THE USE OF HYPOTHESIS.
If the views upheld in this work be correct, all inductive
investigation consists in the marriage of hypothesis and experiment.
When facts are in our possession, we frame an hypothesis to explain
their relations, and by the success of this explanation is the value
of the hypothesis to be judged. In the invention and treatment of
such hypotheses, we must avail ourselves of the whole body of science
already accumulated, and when once we have obtained a probable
hypothesis, we must not rest until we have verified it by comparison
with new facts. We must endeavour by deductive reasoning to anticipate
such phenomena, especially those of a singular and exceptional nature,
as would happen if the hypothesis be true. Out of the infinite number
of experiments which are possible, theory must lead us to select those
critical ones which are suitable for confirming or negativing our
anticipations.
This work of inductive investigation cannot be guided by any system of
precise and infallible rules, like those of deductive reasoning. There
is, in fact, nothing to which we can apply rules of method, because
the laws of nature must be in our possession before we can treat them.
If there were any rule of inductive method, it would direct us to make
an exhaustive arrangement of facts in all possible orders. Given the
specimens in a museum, we might arrive at the best classification by
going systematically through all possible classifications, and, were
we endowed with infinite time and patience, this would be an effective
method. It is the method by which the first simple steps are taken in
an incipient branch of science. Before the dignified name of science is
applicable, some coincidences will force themselves upon the attention.
Before there was a science of meteorology observant persons learned
to associate clearness of the atmosphere with coming rain, and a
colourless sunset with fine weather. Knowledge of this kind is called
*empirical*, as seeming to come directly from experience; and there is
a considerable portion of knowledge which bears this character.
We may be obliged to trust to the casual detection of coincidences
in those branches of knowledge where we are deprived of the aid of
any guiding notions; but a little reflection will show the utter
insufficiency of haphazard experiment, when applied to investigations
of a complicated nature. At the best, it will be the simple identity,
or partial identity, of classes, as illustrated in pages 127 or 134,
which can be thus detected. It was pointed out that, even when a law
of nature involves only two circumstances, and there are one hundred
distinct circumstances which may possibly be connected, there will be
no less than 4,950 pairs of circumstances between which coincidence may
exist. When a law involves three or more circumstances, the possible
number of relations becomes vastly greater. When considering the
subject of combinations and permutations, it became apparent that we
could never cope with the possible variety of nature. An exhaustive
examination of the possible metallic alloys, or chemical compounds, was
found to be out of the question (p. 191).
It is on such considerations that we can explain the very small
additions made to our knowledge by the alchemists. Many of them were
men of the greatest acuteness, and their indefatigable labours were
pursued through many centuries. A few things were discovered by them,
but a true insight into nature, now enables chemists to discover more
useful facts in a year than were yielded by the alchemists during
many centuries. There can be no doubt that Newton was an alchemist,
and that he often laboured night and day at alchemical experiments.
But in trying to discover the secret by which gross metals might be
rendered noble, his lofty powers of deductive investigation were wholly
useless. Deprived of all guiding clues, his experiments were like
those of all the alchemists, purely tentative and haphazard. While his
hypothetical and deductive investigations have given us the true system
of the Universe, and opened the way in almost all the great branches of
natural philosophy, the whole results of his tentative experiments are
comprehended in a few happy guesses, given in his celebrated “Queries.”
Even when we are engaged in apparently passive observation of a
phenomenon, which we cannot modify experimentally, it is advantageous
that our attention should be guided by theoretical anticipations. A
phenomenon which seems simple is, in all probability, really complex,
and unless the mind is actively engaged in looking for particular
details, it is likely that the critical circumstances will be passed
over. Bessel regretted that no distinct theory of the constitution
of comets had guided his observations of Halley’s comet;[418] in
attempting to verify or refute a hypothesis, not only would there be a
chance of establishing a true theory, but if confuted, the confutation
would involve a store of useful observations.
[418] Tyndall, *On Cometary Theory*, Philosophical Magazine, April
1869. 4th Series, vol. xxxvii. p. 243.
It would be an interesting work, but one which I cannot undertake, to
trace out the gradual reaction which has taken place in recent times
against the purely empirical or Baconian theory of induction. Francis
Bacon, seeing the futility of the scholastic logic, which had long
been predominant, asserted that the accumulation of facts and the
orderly abstraction of axioms, or general laws from them, constituted
the true method of induction. Even Bacon was not wholly unaware of
the value of hypothetical anticipation. In one or two places he
incidentally acknowledges it, as when he remarks that the subtlety of
nature surpasses that of reason, adding that “axioms abstracted from
particular facts in a careful and orderly manner, readily suggest and
mark out new particulars.”
