Chapter II: I Introduce My Wife—She Disappears! (4)

“I assure you,” said I, with a sincerity of accent that could not be mistaken, “this so‐called great catastrophe has only taken away the things I did not care for: it gives me here all I love, and nearly everything I desire.”

I looked at him hesitatingly, not yet knowing how far to go. But his look inspired me with courage, and I continued, with emotion:

“Tell me, in your turn, that you regret nothing, that my presence suffices, and I pledge you my word, Lorenzo, this hour will be the happiest of my life.”

Instead of replying directly, he knelt down beside the little divan where I was sitting, and I saw his eyes beaming with the expression that once used to flash from them for an instant, not uncertain and transitory as then, but calm, stable, and profound.

“Ginevra,” said he, “in assuring you to‐day that my reason has been restored to me, that I have for ever recovered from my detestable aberration, that I again look upon you as I did when you first effaced every other image, that I love you as much, yes, a thousand times more than ever, this is not saying enough, this is not telling you what you would perhaps listen to far more gladly than all this.”

I opened my eyes and looked steadily towards him. He felt my soul was trying to read his, and he continued in a low, agitated tone:

“You have made me love in you what is better than yourself. Listen to me.... Long years of indifference had effaced the memory of divine things I had been taught in my childhood. Did you think they could ever be recalled? I had never felt the slightest desire. It is you, Ginevra, who caused their return. Can you realize it?”

O my God! this hour was too happy for earth! It left me only one wish more. It realized to the fullest extent all the cherished dreams of the past, and made me touch at last the summit (alas! always threatening and uncertain) of earthly happiness! No cloud has ever obscured the bright, blessed remembrance! No suffering, no trial, has ever checked the effusion of gratitude I still feel, and which will be eternal!

It will not be difficult to understand that, in this new state of things, our life speedily and sweetly resumed its course. Strange to say, this calm, simple life, exempt from splendor, luxury, and worldly _éclat_, was the precise realization of the secret desire I had always cherished in my soul, the signification of which had been revealed to me in that great day of grace which I may call that of my _true birth_!

It would, therefore, have been an absurdity to speak of sacrifice in the situation in which I now found myself. But Lorenzo did not yet see things in the same light.

“I acknowledge,” said he one day, after some weeks had passed by—“I acknowledge we lack nothing essential, that the waifs from our wreck even afford us a comfortable support, but I wish more than that for you, my Ginevra. I must work for the means of restoring all my folly has deprived you of. The public receives my productions with marked favor. They have all been sold at a fabulous price, except one which I will never part with. Let me alone, therefore, and I promise you the day shall arrive when I will place on your brow a diadem even more brilliant than the one you have lost.”

I made a quick gesture, and was about to express the repugnance such a prospect inspired. But I stopped. It was better, no matter in what way, he should be stimulated by some object to be attained by the laborious efforts to which he devoted all his faculties. I allowed him, therefore, to dream of the jewels he would adorn me with, and enlarge on his plans for the future, while I was sitting beside him in his studio, sometimes reading to him, and sometimes becoming his model again. Whenever he spoke in this way, I smiled without trying to oppose him.

Mme. de Kergy and Diana hastened to see me the day after my arrival. We continued to meet almost daily, and I found in their delightful society the strongest support, the wisest counsels, and an affection which inspired almost unlimited confidence.

As to Gilbert, he was still absent, and not expected to return till the autumn of the following year.

When his mother gave me this information, my first feeling was one of relief. It seemed to me my relations with his family were simplified by his absence, and I could defer all thought as to what I should do at his return. But, when I saw my dear, venerable friend secretly wipe away a tear as she spoke of her son; when she added in a trembling voice that such a separation at her age was a severe trial which afflicted her more than any she had ever known; when Diana afterwards came to tell me with a full heart that Gilbert’s absence was shortening her mother’s days, oh! then my heart sank with profound sorrow, and I felt an ardent, painful desire to repair the evil I had caused—an evil which (whatever may be said) is never altogether involuntary!

Ah! if women would only consider how far their fatal influence sometimes extends, even those who add hardness of heart to their desire to please would become indifferent to the wish. They scarcely hesitate sometimes to sacrifice a man’s career, his abilities, his whole existence. Vanity and pride take pleasure in ravages of this kind. But if their eyes could behold the firesides they quench the light of, the maternal hearts they sadden, the families whose sweet joys they destroy, their trophies would seem bloody, and they might be brought to comprehend the words of the Psalmist which I had humbly learned to repeat: _Ab occultis meis munda me, et ab alienis parce servo tuo._

Lorenzo’s celebrity increased by the productions he now exhibited to the public. The singularity of our position in returning to Paris, under circumstances so different from those which surrounded us when we made our first appearance in the _grand monde_, drew upon us the attention of this very world which would have enticed us from our retreat. But, thank Heaven! I did not have to exert my influence over Lorenzo to induce him to decline it. His pride would have been sufficient, had not his whole time been absorbed in his labors, and it was even with difficulty he consented to accompany me one evening to the Hôtel de Kergy.

