Popular Science Monthly/Volume 48/March 1896/The Failure of Scientific Materialism

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THE complaint has gone up in all ages that so little agreement prevails respecting the most important and most fundamental questions of humanity. Only within our own days has the cry with respect to one of the greatest of these questions been silenced; and although many contradictions are still current, it may yet be said that rarely at any time has a so relatively great unanimity existed concerning the theory of the world of outward phenomena as prevails just now in our scientific century. From the mathematician to the practicing physician, every scientifically thinking man, in answer to the question how he supposes the world is intrinsically constituted, would sum up his view, by saying that the universe is composed of atoms in motion, and that these atoms and the forces operating between them are the ultimate realities of which individual phenomena consist. The phrase can be heard and read in hundredfold repetitions, that no other explanation of the physical world can be found than one that rests upon the "mechanics of atoms"; matter and motion seem to be the ultimate concepts to which the diversity of natural phenomena must be referred. This conception may be called scientific materialism.

I purpose to express my conviction that this so generally accepted conception is untenable; that this mechanical view of the world does not answer the purpose for which it has been formed, and that it is contradictory of indubitable and generally known and recognized truths. There can be no doubt of the conclusion to be drawn from this proposition: this scientifically untenable conception must be given up, and replaced, if possible, by another and better one. I believe that I can answer the question that would naturally be asked here, whether another better view exists, in the affirmative. What I have to say on the subject will therefore be legitimately divided into two parts the destructive and the constructive. It is easier in this case, as in others, to destroy than to build up, and the insufficiency of the usual mechanical view will be easier to demonstrate than the sufficiency of the new one, which I shall call the energistic view. But if I declare at once that this new theory has already had opportunity to show its quality in the field of experimental science, so favorable to calm examination and impartial testing, it will then be able, even if it can not secure conviction of its correctness, to demand recognition of its claim to consideration.

It may not be superfluous for me to announce in the beginning that I contemplate an exclusively scientific discussion. I put away absolutely and unconditionally all conclusions which might be drawn from the result for other, ethical and religious, purposes. I do this, not because I undervalue the importance of such considerations, but because my result has been obtained independently of them, purely on the ground of exact science. Even for the tilling of this ground the word holds good that he who puts hand to the plow and looks back is not made for the kingdom. The naturalist is pledged to declare what he has found, whomsoever it may hurt or help, and we may surely trust that earnest seeking, though it may lead us astray for a little while, will never do it permanently. I do not forget that my attempt places me in contradiction with the opinions of men who have achieved much in science, and to whom we all look up in admiration. I hope you will not impute conceit to me because I differ from them on so important a subject. It is not conceit when the sailor whose post is in the " crow's nest " causes the course of the great ship on which he is only a servant to be turned by the cry of "Breakers ahead!" It is his duty to tell what he sees, and he would fail in this duty if he neglected to do so. In the same sense I have a duty to discharge. Yet none of you is obliged to change his scientific course merely on my call of "Breakers ahead!" Each of you may test whether a reality stands before my eyes, or I am deceived by a vision. But since I believe that the special kind of scientific work which is my calling permits me for the moment to discern certain phenomena more clearly than they appear from other points of view, I should consider it wrong if I failed for reasons outside of it to speak of what I have seen.

In order to set ourselves right in the infinity of the world of phenomena, we pursue always and everywhere the same scientific method. We put like by the side of like, and seek what is common in diversity. In this way is the gradual mastery of the infinity of our phenomenal world achieved, and more effective means for compassing the purpose arise in successive development. From bare comparison we pass to system, from this to laws of Nature, and the most comprehensive form of these is compressed into the general principle. We perceive that the phenomena of the actual world, unlimited as is their diversity, still represent only quite definite and well-marked instances of formally conceivable possibilities. The significance of the laws of Nature consists in the determination of the real cases out of the possible, and the form to which they may all be traced back is the ascertaining of an invariant, a something which remains unalterable, even when all other criterions within the possible bounds defined by the law change. Thus we see that the historical development of scientific views is always associated with the discover}^ and elaboration of such invariants; in them are revealed the milestones of the highway of knowledge which mankind has trodden.

