lowing table, the values of the specific heat s, of the absolute specific heat k, and of the heat expended for internal work i.

If we seek to ascertain in this way the value of k for carbon, we obtain, by taking the atomic weight 12 as a basis, k=0.2, a value which is greater than the value of s heretofore found for graphite and diamond. This circumstance speaks decisively to the effect that, agreeably to Regnault's proposition, we should double the atomic weight of carbon and assume it to be equal to 24; we then have, for the different forms of aggregation of carbon, the values of s, k, and i, exhibited in the following brief table:

The inequality of the specific heat of different forms of aggregation of carbon thus becomes intelligible, from the consideration that at a like elevation of temperature the internal work performed is different, according as we are dealing with diamond, graphite, or charcoal.

In strictness, therefore, the law of Dulong and Petit is, in general, only valid for the absolute specific heat k, which, multiplied by the atomic weight of the element, gives the constant product kp=2.4. The variations which the specific heat of solid elements undergoes, when the temperature is raised, are likewise to be ascribed to a difference in the amount of internal work.

In reference to chemically compounded substances, we have, for ascertaining their absolute capacity of heat K, the equation

P.S
N

(5),

which is found from equation: a if we put K in the place of the experimen

tally determined specific heat S, and the absolute specific heat of the element 2.4 in the place of a. From equation (5) results K=2.4 4.

N
Ρ

For water, for instance,

3

18

we have N=3, P=16+2=18; hence K=2.4 0.4; thus the absolute

From

specific heat of water in a solid, liquid, and gaseous form, is equal to 0.4. these premises we obtain, for the quantity of heat i, which, by an elevation of temperature of 1° C., is expended in internal work,

THE THERMIC MOLECULAR MOTION.

From the equivalency of heat and labor it undoubtedly results that every development of heat by mechanical means must be regarded as the transformation of a bodily motion into a molecular motion; and, conversely, that every performance of work must be considered a transformation of the molecular motion into a bodily motion. This view constitutes the starting point of the mechanical theory of heat, of which the most essential principles, together with some of the most important consequences springing from them, have been discussed in the preceding paragraphs, without reference, however, to the conception which we must form of this molecular movement, whose results are the different phenomena of heat.

For the completion of the mechanical theory there is certainly needed an hypothesis respecting the nature of this molecular action, although many important questions may be and have been solved without one. In the mean time the construction of such an hypothesis has exercised the ingenuity of different physicists, especially of Clausius, Krönig, and Redtenbacher.

Krönig and Clausius (Pogg. Annal., XCIX and c) suppose that the minute molecules of gases and vapors, mere points in proportion to the intervals which separate them, move on with a constant velocity, in right lines, until they impinge against another molecule of the same nature, or against some object to them impenetrable. The pressure of gases against a solid surface is supposed to result from the fact that the molecules in great number continually impinge against the resisting surface and rebound from it. By an increase of temperature the velocity with which the molecules move is augmented; and, in fine, the temperature is assumed to be proportional to the square of that velocity.

In the case of solid bodies, the molecules oscillate about a permanent point of equilibrium; while in the case of fluids this point of equilibrium does not exist; but the molecules, notwithstanding their constant and manifold movements, are restrained to determined distances, and cannot, like the gases, move freely apart from one another.

While the savants just named seek the causes of the phenomena of heat in a movement of the atoms themselves of bodies, Redtenbacher considers the oscillations of the atoms of the ether enveloping the atoms of a body to be the source of those phenomena, as he has explained in his "Dynamiden system," (Manheim, 1857.)

A circumstance which speaks with much force in favor of the views of Krönig and Clausius is that through these views the difference between radiant and sensible heat admits of easy explanation. The former would thus appear to be propagated in a precisely identical manner with the rays of light, by a undulatory movement of the ether, while a vibratory movement of the ponderable atoms of the body would be the source of sensible heat.

The development of the mechanical theory of heat has, within a few years, made such progress that it must soon stand in the same grade with the undulatory theory of light. In proportion, at the same time, as the mathematical theory is advanced towards completion, will it become more and more practicable to reduce the explanation of the particular phenomena of heat, in a generally intelligible form, to the principles of the mechanical theory.

CONTINUOUS VIBRATORY MOVEMENT OF ALL MATTER, PONDERABLE

AND IMPONDERABLE.

BY L. MAGRINI, OF THE MUSEUM OF FLORENCE.