From that time, however, he willingly repeated his visits, attracted by Mme. de Kergy’s dignified cordiality and simplicity of manner as well as by the charm of the intellectual circle of which her _salon_ was the centre—a charm he would have always appreciated had he not been under the influence of another attraction. Now there was no counteracting influence, and he took fresh pleasure every evening in going there to repose after the fatigue of the day and seek something more beneficial to his mind than mere recreation.

A person endowed with noble gifts, who returns to the right path after long going astray, experiences an immense consolation in finding himself in his true element. It would, therefore, be impossible to tell how great Lorenzo’s joy now was, or how eloquently he was able to express it. And nothing could express the feelings with which I listened to him!

The only shadow of my life at this time was my separation from Stella. A thousand times did I urge her to join me, as she was no longer under any obligation to remain at Naples. I felt that the only possible solace for her broken heart would be to leave the place where she had suffered so much; her courageous soul would find a salutary aliment in the great charitable movement at Paris, at that time in all the vigor of its first impulse, given a few years before. I therefore continually urged her to come, but I begged her in vain. An invincible repugnance to leave the place of refuge where she had hidden her grief prevented her from yielding to my wishes.

Thus passed days, weeks, months, yes, even a whole year and more of happiness. The satisfactory life I had dreamed of was now a reality, and the world I once fancied I could reveal to Lorenzo unaided he had discovered himself. It had been revealed to him by trials, humiliation, and labor. The absolute change in his habits, which Lando had once indicated as the only remedy, had, as he had foreseen, produced a beneficial, efficacious, and lasting effect.

But we know one of the anomalies of the human heart is to expect and long for happiness as its right, and yet to be incapable of possessing it a single day in its plenitude without trembling, as if conscious it was not in the nature of things here below for it to endure a long time.

Lorenzo experienced more than most people this melancholy of happiness, which was often increased by too profound a regret for the errors of his life. It partook of the vehemence of his character, and it was sometimes difficult to overcome the sadness awakened by the remembrance of the past.

“Ginevra,” said he one day, “I am far too happy for a man who merits it so little.”

He said this with a gloomy expression. It was the beginning of spring. The air was soft, the sky clear, the lilacs of our little garden were in bloom, and we sat there inhaling the perfume. He repeated:

“Yes, my life is now too happy—too happy, I feel, to be of long duration.” A remark somewhat trite, which is often thrown like a veil over the too excessive brightness of earthly happiness! But I could not repress a shudder as I listened to it. And yet what was there to fear ... to desire ... to refuse ... when I felt the present and the future were in the hands of Him whom I loved more than anything here below?

To Be Concluded Next Month.

A Bit Of Modern Thought On Matter.

We have now accomplished the first portion of our task, by establishing on good philosophical and physical grounds the fundamental truths regarding the essence and the properties of material substance as such. We might, therefore, take up the second part of our treatise, and begin our investigation about the nature of the metaphysical constituents of matter and their necessary relations, in order to ascertain how far the principles of the scholastic doctrine on matter can nowadays be maintained consistently with the principles of natural science. But we think it necessary, before we enter into the study of such a difficult subject, to caution our readers against some productions of modern thinkers, whose speculations on the nature of material things confound all philosophy, and tend by their sophistry to popularize the most pernicious errors. The number of such productions is daily increasing, owing to the efforts of powerful societies, and the philosophical imbecility of the scientific press and of its patrons. The heap of intellectual rubbish thus accumulated, both in Europe and in America, is quite prodigious; to sweep it all away would be like purging the Augean stable—a task which some new Hercules may yet undertake. We shall confine ourselves to a small portion of that task, by scattering to the winds some plausible quibbles we have lately met with in an American scientific magazine.

J. B. Stallo is the author of a series of articles published in the _Popular Science Monthly_ under the title “The Primary Concepts of Modern Physical Science.” He is a clever writer; but his conclusions, owing to a lack of sound philosophy, are not always correct. Some of them are altogether unfounded, others demonstrably false; and many of them, while attempting to revolutionize science, tend to foster downright scepticism. We shall single out a few of those propositions which clash with the common doctrines of modern physics no less than with the common principles of metaphysics; and we hope to show, by their refutation, the incomparable superiority of our old over his new philosophy.

_Indestructibility of matter._—“The indestructibility of matter,” says the writer,(181) “is an unquestionable truth. But in what sense, and upon what grounds, is this indestructibility predicated of matter? The unanimous answer of the atomists is: Experience teaches that all the changes to which matter is subject are but variations of form, and that amid these variations there is an unvarying constant—the mass or quantity of matter. The constancy of the mass is attested by the balance, which shows that neither fusion nor sublimation, neither generation nor corruption, can add to, or detract from, the weight of a body subjected to experiment. When a pound of carbon is burned, the balance demonstrates the continuous existence of this pound in the carbonic acid, which is the product of combustion, and from which the original weight of carbon may be recovered. The quantity of matter is measured by its weight, and this weight is unchangeable.”