One such invariant of universal bearing is found in the idea of mass. This not only gives the constants of astronomical laws, but is not less invariably illustrated in the most incisive changes to which we can subject the objects of the outer world chemical processes. For that reason this idea, as being highly adapted to the position, has been made the center of scientific legitimacy. It was, however, in itself too poor in substance to serve for the representation of the manifold phenomena, and had to be correspondingly extended. This was done by associating with that simple mechanical idea the series of properties, in their proportion, which are experimentally connected with the property of mass. Thus originated the idea of matter, in which was grouped all that was sensibly connected with mass, and continued with it, such as weight, volume, chemical properties, etc., and the physical law of the conservation of mass passed into the metaphysical axiom of the conservation of matter.

It is important to understand that with this extension a multitude of hypothetical elements were introduced into a conception that was in the beginning wholly free from hypotheses. Chemical processes, in particular, must be interpreted in the light of this view against the seeming, not as implying a disappearance of the matter affected by the change and its replacement by new matter with new properties. The theory rather became accepted that even when all the sensible properties of, for example, iron and oxygen disappear in iron oxide, iron and oxygen are nevertheless present in the resultant substance, and have only taken on other properties. We have now become so accustomed to this view tliat it is very hard for us to perceive the strangeness, yes, the absurdity of it. When we reflect that all we know of any particular substance is of its properties, we see that the thought that it is still present, but has no longer any of its properties, is not far removed from pure nonsense. In fact, this purely formal conception only serves to help us harmonize the general facts of chemical processes, particularly the stoichiometrical laws of mass, with the arbitrary conception of a matter unchangeable in itself.

But even with this extended conception of matter and the necessary corollaries besides, we can not comprehend the mass of phenomena not once in inorganic Nature. Matter is thought of as something at rest, unchangeable; in order to reconcile this thought with the view of the constantly changing world, we have to complement it with another, independent of it, which shall bring changeableness to pass. Such a supplementary idea was set forth by Galileo, the creator of scientific physics, in the conception of force, as the constant cause of motion. Galileo had discovered a highly important invariant for the variable phenomena of free and induced falling. By the application of a self-existing gravity, the effects of which continuously accumulate, he made the complete explanation of these processes possible. The pregnancy of this conception was demonstrated by Newton, who, with his thought that the same force was operative as a function of the distance between the heavenly bodies, conquered the whole visible stellar world for science. This advance it was, chiefly, which aroused the conviction that all other physical phenomena could be accounted for in the same way as those of astronomy by the same auxiliary. Then when it resulted, further, at the beginning of our century, through the labors of a number of eminent astronomers, principally French, not only that Newton's law of gravitation could account for the motions of the heavenly bodies in their larger features, but that it sustained the closer and far more thorough second test of accounting for the deviations from the typical forms of motion, the perturbations, the confidence in the fruitfulness of this conception was increased in an extraordinary measure. What could be more readily suggested than the supposition that the theory which had been competent to account so completely for the motions of the great world was also the right and only means of reducing the processes in the smaller world of atoms to scientific control? Thus arose the mechanical view of Nature, according to which all phenomena, especially in inanimate Nature, were traced back ultimately to the motions of atoms under the same laws as were recognized for the heavenly bodies. It was a necessary consequence that this conception of the realm of inorganic Nature should be applied to animate Nature as soon as it was perceived that the same laws which prevailed there could also claim their inviolable right here. This view of the world found its classical expression in Laplace's idea of a "world formula/' by means of which every past and future event could be brought about in a strictly analytical way according to mechanical laws. For such a work, a mind was required which was far superior to the human mind, but was still essentially like it and not fundamentally different from it.

We do not ordinarily remark in how extremely high a measure this generally current view is hypothetical, even metaphysical J but are accustomed, on the other hand, to regard it as the maximum of exact formulation of actual facts. In contradiction to this it should be declared that a confirmation of the consequence that should flow out of this theory that all the non-mechanical processes, like heat, light, electricity, magnetism, and chemism, are really mechanical can not be reached in any single case. It has never been possible in any one of these instances so to account for the actual conditions by a corresponding mechanical system that there should be no remainder.

Mechanical interpretations, it is true, have been given with more or less considerable success to individual phenomena; but when the attempt has been made to account for all the facts in any given field by means of a mechanical conception, it has always and without exception come to pass that an irreconcilable contradiction appeared at some point, between the actual state of the phenomena and that which the mechanical conception would lead us to expect. Such contradictious might remain hidden for a long time; but the history of science teaches us that they will inevitably sooner or later come to light; and that all that we can say with full certainty of such mechanical conceptions or analogies as are usually called mechanical theories of the phenomena in question is that they will at any rate fill the gap for the present.