Nevertheless Bacon’s method, as far as we can gather the meaning of
the main portions of his writings, would correspond to the process of
empirically collecting facts and exhaustively classifying them, to
which I alluded. The value of this method may be estimated historically
by the fact that it has not been followed by any of the great masters
of science. Whether we look to Galileo, who preceded Bacon, to Gilbert,
his contemporary, or to Newton and Descartes, Leibnitz and Huyghens,
his successors, we find that discovery was achieved by the opposite
method to that advocated by Bacon. Throughout Newton’s works, as
I shall show, we find deductive reasoning wholly predominant, and
experiments are employed, as they should be, to confirm or refute
hypothetical anticipations of nature. In my “Elementary Lessons in
Logic” (p. 258), I stated my belief that there was no kind of reference
to Bacon in Newton’s works. I have since found that Newton does once or
twice employ the expression *experimentum crucis* in his “Opticks,” but
this is the only expression, so far as I am aware, which could indicate
on the part of Newton direct or indirect acquaintance with Bacon’s
writings.[419]
[419] See *Philosophical Transactions*, abridged by Lowthorp. 4th
edit. vol. i. p. 130. I find that opinions similar to those in the
text have been briefly expressed by De Morgan in his remarkable
preface to *From Matter to Spirit*, by C.D., pp. xxi. xxii.
Other great physicists of the same age were equally prone to the use
of hypotheses rather than the blind accumulation of facts in the
Baconian manner. Hooke emphatically asserts in his posthumous work
on Philosophical Method, that the first requisite of the Natural
Philosopher is readiness at guessing the solution of phenomena and
making queries. “He ought to be very well skilled in those several
kinds of philosophy already known, to understand their several
hypotheses, suppositions, collections, observations, &c., their various
ways of ratiocinations and proceedings, the several failings and
defects, both in their way of raising and in their way of managing
their several theories: for by this means the mind will be somewhat
more ready at guessing at the solution of many phenomena almost at
first sight, and thereby be much more prompt at making queries, and at
tracing the subtlety of Nature, and in discovering and searching into
the true reason of things.”
We find Horrocks, again, than whom no one was more filled with the
scientific spirit, telling us how he tried theory after theory in order
to discover one which was in accordance with the motions of Mars.[420]
Huyghens, who possessed one of the most perfect philosophical
intellects, followed the deductive process combined with continual
appeal to experiment, with a skill closely analogous to that of Newton.
As to Descartes and Leibnitz, they fell into excess in the use of
hypothesis, since they sometimes adopted hypothetical reasoning to
the exclusion of experimental verification. Throughout the eighteenth
century science was supposed to be advancing by the pursuance of the
Baconian method, but in reality hypothetical investigation was the
main instrument of progress. It is only in the present century that
physicists began to recognise this truth. So much opprobrium had been
attached by Bacon to the use of hypotheses, that we find Young speaking
of them in an apologetic tone. “The practice of advancing general
principles and applying them to particular instances is so far from
being fatal to truth in all sciences, that when those principles are
advanced on sufficient grounds, it constitutes the essence of true
philosophy;”[421] and he quotes cases in which Davy trusted to his
theories rather than his experiments.
[420] Horrocks, *Opera Posthuma* (1673), p. 276.
[421] Young’s *Works*, vol. i. p. 593.
Herschel, who was both a practical physicist and an abstract logician,
entertained the deepest respect for Bacon, and made the “Novum
Organum” as far as possible the basis of his own admirable *Discourse
on the Study of Natural Philosophy*. Yet we find him in Chapter VII.
recognising the part which the formation and verification of theories
takes in the higher and more general investigations of physical
science. J. S. Mill carried on the reaction by describing the Deductive
Method in which ratiocination, that is deductive reasoning, is employed
for the discovery of new opportunities of testing and verifying an
hypothesis. Nevertheless throughout the other parts of his system
he inveighed against the value of the deductive process, and even
asserted that empirical inference from particulars to particulars is
the true type of reasoning. The irony of fate will probably decide
that the most original and valuable part of Mill’s System of Logic is
irreconcilable with those views of the syllogism and of the nature of
inference which occupy the main part of the treatise, and are said to
have effected a revolution in logical science. Mill would have been
saved from much confusion of thought had he not failed to observe that
the inverse use of deduction constitutes induction. In later years
Professor Huxley has strongly insisted upon the value of hypothesis.
When he advocates the use of “working hypotheses” he means no doubt
that any hypothesis is better that none, and that we cannot avoid being
guided in our observations by some hypothesis or other. Professor
Tyndall’s views as to the use of the Imagination in the pursuit of
Science put the same truth in another light.