So far all is right; but he continues: “Such is the fact familiar to every one, and its interpretation equally familiar. To test the correctness of this interpretation we may be permitted slightly to vary the method of verifying it. Instead of burning the pound of carbon, let us simply carry it to the summit of a mountain, or remove it to a lower latitude; is its weight still the same? Relatively it is; it will still balance the original counterpoise. But the absolute weight is no longer the same.... It is thus evident that the constancy, upon the observation of which the assertion of the indestructibility of matter is based, is simply the constancy of a relation, and that the ordinary statement of the fact is crude and inadequate. Indeed, while it is true that the weight of a body is a measure of its mass, this is but a single case of the more general fact that the masses of bodies are inversely as the velocities imparted to them by the action of the same force, or, more generally still, inversely as the accelerations produced in them by the same force. In the case of gravity, the forces of attraction are directly proportional to the masses, so that the action of the forces (_weight_) is the simplest measure of the relation between any two masses as such; but in any inquiry relating to the validity of the atomic theory, it is necessary to bear in mind that this weight is not the equivalent, or rather the presentation, of an absolute substantive entity in one of the bodies (the body weighed), but the mere expression of a relation between two bodies mutually attracting each other. And it is further necessary to remember that this weight may be indefinitely reduced, without any diminution in the mass of the body weighed, by a mere change of its position in reference to the body between which and the body weighed the relation subsists.”

The aim of the author is, as we shall see, to prove that “there are and can be no absolute constants of mass”; hence he endeavors at the very outset to shake our opposite conviction by showing that there is no absolute measure of masses. Such is the drift of the passage we have transcribed.

But we beg to remark that absolute quantities may be known to be absolute independently of any absolute measurement. Three kinds of quantity are conceivable: intensive quantity, which is measured by _degrees_; dimensive quantity, which is measured by _distances_; and numerical quantity, which is measured by discrete _units_. Of course dimensive quantity is altogether relative, inasmuch as it entirely consists of relations, and cannot be measured but by relative and arbitrary measures; but intensive quantity, though measured by arbitrary degrees, is altogether absolute, because it consists of a reality whose value is independent of correlative terms. And in the same manner numerical quantity is altogether absolute, because it consists of absolute units, by which it can be measured, absolutely speaking, though we may fail to reach such units, and are then obliged to measure it by some other standard. Now, the mass, or the quantity of matter in a body, is a numerical quantity; for it consists of a number of primitive units, independent of one another for their essence and for their existence, and therefore absolute in regard to their substantial being. Consequently, every mass of matter has an absolute value corresponding to the number of absolute units it contains; and thus every mass of matter is “an absolute constant of mass.” It is true that we have no means of ascertaining the absolute number of primitive units contained in a given mass; hence we are constrained to measure the quantity of matter by a relative measure—that is, by comparing it with an equal volume of another substance, whose density and weight we assume as the measure of other densities and weights. But does our ignorance of the absolute number of primitive units contained in a given mass interfere with their real existence? or, can our method of measuring change the nature of the thing measured?

We are told that “the weight of a body may be indefinitely reduced without any diminution in the mass of the body weighed.” Would not this show that, contrary to the author’s opinion, the body weighed possesses “an absolute constant of mass”? We are told at the same time that “the weight of a body is a measure of its mass.” This cannot be true, unless, while the mass remains unchanged, the weight also remains unchanged. Hence the author’s idea of carrying the pound of carbon to the summit of a mountain in order to diminish its weight, is inconsistent with the law of measurement, which forbids the employment of two weights and measures for measuring one and the same quantity.

The atomists measure the quantity of matter by its weight, because they know that every particle of matter is subject to gravitation, and therefore that the weights, all other things being equal, are proportionate to the number of primitive particles contained in the bodies. Thus, if a body contains a number, _m_, of primitive particles, and each of these particles is subject to the gravitation, _g_, while another body contains a number, _m´_, of primitive particles subject to the same gravitation, the ratio of the weights of the two bodies will be the same as the ratio of the two masses; for

_mg_ : _m´g_ : : _m_ : _m´_;

and if the two bodies were carried to the summit of a mountain, where the gravitation is reduced to _g´_, the weights would indeed be changed, but their ratio would remain unaltered, and we would still have

_mg´_ : _m´g´_ : : _m_ : _m´_.

Hence, whether we weigh two bodies in the valley or at the summit of the mountain, so long as we keep the same unit of gravitation for both, the ratio of their masses remains the same. This shows that the quantity of matter existing in those bodies implies “a constant of mass” _independent_ of the intensity of gravitation, and that the ratio of the two masses is the ratio of two “absolute” quantities—that is, of two numbers of primitive material units.

It is not true, therefore, that the weight is not “the presentation of an absolute substantive entity,” as the author pretends. Weight implies mass and gravitation, and presents the one as subject to the other. Now, the mass is an “absolute substantive entity,” as we have shown. Nor is it true that weight is “the mere expression of a relation between two bodies mutually attracting each other,” as the author imagines. The pound of carbon is a pound not because of an attraction exercised by the carbon upon the earth, but merely because of the attraction exercised by the earth on the mass of the carbon. Were it otherwise, the mathematical expression of weight should contain, besides the mass of the body weighed and the action of gravity upon it, a third quantity representing the action of the body upon the earth, and the gravitation of the earth towards the body.

