OF THE APPLICATION OF INDUCTIVE TRUTHS.
APHORISM LIII.
_When the theory of any subject is established, the observations and
experiments which are made in applying the science to use and to
instruction, supply a perpetual_ verification _of the theory._
APHORISM LIV.
_Such observations and experiments, when numerous and accurate,
supply also_ corrections _of the_ constants _involved in the theory;
and sometimes_, (_by the Method of Residues_,) additions _to the
theory._
APHORISM LV.
_It is worth considering, whether a continued and connected system
of observation and calculation, like that of astronomy, might not be
employed with advantage in improving our knowledge of other
subjects; as Tides, Currents, Winds, Clouds, Rain, Terrestrial
Magnetism, Aurora Borealis, Composition of Crystals, and many other
subjects._
APHORISM LVI.
_An_ extension _of a well-established theory to the explanation of
new facts excites admiration as a discovery; but it is a discovery
of a lower order than the theory itself._
APHORISM LVII.
_The practical inventions which are most important in Art may be
either unimportant parts of Science, or results not explained by
Science._ {234}
APHORISM LVIII.
_In modern times, in many departments. Art is constantly guided,
governed and advanced by Science._
APHORISM LIX.
_Recently several New Arts have been invented, which may be regarded
as notable verifications of the anticipations of material benefits to
be derived to man from the progress of Science._
1. BY the application of inductive truths, we here mean, according
to the arrangement given in chap. I. of this book, those steps,
which in the natural order of science, follow the discovery of each
truth. These steps are, the _verification_ of the discovery by
additional experiments and reasonings, and its _extension_ to new
cases, not contemplated by the original discoverer. These processes
occupy that period, which, in the history of each great discovery,
we have termed the _Sequel_ of the epoch; as the collection of
facts, and the elucidation of conceptions, form its Prelude.
2. It is not necessary to dwell at length on the processes of the
Verification of Discoveries. When the Law of Nature is once stated,
it is far easier to devise and execute experiments which prove it,
than it was to discern the evidence before. The truth becomes one of
the standard doctrines of the science to which it belongs, and is
verified by all who study or who teach the science experimentally.
The leading doctrines of Chemistry are constantly exemplified by
each chemist in his _Laboratory_; and an amount of verification is
thus obtained of which books give no adequate conception. In
Astronomy, we have a still stronger example of the process of
verifying discoveries. Ever since the science assumed a systematic
form, there have been _Observatories_, in which the consequences of
the theory were habitually compared with the results of observation.
And to facilitate this comparison, _Tables_ of great extent have
been calculated, with immense labour, from each theory, showing the
place which the {235} theory assigned to the heavenly bodies at
successive times; and thus, as it were, challenging nature to deny
the truth of the discovery. In this way, as I have elsewhere stated,
the continued prevalence of an errour in the systematic parts of
astronomy is impossible[49\3]. An errour, if it arise, makes its way
into the tables, into the ephemeris, into the observer's nightly
list, or his sheet of reductions; the evidence of sense flies in its
face in a thousand Observatories; the discrepancy is traced to its
source, and soon disappears for ever.
[Note 49\3: _Hist. Ind. Sc._ b. vii. c. vi. sect. 6.]
3. In these last expressions, we suppose the theory, not only to be
tested, but also to be _corrected_ when it is found to be imperfect.
And this also is part of the business of the observing astronomer.
From his accumulated observations, he deduces more exact values than
had previously been obtained, of the _Constants_ or _Coefficients_
of these Inequalities of which the _Argument_ is already known. This
he is enabled to do by the methods explained in the fifth chapter of
this book; the Method of Means, and especially the Method of Least
Squares. In other cases, he finds, by the Method of Residues, some
new Inequality; for if no change of the Coefficients will bring the
Tables and the observation to a coincidence, he knows that a new
Term is wanting in his formula. He obtains, as far as he can, the
law of this unknown Term; and when its existence and its law have
been fully established, there remains the task of tracing it to its
cause.
4. The condition of the science of Astronomy, with regard to its
security and prospect of progress, is one of singular felicity. It
is a question well worth our consideration, as regarding the
interests of science, whether, in other branches of knowledge also,
_a continued and corrected system, of observation and calculation_,
imitating the system employed by astronomers, might not be adopted.
But the discussion of this question would involve us in a digression
too wide for the present occasion. {236}
5. There is another mode of application of true theories after their
discovery, of which we must also speak; I mean the process of
showing that facts, not included in the original induction, and
apparently of a different kind, are explained by reasonings founded
upon the theory:--_extensions_ of the theory as we may call them.
