Galena, readily splits into cubes, and cubes

are easily placed together so as to fit each other, and fill

the space which they occupy. The same is the case in the

mineral which suggested to Haüy his theory, namely, Calc

Spar. The crystals of this substance are readily divisible

into rhombohedrons, a form like a brick with oblique angles;

and such bricks can be built together so as to produce

crystals of all the immense varieties of form which Calc

Spar presents. This kind of masonry is equally possible in

many other {82} minerals; but as we go through the mineral

kingdom in our survey, we soon find cases which offer

difficulties. Some minerals cleave only in two directions,

some in one only; in such cases we cannot by cleavage obtain

an integrant molecule of definite form; one of its

dimensions, at least, must remain indeterminate and

arbitrary. Again, in some instances, we have more than three

different planes of cleavage, as in Fluor Spar, where we

have four. The solid, bounded by four planes, is a

tetrahedron; or if we take four _pairs_ of parallel faces,

an octahedron. But if we attempt to take either of these

forms for our integrant molecule, we are met by this

difficulty: that a collection of such forms will not fill

space. Perhaps this difficulty will be more readily

conceived by the general reader if it be contemplated with

reference to plane figures. It will readily be seen that a

number of equal squares may be put together so as to fill

the space which they occupy; but if we take a number of

equal regular octagons, we may easily convince ourselves

that no possible arrangement can make them cover a flat

space without leaving blank spots between. In like manner

octahedrons or tetrahedrons cannot be arranged in solid

space so as to fill it. They necessarily leave vacancies.

Hence the structure of Fluor Spar, and similar crystals, was

a serious obstacle in the way of the theory of integrant

molecules. That theory had been adopted in the first

instance because portions of the crystal, obtained by

cleavage, could be built up into a solid mass; but this

ground of the theory failed altogether in such instances as

I have described, and hence the theory, even upon the

representations of its adherents, had no longer any claim to

assent.

The doctrine of Integral Molecules, however, was by no means

given up at once, even in such instances. In this and in

other subjects, we may observe that a theory, once

constructed and carried into detail, has such a hold upon

the minds of those who have been in the habit of applying

it, that they will attempt to uphold it by introducing

suppositions inconsistent with {83} the original foundations

of the theory. Thus those who assert the Atomic Theory,

reconcile it with facts by taking the _halves of atoms_; and

thus the Theory of Integrant Molecules was maintained for

Fluor Spar, by representing the elementary octahedrons of

which crystals are built up, as touching each other only by

the _edges_. The contact of surface with surface amongst

integrant molecules had been the first basis of the theory;

but this supposition being here inapplicable, was replaced

by one which made the theory no longer a representation of

the facts (the cleavages), but a mere geometrical

construction. Although, however, the inapplicability of the

theory to such cases was thus, in some degree, disguised to

the disciples of Haüy, it was plain that, in the face of

such difficulties, the Theory of Integrant Molecules could

not hold its place as a philosophical truth. But it still

answered the purpose (a very valuable one, and one to which

crystallography is much indebted,) of an instrument for

calculating the geometrical relations of the parts of

crystals to each other: for the integrant molecules were

supposed to be placed layer above layer, each layer as we

ascend, _decreasing_ by a certain number of molecules and

rows of molecules; and the calculation of these _laws of

decrement_ was, in fact, the best mode then known of

determining the positions of the faces. The Theory of

Decrements served to express and to determine, in a great

number of the most obvious cases, _the laws of phenomena_ in

crystalline forms, though the Theory of Integrant Molecules

could not be maintained as a just view of the structure of

crystals.

