CHAPTER IX.Of the Application of Inductive Truths.AphorismLIII.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 perpetualverificationof the theory.AphorismLIV.Such observations and experiments, when numerous and accurate, supply alsocorrectionsof theconstantsinvolved in the theory; and sometimes, (by the Method of Residues,) additionsto the theory.AphorismLV.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.AphorismLVI.Anextensionof 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.AphorismLVII.The practical inventions which are most important in Art may be either unimportant parts of Science, or results not explained by Science.234AphorismLVIII.In modern times, in many departments. Art is constantly guided, governed and advanced by Science.AphorismLIX.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, theverificationof the discovery by additional experiments and reasonings, and itsextensionto new cases, not contemplated by the original discoverer. These processes occupy that period, which, in the history of each great discovery, we have termed theSequelof 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 hisLaboratory; 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 beenObservatories, in which the consequences of the theory were habitually compared with the results of observation. And to facilitate this comparison,Tablesof great extent have been calculated, with immense labour, from each theory, showing the place which the235theory 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 impossible49. 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.49Hist. 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 becorrectedwhen 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 theConstantsorCoefficientsof these Inequalities of which theArgumentis already known. This he is enabled to do by the methods explained in thefifthchapter of this book; theMethod of Means, and especially theMethod of Least Squares. In other cases, he finds, by theMethod 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.2365. 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:—extensionsof 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 gravitation50. 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.50Hist. 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 not237forget, however, that there is a great and essential difference between inductive and deductive processes of the mind. The discovery of anewtheory, 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 polarized238light 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 offelicitiesof 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’sInquiry 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 aware51that 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 is239necessary to constitute vapour, and is hence called theconstituent temperature. But these principles were not generally familiar in England till Dr. Wells introduced them into hisEssay 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.51Hist. 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 gunpowder52, from the conversion of its materials into gases. In Mineralogy also we have to apply the240principles 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.52The 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 theNovum Organonin 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 those241practical 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 ancient242doctrine 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 todoas well243as tosee. 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 still244clocks 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 galvanic245battery 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 anEriometer, 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 termedDextrin, 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 modelling246and 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.
CHAPTER IX.Of the Application of Inductive Truths.
AphorismLIII.
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 perpetualverificationof the theory.
AphorismLIV.
Such observations and experiments, when numerous and accurate, supply alsocorrectionsof theconstantsinvolved in the theory; and sometimes, (by the Method of Residues,) additionsto the theory.
AphorismLV.
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.
AphorismLVI.
Anextensionof 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.
AphorismLVII.
The practical inventions which are most important in Art may be either unimportant parts of Science, or results not explained by Science.234
AphorismLVIII.
In modern times, in many departments. Art is constantly guided, governed and advanced by Science.
AphorismLIX.
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, theverificationof the discovery by additional experiments and reasonings, and itsextensionto new cases, not contemplated by the original discoverer. These processes occupy that period, which, in the history of each great discovery, we have termed theSequelof 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 hisLaboratory; 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 beenObservatories, in which the consequences of the theory were habitually compared with the results of observation. And to facilitate this comparison,Tablesof great extent have been calculated, with immense labour, from each theory, showing the place which the235theory 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 impossible49. 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.
49Hist. 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 becorrectedwhen 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 theConstantsorCoefficientsof these Inequalities of which theArgumentis already known. This he is enabled to do by the methods explained in thefifthchapter of this book; theMethod of Means, and especially theMethod of Least Squares. In other cases, he finds, by theMethod 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:—extensionsof 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 gravitation50. 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.
50Hist. 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 not237forget, however, that there is a great and essential difference between inductive and deductive processes of the mind. The discovery of anewtheory, 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 polarized238light 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 offelicitiesof 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’sInquiry 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 aware51that 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 is239necessary to constitute vapour, and is hence called theconstituent temperature. But these principles were not generally familiar in England till Dr. Wells introduced them into hisEssay 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.
51Hist. 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 gunpowder52, from the conversion of its materials into gases. In Mineralogy also we have to apply the240principles 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.
52The 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 theNovum Organonin 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 those241practical 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 ancient242doctrine 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 todoas well243as tosee. 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 still244clocks 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 galvanic245battery 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 anEriometer, 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 termedDextrin, 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 modelling246and 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.