It ought to be pointed out that Neil in his *Art of Reasoning*, a
popular but able exposition of the principles of Logic, published
in 1853, fully recognises in Chapter XI. the value and position of
hypothesis in the discovery of truth. He endeavours to show, too
(p. 109), that Francis Bacon did not object to the use of hypothesis.
The true course of inductive procedure is that which has yielded
all the more lofty results of science. It consists in *Anticipating
Nature*, in the sense of forming hypotheses as to the laws which are
probably in operation; and then observing whether the combinations
of phenomena are such as would follow from the laws supposed. The
investigator begins with facts and ends with them. He uses facts to
suggest probable hypotheses; deducing other facts which would happen if
a particular hypothesis is true, he proceeds to test the truth of his
notion by fresh observations. If any result prove different from what
he expects, it leads him to modify or to abandon his hypothesis; but
every new fact may give some new suggestion as to the laws in action.
Even if the result in any case agrees with his anticipations, he does
not regard it as finally confirmatory of his theory, but proceeds to
test the truth of the theory by new deductions and new trials.
In such a process the investigator is assisted by the whole body of
science previously accumulated. He may employ analogy, as I shall
point out, to guide him in the choice of hypotheses. The manifold
connections between one science and another give him clues to the kind
of laws to be expected, and out of the infinite number of possible
hypotheses he selects those which are, as far as can be foreseen at the
moment, most probable. Each experiment, therefore, which he performs
is that most likely to throw light upon his subject, and even if it
frustrate his first views, it tends to put him in possession of the
correct clue.
*Requisites of a good Hypothesis.*
There is little difficulty in pointing out to what condition an
hypothesis must conform in order to be accepted as probable and
valid. That condition, as I conceive, is the single one of enabling
us to infer the existence of phenomena which occur in our experience.
*Agreement with fact is the sole and sufficient test of a true
hypothesis.*
Hobbes has named two conditions which he considers requisite in an
hypothesis, namely (1) That it should be conceivable and not absurd;
(2) That it should allow of phenomena being necessarily inferred.
Boyle, in noticing Hobbes’ views, proposed to add a third condition,
to the effect that the hypothesis should not be inconsistent with any
other truth on phenomenon of nature.[422] I think that of these three
conditions, the first cannot be accepted, unless by *inconceivable* and
*absurd* we mean self-contradictory or inconsistent with the laws of
thought and nature. I shall have to point out that some satisfactory
theories involve suppositions which are wholly *inconceivable* in
a certain sense of the word, because the mind cannot sufficiently
extend its ideas to frame a notion of the actions supposed to take
place. That the force of gravity should act instantaneously between
the most distant parts of the planetary system, or that a ray of
violet light should consist of about 700 billions of vibrations in a
second, are statements of an inconceivable and absurd character in
one sense; but they are so far from being opposed to fact that we
cannot on any other suppositions account for phenomena observed. But
if an hypothesis involve self-contradiction, or is inconsistent with
known laws of nature, it is self-condemned. We cannot even apply
deductive reasoning to a self-contradictory notion; and being opposed
to the most general and certain laws known to us, the primary laws of
thought, it thereby conspicuously fails to agree with facts. Since
nature, again, is never self-contradictory, we cannot at the same time
accept two theories which lead to contradictory results. If the one
agrees with nature, the other cannot. Hence if there be a law which we
believe with high probability to be verified by observation, we must
not frame an hypothesis in conflict with it, otherwise the hypothesis
will necessarily be in disagreement with observation. Since no law or
hypothesis is proved, indeed, with absolute certainty, there is always
a chance, however slight, that the new hypothesis may displace the
old one; but the greater the probability which we assign to that old
hypothesis, the greater must be the evidence required in favour of the
new and conflicting one.
[422] Boyle’s *Physical Examen*, p. 84.
I assert, then, that there is but one test of a good hypothesis,
namely, *its conformity with observed facts*; but this condition may
be said to involve three constituent conditions, nearly equivalent to
those suggested by Hobbes and Boyle, namely:--
(1) That it allow of the application of deductive reasoning and the
inference of consequences capable of comparison with the results of
observation.
(2) That it do not conflict with any laws of nature, or of mind, which
we hold to be true.
(3) That the consequences inferred do agree with facts of observation.
