Preliminary Discourse on the Study of Natural Philosophy · John F. W. Herschel
(176.) But a law of nature has not that degree of generality which fits it for a stepping-stone to greater inductions, unless it be universal in its application. We cannot rely on its enabling us to extend our views beyond the circle of instances from which it was obtained, unless we have already had experience of its power to do so; unless it actually has enabled us before trial to say what will take place in cases analogous to those originally contemplated; unless, in short, we have studiously placed ourselves in the situation of its antagonists, and even perversely endeavoured to find exceptions to it without success. It is in the precise proportion that a law once obtained endures this extreme severity of trial, that its value and importance are to be estimated; and our next step in the verification of an induction must therefore consist in extending its application to cases not originally contemplated; in studiously varying the circumstances under which our causes act, with a view to ascertain whether their effect is general; and in pushing the application of our laws to extreme cases.
(177.) For example, a fair induction from a great number of facts led Galileo to conclude that the accelerating power of gravity is the same on all sorts of bodies, and on great and small masses indifferently; and this he exemplified by letting bodies of very different natures and weights fall at the same instant from a high tower, when it was observed that they struck the ground at the same moment, abating a certain trifling difference, due, as he justly believed it to be, to the greater proportional resistance of the air to light than to heavy bodies. The experiment could not, at that time, be fairly tried with extremely light substances, such as cork, feathers, cotton, &c. because of the great resistance experienced by these in their fall; no means being then known of removing this cause of disturbance. It was not, therefore, till after the invention of the air-pump that this law could be put to the severe test of an extreme case. A guinea and a downy feather were let drop at once from the upper part of a tall exhausted glass, and struck the bottom at the same moment. Let any one make the trial in the air, and he will perceive the force of an extreme case.
(178.) In the verification of a law whose expression is quantitative, not only must its generality be established by the trial of it in as various circumstances as possible, but every such trial must be one of precise measurement. And in such cases the means taken for subjecting it to trial ought to be so devised as to repeat and multiply a great number of times any deviation (if any exist); so that, let it be ever so small, it shall at last become sensible.
(179.) For instance, let the law to be verified be, that the gravity of every material body is in the direct proportion of its mass, which is only another mode of expressing Galileo’s law above mentioned. The time of falling from any moderate height cannot be measured with precision enough for our purpose: but if it can be repeated a very great multitude of times without any loss or gain in the intervals, and the whole amount of the times of fall so repeated measured by a clock; and if at the same time the resistance of the air can be rendered exactly alike for all the bodies tried, we have here Galileo’s trial in a much more refined state; and it is evident that almost unlimited exactness may be obtained. Now, all this Newton accomplished by the simple and elegant contrivance of enclosing in a hollow pendulum the same weights of a great number of substances the most different that could be found in all respects, as gold, glass, wood, water, wheat, &c., and ascertaining the time required for the pendulum so charged to make a great number of oscillations; in each of which it is clear the weights had to fall, and be raised again successively, without loss of time, through the same identical spaces. Thus any difference, however inconsiderable, that might exist in the time of one such fall and rise would be multiplied and accumulated till they became sensible. And none having been discovered by so delicate a process in any case, the law was considered verified both in respect of generality and exactness. This, however, is nothing to the verifications afforded by astronomical phenomena, where the deviations, if any, accumulate for thousands of years instead of a few hours.
(180.) The surest and best characteristic of a well-founded and extensive induction, however, is when verifications of it spring up, as it were, spontaneously, into notice, from quarters where they might be least expected, or even among instances of that very kind which were at first considered hostile to them. Evidence of this kind is irresistible, and compels assent with a weight which scarcely any other possesses. To give an example: M. Mitscherlich had announced a law to this effect--that the chemical elements of which all bodies consist are susceptible of being classified in distinct groups, which he termed isomorphous groups; and that these groups are so related, that when similar combinations are formed of individuals belonging to two, three, or more of them, such combinations will crystallize in the same geometrical forms. To this curious and important law there appeared a remarkable exception. According to professor Mitscherlich, the arsenic and phosphoric acids are similar combinations coming under the meaning of his law, and their combinations with soda and water, forming the salts known to chemists under the names of arseniate and phosphate of soda, ought, if the law were general, to crystallize in identical shapes. The fact, however, was understood to be otherwise. But lately, Mr. Clarke, a British chemist, having examined the two salts attentively, ascertained the fact that their compositions deviate essentially from that similarity which M. Mitscherlich’s law requires; and that, therefore, the exception in question disappears. This was something: but, pursuing the subject further, the same ingenious enquirer happily succeeded in producing a new phosphate of soda, differing from that generally known in containing a different proportion of water, and agreeing in composition exactly with the arseniate. The crystals of this new salt, when examined, were found by him to be precisely identical in form with those of the arseniate: thus verifying, in a most striking and totally unexpected manner, the law in question, or, as it is called, the law of isomorphism.