The writer proceeds: “Masses find their true and only measure in the action of forces, and the quantitative persistence of the effect of this action is the simple and accurate expression of the fact which is ordinarily described as the indestructibility of matter. It is obvious that this persistence is in no sense explained or accounted for by the atomic theory” (p. 708).

We admit that, owing to our inability to determine the absolute number of primitive elements in a body, we resort to the persistence of the weight in order to ascertain the persistence of a certain quantity of matter in the body. But this does not show that the action of forces is the “only measure” of masses. A mass is a number of material units; its true measure is _one of such units_, and it is only in order to determine the relative number of such units in different bodies that we have recourse to their weights. It is not the quantity of matter that follows the weight of the body, but it is the weight of the body that follows the quantity of matter; and therefore, although we determine the relative quantities of matter by the relation of their weights, it is not the weight that measures the quantity of matter, but it is the quantity of matter that measures the weight. In other terms, the persistence of the mass is merely _known_ through the persistence of the weight, but the persistence of the weight is itself _a consequence_ of the persistence of the mass. Hence the persistence of the mass is perfectly accounted for by the atomic theory, notwithstanding Mr. Stallo’s contrary assertion.

He says: “The hypothesis of ultimate indestructible atoms is not a necessary implication of the persistence of weight, and can at best account for the indestructibility of matter if it can be shown that there is an absolute limit to the compressibility of matter—in other words, that there is an absolutely least volume for every determinate mass” (p. 708). Both parts of this proposition are false. The first is false, because the weight of a body is the result of the gravitation of all its particles; and, therefore, it cannot persist without the persistence of the gravitating particles. The second part also is false, because the persistence of the weight implies the persistence of the mass independently of all considerations concerning a limit of compressibility or an absolute minimum of volume. Hence, whatever the author may say to the contrary, it is quite certain of scientific certainty that there can be, and there is, in all bodies, “an absolute constant of mass.”

_Atomic theory._—The writer objects to the atomic theory on the ground that it does not explain impenetrability, and that it misconceives the nature of reality. He begins by remarking that “the proposition, according to which a space occupied by one body cannot be occupied by another, implies the assumption that space is an absolute, self‐measuring entity, and the further assumption that there is a least space which a given body will absolutely fill so as to exclude any other body” (p. 709). We think that the proposition implies nothing of the kind. The space occupied by one body cannot _naturally_ be occupied by another, because all bodies are made up of molecules which at very small distances repel one another with actions of greater and greater intensities, thus preventing compenetration, while successfully struggling for the preservation of their own individuality. This the molecules can do, whether space can be filled or not, and whether space is a self‐measuring entity or not. Hence the remark of the author has no foundation.

But he continues: “The atomic theory has become next to valueless as an explanation of the impenetrability of matter, since it has been pressed into the service of the undulatory theory of light, heat, etc., and assumed the form in which it is now held by the majority of physicists. According to this form of the theory, the atoms are either mere points, wholly without extension, or their dimensions are infinitely small as compared with the distances between them, whatever be the state of aggregation of the substances into which they enter. In this view, the resistance which a body, _i.e._, a system of atoms, offers to the intrusion of another body is due not to the rigidity or unchangeability of volume of the individual atoms, but to the relation between the attractive and repulsive forces with which they are supposed to be endowed. There are physicists holding this view, who are of opinion that the atomic constitution of matter is consistent with its compenetrability—among them M. Cauchy, who in his _Sept Leçons de physique générale_ (ed. Moigno, Paris, 1868, p. 38), after defining atoms as material points without extension, uses this language: ‘Thus, this property of matter, which we call impenetrability, is explained when we consider the atoms as material points exerting on each other attractions and repulsions which vary with the distances that separate them.... From this it follows that, if it pleased the Author of nature simply to modify the laws according to which the atoms attract or repel each other, we might instantly see the hardest bodies penetrate each other, the smallest particles of matter occupy immense spaces, or the largest masses reduce themselves to the smallest volumes, the entire universe concentrating itself, as it were, in a single point’ ” (p. 710).

We think that the author’s notion of the form in which the atomic theory is now held by physicists is not quite correct. The chemical atoms are now considered as dynamical systems of material points, so that the atomic theory is now scarcely distinguishable from the molecular theory. That such a theory “has become next to valueless as an explanation of the impenetrability of matter” is not true. Of course two primitive elements of matter, if attractive, would, according to the theory, as we understand it, pass through one another; as nothing can oppose their progress except repulsion, which is not to be thought of in the case of attractive elements. But the case is different with molecules; for every molecule of any special substance contains a number of repulsive elements, and possesses a repulsive envelope(182) which resists most effectually all attempt at compenetration on the part of other molecules. Hence the impenetrability of _bodies_ (not of _matter_, as the author says) is a simple result of the molecular constitution of bodies, as explained in the atomic theory of the modern chemists.