*Possibility of Deductive Reasoning.*
As the truth of an hypothesis is to be proved by its conformity with
fact, the first condition is that we be able to apply methods of
deductive reasoning, and learn what should happen according to such
an hypothesis. Even if we could imagine an object acting according to
laws hitherto wholly unknown it would be useless to do so, because we
could never decide whether it existed or not. We can only infer what
would happen under supposed conditions by applying the knowledge of
nature we possess to those conditions. Hence, as Boscovich truly said,
we are to understand by hypotheses “not fictions altogether arbitrary,
but suppositions conformable to experience or analogy.” It follows that
every hypothesis worthy of consideration must suggest some likeness,
analogy, or common law, acting in two or more things. If, in order to
explain certain facts, *a*, *a′*, *a″*, &c., we invent a cause A, then
we must in some degree appeal to experience as to the mode in which A
will act. As the laws of nature are not known to the mind intuitively,
we must point out some other cause, B, which supplies the requisite
notions, and all we do is to invent a fourth term to an analogy. As B
is to its effects *b*, *b′*, *b″*, &c., so is A to its effects *a*,
*a′*, *a″*, &c. When we attempt to explain the passage of light and
heat radiations through space unoccupied by matter, we imagine the
existence of the so-called *ether*. But if this ether were wholly
different from anything else known to us, we should in vain try to
reason about it. We must apply to it at least the laws of motion, that
is we must so far liken it to matter. And as, when applying those laws
to the elastic medium air, we are able to infer the phenomena of sound,
so by arguing in a similar manner concerning ether we are able to infer
the existence of light phenomena corresponding to what do occur. All
that we do is to take an elastic substance, increase its elasticity
immensely, and denude it of gravity and some other properties of
matter, but we must retain sufficient likeness to matter to allow of
deductive calculations.
The force of gravity is in some respects an incomprehensible existence,
but in other respects entirely conformable to experience. We observe
that the force is proportional to mass, and that it acts in entire
independence of other matter which may be present or intervening.
The law of the decrease of intensity, as the square of the distance
increases, is observed to hold true of light, sound, and other
influences emanating from a point, and spreading uniformly through
space. The law is doubtless connected with the properties of space, and
is so far in agreement with our necessary ideas.
It may be said, however, that no hypothesis can be so much as framed
in the mind unless it be more or less conformable to experience. As
the material of our ideas is derived from sensation we cannot figure
to ourselves any agent, but as endowed with some of the properties of
matter. All that the mind can do in the creation of new existences is
to alter combinations, or the intensity of sensuous properties. The
phenomenon of motion is familiar to sight and touch, and different
degrees of rapidity are also familiar; we can pass beyond the limits of
sense, and imagine the existence of rapid motion, such as our senses
could not observe. We know what is elasticity, and we can therefore
in a way figure to ourselves elasticity a thousand or a million times
greater than any which is sensuously known to us. The waves of the
ocean are many times higher than our own bodies; other waves, are
many times less; continue the proportion, and we ultimately arrive
at waves as small as those of light. Thus it is that the powers of
mind enable us from a sensuous basis to reason concerning agents and
phenomena different in an unlimited degree. If no hypothesis then can
be absolutely opposed to sense, accordance with experience must always
be a question of degree.
In order that an hypothesis may allow of satisfactory comparison with
experience, it must possess definiteness and in many cases mathematical
exactness allowing of the precise calculation of results. We must
be able to ascertain whether it does or does not agree with facts.
The theory of vortices is an instance to the contrary, for it did
not present any mode of calculating the exact relations between the
distances and periods of the planets and satellites; it could not,
therefore, undergo that rigorous testing to which Newton scrupulously
submitted his theory of gravity before its promulgation. Vagueness
and incapability of precise proof or disproof often enable a false
theory to live; but with those who love truth, vagueness should
excite suspicion. The upholders of the ancient doctrine of Nature’s
abhorrence of a vacuum, had been unable to anticipate the important
fact that water would not rise more than 33 feet in a common suction
pump. Nor when the fact was pointed out could they explain it, except
by introducing a special alteration of the theory to the effect that
Nature’s abhorrence of a vacuum was limited to 33 feet.
*Consistency with the Laws of Nature.*
In the second place an hypothesis must not be contradictory to
what we believe to be true concerning Nature. It must not involve
self-inconsistency which is opposed to the highest and simplest laws,
namely, those of Logic. Neither ought it to be irreconcilable with
the simple laws of motion, of gravity, of the conservation of energy,
nor any parts of physical science which we consider to be established
beyond reasonable doubt. Not that we are absolutely forbidden to
entertain such an hypothesis, but if we do so we must be prepared to
disprove some of the best demonstrated truths in the possession of
mankind. The fact that conflict exists means that the consequences of
the theory are not verified if previous discoveries are correct, and we
must therefore show that previous discoveries are incorrect before we
can verify our theory.
An hypothesis will be exceedingly improbable, not to say absurd, if
it supposes a substance to act in a manner unknown in other cases;
for it then fails to be verified in our knowledge of that substance.
