Popular Science Monthly/Volume 12/November 1877/The Law of Continuity
WHEN the details of knowledge had in modern times accumulated to so great an extent as to demand some organization of them into principles, thoughtful men cast about for some law which might serve to relate and connect together, in part at least, the multitude of facts and theories which were in an isolated and incoherent state.
At this important stage of scientific development, Galileo was the first to recognize the value of Plato's thought as to the continuous action of natural forces. By arranging in serial order the cases of a law, he showed that phenomena which might be supposed to be radically distinct were really due to one cause; and he said that, where links of connection were unknown, they should be sought for diligently.
Galileo, however, was too busy a man to work out many of the suggestions of the law of continuity, and it remained for Leibnitz to be the first to apply it extensively in the test of physical theories, and in the reduction of fragmentary knowledge to order and intelligibility. He affirmed that nothing passes from one state to another without passing through all intermediate states, and established the truth of his proposition by showing the absurdity of the contrary. If a change were to happen without the lapse of time, the thing changed must be in two different conditions at the same instant, which is manifestly impossible.
From this principle, for example, if it be known that a body at one moment had a temperature of 20°, and at another moment a temperature of 40°, it is certain that at some intervening moment its temperature was 30°. Although this law is so simple when stated as to seem almost axiomatic, yet its cases are frequently so obscure as to have caused much hesitation in its acceptance as a universal or even a widely-operating law. Some of its illustrations, lately discovered, are among the hardest-won triumphs of experimental skill, and have demanded the aid of the most refined modern apparatus.
A typical example of continuity has long been familiar to students of geometry; figures which may differ so much in graphic delineation as the circle, the ellipse, parabola, and hyperbola, may be united by the insensible modifications of surface afforded by the inclination, more and more, of a plane dividing a cone asunder.
Similarly, in mechanics, the arc of a vibrating pendulum may be gradually enlarged by successive impacts until it becomes a circle. The part of a rotation differs generically from a complete one, yet it may approach infinitely near to it, and with only such a difference as exists between one arc and another slightly shorter.
The works on physics issued during the last century abound with distinctions which close and accurate investigations have since removed. Iron was once thought to be the only substance endowable with magnetism; now, not only all the metals, but all bodies whatever, are proved to present this polar force. In like manner, with respect to heat and electricity, conductors and non-conductors were ranged as two opposite classes; this disposition is still practically useful, since most substances conduct either very well or very ill; but it has given way as a precise statement of truth before the demonstration that all substances may be placed in unbroken order as to conductive power. For, while no material transmits either heat or electricity without some resistance, that resistance is in no case indefinitely great.
The transmission of light is another property which is not now confined within a narrow area; transparency is no longer attributed to a few bodies only—air, glass, and the like—it is extended to matter universally, experiment and reason both warranting the belief that any substance whatever, if reduced to a sufficiently thin film, would be pervious to light. Gold, one of the densest metals, can now be deposited by electricity in such tenuity as to be easily penetrated by the solar ray, and, although science is unable to give us any metal but gold in a translucent state, we know the degrees at which such light as passes through every member of the metallic catalogue is refracted. This curious piece of information has been attained by extending to the cases concerned a law, which, as far as experiment has gone, has been found true—namely, that the angle of a ray polarized by reflection always makes 90° with the angle of a refracted ray. Now, the particular angles at which lead, copper, and the rest, polarize light by reflection being observed, a simple calculation tells us how much deflection a beam may undergo in piercing metallic plates. This is an instance of how Science appropriates territory, one might deem ever to be undiscovered, by availing itself of the relationship of laws binding all things together, and interweaving the known and the unknown.
Chemists have taken their acids and alkalies, that were formerly adjudged as possessing qualities diametrically opposite, and now include them in one catalogue, no two consecutive members of which are much more than distinguishable in character. The same order has also been adopted in the electro-chemical arrangement of metals. Upon the possibility of placing all bodies in a continuous list under the head of any property whatever—cohesion, elasticity, and so on—the opinion is now entertained that all matter is capable of receiving, holding, and giving forth, any kind of force.
The varieties of force themselves have been instructively reduced to a single basis—that of motion; electricity, gravity, light, and all the rest, are at present referred to the movement in particular orbits and planes of the ultimate particles which build up all masses. For any sort of force can be converted by suitable means into any other, and all into common mechanical motion. Now, as transformations of energy are incessant in Nature—changes whereby heat becomes electricity, electricity light, and light chemical action—it must be that there are intermediate phases which a body assumes while passing from the manifestation of one of these forces to another. It must be that the ordinary forms of force just named, which seem to be so broadly marked off from each other, must be really united in transmutation by processes of motion too unstable to be caught and detained by our comparatively rude methods of detection and arrest. The extremes of a series we see, the links between elude us.