The history of physical astronomy is full of such events. Thus after
Bradley and Wargentin had observed a certain cycle among the
perturbations of Jupiter's satellites, Laplace explained this cycle
by the doctrine of universal gravitation[50\3]. The long inequality
of Jupiter and Saturn, the diminution of the obliquity of the
ecliptic, the acceleration of the moon's mean motion, were in like
manner accounted for by Laplace. The coincidence of the nodes of the
moon's equator with those of her orbit was proved to result from
mechanical principles by Lagrange. The motions of the
recently-discovered planets, and of comets, shown by various
mathematicians to be in exact accordance with the theory, are
Verifications and Extensions still more obvious.
[Note 50\3: _Hist. Ind. Sc._ b. vii. c. iv. sect. 3.]
6. In many of the cases just noticed, the consistency between the
theory, and the consequences thus proved to result from it, is so
far from being evident, that the most consummate command of all the
powers and aids of mathematical reasoning is needed, to enable the
philosopher to arrive at the result. In consequence of this
circumstance, the labours just referred to, of Laplace, Lagrange,
and others, have been the object of very great and very just
admiration. Moreover, the necessary connexion of new facts, at first
deemed inexplicable, with principles already known to be true;--a
connexion utterly invisible at the outset, and yet at last
established with the certainty of demonstration;--strikes us with
the delight of a new discovery; and at first sight appears no less
admirable than an original induction. Accordingly, men sometimes
appear tempted to consider Laplace and other great mathematicians as
persons of a kindred genius to Newton. We must not {237} forget,
however, that there is a great and essential difference between
inductive and deductive processes of the mind. The discovery of a
_new_ theory, which is true, is a step widely distinct from any mere
development of the consequences of a theory already invented and
established.
7. In the other sciences also, which have been framed by a study of
natural phenomena, we may find examples of the explanation of new
phenomena by applying the principles of the science when once
established. Thus, when the laws of the reflection and refraction of
light had been established, a new and poignant exemplification of
them was found in the explanation of the Rainbow by the reflection
and refraction of light in the spherical drops of a shower; and
again, another, no less striking, when the intersecting Luminous
Circles and Mock Suns, which are seen in cold seasons, were
completely explained by the hexagonal crystals of ice which float in
the upper regions of the atmosphere. The Darkness of the space
between the primary and secondary rainbow is another appearance
which optical theory completely explains. And when we further
include in our optical theory the doctrine of interferences, we find
the explanation of other phenomena; for instance, the Supernumerary
Rainbows which accompany the primary rainbow on its inner side, and
the small Halos which often surround the sun and moon. And when we
come to optical experiments, we find many instances in which the
doctrine of interferences and of undulations have been applied to
explain the phenomena by calculations almost as complex as those
which we have mentioned in speaking of astronomy: with results as
little foreseen at first and as entirely satisfactory in the end.
Such are Schwerdt's explanation of the diffracted images of a
triangular aperture by the doctrine of interferences, and the
explanation of the coloured Lemniscates seen by polarized light in
biaxal crystals, given by Young and by Herschel: and still more
marked is another case, in which the curves are unsymmetrical,
namely, the curves seen by passing polarized {238} light through
plates of quartz, which agree in a wonderful manner with the
calculations of Airy. To these we may add the curious phenomena, and
equally curious mathematical explanation, of Conical Refraction, as
brought to view by Professor Lloyd and Sir W. Hamilton. Indeed, the
whole history both of Physical Optics and of Physical Astronomy is a
series of _felicities_ of this kind, as we have elsewhere observed.
Such applications of theory, and unforeseen explanations of new
facts by complicated trains of reasoning necessarily flowing from
the theory, are strong proof of the truth of the theory, while it is
in the course of being established; but we are here rather speaking
of them as applications of the theory after it has been established.
Those who thus apply principles already discovered are not to be
ranked in their intellectual achievements with those who discover
new principles; but still, when such applications are masked by the
complex relations of space and number, it is impossible not to
regard with admiration the clearness and activity of intellect which
thus discerns in a remote region the rays of a central truth already
unveiled by some great discoverer.
8. As examples in other fields of the application of a scientific
discovery to the explanation of natural phenomena, we may take the
identification of Lightning with electricity by Franklin, and the
explanation of Dew by Wells. For Wells's _Inquiry into the Cause of
Dew_, though it has sometimes been praised as an original discovery,
was, in fact, only resolving the phenomenon into principles already
discovered. The atmologists of the last century were aware[51\3]
that the vapour which exists in air in an invisible state may be
condensed into water by cold; and they had noticed that there is
always a certain temperature, lower than that of the atmosphere, to
which if we depress bodies, water forms upon them in fine drops.