The history of optical theories affords a conspicuous example of these conditions. So long as all optics included nothing more than the phenomena of reflection and refraction, an interpretation was possible under the mechanical scheme proposed by Newton, according to which light consists of small particles which, thrown out straightwise by shining bodies, behaved according to the laws of moving and perfectly elastic masses. That another mechanical view, the undulatory theory proposed by Huygens and Euler, accomplished quite as much, might make the exclusive validity of the former theory doubtful, but could not deprive it of its predominance. But when the phenomena of polarization and interference were discovered, Newton's mechanical conception was found wholly inadequate, and the other, the undulatory theory,

TOL. XLTIII. 42 was received as proved, because the essential facts at least of the new departments were deducible from its premises.

The life of the undulatory theory as a mechanical hj^'pothesis has, however, been a limited one, for it has been borne to the grave in our own time without display, and been replaced by the electromagnetic theory. The cause of its death is shown very plainly when we dissect the corpse. It was carried down by its mechanical constituents. The hypothetical ether, on which the task of undulating was imposed, had to do this under peculiarly hard conditions, for the phenomena of polarization demanded peremptorily that the undulations should be transversal; but such undulations presuppose a rigid body, and Lord Kelvin's calculations have shown, as a final result, that a medium with such properties as this ether must have is not stable; whence the conclusion is inevitable that it can have no physical existence. In order to spare the now accepted electro-magnetic theory of light from such a fate, the lamented Hertz, to whom this theory owes so much, expressly denied that he saw anything else in it than a system of six differential equations. This termination of the evolution speaks more impressively than I ever can against the permanent usefulness of the formerly current mechanical theorizing.

But I hear it said. Those theories have been so fertile. Yes, they have been so through the sum of correct constituents in them, as they have been damaging through their false ones. What were the correct and what the false had to be determined by long and costly experiments. The result of our discussion so far is first a pure negative. We have learned how not to do it, and it seems to be of little use to follow out such negative results. Yet we can point out a gain here, which will not appear worthless to many of you. We find it possible, as we go, to refute critically a view which had no small credit in its time, and caused great concern to many of those interested in the discussion. I refer to the widely known propositions which the eminent physiologist of the University of Berlin, Emil Du Bois-Reymond, made, first twenty-three years ago, on the occasion of the meeting of naturalists at Leipsic, and afterward in some more widely read writings, relative to the prospects of our future knowledge of nature, and which culminated in the famous expression ignordbimus. In the long controversy which followed this address, Du Bois-Reymond, so far as I can see, remained essentially the victor against all attacks, for all his antagonists proceeded from the same principle from which he inferred his ignordbimus, and his conclusions stood as firmly as that principle. This principle, which in the meanwhile had never been brought in question by any one, was the mechanical theory of the world the supposition that the solution of the phenomena in a system of moving mass-points is the end which the theory of Nature is trying to reach. If this principle falls, and we have seen that it must fall, the ignorahimus falls with it, and science again has free course.

I do not believe that you will accept this result with surprise, for, if I can judge from my own experience, hardly a naturalist has seriously believed in the ignorabimus unless he has failed to make clear to himself in what point that in it which is untenable lies. But the gain to the negative criticism of the mechanical theory of the world accruing from the formal laying of that menacing specter may be of some value to many thinkers who have nothing to oppose to the inevitable logic of Du Bois-Reymond 's demonstration.

What is here laid down for the sake of clearness, in respect to these particular discussions, has, however, a considerably wider bearing. The refutation of the mechanical construction of the universe touches the basis of the whole materialistic theory of the world, the terms being taken in the scientific sense. It appears a vain undertaking, with ultimate failure decreed to every earnest effort, to interpret known physical phenomena mechanically; hence the conclusion is unavoidable that the attempt can still less succeed with the vastly more complicated phenomena of organic life. The same contradiction of principle forces itself upon us here, and the supposition that all natural phenomena can be traced back primarily to mechanical factors can not even be designated an available working hypothesis. It is a mere error.