3. The Theory of Integrant Molecules, however, involved this

just and important principle: that a true view of the

intimate structure of crystals must include and explain the

facts of crystallization, that is, crystalline form and

cleavage; and that it must take these into account,

according to their degree of _Symmetry_. So far all theories

concerning the elements of crystals must agree. And it was

soon seen that this was, in reality, all that had been

established by the investigations of Haüy and his school. I

have already, in the {84} _History_, quoted Weiss's

reflections on making this step. 'When in 1809,' he

says[5\7], 'I published my Dissertation, I shared the common

opinion as to the necessity of the assumption, and the

reality of the existence of a primitive form, at least in a

sense not very different from the usual sense of the

expression.' He then proceeds to relate that he sought a

ground for such an opinion, independent of the doctrine of

_Atoms_, which he, in common with a great number of

philosophers of that time in his own country, was disposed

to reject, inclining to believe that the properties of

bodies were determined by _Forces_ which acted in them, and

not by _Molecules_ of which they were composed. He adds,

that in pursuing this train of thought, he found, 'that out

of his Primitive Forms there was gradually unfolded to his

hands that which really governs them, and is not affected by

their casual fluctuations; namely, the Fundamental Relations

of their Dimensions,' or as we now may call them, _Axes of

Symmetry_. With reference to these Axes, he found, as he

goes on to say, that 'a multiplicity of internal

Oppositions, necessarily and mutually interdependent, are

developed in the crystalline mass, each Relation having its

own Polarity; so that the Crystalline Character is

co-extensive with these Polarities.' The character of these

polarities, whether manifested in crystalline faces,

cleavage, or any other incidents of crystallization, is

necessarily displayed in the degree and kind of Symmetry

which the crystal possesses: and thus this Symmetry, in all

our speculations concerning the structure of crystals,

necessarily takes the place of that enumeration of Primitive

Forms which were rejected as inconsistent with observed

facts, and destitute of sound scientific principle.

[Note 5\7: _Acad. Berlin._ 1816, p. 307.]

I may just notice here what I have stated in the History of

Mineralogy[6\7], that the distinction of systems of

crystallization, as introduced by Weiss and Mohs, was

strikingly confirmed by Sir David Brewster's discoveries

respecting the optical properties of minerals. {85} The

splendid phenomena which were produced by passing polarized

light through crystals, were found to vary according as the

crystals were of the Rhombohedral, Square Pyramidal, Oblong

Prismatic, or Tessular System. The Optical Symmetry exactly

corresponded with the Geometrical Symmetry. In the two

former Systems were crystals _uniaxal_ in respect of their

optical properties; the oblong prismatic, was _biaxal_;

while in the tessular, the want of a predominant axis

prevented the phenomena here spoken of from occurring at

all. The optical experiments must have led, and would have

led, to a classification of crystals into the above systems

or something nearly equivalent, even had they not been

already so arranged by attention to their forms.

[Note 6\7: _Hist. Ind. Sc._ b. xv. c. v.]

4. While in Germany Weiss and Mohs with their disciples,

were gradually rejecting what was superfluous in the

previous crystallographical hypotheses, philosophers in

England were also trying to represent to themselves the

constitution of crystals in a manner which should be free

from the obviously arbitrary and untenable fictions of the

Haüyian school. These attempts, however, were not crowned

with much success. One mode of representing the structure of

crystals which suggested itself, was to reject the

polyhedral forms which Haüy gave to his integrant molecules,

and to conceive the elements of crystals as _spheres_, the

properties of the crystal being determined not by the

_surfaces_, but by the _position_ of the elements. This was

done by Wollaston, in the _Philosophical Transactions_ for

1813. He applied this view to the tessular system, in which,

indeed, the application is not difficult; and he showed that

octahedral and tetrahedral figures may be deduced from

symmetrical arrangements of equal spherules. But though in

doing this, he manifested a perception of the conditions of

the problem, he appeared to lose his hold on the real

question when he tried to pass on to other systems of

crystallization. For he accounted for the rhombohedral

system by supposing the spheres changed into _spheroids_.

Such a procedure involved him in a gratuitous and useless

hypothesis: for to what purpose do we introduce the {86}

arrangement of atoms (instead of their figure,) as a mode of

explaining the symmetry of the crystallization, when at the

next step we ascribe to the atom, by an arbitrary fiction, a

symmetry of figure of the same kind as that which we have to

explain? It is just as easy, and as allowable, to assume an

elementary rhombohedron, as to assume elementary spheroids,

of which the rhombohedrons are constructed.

5. Many hypotheses of the same kind might be adduced,

devised both by mineralogists and chemists. But almost all

such speculations have been pursued with a most surprising

neglect of the principle which obviously is the only sound

basis on which they can proceed. The principle is

this:--that _All hypotheses concerning the arrangement of

the elementary atoms of bodies in space must be constructed

with reference to the general facts of crystallization_. The

truth and importance of this principle can admit of no

doubt. For if we make any hypothesis concerning the mode of

connexion of the elementary particles of bodies, this must

be done with the view of representing to ourselves the

forces which connect them, and the results of these forces

as manifested in the properties of the bodies. Now the

forces which connect the particles of bodies so as to make

them crystalline, are manifestly chemical forces. It is only

definite chemical compounds which crystallize; and in

crystals the force of cohesion by which the particles are

held together cannot in any way be distinguished or

separated from the chemical force by which their elements

are combined. The elements are understood to be combined,

precisely because the result is a definite, apparently

homogeneous substance. The properties of the compound bodies

depend upon the elements and their mode of combination; for,

in fact, these include everything on which they can depend.