That the resistance which a body offers to the intrusion of another body is due “not to the rigidity or unchangeability of volume of individual atoms, but to the relation between the attractive and repulsive forces with which they are supposed to be endowed,” is an obvious truth. We do not see by what kind of reasoning the author can infer from it that “the atomic theory has become next to valueless as an explanation of impenetrability.” We rather maintain that the theory is correct, and that no other theory has yet been found which explains impenetrability without assuming much that philosophy condemns. As to M. Cauchy’s views, we remark that, when he defines atoms as “material points without extension,” he does not speak of the chemical atoms, or equivalents, but of the primitive elements of which such atoms or equivalents are composed.

The author says: “The assumption of atoms of different specific gravities proves to be not only futile, but absurd. Its manifest theoretical ineptitude is found to mask the most fatal inconsistencies. According to the mechanical conception which underlies the whole atomic hypothesis, differences of weight are differences of density; and differences of density are differences of distance between the particles contained in a given space. Now, in the atom there is no multiplicity of particles and no void space; hence differences of density or weight are impossible in the case of atoms” (p. 715).

This conclusion would be quite inevitable, if it were true that the atom of the chemists contains no multiplicity of particles and no void space; but the truth is that chemical atoms are nothing but _equivalents_, or _molecules_—that is, dynamical systems of material points intercepting void space. Hence the author’s argument has no foundation. The very fact that men of science unanimously agree in attributing to different atoms a different weight, should have warned Mr. Stallo that the word “atom” could not be considered by them as a simple material point.

The author in his second article (November, 1873) argues against the _actio in distans_. We have given his words in one of our own articles, where we undertook to show that _actio in distans_ cannot be impugned with any good argument.(183) The author, however, we are glad to see, honestly acknowledges that “the transfer of motion from one body to another by impact is no less incomprehensible than the _actio in distans_” (p. 96); which shows that, after having rejected the action at a distance, he is at a loss how to account for any communication or propagation of movement. A little later he quotes a passage of Faraday, which we have given in another place, and in which the English professor considers the atoms as consisting of a mere sphere of power, with a central point having no dimensions. Then he gives his own view of the subject in the following words:

“The true root of all these errors is a total misconception of the nature of reality. All the reality we know is not only spatially finite, but limited in all its aspects; its whole existence lies in relation and contrast, as I shall show more at length in the next article. We know nothing of force, except by its contrast with mass, or (what is the same thing) inertia; and conversely, as I have already pointed out in my first article, we know nothing of mass except by its relation to force. Mass, inertia (or, as it is sometimes, though inaccurately, called, matter _per se_), is indistinguishable from absolute nothingness; for matter reveals its presence, or evinces its reality, only by its action, its force, its tension, or motion. But, on the other hand, mere force is equally nothing; for, if we reduce the mass upon which a given force, however small, acts, until it vanishes—or, mathematically expressed, until it becomes infinitely small—the consequence is that the velocity of the resulting motion is infinitely great, and that the ‘thing’ (if under these circumstances a thing can still be spoken of) is at any given moment neither here nor there, but everywhere—that is, there is no real presence. It is impossible, therefore, to construct matter by a mere synthesis of forces.... The true formula of matter is mass × force, or inertia × force” (p. 103).

The author is greatly mistaken in assuming that those who consider the atoms (primitive elements) as centres of force totally misconceive the nature of reality. That Faraday, notwithstanding his saying that “the substance consists of the powers,” admits with the power the matter also, is evident from his very mention of the _centre_ of the powers; for such a centre is nothing else than _the_ matter, as we have proved above. He says, indeed, that the nucleus of the atom “vanishes”; but by “nucleus” he means the _bulk_ or the continuous material extension of the atom. This bulk, says he, must vanish, inasmuch as the centre of the powers must be a mere unextended point. He therefore denies, not the matter, but only its intrinsic extension.

Mr. Stallo volunteers to show us “the true root” of all our _errors_. According to him, we totally misconceive the nature of reality. “All the reality we know,” he says, “is not only spatially finite, but limited in all its aspects.” About this we will not quarrel, for we admit that all created substances are limited; yet we would ask the author whether he thinks that the range of universal attraction has any known limit in space; and, if so, we would further ask where it is; for we admit our full ignorance of its existence. “We know nothing of force,” he continues, “except by its contrast with mass, or, what is the same thing, inertia.” Our readers know that mass and inertia are not the same thing; the mass is a quantity of matter, while inertia is the incapability of self‐motion. A writer who can confound the two as identical is not competent to correct our _errors_ and to teach us the nature of reality. As to the contrast of force with mass, we have no objection; yet, while speaking of the nature of things, we would prefer to contrast matter with form rather than force with mass. The term _force_ applies to the production of phenomena, and is usually confounded with action and with movement, neither of which is a constituent of substance; whilst the term _mass_ expresses any quantity of matter from a single element up to a mountain; and thus it does not exhibit with precision the matter due to the primitive material substance.