This temperature is the limit of that which is {239} necessary to
constitute vapour, and is hence called the _constituent
temperature_. But these principles were not generally familiar in
England till Dr. Wells introduced them into his _Essay on Dew_,
published in 1814; having indeed been in a great measure led to them
by his own experiments and reasonings. His explanation of Dew,--that
it arises from the coldness of the bodies on which it settles,--was
established with great ingenuity; and is a very elegant confirmation
of the Theory of Constituent Temperature.
[Note 51\3:_Hist. Ind. Sc._ b. x. c. iii. sect. 5.]
9. As other examples of such explanations of new phenomena by a
theory, we may point out Ampère's Theory that Magnetism is
transverse voltaic currents, applied to explain the rotation of a
voltaic wire round a magnet, and of a magnet round a voltaic wire.
And again, in the same subject, when it had been proved that
electricity might be converted into magnetism, it seemed certain
that magnetism might be converted into electricity; and accordingly
Faraday found under what conditions this may be done; though indeed
here, the theory rather suggested the experiment than explained it
when it had been independently observed. The production of an
electric spark by a magnet was a very striking exemplification of
the theory of the identity of these different polar agencies.
10. In Chemistry such applications of the principles of the science
are very frequent; for it is the chemist's business to account for
the innumerable changes which take place in material substances by
the effects of mixture, heat, and the like. As a marked instance of
such an application of the science, we may take the explanation of
the explosive force of gunpowder[52\3], from the conversion of its
materials into gases. In Mineralogy also we have to apply the {240}
principles of Chemistry to the analysis of bodies: and I may
mention, as a case which at the time excited much notice, the
analysis of a mineral called Heavy Spar. It was found that different
specimens of this mineral differed in their crystalline angles about
three degrees and a half; a difference which was at variance with
the mineralogical discovery then recently made, of the constancy of
the angle of the same substance. Vauquelin solved this difficulty by
discovering that the crystals with the different angles were really
minerals chemically different; the one kind being sulphate of
barytes, and the other, sulphate of strontian.
[Note 52\3: The explanation is, that the force is due to the sudden
development of a large volume of nitrogen and carbonic acid gases,
which at the ordinary temperature of the air would occupy a space
equal to about 300 times the bulk of the powder used, but from the
intense heat developed at the moment of the explosion, the
dilatation amounts to at least 1500 times the volume of the
gunpowder employed.]
11. In this way a scientific theory, when once established, is
perpetually finding new applications in the phenomena of nature; and
those who make such applications, though, as we have said, they care
not to be ranked with the great discoverers who establish theories
new and true, often receive a more prompt and general applause than
great discoverers do; because they have not to struggle with the
perplexity and averseness which often encounter the promulgation of
new truths.
12. Along with the verification and extension of scientific truths,
we are naturally led to consider the useful application of them. The
example of all the best writers who have previously treated of the
philosophy of sciences, from Bacon to Herschel, draws our attention
to those instances of the application of scientific truths, which
are subservient to the uses of practical life; to the support, the
safety, the pleasure of man. It is well known in how large a degree
the furtherance of these objects constituted the merit of the _Novum
Organon_ in the eyes of its author; and the enthusiasm with which
men regard these visible and tangible manifestations of the power
and advantage which knowledge may bring, has gone on increasing up
to our own day. And undoubtedly such applications of the discoveries
of science to promote the preservation, comfort, power and dignity
of man, must always be objects of great philosophical as well as
practical interest. Yet we may observe that those {241} practical
inventions which are of most importance in the Arts, have not
commonly, in the past ages of the world, been the results of
theoretical knowledge, nor have they tended very greatly to the
promotion of such knowledge. The use of bread and of wine has
existed from the first beginning of man's social history; yet men
have not had--we may question whether they yet have--a satisfactory
theory of the constitution and fabrication of bread and of wine.