There are no other circumstances than these which can affect

the properties of a body. Therefore all those properties

which have reference to space, namely, the crystalline

properties, cannot depend upon anything else than the

arrangement of the elementary molecules in space. These {87}

properties are the facts which any hypothesis of the

arrangement of molecules must explain, or at least render

conceivable; and all such hypotheses, all constructions of

bodies by supposed arrangements of molecules, can have no

other philosophical object than to account for facts of this

kind. If they do not do this, they are mere arbitrary

geometrical fictions, which cannot be in any degree

confirmed or authorised by an examination of nature, and are

therefore not deserving of any regard.

6. Those philosophers who have endeavoured to represent the

mode in which bodies are constructed by the combination of

their chemical atoms, have often undertaken to show, not

only that the atoms are combined, but also in what positions

and configurations they are combined. And it is truly

remarkable, as I have already said, that they have done

this, almost in every instance, without any consideration of

the crystalline character of the resulting combinations;

from which alone we receive any light as to the relation of

their elements in space. Thus Dr. Dalton, in his _Elements

of Chemistry_, in which he gave to the world the Atomic

Theory as a representation of the doctrine of definite and

multiple proportions, also published a large collection of

Diagrams, exhibiting what he conceived to be the

configuration of the atoms in a great number of the most

common combinations of chemical elements. Now these

hypothetical diagrams do not in any way correspond, as to

the nature of their symmetry, with the compounds, as we find

them displaying their symmetry when they occur crystallized.

Carbonate of lime has in reality a triangular symmetry,

since it belongs to the rhombohedral system; Dr. Dalton's

carbonate of lime would be an oblique rhombic prism or

pyramid. Sulphate of baryta is really two-and-two membered;

Dr. Dalton's diagram makes it two-and-one membered. Alum is

really octahedral or tessular; but according to the diagram

it could not be so, since the two ends of the atom are not

symmetrical. And the same want of correspondence between the

facts and the hypothesis runs through the whole {88} system.

It need not surprise us that the theoretical arrangement of

atoms does not explain the facts of _crystallization_; for

to produce such an explanation would be a second step in

science quite as great as the first, the discovery of the

atomic theory in its _chemical_ sense. But we may allow

ourselves to be surprised that an utter discrepance between

all the facts of crystallization and the figures assumed in

the theory, did not suggest any doubt as to the soundness of

the mode of philosophizing by which this part of the theory

was constructed.

7. Some little accordance between the hypothetical

arrangements of chemical atoms and the facts of

crystallization, does appear to have been arrived at by some

of the theorists to whom we here refer, although by no means

enough to show a due conviction of the importance of the

principle stated above. Thus Wollaston, in the Essay above

noticed, after showing that a symmetrical arrangement of

equal spherules would give rise to octahedral and other

tessular figures, remarks, very properly, that the metals,

which are simple bodies, crystallize in such forms. M.

Ampère[7\7] also, in 1814, published a brief account of an

hypothesis of a somewhat similar nature, and stated himself

to have developed this speculation in a Memoir which has not

yet, so far as I am aware, been published. In this notice he

conceives bodies to be compounded of _molecules_, which,

arranged in a polyhedral form, constitute _particles_. These

_representative forms_ of the particles depend on chemical

laws. Thus the particles of oxygen, of hydrogen, and of

azote, are composed each of four molecules. Hence it is

collected that the particles of nitrous gas are composed of

two molecules of oxygen and two of azote; and similar

conclusions are drawn respecting other substances. These

conclusions, though expressed by means of the polyhedrons

thus introduced, are supported by chemical, rather than by

crystallographical comparisons. The author does, indeed,

appeal to the crystallization of sal {89} ammoniac as an

argument[8\7]; but as _all_ the forms which he introduces

appear to belong to the _tessular_ system of

crystallization, there is, in his reasonings, nothing

distinctive; and therefore nothing, crystallographically

speaking, of any weight on the side of this theory.

[Note 7\7: _Ann. de Chimie_, tom. xc. p. 43.]

[Note 8\7: _Ann. de Chimie_, tom. xc. p. 83.]