(181.) Unexpected and peculiarly striking confirmations of inductive laws frequently occur in the form of residual phenomena, in the course of investigations of a widely different nature from those which gave rise to the inductions themselves. A very elegant example may be cited in the unexpected confirmation of the law of the developement of heat in elastic fluids by compression, which is afforded by the phenomena of sound. The enquiry into the cause of sound had led to conclusions respecting its mode of propagation, from which its velocity in the air could be precisely calculated. The calculations were performed; but, when compared with fact, though the agreement was quite sufficient to show the general correctness of the cause and mode of propagation assigned, yet the whole velocity could not be shown to arise from this theory. There was still a residual velocity to be accounted for, which placed dynamical philosophers for a long time in a great dilemma. At length Laplace struck on the happy idea, that this might arise from the heat developed in the act of that condensation which necessarily takes place at every vibration by which sound is conveyed. The matter was subjected to exact calculation, and the result was at once the complete explanation of the residual phenomenon, and a striking confirmation of the general law of the developement of heat by compression, under circumstances beyond artificial imitation.
(182.) In extending our inductions to cases not originally contemplated, there is one step which always strikes the mind with peculiar force, and with such a sensation of novelty and surprise, as often gives it a weight beyond its due philosophic value. It is the transition from the little to the great, and vice versâ, but especially the former. It is so beautiful to see, for instance, an experiment performed in a watch-glass, or before a blowpipe, succeed, in a great manufactory, on many tons of matter, or, in the bosom of a volcano, upon millions of cubic fathoms of lava, that we almost forget that these great masses are made up of watch-glassfuls, and blowpipe-beads. We see the enormous intervals between the stars and planets of the heavens, which afford room for innumerable processes to be carried on, for light and heat to circulate, and for curious and complicated motions to go forward among them: we look more attentively, and we see sidereal systems, probably not less vast and complicated than our own, crowded apparently into a small space (from the effect of their distance from us), and forming groups resembling bodies of a substantial appearance, having form and outline: yet we recoil with incredulous surprise when we are asked why we cannot conceive the atoms of a grain of sand to be as remote from each other (proportionally to their sizes) as the stars of the firmament; and why there may not be going on, in that little microcosm, processes as complicated and wonderful as those of the great world around us. Yet the student who makes any progress in natural philosophy will encounter numberless cases in which this transfer of ideas from the one extreme of magnitude to the other will be called for: he will find, for instance, the phenomena of the propagation of winds referred to the same laws which regulate the propagation of motions through the smallest masses of air; those of lightning assimilated to the mere communication of an electric spark, and those of earthquakes to the tremors of a stretched wire: in short, he must lay his account to finding the distinction of great and little altogether annihilated in nature: and it is well for man that such is the case, and that the same laws, which he can discover and verify in his own circumscribed sphere of power, should prove available to him when he comes to apply them on the greatest scale; since it is thus only that he is enabled to become an exciting cause in operations of any considerable magnitude, and to vindicate his importance in creation.
(183.) But the business of induction does not end here: its final result must be followed out into all its consequences, and applied to all those cases which seem even remotely to bear upon the subject of enquiry. Every new addition to our stock of causes becomes a means of fresh attack with new vantage ground upon all those unexplained parts of former phenomena which have resisted previous efforts. It can hardly be pressed forcibly enough on the attention of the student of nature, that there is scarcely any natural phenomenon which can be fully and completely explained in all its circumstances, without a union of several, perhaps of all, the sciences. The great phenomena of astronomy, indeed, may be considered exceptions; but this is merely because their scale is so vast that one only of the most widely extending forces of nature takes the lead, and all those agents whose sphere of action is limited to narrower bounds, and which determine the production of phenomena nearer at hand, are thrown into the back ground, and become merged and lost in comparative insignificance. But in the more intimate phenomena which surround us it is far otherwise. Into what a complication of different branches of science are we not led by the consideration of such a phenomenon as rain, for instance, or flame, or a thousand others, which are constantly going on before our eyes? Hence, it is hardly possible to arrive at the knowledge of a law of any degree of generality in any branch of science, but it immediately furnishes us with a means of extending our knowledge of innumerable others, the most remote from the point we set out from; so that, when once embarked in any physical research, it is impossible for any one to predict where it may ultimately lead him.
