The Method of Gradation consists in taking a number of stages of a property in question, intermediate between two extreme cases which appear to be different. This Method is employed to determine whether the extreme cases are really distinct or not.
Aphorism LI.
The Method of Gradation, applied to decide the question, whether the existing geological phenomena arise from existing causes, leads to this result:—That the phenomena do appear to arise from Existing Causes, but that the action of existing causes may, in past times, have transgressed, to any extent, their recorded limits of intensity.
Aphorism LII.
The Method of Natural Classification consists in classing cases, not according to any assumed Definition, but according to the connexion of the facts themselves, so as to make them the means of asserting general truths. 221
Sect. I.—The Law of Continuity.
1. THE Law of Continuity is applicable to quantity primarily, and therefore might be associated with the methods treated of in the last chapter: but inasmuch as its inferences are made by a transition from one degree to another among contiguous cases, it will be found to belong more properly to the Methods of Induction of which we have now to speak.
The Law of Continuity consists in this proposition,—That a quantity cannot pass from one amount to another by any change of conditions, without passing through all intermediate degrees of magnitude according to the intermediate conditions. And this law may often be employed to correct inaccurate inductions, and to reject distinctions which have no real foundation in nature. For example, the Aristotelians made a distinction between motions according to nature, (as that of a body falling vertically downwards,) and motions contrary to nature, (as that of a body moving along a horizontal plane:) the former, they held, became naturally quicker and quicker, the latter naturally slower and slower. But to this it might be replied, that a horizontal line may pass, by gradual motion, through various inclined positions, to a vertical position: and thus the retarded motion may pass into the accelerated; and hence there must be some inclined plane on which the motion downwards is naturally uniform: which is false, and therefore the distinction of such kinds of motion is unfounded. Again, the proof of the First Law of Motion depends upon the Law of Continuity: for since, by diminishing the resistance to a body moving on a horizontal plane, we diminish the retardation, and this without limit, the law of continuity will bring us at the same time to the case of no resistance and to the case of no retardation.
2. The Law of Continuity is asserted by Galileo in a particular application; and the assertion which it 222 suggests is by him referred to Plato;—namely36 that a moveable body cannot pass from rest to a determinate degree of velocity without passing through all smaller degrees of velocity. This law, however, was first asserted in a more general and abstract form by Leibnitz37: and was employed by him to show that the laws of motion propounded by Descartes must be false. The Third Cartesian Law of Motion was this38: that when one moving body meets another, if the first body have a less momentum than the second, it will be reflected with its whole motion: but if the first have a greater momentum than the second, it will lose a part of its motion, which it will transfer to the second. Now each of these cases leads, by the Law of Continuity, to the case in which the two bodies have equal momentums: but in this case, by the first part of the law the body would retain all its motion; and by the second part of the law it would lose a portion of it: hence the Cartesian Law is false.
3. I shall take another example of the application of this Law from Professor Playfair’s Dissertation on the History of Mathematical and Physical Science39. ‘The Academy of Sciences at Paris having (in 1724) proposed, as a Prize Question, the Investigation of the Laws of the Communication of Motion, John Bernoulli presented an Essay on the subject very ingenious and profound; in which, however, he denied the existence of hard bodies, because in the collision of such bodies, a finite change of motion must take place in an instant: an event which, on the principle just explained, he maintained to be impossible.’ And this reasoning was justifiable: for we can form a continuous transition from cases in which the impact manifestly occupies a finite time, (as when we strike a large soft body) to cases in which it is apparently instantaneous. Maclaurin and others are disposed, in order to avoid the conclusion of Bernoulli, to reject the Law of 223 Continuity. This, however, would not only be, as Playfair says, to deprive ourselves of an auxiliary, commonly useful though sometimes deceptive; but what is much worse, to acquiesce in false propositions, from the want of clear and patient thinking. For the Law of Continuity, when rightly interpreted, is never violated in actual fact. There are not really any such bodies as have been termed perfectly hard: and if we approach towards such cases, we must learn the laws of motion which rule them by attending to the Law of Continuity, not by rejecting it.
4. Newton used the Law of Continuity to suggest, but not to prove, the doctrine of universal gravitation. Let, he said, a terrestrial body be carried as high as the moon: will it not still fall to the earth? and does not the moon fall by the same force40? Again: if any one says that there is a material ether which does not gravitate41, this kind of matter, by condensation, may be gradually transmuted to the density of the most intensely gravitating bodies: and these gravitating bodies, by taking the internal texture of the condensed ether, may cease to gravitate; and thus the weight of bodies depends, not on their quantity of matter, but on their texture; which doctrine Newton conceived he had disproved by experiment.