Several physicists, especially Euler and Grove, have supposed that
we might dispense with an ethereal basis of light, and infer from
the interstellar passage of rays that there was a kind of rare gas
occupying space. But if so, that gas must be excessively rare, as we
may infer from the apparent absence of an atmosphere around the moon,
and from other facts known to us concerning gases and the atmosphere;
yet it must possess an elastic force at least a billion times as great
as atmospheric air at the earth’s surface, in order to account for the
extreme rapidity of light rays. Such an hypothesis then is inconsistent
with our knowledge concerning gases.
Provided that there be no clear and absolute conflict with known
laws of nature, there is no hypothesis so improbable or apparently
inconceivable that it may not be rendered probable, or even
approximately certain, by a sufficient number of concordances. In
fact the two best founded and most successful theories in physical
science involve the most absurd suppositions. Gravity is a force which
appears to act between bodies through vacuous space; it is in positive
contradiction to the old dictum that nothing can act but through
some medium. It is even more puzzling that the force acts in perfect
indifference to intervening obstacles. Light in spite of its extreme
velocity shows much respect to matter, for it is almost instantaneously
stopped by opaque substances, and to a considerable extent absorbed
and deflected by transparent ones. But to gravity all media are, as
it were, absolutely transparent, nay non-existent; and two particles
at opposite points of the earth affect each other exactly as if the
globe were not between. The action is, so far as we can observe,
instantaneous, so that every particle of the universe is at every
moment in separate cognisance, as it were, of the relative position of
every other particle throughout the universe at that same moment of
time. Compared with such incomprehensible conditions, the theory of
vortices deals with commonplace realities. Newton’s celebrated saying
*hypotheses non fingo*, bears the appearance of irony; and it was not
without apparent grounds that Leibnitz and the continental philosophers
charged Newton with re-introducing occult powers and qualities.
The undulatory theory of light presents almost equal difficulties
of conception. We are asked by physical philosophers to give up our
prepossessions, and to believe that interstellar space which seems
empty is not empty at all, but filled with *something* immensely
more solid and elastic than steel. As Young himself remarked,[423]
“the luminiferous ether, pervading all space, and penetrating almost
all substances, is not only highly elastic, but absolutely solid!!!”
Herschel calculated the force which may be supposed, according to the
undulatory theory of light, to be constantly exerted at each point in
space, and finds it to be 1,148,000,000,000 times the elastic force
of ordinary air at the earth’s surface, so that the pressure of ether
per square inch must be about seventeen billions of pounds.[424] Yet
we live and move without appreciable resistance through this medium,
immensely harder and more elastic than adamant. All our ordinary
notions must be laid aside in contemplating such an hypothesis; yet it
is no more than the observed phenomena of light and heat force us to
accept. We cannot deny even the strange suggestion of Young, that there
may be independent worlds, some possibly existing in different parts
of space, but others perhaps pervading each other unseen and unknown
in the same space.[425] For if we are bound to admit the conception
of this adamantine firmament, it is equally easy to admit a plurality
of such. We see, then, that mere difficulties of conception must not
discredit a theory which otherwise agrees with facts, and we must only
reject hypotheses which are inconceivable in the sense of breaking
distinctly the primary laws of thought and nature.
[423] Young’s *Works*, vol. i. p. 415.
[424] *Familiar Lectures on Scientific Subjects*, p. 282.
[425] Young’s *Works*, vol. i. p. 417.
*Conformity with Facts.*
Before we accept a new hypothesis it must be shown to agree not only
with the previously known laws of nature, but also with the particular
facts which it is framed to explain. Assuming that these facts are
properly established, it must agree with all of them. A single absolute
conflict between fact and hypothesis, is fatal to the hypothesis;
*falsa in uno, falsa in omnibus*.
Seldom, indeed, shall we have a theory free from difficulties and
apparent inconsistency with facts. Though one real inconsistency
would overturn the most plausible theory, yet there is usually some
probability that the fact may be misinterpreted, or that some supposed
law of nature, on which we are relying, may not be true. It may be
expected, moreover, that a good hypothesis, besides agreeing with
facts already noticed, will furnish us with distinct credentials by
enabling us to anticipate deductively series of facts which are not
already connected and accounted for by any equally probable hypothesis.
We cannot lay down any precise rule as to the number of accordances
which can establish the truth of an hypothesis, because the accordances
will vary much in value. While, on the one hand, no finite number
of accordances will give entire certainty, the probability of the
hypothesis will increase very rapidly with the number of accordances.
Almost every problem in science thus takes the form of a balance of
probabilities. It is only when difficulty after difficulty has been
successfully explained away, and decisive *experimenta crucis* have,
time after time, resulted in favour of our theory, that we can venture
to assert the falsity of all objections.
The sole real test of an hypothesis is its accordance with fact.