(184.) This remark rather belongs to the inverse or deductive process, by which we pursue laws into their remote consequences. But it is very important to observe, that the successful process of scientific enquiry demands continually the alternate use of both the inductive and deductive method. The path by which we rise to knowledge must be made smooth and beaten in its lower steps, and often ascended and descended, before we can scale our way to any eminence, much less climb to the summit. The achievement is too great for a single effort; stations must be established, and communications kept open with all below. To quit metaphor; there is nothing so instructive, or so likely to lead to the acquisition of general views, as this pursuit of the consequences of a law once arrived at into every subject where it may seem likely to have an influence. The discovery of a new law of nature, a new ultimate fact, or one that even temporarily puts on that appearance, is like the discovery of a new element in chemistry. Thus, selenium was hardly discovered by Berzelius in the vitriol works of Fahlun, when it presently made its appearance in the sublimates of Stromboli, and the rare and curious products of the Hungarian mines. And thus it is with every new law, or general fact. It is hardly announced before its traces are found every where, and every one is astonished at its having so long remained concealed. And hence it happens that unexpected lights are shed at length over parts of science that had been abandoned in despair, and given over to hopeless obscurity.
(185.) The verification of quantitative laws has been already spoken of (178.); but their importance in physical science is so very great, inasmuch as they alone afford a handle to strict mathematical deductive application, that something ought to be said of the nature of the inductions by which they are to be arrived at. In their simplest or least general stages (of which alone we speak at present) they usually express some numerical relation between two quantities dependent on each other, either as collateral effects of a common cause, or as the amount of its effect under given numerical circumstances or data. For example, the law of refraction before noticed (§ 22.) expresses, by a very simple relation, the amount of angular deviation of a ray of light from its course, when the angle at which it is inclined to the refracting surface is known, viz. that the sine of the angle which the incident ray makes with a perpendicular to the surface is always to that of the angle made by the refracted ray with the same perpendicular, in a constant proportion, so long as the refracting substance is the same. To arrive inductively at laws of this kind, where one quantity depends on or varies with another, all that is required is a series of careful and exact measures in every different state of the datum and quæsitum. Here, however, the mathematical form of the law being of the highest importance, the greatest attention must be given to the extreme cases as well as to all those points where the one quantity changes rapidly with a small change of the other. The results must be set down in a table in which the datum gradually increases in magnitude from the lowest to the highest limit of which it is susceptible. It will depend then entirely on our habit of treating mathematical subjects, how far we may be able to include such a table in the distinct statement of a mathematical law. The discovery of such laws is often remarkably facilitated by the contemplation of a class of phenomena to be noticed further on, under the head of Collective Instances, (see § 194.) in which the nature of the mathematical expression in which the law sought is comprehended, is pointed out by the figure of some curve brought under inspection by a proper mode of experimenting.
(186.) After all, unless our induction embraces a series of cases which absolutely include the whole scale of variation of which the quantities in question admit, the mathematical expression so obtained cannot be depended upon as the true one, and if the scale actually embraced be small, the extension of laws so derived to extreme cases will in all probability be exceedingly fallacious. For example, air is an elastic fluid, and as such, if enclosed in a confined space and squeezed, its bulk diminishes: now, from a great number of trials made in cases where the air has been compressed into a half, a third, &c. even as far as a fiftieth of its bulk, or less, it has been concluded that “the density of air is proportional to the compressing force,” or the bulk it occupies inversely as that force; and when the air is rarefied by taking off part of its natural pressure, the same is found to be the case, within very extensive limits. Yet it is impossible that this should be, strictly or mathematically speaking, the true law; for, if it were so, there could be no limit to the condensation of air, while yet we have the strongest analogies to show that long before it had reached any very enormous pitch the air would be reduced into a liquid, and even, perhaps, if pressed yet more violently, into a solid form.
