are at rest in solid bodies, and also in liquids; but there is no resting place for them between the solid and the liquid state. Therefore, between the first attractive and second repellent forces there is a sphere of forces in Unstable Equilibrium.

If heat be applied to a liquid it is expanded—that is, its atoms are forced further apart. As the heat is increased the liquid is expanded more and more, until the atoms are separated beyond the limits of the action of the second sphere of attractive force; when they instantly are violently thrust apart, several hundred times as far as they were before, and the liquid becomes a gas. Experiments on gases show the following facts:

1. They may be diminished in bulk by pressure.

2. Increased pressure produces increased diminution, until, in some cases, the gas becomes a liquid again.

3. As the pressure is removed, the gas recovers its original bulk.

4. If all pressure be removed the gas continues to expand, as far as experiments have been made. Here we find evidence of a third sphere of repellent force.

Reasoning here as in the case of the transition of matter from the solid to the liquid state, there must be a position of equilibrium between the second attractive and third repellent forces; but, as the forces act away from the position of equilibrium, the equilibrium must be unstable and the atoms cannot rest at this distance apart. Thus, experiment demonstrates the existence of two other concentric spheres of force, namely, A second sphere of forces in Unstable Equilibrium, and a third Sphere of Repellent Force.

Great as has been the relative separation of the atoms in passing through the changes described, they are still separated by only inappreciable distances. All the spheres of forces already described act within a containing sphere so small as to be invisible, even by the aid of the most powerful miscroscope. But all experimenters concur in the fact that, at sensible distances apart, all atoms attract each other. Hence there must be, between the third repellent and third attractive spheres, a third sphere of equilibrium. This is shown in the figure. The heavy lines indicate repellent forces. As the third repel lent and attractive forces of both atoms operate toward this FOURTH SERIES, VOL. XXV.-41

third position of equilibrium it must be stable, and the atoms can rest in this position.

Matter, with its atoms sustaining this relation to each other, has never been experimented upon; but there is a satisfactory evidence of its existence as an exceedingly attenuated interstellar medium. It is this medium which transmits light and other forces from the sun and stars. But the phenomena of light demand, for their existence, that the contiguous atoms of the transmitting medium be nearer together than any sensible distance. Therefore this interstellar medium is an instance of matter whose atoms are separated by their third spheres of forces in stable equilibrium.

Collecting now the results from the beginning, we have: 1. Every atom of matter is endowed with a Force nature. 2. The force is in four conditions: Repulsion, Attraction, Stable, and Unstable Equilibrium.

3. The forces act through spaces which may

by hollow concentric spheres or spheroids.

be represented

4. These forces are grouped in three sets, of three forces in each set, arranged invariably in the following order from the center: Repellent, Stable Equilibrium, and Attractive.

5. The middle set is separated from each of the others by a sphere of forces in unstable equilibrium.

In addition to these eleven spheres of force there may be others, binding the bodies of the universe together in groups separated by other spheres of balanced forces, in such a manner as to render impossible any "crash of worlds" of greater magnitude than that of the bodies of the same planetary system. The probability, or even the necessity, for such balancing of forces will not be discussed in this paper.

Scientific men consider it "difficult to correlate force with matter." Is it not justifiable to go a step further and consider it impossible? Can there be any impropriety in saying that every atom of matter has an immaterial nature? This nature cannot be a resultant, but is rather an endowment of matter, if it be not matter itself, as is much more probable. It is not enough to say that this immaterial nature is force. It is

rather a definitely organized system of forces having reference to definite ends.

The preceding experiments and deductions furnish at once the following definitions:

1. When the atoms of a body are separated by their first spheres of forces in stable equilibrium, the body is a solid. 2. When the atoms of a body are separated by their second spheres of forces in stable equilibrium, the body is a liquid.

3. When the atoms of a body are separated by their third spheres of forces in stable equilibrium, the body is an etheroid. (Interstellar matter.)

4. When the atoms of a body are separated by their third spheres of repellent force, the body is a gas. It is only external pressure which prevents a gas from becoming an etheroid.