The following fact bears most plainly against this error: Mechanical equations all have the property of permitting the exchange of the sign of time that is, the theoretically perfected mechanical processes can as well go backward as forward. In a purely mechanical world there are therefore no earlier and later in the sense of our world: the tree might be changed into a twig or a seed, the butterfly to a caterpillar, and the old man to a child. The mechanical theory has no explanation of the fact that this does not take place, and, on account of the property of mechanical equations which we have mentioned, can have none. The actual irreversibility of real phenomena also demonstrates the existence of processes that are not representable by mechanical equations; and with this the condemnation of scientific materialism is pronounced.

It thus appears to result certainly from these considerations that we shall have finally to renounce the hope of explaining the physical world intuitively by tracing its phenomena back to a mechanics of the atoms. But, I hear it said, if the conception of moving atoms is taken away from us, what means is left of forming a picture of the reality? To sucli a question I miglit reply, "Thou shalt not make unto thee any image or any likeness! " Our object is not to see the world in a more or less darkened or distorted glass, but as immediately as the constitution of our mind will permit. To set realities, demonstrable and measurable magnitudes, in definite relations with one another, so that when one is given the others will follow that is the purpose of science, and it can not be fulfilled by the substitution of any hypothetical figure, but only by the demonstration of the mutual dependencies of measurable magnitudes.

This road is undoubtedly long and toilsome, but it is the only permissible one. We do not have to go upon it, however, despairing of ourselves seeing the end of it, and merely hoping that it may lead our children to the desired heights. No, we ourselves are the happy ones, and the most hopeful scientific gift which the departing century can offer the dawning one is the replacement of the mechanical theory by the energistic.

I lay at this point great weight on the declaration which I make that we are not dealing with some fresh novelty, first given in our time. No, we have been in possession of the truth for half a century without knowing it. If there ever was a place for the expression "mysteriously evident," it is here; we can read it every day, and do not understand it.

When fifty-three years ago Julius Robert Mayer first discovered the equivalence of the different natural forces, or, as we should say now, of the various forms of energy, he made a great advance toward an ultimate solution of the problem. But, according to a constantly recurring law in universal thought, a new fact is never accepted in its primary clearness and simplicity. The receiver, who has not inwardly felt the advance, but has taken it in from without, strives first of all things to connect the new as well as he can with what is already existing. Hence the new thought is obscured, and, although not exactly falsified, is robbed of the best of its force. So strong is this peculiarity of thought that it does not even leave the discoverer free; as even the powerful mind of Copernicus was competent to let the sun and earth change places in their motions, but not to comprehend the simple motions of the other planets; to account for these he adhered to the received theory of epicycles. So it was with Mayer. Hence, as it nearly always is, the work of the next generation consists, not in harvesting the results of the ne.w knowledge, but rather in removing again, piece by piece, the involuntary additions that do not belong to the subject, till at last the fundamental thought can come out in its whole plain identity.

A similar development can be perceived, even in our case. After J. R. Mayer had- defined the law of equivalence, his theory of the equivalent transformability of the different forms of energy was too paradoxical in its simplicity to be immediately accepted. Rather have the three johysicists to whom we are most indebted for the continued study of the law Helmholtz, Clausius, and Lord Kelvin believed that it must be interpreted as implying that all the different forms of energy are fundamentally the same mechanical energy. In this way, what was regarded as most pressing close connection with the prevailing mechanical conception of Nature was reached; but a decisive side of the new thought was lost.

It required a half century for the idea to mature that this hypothetical addition to the law of energy did not give depth to the theory, but detracted from it on its most significant side its freedom from all arbitrary hypothesis. And not even the recognition of this methodical circumstance, but the ultimate failure of all attempts satisfactorily to explain all the other forms of energy mechanically, has been, so far as our advance has as yet proceeded, the decisive reason for giving up the mechanical explanation.

You are impatient to learn how it is possible to form, by means of so abstract an idea as energy, a theory of the world that can compare in clearness and intuitiveness with the mechanical theory. I do not find the answer hard. What do we know of the physical world? Evidently only what our organs of sense permit to reach us from it. But what are the conditions under which these organs act? Turn things as we will, we find nothing common but that the sense organs react upon differences of energy between them and the surroundings. In a world the temperature of which is everywhere that of our body, we would know nothing of heat, just as we have no idea of the constant atmospheric pressure under which we live, and as we never gain knowledge of it till we establish a different pressure.