Translated for the Smithsonian Institution.*

It would be at once curious and instructive, could we unite in one point of view the different reflections of mankind on the phenomena of nature. What variety in ideas! what differences among men! what contrasts between nationalities! If the paths which the human mind pursues could be clearly traced, and it were possible to examine them, we should perhaps discover the reasons which cause men at one time to affirm, as if with intuitive certainty, a principle pregnant with consequences, destined to be confirmed by facts, while at other times they hesitate, go astray, and lose the truth even when earnestly seeking it.

Our senses, even with the help of the most perfect instruments, reveal to us but very little about nature; but the sensations derived from the impressions made on our organs by exterior objects are transmitted to the understanding, which co-ordinates them and draws from them the most rational and rigorous deductions; the small number of facts which our senses thus teach us, afford us the best means of extending our knowledge regarding the external world. We might repine, with some justice, at the imperfection of our senses: our ears might be more impressible, our sense of smell more susceptible; our sight might be even more piercing than it actually is with the aid of optical instruments. Yet it is not difficult to convince ourselves that it is not the senses which deceive us, and that the error proceeds from the deductions formed by the understanding.

An oar, piercing obliquely a horizontal surface of water, appears to us to be broken at the point where it issues from the water. The eye really receives the impressions of the light as if the oar were broken. But if our mind were to conclude from this optical phenomenon that we beheld a broken oar, it would not be the eye which was in fault, but the understanding, which deceives itself by a conclusion without verifying the other characters of a broken oar. The philosophers who impute error to the eye ought, on the contrary, to regard this indication as a signal service; since, without touching on other propertiesthe knowledge of which does not pertain to its province-the eye does in fact faithfully represent to us the real course of the luminous rays which pass from the water into the air.

This example, and a multitude of others of the same kind which might be cited, teach us that it is very difficult for us to pronounce a correct judgment in taking our first sensations as a basis. It is necessary to wait till new facts add themselves to the old, and disclose the relations which lead to the common principle of all the phenomena of the same order. Mathematical truths are pure conceptions which obey the necessary laws of reasoning; it is not the same case with the physical sciences, the study of which rests not on axioms furnished by reason, nor on principles which can be directly drawn from the understanding. Nature presents us complex phenomena which we must examine minutely, in order to analyze them and discover their cause; if we would not deviate from reality and truth, we must accept the descriptive language of the sensations. The sensations furnish us the data, and the tendency which we have to attribute them to external causes, conducts us from analogy to principles. In reality, the

* From Revue des Cours Scientifiques: Paris, No. 49, Nov. 2, 1867.

world is composed of objects which we know only by the impressions they produce on our senses. Matter is the unknown principle of which they are formed, the cause of the properties which they manifest, and of the sensations which reveal them to us. But when we wish to study an object, it is proper to commence by defining it; we should therefore ask ourselves, first of all, what is the true constitution of matter?

In considering the scale of magnitudes and the extreme divisibility of bodies, we find that we can form two hypotheses on the constitution of matter. We may admit that it is divisible to infinity, and consequently conceive of a body as a continuous mass, as a veritable geometric solid; or again, we may suppose that by continuing to divide more and more the fragments of a body, we shall arrive at an ultimate particle-an atom. On this last hypothesis, matter would be but an assemblage of atoms, grouped in distinct elementary molecules, placed one beside another without touching, and endowed with the faculty of approaching to or withdrawing from one another.

If we interrogate chemistry before making a choice between these two hypotheses, it will reply that if matter is continuous, that is to say, not capable of being resolved into indivisible elements, the idea of chemical combinations becomes essentially obscure. On the contrary, all the known laws of combination become evident consequences, logical corollaries of the hypothesis which considers matter as formed by the union of a great number of small indivisible masses; it is easy, in effect, to comprehend that the atoms of two simple bodies may, in uniting, form mixed molecules and give rise to new bodies.

The propagation of heat and of light in the Torricellian vacuum and in the planetary spaces, compels us to admit the existence of another highly subtle species of matter, infinitely more diffused and universal than ponderable matter, and which we are led to consider as the principal agent of physical nature.

We shall endeavor to prove, on this occasion, that movement is a fundamental property of matter in whatsoever state it exists, ponderable or imponderable; and if movement exists to-day in all the particles of matter, it has, of necessity, always existed. Without movement it is impossible for our mind to conceive any modification whatever in the state of things. No action of bodies can be manifested without our being able to affirm that this action consists in a particular mode of movement. We shall proceed, as those who transport themselves to some elevation in order to embrace the view of a vast region, to cast a comprehensive glance on the phenomena offering more particularly the proof of the interior movement which constantly animates the molecules. Let us remark at once, that this movement is for us an ultimate fact, of which as yet we know not the reason.