The kinds of motion to which are given names in our works on physics are, perhaps, only the stable varieties of an indefinitely great number. The swiftness of the transitions from one stable form to another may explain and excuse the notion long held that the different kinds of force were individual entities, unrelated to each other.
Here one of the chief lessons taught us by the law of continuity comes in: we are confronted by a variety of seemingly isolated forces; we find them taking on indifferently one another's forms; and, although we know not how they do so, yet we can see the danger of over-estimating the apparent, while much more may be present though hidden from our sight. The comprehension of all the varieties of force under the one category of motion is hardly fraught with any deduction more suggestive than that which inclines us to acknowledge that mere permanence has hitherto unduly influenced our ideas of what the modes of motion may be in extent and diversity. The existence of electricity was unsuspected, except in the case of rubbed amber, until within a few generations; the fleeting character of the force evading the scrutiny of the majority of the acutest investigators of Nature who have lived.
The noble generalization of the conservation of energy affords another fact and hint of much value. It tells us of the radical identity of all sorts of force, whether as that of the descending clock-weight; or in a simple form of much fixity, as that of heat; or evanescent and easily convertible, as electricity; or intricate and with many paths of working, as chemical affinity; or beyond the reach of any but vague and general means of examination, as the forces of nerve and brain. Every one of these is within the jurisdiction of the laws of mechanics, even when the motions are so exalted in degree and dignity as to seem of other stock than their real parents. Or, to change the metaphor, the tortuous labyrinth of the whole series diverges by clear and continuous avenues from one simple highway, where the elementary laws of motion are visibly obeyed.
The consistences of matter, as well as its properties, illustrate in a remarkable manner the principle of continuity. Sir William Herschel long ago ventured on general grounds to predict that the solid, liquid, and gaseous states of matter would be found to shade off imperceptibly into each other. Twenty years afterward, the labors of Prof. Andrews, of Belfast, proved the great astronomer right. By the most ingenious appliances, he detained for convenient inspection processes of transition from gas to liquid, which, in their ordinary progress, coalesce so abruptly as to seem instantaneous. In some familiar cases we can perceive changes of the same kind going on; as, for example, in the melting of wax we can follow the alteration from brittle hardness to plasticity, and thence to viscosity and liquefaction. From facts such as these, here very briefly indicated, has arisen the conviction that all matter can assume any of the three consistences. Faraday liquefied, by cold and great pressure, several of what had been called permanent gases, and improvements in the means of producing pressure and cold will doubtless enable us in the future to liquefy the remainder. Although the greatest heat we can bring to bear on carbon does not fuse it, still the tendency of our knowledge is to induce us to believe that coal in burning for a brief instant, too short for observation, exists in the liquid state. A second of time is divisible into millionths quite as perfectly as a geological cycle.
The thread of continuity has, in a variety of cases, been established in the laboratory. No two physical facts would seem to stand more decidedly apart than chemical union and mechanical admixture, yet we find them inextricably joined when we add sulphuric acid and water together. In all possible percentages do these liquids chemically combine, and this at variance with the generally-obeyed law of definite proportions. The same departure from the usual rule also obtains among other complex unions, and corroborates what first principles affirm—namely, that chemical forces are but intense and involved mechanical ones.
In the progress of science there has been much speculation as to the method by which light, electricity, and gravitation, are propagated through space. It is the old question again, "Can matter act where it is not?" Newton found the idea inconceivable, and imagined an ether as the vehicle of motions between the suns and planets of the universe. This position has been criticised by Mill, who says that inconceivableness is no test of truth, and who asserts, with a lack of his usual caution, that scarcely any living thinker of eminence now doubts that matter can act where it is not. What light have recent researches shed upon this interesting question, heretofore little more than metaphysical?
The solar atmosphere has been found to extend to more than half a radius beyond its surface; at the top of its corona, high above the hydrogen, there are vast masses of a gas which emits a simple, green ray, not corresponding with that of any known substance. In auroral displays on earth, in the uppermost regions of our atmosphere, the same simple ray has been detected; whence it has been supposed that atmospheres are not restrictedly planetary nor solar, but continuous and cosmical; and that it may be a gas indefinitely rarefied that conveys to us through the depths of space not only light-motion, but the yet more inappreciable tremors of electricity and gravitation.