(187.) Laws thus derived, by the direct process of including in mathematical formulæ the results of a greater or less number of measurements, are called “empirical laws.” A good example of such a law is that given by Dr. Young (Phil. Trans. 1826,) for the decrement of life, or the law of mortality. Empirical laws in this state are evidently unverified inductions, and are to be received and reasoned on with the utmost reserve. No confidence can ever be placed in them beyond the limits of the data from which they are derived; and even within those limits they require a special and severe scrutiny to examine how nearly they do represent the observed facts; that is to say, whether, in the comparison of their results with the observed quantities, the differences are such as may fairly be attributed to error of observation. When so carefully examined, they become, however, most valuable; and frequently, when afterwards verified theoretically by a deductive process (as will be explained in our next chapter), turn out to be rigorous laws of nature, and afford the noblest and most convincing supports of which theories themselves are susceptible. The finest instances of this kind are the great laws of the planetary motions deduced by Kepler, entirely from a comparison of observations with each other, with no assistance from theory. These laws, viz. that the planets move in ellipses round the sun; that each describes about the sun’s centre equal areas in equal times; and that in the orbits of different planets the squares of the periodical times are proportional to the cubes of the distances; were the results of inconceivable labour of calculation and comparison: but they amply repaid the labour bestowed on them, by affording afterwards the most conclusive and unanswerable proofs of the Newtonian system. On the other hand, when empirical laws are unduly relied on beyond the limits of the observations from which they were deduced, there is no more fertile source of fatal mistakes. The formulæ which have been empirically deduced for the elasticity of steam (till very recently), and those for the resistance of fluids, and other similar subjects, have almost invariably failed to support the theoretical structures which have been erected on them.
(188.) It is a remarkable and happy fact, that the shortest and most direct of all inductions should be that which has led at once, or by very few steps, to the highest of all natural laws,--we mean those of motion and force. Nothing can be more simple, precise, and general, than the enunciation of these laws; and, as we have once before observed, their application to particular facts in the descending or deductive method is limited by nothing but the limited extent of our mathematics. It would seem, then, that dynamical science were taken thenceforward out of the pale of induction, and transformed into a matter of absolute à priori reasoning, as much as geometry; and so it would be, were our mathematics perfect, and all the data known. Unhappily, the first is so far from being the case, that in many of the most interesting branches of dynamical enquiry they leave us completely at a loss. In what relates to the motions of fluids, for instance, this is severely felt. We can include our problems, it is true, in algebraical equations, and we can demonstrate that they contain the solutions; but the equations themselves are so intractable, and present such insuperable difficulties, that they often leave us quite as much in the dark as before. But even were these difficulties overcome, recourse to experience must still be had, to establish the data on which particular applications are to depend; and although mathematical analysis affords very powerful means of representing in general terms the data of any proposed case, and afterwards, by comparison of its results with fact, determining what those data must be to explain the observed phenomena, still, in any mode of considering the matter, an appeal to experience in every particular instance of application is unavoidable, even when the general principles are regarded as sufficiently established without it. Now, in all such cases of difficulty we must recur to our inductive processes, and regard the branches of dynamical science where this takes place as purely experimental. By this we gain an immense advantage, viz. that in all those points of them where the abstract dynamical principles do afford distinct conclusions, we obtain verifications for our inductions of the highest and finest possible kind. When we work our way up inductively to one of these results, we cannot help feeling the strongest assurance of the validity of the induction.
(189.) The necessity of this appeal to experiment in every thing relating to the motions of fluids on the large scale has long been felt. Newton himself, who laid the first foundations of hydrodynamical science (so this branch of dynamics is called), distinctly perceived it, and set the example of laborious and exact experiments on their resistance to motion, and other particulars. Venturi, Bernoulli, and many others, have applied the method of experiment to the motions of fluids in pipes and canals; and recently the brothers Weber have published an elaborate and excellent experimental enquiry into the phenomena of waves. One of the greatest and most successful attempts, however, to bring an important, and till then very obscure, branch of dynamical enquiry back to the dominion of experiment, has been made by Chladni and Savart in the case of sound and vibratory motion in general; and it is greatly to be wished that the example may be followed in many others hardly less abstruse and impracticable when theoretically treated. In such cases the inductive and deductive methods of enquiry may be said to go hand in hand, the one verifying the conclusions deduced by the other; and the combination of experiment and theory, which may thus be brought to bear in such cases, forms an engine of discovery infinitely more powerful than either taken separately. This state of any department of science is perhaps of all others the most interesting, and that which promises the most to research.
(190.) It can hardly be expected that we should terminate this division of our subject without some mention of the “prerogatives of instances” of Bacon, by which he understands characteristic phenomena, selected from the great miscellaneous mass of facts which occur in nature, and which, by their number, indistinctness, and complication, tend rather to confuse than to direct the mind in its search for causes and general heads of induction. Phenomena so selected on account of some peculiarly forcible way in which they strike the reason, and impress us with a kind of sense of causation, or a particular aptitude for generalization, he considers, and justly, as holding a kind of prerogative dignity, and claiming our first and especial attention in physical enquiries.