5. The evidence of the Law of Continuity resides in the universality of those Ideas, which enter into our apprehension of Laws of Nature. When, of two quantities, one depends upon the other, the Law of Continuity necessarily governs this dependence. Every philosopher has the power of applying this law, in proportion as he has the faculty of apprehending the Ideas which he employs in his induction, with the same clearness and steadiness which belong to the fundamental ideas of Quantity, Space and Number. To those who possess this faculty, the Law is a Rule of very wide and decisive application. Its use, as has appeared in the above examples, is seen rather in the disproof of erroneous views, and in the correction of false propositions, 224 than in the invention of new truths. It is a test of truth, rather than an instrument of discovery.
Methods, however, approaching very near to the Law of Continuity may be employed as positive means of obtaining new truths; and these I shall now describe.
Sect. II.—The Method of Gradation.
6. To gather together the cases which resemble each other, and to separate those which are essentially distinct, has often been described as the main business of science; and may, in a certain loose and vague manner of speaking, pass for a description of some of the leading procedures in the acquirement of knowledge. The selection of instances which agree, and of instances which differ, in some prominent point or property, are important steps in the formation of science. But when classes of things and properties have been established in virtue of such comparisons, it may still be doubtful whether these classes are separated by distinctions of opposites, or by differences of degree. And to settle such questions, the Method of Gradation is employed; which consists in taking intermediate stages of the properties in question, so as to ascertain by experiment whether, in the transition from one class to another, we have to leap over a manifest gap, or to follow a continuous road.
7. Thus for instance, one of the early Divisions established by electrical philosophers was that of Electrics and Conductors. But this division Dr. Faraday has overturned as an essential opposition. He takes42 a Gradation which carries him from Conductors to Non-conductors. Sulphur, or Lac, he says, are held to be non-conductors, but are not rigorously so. Spermaceti is a bad conductor: ice or water better than spermaceti: metals so much better that they are put in a different class. But even in metals the transit of the electricity is not instantaneous: we have in them proof of a retardation of the electric current: ‘and what 225 reason,” Mr. Faraday asks, “why this retardation should not be of the same kind as that in spermaceti, or in lac, or sulphur? But as, in them, retardation is insulation, [and insulation is induction43] why should we refuse the same relation to the same exhibitions of force in the metals?”
The process employed by the same sagacious philosopher to show the identity of Voltaic and Franklinic electricity, is another example of the same kind44. Machine [Franklinic] electricity was made to exhibit the same phenomena as Voltaic electricity, by causing the discharge to pass through a bad conductor, into a very extensive discharging train: and thus it was clearly shown that Franklinic electricity, not so conducted, differs from the other kinds, only in being in a state of successive tension and explosion instead of a state of continued current.
Again; to show that the decomposition of bodies in the Voltaic circuit was not due to the Attraction of the Poles45, Mr. Faraday devised a beautiful series of experiments, in which these supposed Poles were made to assume all possible electrical conditions:—in some cases the decomposition took place against air, which according to common language is not a conductor, nor is decomposed;—in others, against the metallic poles, which are excellent conductors but undecomposable;—and so on: and hence he infers that the decomposition cannot justly be considered as due to the Attraction, or Attractive Powers, of the Poles.
8. The reader of the Novum Organon may perhaps, in looking at such examples of the Rule, be reminded of some of Bacon’s Classes of Instances, as his instantiæ absentiæ in proximo, and his instantiæ migrantes. But we may remark that Instances classed and treated as Bacon recommends in those parts of his work, could hardly lead to scientific truth. His 226 processes are vitiated by his proposing to himself the form or cause of the property before him, as the object of his inquiry; instead of being content to obtain, in the first place, the law of phenomena. Thus his example46 of a Migrating Instance is thus given. “Let the Nature inquired into be that of Whiteness; an Instance Migrating to the production of this property is glass, first whole, and then pulverized; or plain water, and water agitated into a foam; for glass and water are transparent, and not white; but glass powder and foam are white, and not transparent. Hence we must inquire what has happened to the glass or water in that Migration. For it is plain that the Form of Whiteness is conveyed and induced by the crushing of the glass and shaking of the water.” No real knowledge has resulted from this line of reasoning:—from taking the Natures and Forms of things and of their qualities for the primary subject of our researches.
9. We may easily give examples from other subjects in which the Method of Gradation has been used to establish, or to endeavour to establish, very extensive propositions. Thus Laplace’s Nebular Hypothesis,—that systems like our solar system are formed by gradual condensation from diffused masses, such as the nebulæ among the stars,—is founded by him upon an application of this Method of Gradation. We see, he conceives, among these nebulæ, instances of all degrees of condensation, from the most loosely diffused fluid, to that separation and solidification of parts by which suns, and satellites, and planets are formed: and thus we have before us instances of systems in all their stages; as in a forest we see trees in every period of growth. How far the examples in this case satisfy the demands of the Method of Gradation, it remains for astronomers and philosophers to examine.