The ordinary definitions of the interstellar ether are open to the objections urged by Mill, because of a dread there seems to be abroad of ascribing materiality to it; while its infinitesimal materiality is not only within the bounds of possibility, but well agrees with the facts. All motion takes time; light has a measurable velocity; chemical action of the most violent kind and even explosions are not instantaneous. Were it otherwise, the hypothesis of no medium or of an immaterial one might be entertained. Now, the decidedness in amount of a body's weight as a mass, or in its particles, has no necessary connection with its efficiency as a medium of motion. Just the reverse: we find that as matter is smaller and lighter in its ultimate parts or gross masses, the more rapidly can it communicate motion, and the greater is its capacity for motion. It is a familiar fact that, in the use of machinery, a small wheel can, proportionately to its weight, contain and transmit more motion than a large one, the plain reason of which is that it can be driven at a higher peripheral speed, its smaller bulk causing less centrifugal strain at the axis than if it were larger.
Sound travels nearly four times faster in hydrogen than in air, and in quickness of elastic recoil it is, when compressed, preferable to air in the same degree. Its extraordinary chemical energy, far transcending that of denser gases, is a fact of parallel bearing.
If we can imagine a gas as much thinner than hydrogen as the square of light's velocity exceeds the speed of sound in hydrogen (about 4,000 feet a second), we have a reasonable presentation of what the luminous medium may be—its marvelous tenuity being vastly more than compensated by the mobility of its molecules. And, therefore, the most subtile aëriform fluid conceivable is of enormously more utility in propagating impulses from star to star than solid steel would be. The ether of space perhaps sustains some such relation to a gas as a gas does to a liquid; and the current disputes as to the materiality or immateriality of a cosmic medium recall very suggestively the days, not very distant, when wise men doubted the materiality of air, and the still more recent times when it was found that gases other than air had existence.
Some further speculations, enkindled by the green ray observed in the sunshine, may be here presented as relevant to the subject. Dumas, the eminent French chemist, sought by very careful determination to prove that all atomic weights were exact multiples of that of hydrogen. He found them to be multiples of a number one-fourth that of hydrogen, whence the tenuous masses which lie above the hydrogen on the sun's surface are supposed to be one-fourth the specific gravity of the lightest gas we commonly know. And, as the spectrum it yields is the simplest known or even possible, it is thought that this new unit of the atomic scale may be primal matter, and the source of all material forms. This conjecture is not unsupported by other considerations, for, in the four kinds of stars regarded in the order of their brightness and heat, there is a progressively increasing variety of gases as they approach a lower temperature—a suggestion this as to the origin of our sixty-three so-called elements in chemistry.
In domains above the plane of physics, we can observe many beautiful cases of the law of continuity. On a window-pane in winter we can notice structural forces beginning their work where there has been, as far as we could see, no structure. We may breathe on the glass, and no microscope can there reveal any definite direction in the disposal of the moisture. Yet, from it a symmetrical architecture of frost slowly arises. We may take a crystal just deposited from a solution, break off a corner from it, and replace it in the liquid whence it came, when the damage will be accurately repaired.
Between the inorganic and the organic kingdoms of Nature the old partition-walls have at many points been removed. Formic acid, such as ants secrete, has been made artificially by the synthesis of its elements; and so have other products, formerly regarded as purely organic. Prof. Huxley maintains the opinion that, in the past, highly-complex chemical compounds have passed into the state of what he calls protoplasm, the simplest basis of organic life. The controversy about spontaneous generation is not whether the organic is contained and potential in the inorganic, but whether the transition can be artificially effected now.
Plants, like the fly-catcher, which closes on venturesome insects and absorbs their juices, show us how powers, commonly supposed to be exclusively animal, may be shared by members of the vegetable world. The sensitive-plant has something very like the nervous system which marks the highest types of life, for it not only shrinks when rudely touched, but also when exposed to fumes of chloroform. In the same direction points what in plants generally seems to parallel instinct in animals. If a layer of soil near the surface of the ground be unusually rich and moist, the rootlets in growth are spread almost wholly along that layer, while in any other case they descend. The tendrils of vines find points for attachment an inch or two from their stems; in cellars and caverns the feeble sprouts grow toward the light which they seem to feel is their life.
Is not all this conformable to the law by which motion takes the path of least resistance, as in the case of the waters of a broken reservoir descending to a valley by the shortest channel; or discharges of electricity harmlessly betaking themselves to the earth through a purposely-exposed conductor?
Instinct, especially in insects, borders on and at times invades the higher realm of intelligence. The shapes of birds'-nests, waxcells, and so on, are not rigidly invariable, but are always more or less adapted to circumstances. Glass rods have been placed in a beehive, and the little workers to avoid them have sprung all sorts of buttresses and arches, such probably as neither they nor any of their progenitors ever undertook before.