Celestial mechanics has explained all the perturbations of the movement of the planets, by admitting the necessary presence of unknown orbs at the limits of the solar system; observation has verified the existence of those bodies. Thanks to numerous and complete verifications of this kind, mechanics has succeeded in rendering extremely probable, not to say absolutely certain, the principle of gravitation, and in establishing in a definitive manner the law of Newton. The law of continuity in nature forces us to admit that the same principle extends to all that exists; it governs the constitution and movements of celestial bodies; it binds the satellites to their planets and the planets to the sun; it controls all the bodies which revolve one around another within a determinate radius; it also acts on each molecule, on each atom, at minute distances which escape our gross senses and all our means of direct observation.

[The name gravitation has been given to that force or tendency of masses to approach each other with an intensity which varies inversely as the square of the distance and directly as the quantity of matter. The force which acts between the particles, though perhaps of the same character, is governed by a different law, and hence has received a different name, that of cohesion.-J. H.]

But if the dimensions of molecules are extremely small, the distances which separate them are relatively very great, insomuch that, according to the sugges tive idea of Laplace, a molecule may be compared to a star, and molecular gravitation to universal gravitation. It results from this that the movements of molecules may be compared to the movements of the stars, and it is thus that modern physics has raised itself to the height of mechanics. It is interesting to see a solid body suddenly obey the laws of attraction at the moment when it enters within the sphere of influence of a liquid; the effect is still produced when the liquid does not moisten the solid.

Cohesion, which may be considered a modification of gravitation, acts with different degrees of intensity on different bodies. All the degrees of intensity which separate the least dense fluid from the most condensed solid, form only some of the intermediate terms of an indefinite series, of which the ultimate parts, eminently solid, the ponderable atoms represent one of the extremities; at the other are found the matter of the nebula and the molecules of the ether itself. It is these ponderable atoms, subject as they all are to the attraction of the neighboring atoms and to that of the ether which surrounds them with a species of atmosphere, that produce thermal, electrical, and optical phenomena.

Under the relatively variable influence of these phenomena, bodies must continually undergo modifications in their internal structure. In effect, what varieties of forms invest quartz and feldspar in their slow and gradual passage from a vitreous to a tophaceous state! And not only stones, originally resistant, which become friable, but flexible substances which become more and more rigid; calcareous concretions which from a fibrous texture acquire a lamellar texture; siliceous incrustations, primitively friable, which are transformed into a fibrous tissue, &c.; are there not here positive proofs that, even in the most compact bodies, the molecular grouping undergoes incessant transformations? In these continual transformations, we cannot neglect the action of gravitation. Pictet has evinced it by showing the shortening which a metallic rod undergoes by resting vertically on its lower extremity. It is known, also, that the sheets of lead with which the roofs of certain buildings are covered grow thinner with time in their upper part, and become denser in their lower part. Hence it results that the particles of a metal tend, like those of & liquid, to place themselves on a level, by yielding slowly, but in a continuous manner, to the force of terrestrial gravitation.

Oil placed in a mixture of water and alcohol, having the same density with itself, is subject only to the molecular attraction of its own matter, and of the medium in which it displaces its bulk without mingling therewith. It maintains. itself in equilibrium and keeps the position in which it is placed; being thus withdrawn from the terrestrial gravitation, it takes the spherical form which satisfies all the conditions of a force acting equally in all directions.

Among the expedients which enabled M. Plateau to obtain a certain number of geometrical figures under the influence of the molecular attraction, I will cite one which led to effects truly curious. If, through one of the small spheres of oil placed in a mixture of water and alcohol, we pass a small metallic rod, to which we communicate a rotary movement, this movement is suddenly transmitted to the whole mass of oil. The little sphere, by virtue of the centrifugal force, becomes flattened in proportion as it revolves more rapidly. Such is also the cause to which we usually attribute the flattening of the terrestrial sphere. When we continue to increase the velocity of rotation, the flattening is enhanced to such a degree that the sphere grows hollow, and of a sudden separates into two parts: the interior part, which is a sphere, remains at the centre of the second part, which has the form of a ring. It is impossible to witness the forma tion of this ring without recalling that of Saturn, which doubtless must have formed itself after the same manner. Thus the same cause which gives rise to the limpid drops of dew which sparkle on the leaves of plants, and which com