(191.) We have already observed that, in forming inductions, it will most commonly happen that we are led to our conclusions by the especial force of some two or three strongly impressive facts, rather than by affording the whole mass of cases a regular consideration; and hence the need of cautious verification. Indeed, so strong is this propensity of the human mind, that there is hardly a more common thing than to find persons ready to assign a cause for every thing they see, and, in so doing, to join things the most incongruous, by analogies the most fanciful. This being the case, it is evidently of great importance that these first ready impulses of the mind should be made on the contemplation of the cases most likely to lead to good inductions. The misfortune, however, is, in natural philosophy, that the choice does not rest with us. We must take the instances as nature presents them. Even if we are furnished with a list of them in tabular order, we must understand and compare them with each other, before we can tell which are the instances thus deservedly entitled to the highest consideration. And, after all, after much labour in vain, and groping in the dark, accident or casual observation will present a case which strikes us at once with a full insight into a subject, before we can even have time to determine to what class its prerogative belongs. For example, the laws of crystallography were obscure, and its causes still more so, till Haüy fortunately dropped a beautiful crystal of calcareous spar on a stone pavement, and broke it. In piecing together the fragments, he observed their facets not to correspond with those of the crystal in its entire state, but to belong to another form; and, following out the hint offered by a “glaring instance” thus casually obtruded on his notice, he discovered the beautiful laws of the cleavage, and the primitive forms of minerals.
(192.) It has always appeared to us, we must confess, that the help which the classification of instances, under their different titles of prerogative, affords to inductions, however just such classification may be in itself, is yet more apparent than real. The force of the instance must be felt in the mind, before it can be referred to its place in the system; and, before it can be either referred or appretiated, it must be known; and when it is appretiated, we are ready enough to interweave it in our web of induction, without greatly troubling ourselves with enquiring whence it derives the weight we acknowledge it to have in our decisions. However, since much importance is usually attached to this part of Bacon’s work, we shall here give a few examples to illustrate the nature of some of his principal cases. One, of what he calls “glaring instances,” has just been mentioned. In these, the nature or cause enquired into, (which in this case is the cause of the assumption of a peculiar external form, or the internal structure of a crystal,) “stands naked and alone, and this in an eminent manner, or in the highest degree of its power.” No doubt, such instances as these are highly instructive; but the difficulty in physics is to find such, not to perceive their force when found.
(193.) The contrary of glaring are “clandestine instances,” where “the nature sought is exhibited in its weakest and most imperfect state.” Of this, Bacon himself has given an admirable example in the cohesion of fluids, as a clandestine instance of the “nature or quality of consistence, or solidity.” Yet here, again, the same acute discrimination which enabled Bacon to perceive the analogy which connects fluids with solids, through the common property of cohesive attraction, would, at the same time, have enabled him to draw from it, if properly supported, every consequence necessary to forming just notions of the cohesive force; nor does its reference to the class of clandestine instances at all assist in bringing forward and maturing the final results. When, however, the final result is obtained,--when our induction is complete, and we would verify it,--this class of instances is of great use, being, in fact, frequently no other than that of extreme cases, such as we have already spoken of (in § 177.); which, by placing our conclusions, as it were, in violent circumstances, try their temper, and bring their vigour to the test.
(194.) Bacon’s “collective instances” (instantiæ unionis), are no other than general facts, or laws of some degree of generality, and are themselves the results of induction. But there is a species of collective instance which Bacon does not seem to have contemplated, of a peculiarly instructive character; and that is, where particular cases are offered to our observation in such numbers at once as to make the induction of their law a matter of ocular inspection. For example, the parabolic form assumed by a jet of water spouted from a round hole, is a collective instance of the velocities and directions of the motions of all the particles which compose it seen at once, and which thus leads us, without trouble, to recognize the law of the motion of a projectile. Again, the beautiful figures exhibited by sand strewed on regular plates of glass or metal set in vibration, are collective instances of an infinite number of points which remain at rest while the remainder of the plate vibrates; and in consequence afford us, as it were, a sight of the law which regulates their arrangement and sequence throughout the whole surface. The beautifully coloured lemniscates seen around the optic axes of crystals exposed to polarized light afford a superb example of the same kind, pointing at once to the general mathematical expression of the law which regulates their production. Of such collective instances as these, it is easy to see the importance, and its reason. They lead us to a general law by an induction which offers itself spontaneously, and thus furnish advanced points in our enquiries; and when we start from these, already “a thousand steps are lost.”