Natural history, in the discussions which have recently shaken the world, illustrates how difficult, if not impossible, is the task of trying to draw lines of demarkation, hard and fast, in Nature. The arguments pro and con as to what constitutes a true species might be gathered into a very bulky volume, and the end of the discussion is not yet.
The probability of truth, on the side of those naturalists who affirm the principle of continuity as explaining the genesis of species, has been strengthened by that principle being made the basis of the best method of zoölogical classification yet produced.
Profs. Huxley and Haeckel describe a tree of life: the main branches of it are the great classes; the divergent limbs, the families; and the minor branches, the species. The wide gaps between the groups of organisms now extant are in considerable measure bridged by recourse to fossils, and the suggestions of embryology—which science studies the phases an animal passes through from conception to birth, and observes the affiliations indicated in antenatal history.
As the gulfs existing between living things present the most formidable difficulty in the way of the reception of the principle of continuity in its broadest claims, it may be admissible here to present some of the explanations given by Lyell and others to account for the fact that so many links of genetic connection are missing. It is most important to a species that it should preserve and intensify some definite method of subsistence—a habit of diving, climbing, swimming, digging, or of catching some particular prey, or finding and living on some special plant. There is a natural premium set upon some expertness of this kind, which we must mark is very apt to run in a narrow groove; and there is a yet greater reward for any new expertness, the occupying of a new field of animal possibility, or an adaptation to circumstances changed by the great forces of Nature—as in the mighty revolutions brought about by astronomical and geological causes. In periods of transition we can well imagine that an elasticity in stationary circumstances, usually all but dormant in an organism, comes into play with all its power; and hence that the type fit for the new conditions is, comparatively speaking, soon formed and fixed. We may thus understand how it is that a wide diversity among living forms has been brought about, and why it is that few fossils intermediate between them have been discovered. Some very striking ones have been unearthed, but it would be an unwarrantable digression to describe them in a paper of these limits.
The remote extremes which may be joined together by gentle and imperceptible modifications are well illustrated in the facts of ordinary growth. Newton had once to be taught that two and two make four, yet from that day to the culmination of his powers there was no abrupt accession of knowledge or insight. He came by steady advances from the ignorance of a babe to the full stature of the first physical philosopher in Europe.
All this teaches us the supreme importance of looking at things in their dynamic as well as in their static aspect; of regarding the mechanics not less earnestly than the geometry of Nature. For differences in degree may gradually accumulate until they become differences in kind. We have seen how various sources of obscurity may veil processes of genesis, and lead any but a minute and careful observer to mistake a new form for a new identity. We have noticed how the possession of qualities usually in extremes may conceal the fact that the qualities are general—as in the magnet, which is but an exaggerated case of any mass whatever.
We have noticed how the vast differences in the time required in transmutation may tend to confuse the similarity of two cases of a law. The embrowning of a pine fence in the course of years is due to the same cause which chars in a few minutes the same wood when used as fuel. We have remarked, also, the enormous differences in the stability of natural forces: some of them, as heat, are metamorphosed with great difficulty; others, as electricity, are of very weak permanence; and others, again, in whose existence we have good reasons to believe, are too evanescent to be detected by the keenest scrutiny.
It has also appeared that mere complexity of resultant lines, as simple forces interact, may yield the erroneous supposition that new and higher causes than the real ones have come into action.
It has been briefly stated how diverse properties merge into one another, and various consistencies overpass the bounds of common definition; and, leaving the region of fact for that of speculation, it has been shown how the principle of continuity may account for the genesis of our chemical elements, and the transfer of impulses across the diameter of the heavens.
All these facts, probabilities, and suggestions, lead to the conviction that continuity is a universal law; that it prevails everywhere, and has prevailed throughout all time; that its present innumerable and intricate threads have been spun forth from the simplest conceivable state of matter and motion, which from the beginning have been subject to a uniform code of law—a code of law growing more complicated with time by the interaction and mutual influence of primitive principles.
The study of continuity presents many results very pertinent to the great question, "How has Nature assumed the infinite beautiful forms which engage our attention and admiration to-day?" The probabilities in favor of the solution offered by the evolution theory are much enhanced when we consider how insignificant in area, and transient in operation, are many of the bridges connecting together the islands and continents of forces and life.
As we trace out with great pains the unbroken links stretching between the most diverse facts and appearances, links which a cursory view would never discover, we find that that theory which supposes a community of origin and descent for all that now is, has a remarkable body of evidence adducible in its favor.
That Nature has arrived at its present state by the continuous action of forces such as are now at work around us, has become so widely-prevalent a conviction that Mill said, speaking of the inclusion of special laws in general ones convergently, that the question Science now asks is, "What are the fewest and simplest assumptions which, being granted, the existing order of Nature would follow?"