8. Any hypothesis which should introduce any principle of

chemical order among the actual forms of minerals, would

well deserve attention. At first sight, nothing can appear

more anomalous than the forms which occur. We have, indeed,

one broad fact, which has an encouraging aspect, the

tessular forms in which the pure metals crystallize. The

highest degree of chemical and of geometrical simplicity

coincide: irregularity disappears precisely where it is

excluded by the consideration above stated, that the

symmetry of chemical composition must determine the symmetry

of crystalline form[9\7].

[Note 9\7: Inasmuch as this law, that the simple metals

crystallize in tessular forms, is the most signal example of

that connexion between the chemical nature of a body and its

crystalline form, I in the former Edition stated it with as

much generality as I could find any ground for, and I should

have been glad if I could have added confirmation of the

law, derived from later observations. But the most recent

investigations of crystallographers appear to have afforded

exceptions rather than examples of the rule. Arsenic and

Tellurium are said to be _rhombohedral_. Antimony, stated by

Haüy to be octahedral (and therefore tessular), has been

found by more modern observers to be _rhombohedral_. Tin has

been obtained by Professor Miller in beautiful crystals

belonging to the _pyramidal_ system. Professor Nöggerath has

observed in Zinc, after cooling from fusion, hexagonal

cleavage, rendering it probable that the mineral

crystallized in _rhombohedrons_ having their axes vertical,

like ice. G. Rose conceives it highly probable that Osmium

and Iridium are _rhombohedral_. (Poggendorf. Bd. liv.)

But all the more perfect metals are tessular; namely, Gold,

Silver, Mercury, Platinum, Iron, Copper; also Bismuth [?]

Perhaps the observation in which the crystallization of Zinc

is affected by its position is, on that very account, no

sufficient evidence of its free crystallization. We can

hardly conceive a collection of perfectly simple, similar

particles to crystallize so as to have one pre-eminent axis,

without some extraneous action affecting them.]

But if we go on to any other class of crystalline forms, we

soon find ourselves lost in our attempts to {90} follow any

thread of order. We have indeed many large groups connected

by obvious analogies; as the rhombohedral carbonates of

lime, magnesia, iron, manganese;--the prismatic carbonates

and sulphates of lime, baryta, strontia, lead. But even in

these, we cannot form any plausible hypothesis of the

arrangement of the elements; and in other cases to which we

naturally turn, we can find nothing but confusion. For

instance, if we examine the oxides of metals:--those of iron

are rhombohedral and tessular; those of copper, tessular;

those of tin, of titanium, of manganese, square pyramidal;

those of antimony, prismatic; and we have other forms for

other substances.

It may be added, that if we take account of the optical

properties which, as we have already stated, have constant

relations to the crystalline forms, the confusion is still

further increased; for the optical dimensions vary in

amount, though not in symmetry, where chemistry can trace no

difference of composition.

9. We will not quit the subject, however, without noticing

the much more promising aspect which it has assumed by the

detection of such groups as are referred to in the last

article; or in other words, by Mitscherlich's discovery of

_Isomorphism_. According to that discovery, there are

various elements which may take the place of each other in

crystalline bodies, either without any alteration of the

crystalline form, or at most with only a slight alteration

of its dimensions. Such a group of elements we have in the

earths lime and magnesia, the protoxides of iron and

manganese: for the carbonates of all these bases occur

crystallized in forms of the rhombohedral system, the

characteristic angle being nearly the same in all. Now lime

and magnesia, by the discoveries of modern chemistry, are

really oxides of metals; and therefore all these carbonates

have a similar chemical constitution, while they have also a

similar crystalline form. Whether or no we can devise any

arrangement of molecules by which this connexion of the

chemical and the geometrical property can be represented, we

cannot help {91} considering the connexion as an extremely

important fact in the constitution of bodies; and such facts

are more likely than any other to give us some intelligible

view of the relations of the ultimate parts of bodies. The

same may be said of all the other isomorphous or

plesiomorphous groups[10\7]. For instance, we have a number

of minerals which belong to the same system of

crystallization, but in which the chemical composition

appears at first sight to be very various: namely, spinelle,

pleonaste, gahnite, franklinite, chromic iron oxide,

magnetic iron oxide: but Abich has shown that all these may

be reduced to a common chemical formula;--they are bioxides

of one set of bases, combined with trioxides of another set.

Perhaps some mathematician may be able to devise some

geometrical arrangement of such a group of elements which

may possess the properties of the tessular system.