Again; this method was used with great success by Macculloch and others to refute the opinion, put in currency by the Wernerian school of geologists, that 227 the rocks called trap rocks must be classed with those to which a sedimentary origin is ascribed. For it was shown that a gradual transition might be traced from those examples in which trap rocks most resembled stratified rocks, to the lavas which have been recently ejected from volcanoes: and that it was impossible to assign a different origin to one portion, and to the other, of this kind of mineral masses; and as the volcanic rocks were certainly not sedimentary, it followed, that the trap rocks were not of that nature.
Again; we have an attempt of a still larger kind made by Sir C. Lyell, to apply this Method of Gradation so as to disprove all distinction between the causes by which geological phenomena have been produced, and the causes which are now acting at the earth’s surface. He has collected a very remarkable series of changes which have taken place, and are still taking place, by the action of water, volcanoes, earthquakes, and other terrestrial operations; and he conceives he has shown in these a gradation which leads, with no wide chasm or violent leap, to the state of things of which geological researches have supplied the evidence.
10. Of the value of this Method in geological speculations, no doubt can be entertained. Yet it must still require a grave and profound consideration, in so vast an application of the Method as that attempted by Sir C. Lyell, to determine what extent we may allow to the steps of our gradation; and to decide how far the changes which have taken place in distant parts of the series may exceed those of which we have historical knowledge, without ceasing to be of the same kind. Those who, dwelling in a city, see, from time to time, one house built and another pulled down, may say that such existing causes, operating through past time, sufficiently explain the existing condition of the city. Yet we arrive at important political and historical truths, by considering the origin of a city as an event of a different order from those daily changes. The causes which are now working to produce geological results, may be supposed to have been, at some former epoch, so far exaggerated in their operation, that the changes 228 should be paroxysms, not degrees;—that they should violate, not continue, the gradual series. And we have no kind of evidence whether the duration of our historical times is sufficient to give us a just measure of the limits of such degrees;—whether the terms which we have under our notice enable us to ascertain the average rate of progression.
11. The result of such considerations seems to be this:—that we may apply the Method of Gradation in the investigation of geological causes, provided we leave the Limits of the Gradation undefined. But, then, this is equivalent to the admission of the opposite hypothesis: for a continuity of which the successive intervals are not limited, is not distinguishable from discontinuity. The geological sects of recent times have been distinguished as uniformitarians and catastrophists: the Method of Gradation seems to prove the doctrine of the uniformitarians; but then, at the same time that it does this, it breaks down the distinction between them and the catastrophists.
There are other exemplifications of the use of gradations in Science which well deserve notice: but some of them are of a kind somewhat different, and may be considered under a separate head.
Sect. III. The Method of Natural Classification.
12. The Method of Natural Classification consists, as we have seen, in grouping together objects, not according to any selected properties, but according to their most important resemblances; and in combining such grouping with the assignation of certain marks of the classes thus formed. The examples of the successful application of this method are to be found in the Classificatory Sciences through their whole extent; as, for example, in framing the Genera of plants and animals. The same method, however, may often be extended to other sciences. Thus the classification of Crystalline Forms, according to their Degree of Symmetry, (which is really an important distinction,) as introduced by Mohs and Weiss, was a great improvement 229 upon Haüy’s arbitrary division according to certain assumed primary forms. Sir David Brewster was led to the same distinction of crystals by the study of their optical properties; and the scientific value of the classification was thus strongly exhibited. Mr. Howard’s classification of Clouds appears to be founded in their real nature, since it enables him to express the laws of their changes and successions. As we have elsewhere said, the criterion of a true classification is, that it makes general propositions possible. One of the most prominent examples of the beneficial influence of a right classification, is to be seen in the impulse given to geology by the distinction of strata according to the organic fossils which they contain47: which, ever since its general adoption, has been a leading principle in the speculations of geologists.
