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show such a pressure-effect produced by atomic motion, where elastic rings are converted into the hexagonal forms of crystals. Cohesion (as now is generally supposed) is only gravitation * by contact. From the above considerations, it becomes easy to understand that elastic crystal forms can sometimes change into non-crystalline forms ; so some crystallizable metals, such as iron and zinc, lose all crystalline structure by rolling and hammering, and become ductile. Crystalline sulphur can, by mere warming, pass over into a sort of indiarubber sulphur. It is evident in fact that the irregular arrangement of the elastic molecules of a substance favours the gliding of the molecules over each other ; while, on the other hand, the regularly arranged molecules which are in contact at their boundaries (corresponding to crystalline structure) cannot be displaced at all without separating entirely : take for instance crystallized cast-iron and some other metals.

The freedom allowed to the molecules to arrange themselves in the case of solutions may be favourable for the production of crystalline structure, while rolling, hammering, &c., manifestly forces the molecules to aggregate in an irregular

When elastic molecules of very open structure cross each other irregularly in all directions, or are arranged in parallel layers (as produced by the rolling of a metal), then it becomes obvious that a subsequent displacement of the molecules, as by a tensile-stress for example, does not necessarily produce actual severance ;

but the atomic streams—from the very nature of this cause-can easily produce contact in fresh places, and so a gliding of molecules over each other is possible, without separation. So a bar of malleable iron gradually lengthens itself under a tensile-stress. On the other hand, because crystalline structure prevents all gliding of the molecules, it becomes impossible in this case for the atomic streams to cause contact in fresh places. The attempt to stretch a cast-iron bar, then, means separation of the molecules. I will not pursue these considerations more at length here : they may well be thought out into greater detail.

It may just be remarked, in passing, how elastic rings, fig. 2, can at first repel each other, merely on account of their elasticity of form ; and how in fig. 3, if the molecules are made to approach closer by force, this has as a consequence

* A fact observed by Prof. Dewar may be favourable to this view. The cohesion of metallic wires does not diminish rather the contrary) by a cold of – 180° C. that of liquid oxygen. Now cooling of the metal could manifestly have no influence on the atomic streams, which are independent,

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that the pressure of the atomic streams over the enlarged surface of contact overcomes the elasticity of form, and the Fig. 2.

Fig. 3.

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molecules cohere (which one calls “ attraction”). As the converse of this, when the molecules are by a tensile-stress pulled nearly apart : then their elasticity of form can make the molecules suddenly spring apart of themselves, as, for instance, " unbreakable” glass flies into dust, when the molecular equilibrium is upset by a very sharp blow. Also, in general, if something is broken, the pieces will not readily unite of themselves, when placed in contact. The natural elasticity of shape of the elastic molecules causes an initial repulsion. By suitable assumption regarding thickness, stiffness, &c., of these ring-like molecular forms, the differences between the “chemical affinity” of different molecules might doubtless be accounted for.

Some may think that the above considerations are too simple to contain truth. Nevertheless one may rightly ask whether it is not precisely simplicity that one in general seeks in mechanism ? The elucidation may serve as initial explanation of certain obscure facts, which may develop itself further.

Respecting the elasticity of molecules (or atoms) Lord Kelvin makes the following observation :

“We are forbidden by the modern physical theory of the conservation of energy to assume inelasticity, or anything short of perfect elasticity, in the ultimate molecules” (Phil. Mag. May 1873, p. 329).

The conception of elastic molecules (also illustrated in a striking manner by spectroscopic observations) appears, as said, to be a very practical conception for Physics, which is much needed. By this assumption the almost inconceivable idea of the sharp blows of "infinitely hard” molecules is avoided. On account of the perfect elasticity, all motions take place with “elegance" and smoothness, which permits a mobile equilibrium in nature, and (without due precautions) may well deceive the senses into the idea that in so-called space” all is in repose.

It is a known consequence of the Newtonian law of gravitation, that the increase of attraction by diminution of distance is so small that two massive bodies, when they touch

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each other, attract each other so much the less the smaller they are ; which one at once sees in the case of two spheres in contact, and can also demonstrate for bodies of other shapes. It, therefore, one attributes a massive structure to molecules, then, for the explanation of cohesion and chemical affinity. forces must be assumed which, by diminution of distance, increase quicker in intensity than according to the Newtonian gravitation law. On the other hand, the attraction of two cylinders of finite length and infinitely small section becomes infinitely great so soon as they touch each other. It is possible, therefore, on the basis of the here assumed open structure of matter, also to account for cohesion, adhesion, and chemical affinity, without necessarily having recourse to forces which, with diminished distance, augment quicker in intensity than the Newtonian law of gravity demands.

The Theory of Isenkrahe. Two years after the present writer's first published paper, appeared the gravitation theory of Dr. Isenkrahe*, which attempts an explanation of gravity based on the kinetic theory of gases, and which seems in Germany to have become very well known. The author of this theory makes no mention of my theory, and it doubtless escaped his attention at that time.