From a very early period there have been workers in metal: yet who
could tell upon what principles depended the purifying of gold and
silver by the fire, or the difference between iron and steel? In
some cases, as in the story of the brass produced by the Corinthian
conflagration, some particular step in art is ascribed to a special
accident; but hardly ever to the thoughtful activity of a scientific
speculator. The Dyeing of cloths, the fabrication and colouring of
earthenware and glass vessels was carried to a very high degree of
completeness; yet who had any sound theoretical knowledge respecting
these processes? Are not all these arts still practised with a
degree of skill which we can hardly or not at all surpass, by
nations which have, properly speaking, no science? Till lately, at
least, if even now the case be different, the operations by which
man's comforts, luxuries, and instruments were produced, were either
mere practical processes, which the artist practises, but which the
scientist cannot account for; or, as in astronomy and optics, they
depended upon a small portion only of the theoretical sciences, and
did not tend to illustrate, or lead to, any larger truths. Bacon
mentions as recent discoveries, which gave him courage and hope with
regard to the future progress of human knowledge, the invention of
gunpowder, glass, and printing, the introduction of silk, and the
discovery of America. Yet which of these can be said to have been
the results of a theoretical enlargement of human knowledge? except
perhaps the discovery of the New World, which was in some degree the
result of Columbus's conviction of the globular form of the earth.
This, however, was not a recent, but a very ancient {242} doctrine
of all sound astronomers. And which of these discoveries has been
the cause of a great enlargement of our theoretical
knowledge?--except any one claims such a merit for the discovery of
printing; in which sense the result is brought about in a very
indirect manner, in the same way in which the progress of freedom
and of religion may be ascribed as consequences to the same
discovery. However great or striking, then, such discoveries have
been, they have not, generally speaking, produced any marked advance
of the Inductive Sciences in the sense in which we here speak of
them. They have increased man's power, it may be: that is, his power
of adding to his comforts and communicating with his fellow-men. But
they have not necessarily or generally increased his theoretical
knowledge. And, therefore, with whatever admiration we may look upon
such discoveries as these, we are not to admire them as steps in
Inductive Science.
And on the other hand, we are not to ask of Inductive Science, as a
necessary result of her progress, such additions as these to man's
means of enjoyment and action. It is said, with a feeling of
triumph, that Knowledge is Power: but in whatever sense this may
truly be said, we value Knowledge, not because it is Power but
because it is Knowledge; and we estimate wrongly both the nature and
the dignity of that kind of science with which we are here
concerned, if we expect that every new advance in theory will
forthwith have a market value:--that science will mark the birth of
a new Truth with some new birthday present, such as a softer stuff
to wrap our limbs, a brighter vessel to grace our table, a new mode
of communication with our friends and the world, a new instrument
for the destruction of our enemies, or a new region which may be the
source of wealth and interest.
13. Yet though, as we have said, many of the most remarkable
processes which we reckon as the triumphs of Art did not result from
a previous progress of Science, we have, at many points of the
history of Science, applications of new views, to enable man to _do_
as well {243} as to _see_. When Archimedes had obtained clear views
of the theory of machines, he forthwith expressed them in his bold
practical boast; 'Give me whereon to stand, and I will move the
earth.' And his machines with which he is said to have handled the
Roman ships like toys, and his burning mirrors with which he is
reported to have set them on fire, are at least possible
applications of theoretical principles. When he saw the waters
rising in the bath as his body descended, and rushed out crying, 'I
have found the way;' what he had found was the solution of the
practical question of the quantity of silver mixed with the gold of
Hiero's crown. But the mechanical inventions of Hero of Alexandria,
which moved by the force of air or of steam, probably involved no
exact theoretical notions of the properties of air or of steam. He
devised a toy which revolved by the action of steam; but by the
force of steam exerted in issuing from an orifice, not by its
pressure or condensation. And the Romans had no arts derived from
science in addition to those which they inherited from the Greeks.
They built aqueducts, not indeed through ignorance of the principles
of hydrostatics, as has sometimes been said; for we, who know our
hydrostatics, build aqueducts still; but their practice exemplified
only Archimedean hydrostatics. Their clepsydras or water-clocks were
adjusted by trial only. They used arches and vaults more copiously
than the Greeks had done, but the principle of the arch appears, by
the most recent researches, to have been known to the Greeks. Domes
and groined arches, such as we have in the Pantheon and in the Baths
of Caracalla, perhaps they invented; certainly they practised them
on a noble scale. Yet this was rather practical skill than
theoretical knowledge; and it was pursued by their successors in the
middle ages in the same manner, as practical skill rather than
theoretical knowledge. Thus were produced flying buttresses,
intersecting pointed vaults, and the other wonders of mediæval
architecture. The engineers of the fifteenth century, as Leonardo da
Vinci, began to convert their practical into theoretical knowledge
of Mechanics; but still {244} clocks and watches, flying machines
and printing presses involved no new mechanical principle.