“Mass, or matter _per se_, is indistinguishable from absolute nothingness.” Of course, matter _per se_—that is, without form—cannot exist. In the same manner “mere force is equally nothing”—that is, the material form, which is the principle of action, has no separate existence without its matter. This every one admits, though not on the grounds suggested by Mr. Stallo. “If we reduce,” says he, “the mass upon which a given force, however small, acts, until it vanishes—or, mathematically expressed, until it becomes infinitely small—the consequence is that the velocity of the resulting motion is infinitely great.” We deny this consequence, as well as the supposition from which it is inferred. Masses are numbers of material elements, or units. When such units are reached, the division is at an end, because those primitive units are without dimensions. Hence the extreme limit of the reduction of masses is not an infinitesimal quantity of mass, as the author imagines, but an absolute finite unit; for this unit, when repeated a finite number of times, gives us a finite quantity of mass. But, even supposing that the hypothesis of the author might be entertained (and it must be entertained by all those who consider matter as materially continuous), his consequence would still be false. For, let there be a continuous atom having finite dimensions. If such an atom is acted on, say by gravity, it will acquire a finite velocity. Now, it is evident that, when the atom has a finite velocity, every infinitesimal portion of it will have a finite velocity. Therefore the action which produces a finite velocity in the finite mass of the atom, produces a finite velocity in the infinitesimal masses of which the atom is assumed to consist. The error of the author arises from his confounding quantity of movement with action. A quantity of movement is a product of a mass into its velocity; and evidently the product cannot remain constant, unless the velocity increases in the same ratio as the mass decreases. The action, on the contrary, is _directly_ proportional to the mass; and therefore, in the author’s hypothesis, the consequence should have been the very opposite of that which he enounces; that is, the velocity acquired by an infinitesimal mass would still be finite instead of infinitely great. But, as we have said, the hypothesis itself is inadmissible, because only continuous quantity can be reduced to infinitesimals, whilst masses are not continuous but discrete quantities.

That it is impossible “to construct matter by a mere synthesis of forces” is undeniable; but there was no need of arguing a point which no one contests. The author should rather have given us his ground for asserting that “the true formula of matter is _mass multiplied by force_.” This assertion can by no means be made good. All physicists know that mass multiplied by force represents nothing but a quantity of movement; and the author will not pretend, we presume, that matter is a quantity of movement. The true formula of matter is its essential definition; and it is not a mathematical but a metaphysical product, or rather a metaphysical ratio, as we have shown in another place. Material substance is _matter actuated by its substantial form_, and nothing else.

The author continues thus: “We now have before us in full view one of the fundamental fallacies of the atomic theory. This fallacy consists in the delusion that the conceptual constituents of matter can be grasped as separate and real entities. The corpuscular atomists take the element of inertia, and treat it as real by itself: while Boscovich, Faraday, and all those who define atoms as _centres of force_, seek to realize the corresponding element, force, as an entity by itself. In both cases elements of reality are mistaken for kinds of reality” (p. 103).

It is rather singular that a man who is so little at home in questions about matter should undertake to point out the fallacies and delusions of the best informed. Is it true that Boscovich, Faraday, and others of the same school, consider force as an entity by itself? And is it true that the corpuscular atomists treat the element of inertia as real by itself? There is much to be said against corpuscular atomists for other reasons, but they cannot surely be accused of maintaining that the element of inertia—that is, the mass of the atom—can exist separately without any inherent power, as they uniformly teach that their atoms are endowed with resisting powers. The accusation brought against Boscovich, Faraday, and others, is still more glaringly unjust. They do not seek to realize force “as an entity by itself”; on the contrary, when they define the atoms as centres of force, they manifestly teach that both the force and its centre are indispensable for the constitution of a primitive atom. And, since by the word _force_ they mean the principle of activity (the form), and in the centre they recognize the principle of passivity (the matter), we cannot but conclude that the accusation has no ground, and that the fallacy and the delusion is on the side of Mr. Stallo himself.

Moreover, is it true that _mass_ and _force_, or, to speak more accurately, the matter and the form, are nothing more than “the _conceptual_ constituents” of material substance? This the author assumes as the base of his argumentation; yet it is plain that, if the constituents of a thing are only conceptual, the thing they constitute cannot be anything else than a conceptual being—that is, a being of reason. We must therefore either deny the reality of matter or concede that its constituents are more than conceptual. Could not the author perceive that, if mass is a mere concept, and force another mere concept, their alliance gives nothing but two concepts, and that the reality of the external world becomes a dream?

We live in times when men of a certain class presume to discuss metaphysical subjects without previous study and without a sufficient acquaintance with the first notions of metaphysics. One of these first notions is that all real being has real constituents. Such constituents, when known to us, are the object of our conceptions, and consequently they may become conceptual; but they do not cease to be real outside of our mind. Were we to conceive matter as separated from its form, or form as deprived of its matter, nothing real would correspond to our conception; for nowhere can real matter be found without a form, or a real form without its matter. Hence form without matter and matter without form are at best beings of reason. But when we conceive the matter as it is under its form, or the form as it is terminated to its matter, we evidently conceive the real constituents of material substance as they are in nature—that is, as metaphysical realities contained in the physical being. Does it follow that “elements of reality,” as the author objects, “are mistaken for kinds of reality”? By no means. The constituents of physical reality are themselves metaphysical realities, but they are not exactly two kinds of reality, because they belong both to the same essence which cannot be of two kinds. Hence the matter and the substantial form, or, in general, act and potency, notwithstanding their real metaphysical opposition and distinction, are one essence, one kind, and one being. But let us go back to our author.