Descartes’ celebrated system of vortices is exploded, not because it
was intrinsically absurd and inconceivable, but because it could not
give results in accordance with the actual motions of the heavenly
bodies. The difficulties of conception involved in the apparatus of
vortices, are child’s play compared with those of gravitation and
the undulatory theory already described. Vortices are on the whole
plausible suppositions; for planets and satellites bear at first sight
much resemblance to objects carried round in whirlpools, an analogy
which doubtless suggested the theory. The failure was in the first and
third requisites; for, as already remarked, the theory did not allow
of precise calculation of planetary motions, and was thus incapable of
rigorous verification. But so far as we can institute a comparison,
facts are entirely against the vortices. Newton did not ridicule the
theory as absurd, but showed[426] that it was “pressed with many
difficulties.” He carefully pointed out that the Cartesian theory was
inconsistent with the laws of Kepler, and would represent the planets
as moving more rapidly at their aphelia than at their perihelia.[427]
The rotatory motion of the sun and planets on their own axes is in
striking conflict with the revolutions of the satellites carried round
them; and comets, the most flimsy of bodies, calmly pursue their
courses in elliptic paths, irrespective of the vortices which they pass
through. We may now also point to the interlacing orbits of the minor
planets as a new and insuperable difficulty in the way of the Cartesian
ideas.
[426] *Principia*, bk. iii. Prop. 43. General Scholium.
[427] Ibid. bk. ii. Sect. ix. Prop. 53.
Newton, though he established the best of theories, was also capable
of proposing one of the worst; and if we want an instance of a theory
decisively contradicted by facts, we have only to turn to his views
concerning the origin of natural colours. Having analysed, with
incomparable skill, the origin of the colours of thin plates, he
suggests that the colours of all bodies are determined in like manner
by the size of their ultimate particles. A thin plate of a definite
thickness will reflect a definite colour; hence, if broken up into
fragments it will form a powder of the same colour. But, if this be
a sufficient explanation of coloured substances, then every coloured
fluid ought to reflect the complementary colour of that which it
transmits. Colourless transparency arises, according to Newton, from
particles being too minute to reflect light; but if so, every black
substance should be transparent. Newton himself so acutely felt this
last difficulty as to suggest that true blackness is due to some
internal refraction of the rays to and fro, and an ultimate stifling
of them, which he did not attempt to explain further. Unless some
other process comes into operation, neither refraction nor reflection,
however often repeated, will destroy the energy of light. The theory
therefore gives no account, as Brewster shows, of 24 parts out of 25 of
the light which falls upon a black coal, and the remaining part which
is reflected from the lustrous surface is equally inconsistent with the
theory, because fine coal-dust is almost entirely devoid of reflective
power.[428] It is now generally believed that the colours of natural
bodies are due to the unequal absorption of rays of light of different
refrangibility.
[428] Brewster’s *Life of Newton*, 1st edit. chap. vii.
*Experimentum Crucis.*
As we deduce more and more conclusions from a theory, and find them
verified by trial, the probability of the theory increases in a rapid
manner; but we never escape the risk of error altogether. Absolute
certainty is beyond the powers of inductive investigation, and the
most plausible supposition may ultimately be proved false. Such is the
groundwork of similarity in nature, that two very different conditions
may often give closely similar results. We sometimes find ourselves
therefore in possession of two or more hypotheses which both agree
with so many experimental facts as to have great appearance of truth.
Under such circumstances we have need of some new experiment, which
shall give results agreeing with one hypothesis but not with the other.
Any such experiment which decides between two rival theories may be
called an *Experimentum Crucis*, an Experiment of the Finger Post.
Whenever the mind stands, as it were, at cross-roads and knows not
which way to select, it needs some decisive guide, and Bacon therefore
assigned great importance and authority to instances which serve in
this capacity. The name given by Bacon has become familiar; it is
almost the only one of Bacon’s figurative expressions which has passed
into common use. Even Newton, as I have mentioned (p. 507), used the
name.
I do not think, indeed, that the common use of the word at all agrees
with that intended by Bacon. Herschel says that “we make an experiment
of the crucial kind when we form combinations, and put in action
causes from which some particular one shall be deliberately excluded,
and some other purposely admitted.”[429] This, however, seems to be
the description of any special experiment not made at haphazard.
Pascal’s experiment of causing a barometer to be carried to the top of
the Puy-de-Dôme has often been considered as a perfect *experimentum
crucis*, if not the first distinct one on record;[430] but if so, we
must dignify the doctrine of Nature’s abhorrence of a vacuum with
the position of a rival theory. A crucial experiment must not simply
confirm one theory, but must negative another; it must decide a mind
which is in equilibrium, as Bacon says,[431] between two equally
plausible views. “When in search of any nature, the understanding comes
to an equilibrium, as it were, or stands suspended as to which of two
or more natures the cause of nature inquired after should be attributed
or assigned, by reason of the frequent and common occurrence of several
natures, then these Crucial Instances show the true and inviolable
association of one of these natures to the nature sought, and the
uncertain and separable alliance of the other, whereby the question
is decided, the former nature admitted for the cause, and the other
rejected. These instances, therefore, afford great light, and have a
kind of overruling authority, so that the course of interpretation will
sometimes terminate in them, or be finished by them.”