14. But from this time the advances in Science generally produced,
as their result, new inventions of a practical kind. Thus the
doctrine of the weight of air led to such inventions as the
barometer used as a Weather-glass, the Air-pump with its train of
curious experiments, the Diving-Bell, the Balloon. The telescope was
perhaps in some degree a discovery due to accident, but its
principles had been taught by Roger Bacon, and still more clearly by
Descartes. Newton invented a steady thermometer by attending to
steady laws of nature. And in the case of the improvements of the
steam engine made by Watt, we have an admirable example how superior
the method of improving Art by Science is, to the blind gropings of
mere practical habit.
Of this truth, the history of most of the useful arts in our time
offers abundant proofs and illustrations. All improvements and
applications of the forces and agencies which man employs for his
purposes are now commonly made, not by blind trial but with the
clearest theoretical as well as practical insight which he can
obtain, into the properties of the agents which he employs. In this
way he has constructed, (using theory and calculation at every step
of his construction,) steam engines, steam boats, screw-propellers,
locomotive engines, railroads and bridges and structures of all
kinds. Lightning-conductors have been improved and applied to the
preservation of buildings, and especially of ships, with admirable
effect, by Sir Wm. Snow Harris, an experimenter who has studied with
great care the theory of electricity. The measurement of the
quantity of oxygen, that is, of vital power, in air, has been taught
by Cavendish, and by Dr Ure a skilful chemist of our time. Methods
for measuring the bleaching power of a substance have been devised
by eminent chemical philosophers, Gay Lussac and Mr Graham. Davy
used his discoveries concerning the laws of flame in order to
construct his Safety Lamp:--his discoveries concerning the galvanic
{245} battery in order to protect ships' bottoms from corrosion. The
skilled geologist has repeatedly given to those who were about to
dig for coal where it could have no geological place, advice which
has saved them from ruinous expence. Sir Roderick Murchison, from
geological evidence, declared the likelihood of gold being found
abundantly in Australia, many years before the diggings began.
Even the subtle properties of light as shewn in the recent
discoveries of its interference and polarization, have been applied
to useful purposes. Young invented an _Eriometer_, an instrument
which should measure the fineness of the threads of wool by the
coloured fringes which they produce; and substances which it is
important to distinguish in the manufacture of sugar, are
discriminated by their effect in rotating the plane of polarization
of light. One substance has been termed _Dextrin_, from its
impressing a right-handed rotation on the plane of polarization.
And in a great number of Arts and Manufactures, the necessity of a
knowledge of theory to the right conduct of practice is familiarly
acknowledged and assumed. In the testing and smelting of metals, in
the fabrication of soap, of candles, of sugar; in the dyeing and
printing of woollen, linen, cotton and silken stuffs; the master
manufacturer has always the scientific chemist at his elbow;--either
a 'consulting chemist' to whom he may apply on a special occasion,
(for such is now a regular profession;) or a chemist who day by day
superintends, controls, and improves the processes which his workmen
daily carry on. In these cases, though Art long preceded Science,
Science now guides, governs and advances Art.
15. Other Arts and manufactures which have arisen in modern times
have been new creations produced by Science, and requiring a
complete acquaintance with scientific processes to conduct them
effectually and securely. Such are the photographic Arts, now so
various in their form; beginning with those which, from their
authors, are called Daguerrotype and Talbotype. Such are the Arts of
Electrotype modelling {246} and Electrotype plating. Such are the
Arts of preparing fulminating substances; gun-cotton; fulminate of
silver, and of mercury; and the application of those Arts to use, in
the fabrication of percussion-caps for guns. Such is the Art of
Electric Telegraphy, from its first beginning to its last great
attempt, the electric cord which connects England and America. Such
is the Art of imitating by the chemistry of the laboratory the
vegetable chemistry of nature, and thus producing the flavour of the
pear, the apple, the pine-apple, the melon, the quince. Such is the
Art of producing in man a temporary insensibility to pain, which was
effected first through the means of sulphuric ether by Dr Jackson of
America, and afterwards through the use of chloroform by Dr Simpson
of Edinburgh. In these cases and many others Science has endowed man
with New Arts. And though even in these Arts, which are thus the
last results of Science, there is much which Science cannot fully
understand and explain; still, such cases cannot but be looked upon
as notable verifications of the anticipations of those who In former
times expected from the progress of Science a harvest of material
advantages to man.
We must now conclude our task by a few words on the subject of
inductions involving Ideas ulterior to those already considered.
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