You will admit this, but you will not therefore give up matter, because energy must have a bearer. But I ask you, why? When all that we learn of the outer world are conditions of its energy, what ground have we for presuming anything in this same outer world of which we have never learned anything? Yes, I may be answered, energy is only something thought of, an abstraction, while matter is real. I reply: The contrary! Matter is a thing of thought, which we have constructed for ourselves, rather imperfectly, to represent what is permanent in the change of phenomena. Now that we begin to comprehend that the effective thing that is, that which affects us is only energy, we have to determine in what relations the two stand; and the result is indubitable that the predicate of reality can be ascribed only to energy. This decisive side of the new theory will come more plainly into view if I present the concept in a brief historical sketch. We have already seen that the progress of science is marked by the discovery of more and more general invariants; and I have shown how the first of these unchangeable entities, mass, has expanded into matter that is, mass endowed with volume, weight, and chemical properties. Yet this idea was obviously insufficient from the beginning to cover the incessant variability of phenomena; and since Galileo's time, that of force has been added as a means of accounting for it. Yet force was destitute of the property of unchangeableness; and after functions were found in mechanics, in living force, and work which manifested themselves as partial invariants, Mayer discovered in energy the most universal invariant, dominating over the whole domain of the physical forces.

Conformably to this historical development, matter and energy continued existing together, and all that we could say of their mutual relations was that they mostly appeared with one another, or that matter was the bearer or the vessel of energy.

Are matter and energy, then, really different from one another like, for instance, body and soul? Or is not rather what we know and express of matter already comprised in the idea of energy, so that we can represent all phenomena with this one entity? In my opinion the answer can not be doubtful. What is included in the idea of matter is, first, mass that is, the capacity for momentum; next, volume, or space-filling energy; then gravity, or the peculiar kind of static energy which is manifested in general weight; and, lastly, chemical properties, or chemical energy. We still have only energy; and if we think on about these various kinds of matter, there is nothing else left us, not even the space it occupies, for this, too, is knowable only by the application of energy, which is required to compress matter within it. Hence matter is nothing but a spatially contiguous group of different eaergies, and all that we can predicate of it we predicate only of these energies.

What I am at pains to assert here is so important that you will pardon me if I try to approach the subject more closely from another side. Permit me, therefore, to take the most drastic example I can find. Imagine that you are struck with a stick. What do you feel, the stick or its energy? The only possible answer is the energy, for the stick is the most harmless thing in the world, so long as it is not made to strike. But we can also run against a stick at rest. Very true; and what we feel then is, as I have already declared, the difference in the conditions of energy as opposed to our sense organs; and it is therefore all the same whether the stick is struck against us or we are pushed against the stick. If both have the same velocity, and that in the same direction, then the stick exists no more for our feeling, for it can not come in contact with us and effect an exchange of energies.

These premises show, I hope, that all that it has hitherto been possible to represent with the aid of the ideas of matter and force can be represented, and much better, by means of the idea of energy; all that is required is a transference of the properties and laws which have been ascribed to the former to the latter. We further gain the very great advantage of avoiding the contradictions which were attached to the former mode of conception, and which I have exposed in the former part of my thesis. While we make no other supposition concerning the connection of the different kinds of energy with one another than that given through the law of the conservation of forces, we gain liberty to study objectively the various properties appertaining to these several kinds of energy, and can thus, by the rational consideration and arrangement of these properties, set up a system of sorts of energy which will reveal to us exactly the similarities as well as the differences between them, and will therefore carry us scientifically much further than can be done by the obliteration of these differences by the hypothetical assumption of their intrinsic identity. We find a good exemplification of this position in the kinetic theory of gases, which is now almost universally accepted, according to which the pressure of a gas arises from the collisions among its moving particles. Now, pressure possesses no special direction: a gas presses equally in all directions, but a collision is dependent on a moving object, and the motion has a definite direction. Consequently, there can be no turning back of one of the bodies immediately upon the others. The kinetic hypothesis deals with this difficulty by artificially neutralizing the properties of direction appertaining to the collisions through the assumption that the collisions take place equally in all directions without distinction. In this case the artificial adaptation of the properties of the different energies may be successful, but in other cases it is not quite possible. Thus, for example, the factors of electric energy tension and quantity are magnitudes which I might propose to call polar; that is, they are not only designated by a numerical value, but they also possess a sign of such form that two equal magnitudes of opposite signs add up as nothing, and not as of double value. Such purely polar magnitudes are not known in mechanics. This is the reason why it will never be possible to find even a barely passable mechanical hypothesis for electrical phenomena. If such a mechanical entity with properties of polarity could be constructed which is perhaps not impossible, and is at any rate worth a thorough investigation then we should have the material for illustrating at least one side of electricity mechanically. It may, indeed, be said here with certainty that only one side is considered, and that here also the defectiveness, without exception, of all mechanical hypotheses is demonstrated, and the full completion of the figure prevented.