[429] *Discourse on the Study of Natural Philosophy*, p. 151.
[430] Ibid. p. 229.
[431] *Novum Organum*, bk. ii. Aphorism 36.
The long-continued strife between the Corpuscular and Undulatory
theories of light forms the best possible illustration of an
Experimentum Crucis. It is remarkable in how plausible a manner both
these theories agreed with the ordinary laws of geometrical optics,
relating to reflection and refraction. According to the first law of
motion a moving particle proceeds in a perfectly straight line, when
undisturbed by extraneous forces. If the particle being perfectly
elastic, strike a perfectly elastic plane, it will bound off in such
a path that the angles of incidence and reflection will be equal.
Now a ray of light proceeds in a straight line, or appears to do
so, until it meets a reflecting body, when its path is altered in a
manner exactly similar to that of the elastic particle. Here is a
remarkable correspondence which probably suggested to Newton’s mind
the hypothesis that light consists of minute elastic particles moving
with excessive rapidity in straight lines. The correspondence was found
to extend also to the law of simple refraction; for if particles of
light be supposed capable of attracting matter, and being attracted
by it at insensibly small distances, then a ray of light, falling on
the surface of a transparent medium, will suffer an increase in its
velocity perpendicular to the surface, and the law of sines is the
consequence. This remarkable explanation of the law of refraction had
doubtless a very strong effect in leading Newton to entertain the
corpuscular theory, and he appears to have thought that the analogy
between the propagation of rays of light and the motion of bodies was
perfectly exact, whatever might be the actual nature of light.[432]
It is highly remarkable, again, that Newton was able to give by his
corpuscular theory, a plausible explanation of the inflection of light
as discovered by Grimaldi. The theory would indeed have been a very
probable one could Newton’s own law of gravity have applied; but this
was out of the question, because the particles of light, in order that
they may move in straight lines, must be devoid of any influence upon
each other.
[432] *Principia*, bk. i. Sect. xiv. Prop. 96. Scholium. *Opticks*,
Prop. vi. 3rd edit. p. 70.
The Huyghenian or Undulatory theory of light was also able to explain
the same phenomena, but with one remarkable difference. If the
undulatory theory be true, light must move more slowly in a dense
refracting medium than in a rarer one; but the Newtonian theory assumed
that the attraction of the dense medium caused the particles of light
to move more rapidly than in the rare medium. On this point, then,
there was complete discrepancy between the theories, and observation
was required to show which theory was to be preferred. Now by simply
cutting a uniform plate of glass into two pieces, and slightly
inclining one piece so as to increase the length of the path of a ray
passing through it, experimenters were able to show that light does
move more slowly in glass than in air.[433] More recently Fizeau and
Foucault independently measured the velocity of light in air and in
water, and found that the velocity is greater in air.[434]
[433] Airy’s *Mathematical Tracts*, 3rd edit. pp. 286–288.
[434] Jamin, *Cours de Physique*, vol. iii. p. 372.
There are a number of other points at which experience decides against
Newton, and in favour of Huyghens and Young. Laplace pointed out that
the attraction supposed to exist between matter and the corpuscular
particles of light would cause the velocity of light to vary with the
size of the emitting body, so that if a star were 250 times as great
in diameter as our sun, its attraction would prevent the emanation of
light altogether.[435] But experience shows that the velocity of light
is uniform, and independent of the magnitude of the emitting body,
as it should be according to the undulatory theory. Lastly, Newton’s
explanation of diffraction or inflection fringes of colours was only
*plausible*, and not true; for Fresnel ascertained that the dimensions
of the fringes are not what they would be according to Newton’s theory.
[435] Young’s *Lectures on Natural Philosophy* (1845), vol. i. p. 361.
Although the Science of Light presents us with the most beautiful
examples of crucial experiments and observations, instances are
not wanting in other branches of science. Copernicus asserted, in
opposition to the ancient Ptolemaic theory, that the earth moved round
the sun, and he predicted that if ever the sense of sight could be
rendered sufficiently acute and powerful, we should see phases in
Mercury and Venus. Galileo with his telescope was able, in 1610 to
verify the prediction as regards Venus, and subsequent observations
of Mercury led to a like conclusion. The discovery of the aberration
of light added a new proof, still further strengthened by the more
recent determination of the parallax of fixed stars. Hooke proposed
to prove the existence of the earth’s diurnal motion by observing the
deviation of a falling body, an experiment successfully accomplished by
Benzenberg; and Foucault’s pendulum has since furnished an additional
indication of the same motion, which is indeed also apparent in the
trade winds. All these are crucial facts in favour of the Copernican
theory.