13. The mode in which, in this and in other cases, the Method of Natural Classification directs the researches of the philosopher, is this:—his arrangement being adopted, at least as an instrument of inquiry and trial, he follows the course of the different members of the classification, according to the guidance which Nature herself offers; not prescribing beforehand the marks of each part, but distributing the facts according to the total resemblances, or according to those resemblances which he finds to be most important. Thus, in tracing the course of a series of strata from place to place, we identify each stratum, not by any single character, but by all taken together;—texture, colour, fossils, position, and any other circumstances which offer themselves. And if, by this means, we come to ambiguous cases, where different indications appear to point different ways, we decide so as best to preserve undamaged those general relations and truths which constitute the value of our system. Thus although we consider the organic fossils in each stratum as its most important characteristic, we are not prevented, by the disappearance of some fossils, or the addition of others, or by the total absence of fossils, 230 from identifying strata in distant countries, if the position and other circumstances authorize us to do so. And by this Method of Classification, the doctrine of Geological Equivalents48 has been applied to a great part of Europe.
14. We may further observe, that the same method of natural classification which thus enables us to identify strata in remote situations, notwithstanding that there may be great differences in their material and contents, also forbids us to assume the identity of the series of rocks which occur in different countries, when this identity has not been verified by such a continuous exploration of the component members of the series. It would be in the highest degree unphilosophical to apply the special names of the English or German strata to the rocks of India, or America, or even of southern Europe, till it has appeared that in those countries the geological series of northern Europe really exists. In each separate country, the divisions of the formations which compose the crust of the earth must be made out, by applying the Method of Natural Arrangement to that particular case, and not by arbitrarily extending to it the nomenclature belonging to another case. It is only by such precautions, that we can ever succeed in obtaining geological propositions, at the same time true and comprehensive; or can obtain any sound general views respecting the physical history of the earth.
15. The Method of Natural Classification, which we thus recommend, falls in with those mental habits which we formerly described as resulting from the study of Natural History. The method was then termed the Method of Type, and was put in opposition to the Method of Definition.
The Method of Natural Classification is directly opposed to the process in which we assume and apply arbitrary definitions; for in the former Method, we find our classes in nature, and do not make them by marks of our own imposition. Nor can any advantage 231 to the progress of knowledge be procured, by laying down our characters when our arrangements are as yet quite loose and unformed. Nothing was gained by the attempts to define Metals by their weight, their hardness, their ductility, their colour; for to all these marks, as fast as they were proposed, exceptions were found, among bodies which still could not be excluded from the list of Metals. It was only when elementary substances were divided into Natural Classes, of which classes Metals were one, that a true view of their distinctive characters was obtained. Definitions in the outset of our examination of nature are almost always, not only useless, but prejudicial.
16. When we obtain a Law of Nature by induction from phenomena, it commonly happens, as we have already seen, that we introduce, at the same time, a Proposition and a Definition. In this case, the two are correlative, each giving a real value to the other. In such cases, also, the Definition, as well as the Proposition, may become the basis of rigorous reasoning, and may lead to a series of deductive truths. We have examples of such Definitions and Propositions in the Laws of Motion, and in many other cases.
17. When we have established Natural Classes of objects, we seek for Characters of our classes; and these Characters may, to a certain extent, be called the Definitions of our classes. This is to be understood, however, only in a limited sense: for these Definitions are not absolute and permanent. They are liable to be modified and superseded. If we find a case which manifestly belongs to our Natural Class, though violating our Definition, we do not shut out the case, but alter our definition. Thus, when we have made it part of our Definition of the Rose family, that they have alternate stipulate leaves, we do not, therefore, exclude from the family the genus Lowæa, which has no stipulæ. In Natural Classifications, our Definitions are to be considered as temporary and provisional only. When Sir C. Lyell established the distinctions of the tertiary strata, which he termed Eocene, Miocene, and Pliocene, he took a numerical criterion 232 (the proportion of recent species of shells contained in those strata) as the basis of his division. But now that those kinds of strata have become, by their application to a great variety of cases, a series of Natural Classes, we must, in our researches, keep in view the natural connexion of the formations themselves in different places; and must by no means allow ourselves to be governed by the numerical proportions which were originally contemplated; or even by any amended numerical criterion equally arbitrary; for however amended, Definitions in natural history are never immortal. The etymologies of Pliocene and Miocene may, hereafter, come to have merely an historical interest; and such a state of things will be no more inconvenient, provided the natural connexions of each class are retained, than it is to call a rock oolite or porphyry, when it has no roelike structure and no fiery spots.
The Methods of Induction which are treated of in this and the preceding chapter, and which are specially applicable to causes governed by relations of Quantity or of Resemblance, commonly lead us to Laws of Phenomena only. Inductions founded upon other ideas, those of Substance and Cause for example, appear to conduct us somewhat further into a knowledge of the essential nature and real connexions of things. But before we speak of these, we shall say a few words respecting the way in which inductive propositions, once obtained, may be verified and carried into effect by their application.
CHAPTER IX.
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 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.
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 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.
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 aware51 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.
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 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.
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.