The gravitation theory of Dr. Isenkrahe is founded on inelastic collision, which obviously involves the annihilation of energy, whereby the gas producing gravity would, after a certain (even very long) epoch, come to rest, and so gravitation cease to exist.

In a plausible enough way (at first sight at least) the author despises elasticity as a qualitas occulta, which, as he thinks, needs an explanation just as much as gravity itself. It seems, however, to have been overlooked that elasticity (at the encounters of molecules) is already demonstrated to exist by the principle of the conservation of energy, and of the centre of mass. The explanation of elasticity is a deeper one than the explanation of gravitation : therefore let us advance from step to step forward in the elucidation, without pushing on in too great a hurry.

All the consequences of the kinetic theory of gases are already built on the assumption of elasticity : the application of this principle to the smaller particles is therefore to be viewed as a perfectly natural and logical consequence. In fact the gravitation pressure by the encounters of elastic particles is explained quite as completely as the air-pressure is explained by the encounters of such particles (molecules). If one only accepts as valid the two principles of the conservation of energy and of the centre of mass, then one must attribute elasticity as well to the ather as to gas molecules, without being troubled about the further explanation of its nature.

* Das Räthsel von der Schwerkraft, by Dr. C. Isenkrahe. (Vieweg & Sohn, Braunschweig, 1879.)

Therefore I have without hesitation regarded molecules of open structure as elastic, which implies that by the impact of such molecules no energy is annihilated. Dr. Isenkrahe regards the molecules of bodies as absolutely hard solid spheres which, in order that gravity by atomic encounters (i. e. its proportionality to mass) may be explained, must be far apart from each other. How can one imagine to oneself a structure composed of perfectly hard molecules situated far apart which shall have only tolerable stiffness and stability ? Such a body made up of widely separated spherical molecules, if no other forces but gravity acted, could at the most behave like a gas, but never as a solid or liquid body.

On the other hand, elastic molecules of open structure may be made to cohere at their boundaries by the pressure of the smaller atoms, which at the same time easily fly through the open parts of the structure. Have we not here at least a groundwork for the conceptions upon which we may hope to build further ?

Dr. Isenkrahe gives no limits for the value of the mean length of path, whereas it seems to me to be a very important point of my theory, that the mean length of path must be assumed great in comparison with the planetary distances.

Concerning the calculations which Dr. Isenkrahe attaches to his theory, Dr. A. M. Bock, who made the theory of Isenkrahe the basis of his ‘Inaugural Dissertation'*, expresses himself as follows:

"The aim and the purpose of the atomic æther theory, namely to construct universal gravitation, is, as mentioned in the introduction to the Räthsel von der Schwerkraft, not fully attained. There is no formula deduced from which, as a starting-point, one could follow out the theory further. One sees oneself forced therefore, in the sense of ihe theory, to deduce an (if only in some measure rigorous) expression for the attraction (p. 18, under the paragraph-title Die Anziehung zweier Körper).

On the developments and modifications which Dr. Isenkrahe's calculations received through Dr. Bock I allow myself

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* Wolf & Sohn, Munich, 1891.

no opinion. The bases of them are nevertheless quite unaltered, and therefore open to the same objections ; namely, he sets himself in contradiction with the principle of the conservation of energy, which, moreover, Dr. Bock himself admits.

Hamburg, 1894.

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APPENDIX (added Jan. 1895).-All who have thought on the subject know that, in the case of a falling body, the motion generated comes from the æther, according to any dynamical explanation of gravitation : and when the body strikes the earth's surface, shaking its molecules into vibration by the concussion, these ("heat") vibrations develop waves in the æther, or are “ radiated” away. So we have a cyclical process here, where motion passes from a material agent and back again to that agent, in a circle.

In accordance with the above we see, then, that stars or stellar suns do not "pour their heat unrequited into space," but return their stores of motion to the source whence they were obtained. For if gravity be caused by a material agent, and if solar energy be derived from gravity, then manifestly solar energy is returning only to its original source, to be again available for generating heat (through gravitation) in some other regions of the universe.

Evidently, if chemical action be caused by a material medium, then an animal or a steam-engine lifting a weight is an instance (again) of motion coming from a material substance, and going back to it in a circle at the same time. A locomotive, as we know, converts all its energy into heat (which is radiated into the æther) as it progresses with its train: so clearly we have the cyclical process of exchange of motion again here: the same being true of work derived from falling water (cataracts) or from winds. If, finally, one pure speculation be permitted, we might suggest that overgrown stars may, towards their centres, become from excessive compression inadequately penetrable by the atoms of the æthereal gas, and so the overgrown masses be broken up by conversion of the æthereal motion into heat. Thus cyclical change would apply to the Universe generally: the stellar bodies constituting in sum a gigantic grained gas inside an excessively fine atomic one. For the tentative development of this idea, a paper in the Philosophical Magazine, August 1879, also Sitzungsberichte, April 1883, Vienna, may be mentioned. So it appears that the Universe may at present in the same sense as a gas is) be in equilibrium of temperature.

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