The following diagram presents a linear segment of the eleven spheres of force, in their relative positions. The arrows denote the directions of the action; the spaces between their points denote the positions of stable equilibrium; the other spaces denote the positions of unstable equilibrium.

Since a liquid occupies only a little more space than the solid from which it was derived; a gas, many hundred times the space of the liquid from which it was derived; an etheroid, many million times the space of the gas from which it was derived, it follows that the thickness of the force-shells rapidly increases outward. While the whole space occupied by ten of the concentric spheres is inappreciable to the senses, the eleventh extends beyond the limits of our solar system.

Let it be remembered that not one of the preceding propositions is merely theoretical. Every one of them is the general statement of a fact, proved by direct experiment. A few additional facts, which all experiments concur in establishing, will now be given :

1. The spheres of force are mutually interpenetrable.

2. All these forces surround every atom, at all times and under all circumstances.

3. In the same kind of atoms they are identical in every particular.

4. In atoms of different kinds they differ in one or more of the following particulars: The thickness of the force-shell; the amount of the force; the tension of the force; the distribution of the force.

The amount and distribution of the force may be illustrated by the diagrams below, where the width of the figure represents the amount of the force, and the form represents the distribution.

1. The apex represents the position nearest that of equilibrium. In these illustrations the increase is uniform, but much more rapid in A than in B. They differ in quantity only.

2. In this case the force increases slowly at first,

^^ then more rapidly.

Λ

3. Here the increase is rapid at first, then more slowly.

The three cases differ from each other in the distribution of the force.

An effort may now be made to ascertain whether the results obtained can contribute any thing toward answering the question, What causes the properties of matter? A few examples, showing how the spheres of force must produce the properties which matter actually exhibits, will be sufficient to show the manner of applying what has been done to the solution of the question. The application is chiefly to solids.

1. If the shell of repellent force be thin, there will evidently be more atoms in a given space, and the body must be dense.

2. If the force increase "rapidly at first" it will be difficult to press the atoms nearer together, and the body must be hard.

3. If both the attractive and repellent forces be strong and increase "rapidly at first," the body will strongly resist tension and pressure, and must be hard and strong.

4. If, in addition to the last, the shell of equilibrium be thin, the atoms can be moved only a short distance with regard to each other without being torn asunder, and the body must be also brittle.

5. If the shell of equilibrium be thick, the rest as in the last

case, it is evident that the atoms may have considerable motion with regard to one another without parting, and the body must be not only dense, hard, and strong, but also malleable, flexible, and inelastic.

6. If both the repellent and attractive forces increase "slowly at first," the atoms may be pressed nearer together or drawn further apart easily, and the body must be elastic to both traction and pressure.

7. If the attractive force be weak and its shell thip, the atoms will be easily driven beyond the distance of unstable equilibrium, and the solid must be easily fusible.

8. If the attractive force be weak and its shell thick, the atoms must separate further before escaping from it, and the body will, before melting, greatly expand and soften.

9. If the tension of all the forces be such as to harmonize their vibrations easily with those required to produce white light, such vibrations will be easily transmitted through the body, and it must be transparent and colorless.

10. If the force vibrations can harmonize easily only with those required to produce one color, as red, blue, etc., such vibrations only will be transmitted, and the body must be transparent and colored.

11. If the outer forces of the atoms have a tension which harmonizes with the vibrations which cause only one color, and the inner ones, owing to their action upon one another, can harmonize only with another color, the one set of vibrations must be reflected and only the other set transmitted; and the body must therefore be transparent, but will be of the one color by reflected light, and of the other by transmitted light.

12. If the outer forces can harmonize with all light vibrations, and the inner ones, owing to their mutual interferences, with none, the body must be opaque and white.

13. If the outer forces can harmonize with only some of the light vibrations, and the inner ones with none, the body evidently must be opaque but colored.

14. If none of the forces can harmonize with any light vibrations, the body must be black.

15. If the sphere of stable equilibrium of one kind of atom can be forced, with its atom, inside of the corresponding sphere