Hypothetical arrangements of atoms, thus expressing both the

chemical and the crystalline symmetry which we know to

belong to the substance, would be valuable steps in

analytical science; and when they had been duly verified,

the hypotheses might easily be divested of their atomic

character.

[Note 10\7: See _Hist. Ind. Sc._ b. xv. c. vi.]

Thus, as we have already said, mineralogy, understood in its

wider sense, as the counterpart of chemistry, has for one of

its main objects to discover those Relations of the Elements

of bodies which have reference to Space. In this research,

the foundation of all sound speculation is the kind and

degree of Symmetry of form which we find in definite

chemical compounds: and the problem at present before the

inquirer is, to devise such arrangements of molecules as

shall answer the conditions alike of Chemistry and of

Crystallography.

We now proceed to the Classificatory Sciences, of which

Mineralogy is one, though hitherto by far the least

successful.

BOOK VIII.

THE

PHILOSOPHY

OF THE

CLASSIFICATORY SCIENCES.

WHERE a certain apparent difference between things (although

perhaps in itself of little moment) answers to we know not

what number of other differences, pervading not only their

known properties but properties yet undiscovered, it is not

optional but imperative to recognise this difference as the

foundation of a specific distinction.

JOHN S. MILL, _System of Logic_, b. 1, ch. vii. § 4.

BOOK VIII.

THE PHILOSOPHY OF THE CLASSIFICATORY SCIENCES.

CHAPTER I.

THE IDEA OF LIKENESS AS GOVERNING THE USE OF COMMON NAMES.

1. _Object of the Chapter._--NOT only the Classificatory

Sciences, but the application of names to things in the

rudest and most unscientific manner, depends upon our

apprehending them as _like_ each other. We must therefore

endeavour to trace the influence and operation of the Idea

of Likeness in the common use of language, before we speak

of the conditions under which it acquires its utmost

exactness and efficacy.

It will be my object to show in this, as in previous cases,

that the impressions of sense are apprehended by acts of the

mind; and that these mental acts necessarily imply certain

relations which may be made the subjects of speculative

reasoning. We shall have, if we can, to seize and bring into

clear view the principles which the relation of _like_ and

_unlike_ involves, and the mode in which these principles

have been developed.

2. _Unity of the Individual._--But before we can attend to

several things as like or unlike, we must be able to

apprehend each of these by itself as _one thing_. {96} It

may at first sight perhaps appear that this apprehension

results immediately from the impressions on our senses,

without any act of our thoughts. A very little attention,

however, enables us to see that thus to single out special

objects requires a mental operation as well as a sensation.

How, for example, without an exertion of mental activity,

can we see one tree, in a forest where there are many? We

have, spread before us, a collection of colours and forms,

green and brown, dark and light, irregular and straight:

this is all that sensation gives or can give. But we

associate one brown trunk with one portion of the green

mass, excluding the rest, although the neighbouring leaves

are both nearer in contiguity and more similar in appearance

than is the stem. We thus have before us one tree; but this

unity is given by the mind itself. We see the green and the

brown, but we must _make_ the tree before we can see _it_.

That this composition of our sensations so as to form _one

thing_ implies an act of our own, will perhaps be more

readily allowed, if we once more turn our attention to the

manner in which we sometimes attempt to imitate and record

the objects of sight, by drawing. When we do this, as we

have already observed, we mark this unity of each object, by

drawing a line to separate the parts which we include from

those which we exclude;--an _Outline_. This line corresponds

to nothing which we see; the beginner in drawing has great

difficulty in discerning it; he has in fact to make it. It

is, as has been said by a painter of our own time[1\8], a

fiction: but it is a fiction employed to mark a real act of

the mind; to designate the singleness of the object in our

conception. As we have said elsewhere, we see lines, but

especially outlines, by mentally drawing them ourselves.

[Note 1\8: Phillips _On Painting_,--Design.]

The same act of conception which the outline thus represents

and commemorates in visible objects,--the same combination

of sensible impressions into a unit,--is exercised also with

regard to the objects of all {97} our senses: and the

singleness thus given to each object, is a necessary

preliminary to its being named or represented in any other

way.

But it may be said, Is it then by an arbitrary act of our

own that we put together the branches of the same tree, or

the limbs of the same animal? Have we equally the power and

the right to make the branch of the fir a part of the

neighbouring oak? Can we include in the outline of a man any

object with which he happens to be in contact?