(195.) A fine example of a collective instance is that of the system of Jupiter or Saturn with its satellites. We have here, in miniature, and seen at one view, a system similar to that of the planets about the sun; of which, from the circumstance of our being involved in it, and unfavourably situated for seeing it otherwise than in detail, we are incapacitated from forming a general idea but by slow progressive efforts of reason. Accordingly, the contemplation of the circumjovial planets (as they were called) most materially assisted in securing the admission of the Copernican system.
(196.) Of “Crucial instances” we have also already spoken, as affording the readiest and securest means of eliminating extraneous causes, and deciding between rival hypotheses. Owing to the disposition of the mind to form hypotheses, and to prejudge cases, it constantly happens that, among all the possible suppositions which may occur, two or three principal ones occupy us, to the exclusion of the rest; or it may be that, if we have been less precipitate, out of a great multitude rejected for obvious inapplicability to some one or other case, two or three of better claims remain for decision; and this such instances enable us to do. One of the instances cited by Bacon in illustration of his crucial class is very remarkable, being neither more nor less than the proposal of a direct experiment to determine whether the tendency of heavy bodies downwards is a result of some peculiar mechanism in themselves, or of the attraction of the earth “by the corporeal mass thereof, as by a collection of bodies of the same nature.” If it be so, he says, “it will follow that the nearer all bodies approach to the earth, the stronger and with the greater force and velocity they will tend to it; but the farther they are, the weaker and slower:” and his experiment consists in comparing the effect of a spring and a weight in keeping up the motions of two “clocks,” regulated together, and removed alternately to the tops of high buildings and into the deepest mines. By clocks he could not have meant pendulum clocks, which were not then known, (the first made in England was in 1662,) fly-clocks, so that the comparison, though too coarse, was not contrary to sound mechanical principles. In short, its principle was the comparison of the effect of a spring with that of a weight, in producing certain motions in certain times, on heights and in mines. Now, this is the very same thing that has really been done in the recent experiments of professors Airy and Whewell in Dolcoath mine: a pendulum (a weight moved by gravity) has been compared with a chronometer balance, moved and regulated by a spring. In his 37th aphorism, Bacon also speaks of gravity as an incorporeal power, acting at a distance, and requiring time for its transmission; a consideration which occurred at a later period to Laplace, in one of his most delicate investigations.
(197.) A well chosen and strongly marked crucial instance is, sometimes, of the highest importance; when two theories, which run parallel to each other (as is sometimes the case) in their explanation of great classes of phenomena, at length come to be placed at issue upon a single fact. A beautiful instance of this will be cited in the next section. We may add to the examples above given of such instances, that of the application of chemical tests, which are almost universally crucial experiments.
(198.) Bacon’s “travelling instances” are those in which the nature or quality under investigation “travels,” or varies in degree; and thus (according to § 152.) afford an indication of a cause by a gradation of intensity in the effect. One of his instances is very happy, being that of “paper, which is white when dry, but proves less so when wet, and comes nearer to the state of transparency upon the exclusion of the air, and admission of water.” In reading this, and many other instances in the Novum Organum, one would almost suppose (had it been written) that its author had taken them from Newton’s Optics.
(199.) The travelling instances, as well as what Bacon terms “frontier instances,” are cases in which we are enabled to trace that general law which seems to pervade all nature--the law, as it is termed, of continuity, and which is expressed in the well known sentence, “Natura non agit per saltum.” The pursuit of this law into cases where its application is not at first sight obvious, has proved a fertile source of physical discovery, and led us to the knowledge of an analogy and intimate connection of phenomena between which at first we should never have expected to find any.
(200.) For example, the transparency of gold leaf, which permits a bluish-green light to pass through it, is a frontier instance between the transparency of pellucid bodies and the opacity of metals, and it prevents a breach of the law of continuity between transparent and opake bodies, by exhibiting a body of the class generally regarded the most opake in nature, as still possessed of some slight degree of transparency. It thus proves that the quality of opacity is not a contrary or antagonist quality to that of transparency, but only its extreme lowest degree.
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End of part 10 of 17
Continue readingPart II, Chapter 7: Of the Higher Degrees of Inductive Generalization, and of the Formation and Verification of Theories
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