In his third article (December, 1873) he says: “The ordinary mechanical explanation of the molecular states of matter, or states of aggregation, on the basis of the atomic theory, proceeds on the assumption that the molecular states are produced by the conflict of antagonistic central forces—molecular attraction and repulsion—the preponderance of the one or the other of which gives rise to the solid and gaseous forms, while their balance or equilibrium results in the liquid state. The utter futility of this explanation is apparent at a glance. Even waiving the considerations presented by Herbert Spencer (_First Principles_, p. 60 et seq.), that, in view of the necessary variation of the attractive and repulsive forces in the inverse ratio of the squares of the distances, the constituent atoms of a body, if they are _in equilibrio_ at any particular distance, must be equally _in equilibrio_ at all other distances, and that their density or state, therefore, must be invariable; and admitting that the increase or diminution of the repulsive force, _heat_, may render the preponderance of either force, and thus the change of density or state of aggregation, possible, what becomes of the liquid state as corresponding to the exact balance of these two forces in the absence of external coercion? The exact balance of the two opposing forces is a mere mathematical limit, which must be passed with the slightest preponderance of either force over the other. All bodies being subject to continual changes of temperature, the equilibrium can at best be but momentary; it must of necessity be of the most labile kind” (p. 223).

This argument against the atomic theory would be very good, if its premises were not deceptive. Mr. Stallo, unfortunately, relies too much on the terminology of physical writers, which is not always correct. Thus, it is not true that the solid form is the result of an actual preponderance of attraction between the molecules. If attraction prevailed, the molecules would not remain in their relative position, but would move in the direction of the attraction. The truth is that molecules, whether in the solid or in the liquid form, are in equilibrium of position; accordingly, neither attraction nor repulsion actually prevails between them.

Their position of equilibrium is determined by their own constitution, and may change; for the molecules admit of accidental changes in their constitution. Hence the distance of relative equilibrium is not necessarily constant, but changes with the change of state of each molecule. This shows that bodies, whether solid or liquid, can retain their solid or liquid form while subjected to considerable molecular changes, and that therefore neither the solid nor the liquid form is necessarily impaired by “the changes of temperature” or other molecular movements. The molecules of bodies attract each other when their distance is great, and repel each other when their distance has become very small; whence we immediately infer that there is for every kind of molecules a distance which marks the limit of their mutual attraction and repulsion, and that at such a distance the molecules must find their position of equilibrium. A body will be solid when, its molecules being in the position of relative equilibrium, from a small increase of their distance an attraction arises, which does not allow of the molecules being easily separated or arranged in a different order around one another. A body will be liquid when, its molecules being in the position of relative equilibrium, from a small increase of their distance a weak attraction arises, which allows of the molecules being easily separated or easily arranged, without separation, in a different manner around one another. A body will be expansive and fluid when its free molecules are at a distance sensibly less than that of relative equilibrium, and therefore repel each other, and are in need of exterior pressure to be kept at such a distance. But we must not forget that the distance of relative equilibrium varies with the intrinsic dynamical variation of the molecules, and that therefore “the exact balance of the two opposing forces is _not_ a mere mathematical limit,” but is comprised between two mathematical limits determined by the amount of the variations of which each species of molecules is susceptible before settling into a different form.

Having thus disposed of the main argument by which the author wished to show “the utter futility” of the ordinary mechanical explanation of the molecular states of matter on the basis of the atomic theory, we may add a few words concerning Herbert Spencer’s argument alluded to by the author. The law of actions inversely proportional to the squares of the distances is true for each primitive element of matter, but it is not applicable to molecules acting at molecular distances, as we have proved in another place.(184) Hence Spencer’s argument, which assumes the contrary, is entirely worthless. On the other hand, were the argument admissible, we do not see how the proposition, “The constituent atoms of a body, if they are _in equilibrio_ at any particular distance, must be equally _in equilibrio_ at all other distances,” can justify the conclusion that “their density or state must be invariable.” It seems to us that a change of molecular distances must entail a change of density; but, of course, we are behind our age.