Such suppositions are manifestly absurd. And the answer is,

that though we give unity to objects by an act of thought,

it is not by an _arbitrary_ act; but by a process subject to

certain conditions;--to conditions which exclude such

incongruous combinations as have just been spoken of.

What are these conditions which regulate our apprehension of

an object as one?--which determine what portion of our

impressions does, and what portion does not belong to the

same thing?

3. _Condition of Unity._--I reply, that the primary and

fundamental condition is, that we must be able to make

intelligible assertions respecting the object, and to

entertain that belief of which assertions are the

exposition. A tree _grows_, _sheds_ its leaves in autumn,

and _buds_ again in the spring, _waves_ in the wind, or

_falls_ before the storm. And to the tree belong all those

parts which must be included in order that such

declarations, and the thought which they convey, shall have

a coherent and permanent meaning. Those are _its_ branches

which wave and fall with _its_ trunk; those are _its_ leaves

which grow on _its_ branches. The permanent connexions which

we observe,--permanent, among unconnected changes which

affect the surrounding appearances,--are what we bind

together as belonging to one object. This permanence is the

condition of our conceiving the object _as_ one. The

connected changes may always be described by means of

assertions; and the connexion is seen in the identity of the

subject of successive predications; in the possibility of

applying many verbs to one substantive. We may {98}

therefore express the condition of the unity of an object to

be this: that _assertions concerning the object shall be

possible_: or rather we should say, that the acts of belief

which such assertions enunciate shall be possible.

It may seem to be superfluous to put in a form so abstract

and remote, the grounds of a process apparently so simple as

our conceiving an object to be one. But the same condition

to which we have thus been led, as the essential principle

of the unity of objects, namely, that propositions shall be

possible, will repeatedly occur in the present chapter; and

it may serve to illustrate our views, to show that this

condition pervades even the simplest cases.

4. _Kinds._--The mental synthesis of which we have thus

spoken, gives us our knowledge of _individual_ things; it

enables me to apprehend that particular tree or man which I

now see, or, by the help of memory, the tree or the man I

saw yesterday. But the knowledge with which we have mainly

here to do is not a knowledge of individuals but of kinds;

of such classes as are indicated by common names. We have to

make assertions concerning a tree or a man in general,

without regarding what is peculiar to this man or that tree.

Now it is clear that certain individual objects are all

called _man_, or all called _tree_, in virtue of some

resemblance which they have. If we had not the power of

perceiving in the appearances around us, likeness and

unlikeness, we could not consider objects as distributed

into kinds at all. The impressions of sense would throng

upon us, but being uncompared with each other, they would

flow away like the waves of the sea, and each vanish from

our contemplation when the sensation faded. That we do

apprehend surrounding objects as belonging to permanent

kinds, as being men and horses, oaks and roses, arises from

our having the idea of likeness, and from our applying it

habitually, and so far as such a classification requires.

Not only can we employ the idea of likeness in this manner,

but we apply it incessantly and universally to {99} the

whole mass and train of our sensations. For we have no

external sensations to which we cannot apply some language

or other; and all language necessarily implies recognition

of resemblances. We cannot call an object _green_ or _round_

without comparing in our thoughts its colour or its shape,

with a shape and a colour seen in other objects. All our

sensations, therefore, without any exception of kind or

time, are subject to this constant process of

classification; and the idea of likeness is perpetually

operating to distribute them into kinds, at least so far as

the use of language requires.

We come then again to the question, Upon what principle,

under what conditions, is the Idea of Likeness thus

operative? What are the limits of the classes thus formed?

Where does that similarity end, which induces and entitles

us to call a thing a _tree_? What universal rule is there

for the application of common names, so that we may not

apply them wrongly?

5. _Not made by Definitions._--Perhaps some one might expect

in answer to these inquiries a definition or a series of

definitions;--might imagine that some description of a tree

might be given which might show when the term was applicable

and when it was not; and that we might construct a body of

rules to which such descriptions must conform. But on

consideration it will be clear that the real solution of our

difficulty cannot be obtained in such a manner. For _first_;

such descriptions must be given in words, and must therefore

suppose that we have already satisfied ourselves how words

are to be used. If we define a tree to be 'a living thing

without the power of voluntary motion,' we shall be called

upon to define 'a living thing;' and it is manifest that

this renewal of the demand for definition might be repeated

indefinitely; and, therefore, we cannot in this way come to

a final principle. And in the _next_ place, most of those

who use language, even with great precision and consistency,

would find it difficult or impossible to give good

definitions even of a few of the general names which they

use; and therefore their practice cannot be regulated by any

{100} tacit reference to such definitions. That definitions

of terms are of great use and importance in their right

place, we shall soon see; but their place is not to regulate

the use of common language.