*Descriptive Hypotheses.*
There are hypotheses which we may call *descriptive hypotheses*,
and which serve for little else than to furnish convenient names.
When a phenomenon is of an unusual kind, we cannot even speak of
it without using some analogy. Every word implies some resemblance
between the thing to which it is applied, and some other thing, which
fixes the meaning of the word. If we are to speak of what constitutes
electricity, we must search for the nearest analogy, and as electricity
is characterised by the rapidity and facility of its movements, the
notion of a fluid of a very subtle character presents itself as
appropriate. There is the single-fluid and the double-fluid theory of
electricity, and a great deal of discussion has been uselessly spent
upon them. The fact is, that if these theories be understood as more
than convenient modes of describing the phenomena, they are altogether
invalid. The analogy extends only to the rapidity of motion, or rather
the fact that a phenomenon occurs successively at different points of
the body. The so-called electric fluid adds nothing to the weight of
the conductor, and to suppose that it really consists of particles of
matter is even more absurd than to reinstate the corpuscular theory
of light. A far closer analogy exists between electricity and light
undulations, which are about equally rapid in propagation. We shall
probably continue for a long time to talk of the *electric fluid*, but
there can be no doubt that this expression represents merely a phase of
molecular motion, a wave of disturbance. The invalidity of these fluid
theories is shown moreover in the fact that they have not led to the
invention of a single new experiment.
Among these merely descriptive hypotheses I should place Newton’s
theory of Fits of Easy Reflection and Refraction. That theory did not
do more than describe what took place. It involved no analogy to other
phenomena of nature, for Newton could not point to any other substance
which went through these extraordinary fits. We now know that the true
analogy would have been waves of sound, of which Newton had acquired in
other respects so complete a comprehension. But though the notion of
interference of waves had distinctly occurred to Hooke, Newton failed
to see how the periodic phenomena of light could be connected with the
periodic character of waves. His hypothesis fell because it was out
of analogy with everything else in nature, and it therefore did not
allow him, as in other cases, to descend by mathematical deduction to
consequences which could be verified or refuted.
We are at freedom to imagine the existence of a new agent, and to
give it an appropriate name, provided there are phenomena incapable
of explanation from known causes. We may speak of *vital force* as
occasioning life, provided that we do not take it to be more than a
name for an undefined something giving rise to inexplicable facts, just
as the French chemists called Iodine the Substance X, so long as they
were unaware of its real character and place in chemistry.[436] Encke
was quite justified in speaking of the *resisting medium* in space so
long as the retardation of his comet could not be otherwise accounted
for. But such hypotheses will do much harm whenever they divert us from
attempts to reconcile the facts with known laws, or when they lead us
to mix up discrete things. Because we speak of vital force we must not
assume that it is a really existing physical force like electricity; we
do not know what it is. We have no right to confuse Encke’s supposed
resisting medium with the basis of light without distinct evidence of
identity. The name protoplasm, now so familiarly used by physiologists,
is doubtless legitimate so long as we do not mix up different
substances under it, or imagine that the name gives us any knowledge
of the obscure origin of life. To name a substance protoplasm no more
explains the infinite variety of forms of life which spring out of the
substance, than does the *vital force* which may be supposed to reside
in the protoplasm. Both expressions are mere names for an inexplicable
series of causes which out of apparently similar conditions produce the
most diverse results.
[436] Paris, *Life of Davy*, p. 274.
Hardly to be distinguished from descriptive hypotheses are certain
imaginary objects which we frame for the ready comprehension of
a subject. The mathematician, in treating abstract questions of
probability, finds it convenient to represent the conditions by a
concrete hypothesis in the shape of a ballot-box. Poisson proved the
principle of the inverse method of probabilities by imagining a number
of ballot-boxes to have their contents mixed in one great ballot-box
(p. 244). Many such devices are used by mathematicians. The Ptolemaic
theory of *cycles* and *epi-cycles* was no grotesque and useless work
of the imagination, but a perfectly valid mode of analysing the motions
of the heavenly bodies; in reality it is used by mathematicians at the
present day. Newton employed the pendulum as a means of representing
the nature of an undulation. Centres of gravity, oscillation, &c.,
poles of the magnet, lines of force, are other imaginary existences
employed to assist our thoughts (p. 364). Such devices may be called
*Representative Hypotheses*, and they are only permissible so far as
they embody analogies. Their further consideration belongs either to
the subject of Analogy, or to that of language and representation,
founded upon analogy.