_Relativity of material realities._—“It has been a favorite tenet, not only of metaphysicians, but of physicists as well, that reality is cognizable only as absolute, permanent, and invariable, or, as the metaphysicians of the XVIth and XVIIth centuries expressed it, _sub specie æterni et abroluti_. This proposition,” Mr. Stallo continues, “like so many others which have served as pillars of imposing metaphysical structures, is the precise opposite of the truth” (p. 223). Do you understand, reader? Metaphysicians and physicists of all centuries count for nothing; they were blind, every one of them; but a great luminary has appeared at last, a Mr. J. B. Stallo, whose superior wisdom, if not philosophical infallibility, opens a new era of thought, and dispels the darkness which has been thickening around us up to the present day. Yet even the sun has spots; and Mr. Stallo will permit us to remark that his statement of the metaphysical doctrine of the ancients is not altogether correct. They did not teach “that reality is cognizable _only_ as absolute, permanent, and invariable”; they well knew and taught that there were realities cognizable, both relative and changeable. Substance, of course, was considered by them, and it is still considered by us, as an absolute reality; but they never imagined that the essence of such a reality was cognizable except through its constituent principles as related to one another, and therefore through an intelligible relation. This relation, as intelligible, was considered necessary and invariable, but, as an actual reality in nature, was considered contingent and changeable; the intelligible essence of things was known _sub specie æterni_, but their existence was known _sub specie contingentis_. Now, on what ground does Mr. Stallo impugn this doctrine? How does he prove that it is “the precise opposite of truth”? Alas! we should be exceedingly simple were we to expect proofs. Progress consists nowadays of stout assertions on the part of the writer, and of a silly credulity on that of most readers. Hence our author, instead of proving what he had rashly asserted, gives us a strain of other assertions equally rash and ridiculously absurd.

He says: “All material reality is, in its nature, not absolute, but essentially relative. All material reality depends upon determination; and determination is essentially limitation, as even Spinoza well knew. A thing ‘in and by itself’ is an impossibility” (_ibid._) Spinoza! a great authority indeed! But we should like to know how the proposition, “Determination is essentially limitation,” can lead to the conclusion that “a thing in itself and by itself is an impossibility.” To make a logical connection between the two propositions, it would be necessary to assume that “nothing finite can be in itself and by itself.” But the assumption is so foolish that even Spinoza, who based on it his revolting system of Pantheism, could never support it except by a false definition of substance, and by giving to the phrases “in itself” and “by itself” an extravagant interpretation, which proved, if not his malice and bad faith, at least his profound philosophical ignorance. Let Mr. Stallo consult any good philosophical treatise on this subject, and he will see how stolid a man must be to fall a victim to the gross sophistry of the Jewish dogmatizer.

What shall we say of the other assertion, “All material reality is, in its nature, not absolute, but essentially relative”? Can anything be _relative_ without at the same time being _absolute_? Can relation exist without two absolute terms? Relativity connects one absolute thing with another; the things thus connected acquire a relative mode of being, but they do not for that lose their absolute being. Thus Mr. Stallo may be an American citizen without ceasing to be a man, though he cannot be a citizen without being endued with a relation not involved in his nature as roan. So, also, husband and wife are essentially relative; yet we hope the author will not say that the relative _Husband_ annihilates the absolute _Man_, or that the relative _Wife_ excludes the absolute _Woman_.

These remarks apply to all relations, whether merely accidental or founded in the essence of things. Pantheists imagine that creatures cannot have any absolute being, because their being is essentially dependent, and therefore relative. They should consider that a creature is a _created being_—that is, a being related to its Creator. Such a creature, inasmuch as it is a being, _is_; and inasmuch as it is related, _connotes_ its Maker. Now, to be and to connote are not identical. The first means _existence_, the second _dependence_; the first is perfectly complete in the creature itself, the second is incomplete without a correlative term; and therefore the creature is in possession of absolute being, while it is endued with an essential relativity. Take away the absolute being; nothing will remain of which any relativity may be predicated.

Perhaps the author, when pronouncing that “all material reality is in its nature essentially relative,” alludes to the essential constitution of material realities, and to the essential relation of matter and form. If such is his meaning, the utmost he can claim is that the reality of the form is essentially connected with the matter, and the reality of the matter essentially connected with the form. This every one will concede; but no one will infer that therefore the reality which results from the conspiration of matter and form is not an absolute reality. For as the matter and the form are the principles of one essence, and as their mutual relativity connotes nothing extrinsic to the same essence, but finds in it its adequate consummation, it is evident that the resulting reality is intrinsically complete, and subsistent in its individuality. Hence this resulting reality is an _absolute_ reality; and only as such can it become the subject of relativity, and acquire the denomination of _relative_.

Our author, entirely taken up by Spinoza’s views, proceeds in the following strain: “All quality is relation; all action is reaction; all force is antagonism; all measure is a ratio between terms neither of which is absolute; every objectively real thing is a term in numberless series of mutual implications, and its reality outside of these series is utterly inconceivable. A material entity, absolute in any of its aspects, would be nothing less than a finite infinitude. There is no absolute material quality, no absolute material substance, no absolute physical unit, no absolutely simple physical entity, no absolute constant, no absolute standard either of quantity or quality, no absolute motion, no absolute rest, no absolute time, no absolute space.... There is and can be no physical real thing which is absolutely simple” (p. 225).

This string of blunders needs no refutation, as no reader who has a modicum of common sense can be deceived by what is evidently false. Yet, as to the assertion that “there is and can be no physical real thing which is absolutely simple,” it must be observed that there are two kinds of simplicity, as there are two kinds of composition. A being is physically simple when it is free from physical composition; whilst it is metaphysically simple, if it has no metaphysical components. Now, God alone is free from metaphysical as well as physical composition; and therefore God alone is absolutely simple. Hence, created beings, though physically simple, are always metaphysically compound.