What then, once more, is this regulative principle? What

rules do men follow in the use of words, so as commonly to

avoid confusion and ambiguity? How do they come to

understand each other so well as they ordinarily do,

respecting the limits of classes never defined, and which

they cannot define? What is the common Convention, or

Condition to which they conform?

6. _Condition of the Use of Terms._--To this we reply, that

the Condition which regulates the use of language, is, that

it shall be capable of being used;--that is, that general

assertions shall be possible. The term _tree_ is applicable

as far as it is useful in expressing our knowledge

concerning trees:--thus we know that trees are fixed in the

ground, have a solid stem, branches, leaves, and many other

properties. With regard to all the objects which surround

us, we have an immense store of knowledge of such

properties, and we employ the names of the objects in such a

manner as enables us to express these properties.

But the connexion of such properties is variable and

indefinite. Some properties are constantly combined, others

occasionally only. The leaves of different oaks resemble

each other, the branches resemble far less, and may differ

very widely. The term _oak_ does not enable us to say that all

oaks have straight branches or all crooked. Terms can only

express properties as far as they are constant. Not only,

therefore, the accumulation of a vast mass of knowledge of

the properties and attributes of objects, but also an

observation of the habitual _connexion_ of such properties

is needed, to direct us to the consistent application of

terms:--to enable us to apply them so as to express truths.

But here again we are largely provided with the requisite

knowledge and observation by the common course of our

existence. The unintermitting stream of experience supplies

us with an incalculable {101} amount of such observed

connexions. All men have observed that the associations of

the same form of leaves are more constant than of the same

form of branches;--that though persons walk in different

attitudes, none go on all fours; and thus the term _oak_ is

so applied as to include those cases in which the leaves are

alike in form though the branches be unlike; and though we

should refuse to apply the term _man_ to a class of

creatures which habitually and without compulsion used four

legs, we make no scruple of affixing it to persons of very

different figures. The whole of human experience being

composed of such observed connexions, we have thus materials

even for the immense multiplicity of names which human

language contains; all which names are, as we have said,

regulated in their application by the condition of their

expressing such experience.

Thus amid the countless combinations of properties and

divisions of classes which the structure of language

implies, scarcely any are arbitrary or capricious. A word

which expressed a mere wanton collection of unconnected

attributes could hardly be called a _word_; for of such a

collection of properties no truth could be asserted, and the

word would disappear, for want of some occasion on which it

could be used. Though much of the fabric of language

appears, not unnaturally, fantastical and purely

conventional, it is in fact otherwise. The associations and

distinctions of phraseology are not more fanciful than is

requisite to make them correspond to the apparent caprices

of nature or of thought; and though much in language may be

called conventional, the conventions exist for the sake of

expressing some truth or opinion, and not for their own

sake. The principle, that _the condition of the use of terms

is the possibility of general, intelligible, consistent

assertions_, is true in the most complete and extensive sense.

7. _Terms may have different Uses._--The Terms with which we

are here most concerned are Names of Classes of natural

objects; and when we say that the principle and the limit of

such Names are their use in expressing propositions

concerning the classes, it is {102} clear that much will

depend on the kind of propositions which we mainly have to

express: and that the same name may have different limits,

according to the purpose we have in view. For example, is

the _whale_ properly included in the general term _fish_?

When men are concerned in catching marine animals, the main

features of the process are the same however the animals may

differ; hence whales are classed with fishes, and we speak

of the _whale-fishery_. But if we look at the analogies of

organization, we find that, according to these, the whale is

clearly not a fish, but a _beast_, (confining this term, for

the sake of distinctness, to suckling beasts or _mammals_).

In Natural History, therefore, the whale is not included

among fish. The indefinite and miscellaneous propositions

which language is employed to enunciate in the course of

common practical life, are replaced by a more coherent and

systematic collection of properties, when we come to aim at

scientific knowledge. But we shall hereafter consider the

principle of the classifications of Natural History; our

present subject is the application of the Idea of Likeness

in common practice and common language.

8. _Gradation of Kinds._--Common names, then, include many

individuals associated in virtue of resemblances, and of

permanently connected properties; and such names are

applicable as far as they serve to express such properties.