When we have really traced the laws of natural phenomena back to the laws of corresponding kinds of energy, what advantage have we gained? First, the very important point that a science free from hypothesis is possible. We inquire no longer for forces which we can not exhibit, acting between atoms which we can not observe, but we ask, when we would judge respecting a process, concerning the kind and number of the energies going into it and issuing from it. We can measure them, and all that it is necessary to know can be expressed in that form. How enormous a methodical advantage that is will be clear to everybody whose scientific conscience has suffered from the unceasing amalgamation of fact and hypothesis which the physics and chemistry of the present offer as rational science. The energistic is the way in which Kirchhoff's variously misunderstood demand for replacing what is called the theory of Nature by the description of phenomena can be fulfilled in its right sense. With this freedom from hypothesis of energistic science is at the same time associated a simplicity which, it can be said without hesitation, has not been reached before. I have already pointed to the philosophical significance of this simple principle in the comprehension of natural phenomena. It lies in the nature of the matter, but might also well be declared on other considerations, that an immense advantage will result to the teaching and comprehension of science by means of this philosophical simplification. To cite only one example, we might assert that all equations, without exception, which relate two or more different kinds of phenomena to one another, must be equations between magnitudes of energy, else they are not possible. This is a consequence of the fact that besides the conceptions space and time, energy is the only entity that is common to the different fields, and in fact to all, without exception; comparisons can not be made between different fields otherwise than by the portions of energy that come into question.

I shall have to refrain from showing here how an immense number of relations, a part of which were already known and a part are new, can be immediately written down by means of this view, while formerly they had to be deduced by more or less detailed calculations. I can not either set before you in comparison the new sides which other already, if not so perfectly known propositions of thermodynamics, the most extended part of ener- gistics, have exhibited in the light of the general theory of energy. All these things must indeed be so, if what I have said to you of the significance of the new theory is well founded. I need not revert to this again.

But I can not forbear proposing a final question. When we have succeeded in grasping a significant and fruit-bearing truth in its entire, even magnitude, we are only too easily inclined to regard all as likewise concluded in its circle which comes within the field in question. We see this fault perpetrated every day in science, and the opinion which I have devoted half of the time allotted to me in contesting has grown out of just such an error. We shall therefore have to ask ourselves at once. Is the energy which is so necessary and useful for the understanding of Nature also sufiicient for that object? Or are there phenomena which can not be wholly accounted for by the laws of energy as they are yet known?

I believe that the responsibility which I have assumed toward you through my thesis can not be better discharged than by my declaring that these questions must be answered with a denial of the universal competency of energy. Immense as are the advantages which the energistic theory of the world has over the mechanical or the naturalistic, there can still, it seems to me, some points be indicated which are not covered by the acknowledged principles of energistics, and which, therefore, point to the existence of principles transcending these. Energistics will exist by the side of these new principles. Only it is not, as we must already perceive, to be the future most comprehensive principle for the mastering of natural phenomena, but will be manifest, presumably, as a particular instance of still more general conditions, of the form of which we at this time can certainly have hardly a foreboding.

I do not apprehend that what I have said has depreciated the mental advance for which so much has been claimed; I have myself extolled that advance. For it has more than once occurred to us that science can never and nowhere recognize any limits to its progress, and even in the midst of the contest for a new possession the eye should not be blind to the fact that beyond the ground we have succeeded in winning extend other stretches that must be acquired later on. In the former time we could put up with the dust and smoke of the conflict preventing our looking into the narrow limits of the battlefield. To-day this is no longer permissible; to-day we shoot with smokeless powder or, at least, ought to and have, therefore, with the possibility, also the duty, of not falling into the errors of earlier epochs.


  1. An address delivered before the third general session of the meeting of the Society of German Naturalists and Physicians, at Lubeck, on September 20, 1895.