These collections of individuals are termed _Kinds_,

_Sorts_, _Classes_.

But this association of particulars is capable of degrees.

As individuals by their resemblances form Kinds, so kinds of

things, though different, may resemble each other so as to

be again associated in a higher Class; and there may be

several successive steps of such classification. _Man_,

_horse_, _tree_, _stone_, are each a name of a Kind; but

_animal_ includes the two first and excludes the others;

_living thing_ is a term which includes _animal_ and _tree_

but not _stone_; _body_ includes all the four. And such a

subordination of kinds may be traced very widely in the

arrangements of language. {103}

The condition of the use of the wider is the same as that of

the narrower Names of Classes;--they are good as far as they

serve to express true propositions. In common language,

though such an order of generality may in a variety of

instances be easily discerned, it is not systematically and

extensively referred to; but this subordination and

graduated comprehensiveness is the essence of the methods

and nomenclatures of Natural History, as we shall soon have

to show.

But such subordination is not without its use, even in

common cases, and when it is expressed in the terms of

common language. Thus _organized body_ is a term which

includes plants and animals; _animal_ includes beasts,

birds, fishes; _beast_ includes horses and dogs; _dogs_,

again, are greyhounds, spaniels, terriers.

9. _Characters of Kinds._--Now when we have such a Series of

Names and Classes, we find that we take for granted

irresistibly that each class has some _Character_ which

distinguishes it from other classes included in the superior

division. We ask what kind of beast a dog is; what kind of

animal a beast is; and we assume that such questions admit

of answer;--that each kind has some mark or marks by which

it may be described. And such descriptions may be given: an

animal is an organized body _having sensation and volition_;

man is a _reasonable_ animal. Whether or no we assent to the

exactness of these definitions, we allow the propriety of

their form. If we maintain these definitions to be wrong, we

must believe some others to be right, however difficult it

may be to hit upon them. We entertain a conviction that

there must be, among things so classed and named, a

possibility of defining each.

Now what is the foundation of this postulate? What is the

ground of this assumption, that there must exist a

definition which we have never seen, and which perhaps no

one has seen in a satisfactory form? The knowledge of this

definition is by no means necessary to our using the word

with propriety; for any one can make true assertions about

dogs, but who can define a {104} dog? And yet if the

definition be not necessary to enable us to use the word,

why is it necessary at all? I allow that we possess an

indestructible conviction that there must be such a

character of each kind as will supply a definition; but I

ask, on what this conviction rests.

I reply, that our persuasion that there must needs be

characteristic marks by which things can be defined in

words, is founded on the assumption of _the necessary

possibility of reasoning_.

The reference of any object or conception to its class

without definition, may give us a persuasion that it shares

the properties of its class, but such classing does not

enable us to reason upon those properties. When we consider

man as an animal, we ascribe to him in thought the

appetites, desires, affections, which we habitually include

in our notion of animal: but except we have expressed these

in some definition or acknowledged description of the term

_animal_, we can make no use of the persuasion in

ratiocination. But if we have described animals as 'being

impelled to action by appetites and passions,' we can not

only think, but say, 'man is an animal, and therefore he is

impelled to act by appetites and passions.' And if we add a

further definition, that 'man is a reasonable animal,' and

if it appear that 'reason implies conformity to a rule of

action,' we can then further infer that man's nature is to

conform the results of animal appetite and passion to a rule

of action.

The possibility of pursuing any such train of reasoning as

this, depends on the definitions, of _animal_ and of _man_,

which we have introduced; and the possibility of reasoning

concerning the objects around us being inevitably assumed by

us from the constitution of our nature, we assume

consequently the possibility of such definitions as may thus

form part of our deduction, and the existence of such

defining characters.

10. _Difficulty of Definitions._--But though men are, on

such grounds, led to make constant and importunate _demands_

for definitions of the terms which they employ in their

speculations, they are, in fact, far {105} from being able

to carry into complete effect the postulate on which they

proceed, that they must be able to find definitions which by

logical consequence shall lead to the truths they seek. The

postulate overlooks the process by which our classes of

things are formed and our names applied. This process

consisting, as we have already said, in observing permanent

connexions of properties, and in fixing them by the

attribution of names, is of the nature of the process of

Induction, of which we shall afterwards have to speak. And

the postulate is so far true, that this process of induction

being once performed, its result may usually be expressed by

means of a few definitions, and may thus lead by a deduction

to a train of real truths.

5. _Controversy of the Composition of Water._--There is