Sphere of action.—The next question is: Has matter a sphere of action? That is, Does a primitive element of matter act around itself with equal intensity on all other elements equally distant from it?
The answer must be affirmative.
And first, since the active principle of material substance is destined, as above stated, to produce local movement, it is evident that its action must proceed from a term marking a point in space, and reach other terms marking other similar points. Local movement, in fact, cannot be produced, unless the term acted on be determined by the agent to follow a certain direction; for the direction of the movement must be imparted by the agent which imparts the movement. Now, the direction of the movement, and of the action which causes it, cannot evidently be conceived without two distinct points, the one marked in space by the agent, the other by the patient. Hence the exertion of the active power of matter necessarily proceeds from a point in space to other points in space. Whether such points be rigorously unextended and mathematically indivisible we shall inquire in another article; our object at present is only to show the necessity of a local term from which the direction of the action has to proceed towards other local terms.
This being understood, we can now show that the point from which the action of a material element is directed is the centre of a sphere of activity, or, in other terms, that the primitive elements of matter act in a sphere of which they occupy the centre. This proposition implies that material elements not only act all around, or in every direction, but also that they act with equal intensity at equal distances. This we show in the following manner.
The earth, the planets, and the sun act in all directions, and the intensity of their respective actions, all other things being equal, depends on their distance from the bodies acted on; so that, all other things being equal, to equal distances equal actions correspond. That such actions really proceed from the earth, the planets, and the sun respectively there can be no doubt. For to no other sources can the actions be referred than to those bodies from which both their direction and their intensity proceed. Now, the action by which a planet is attracted is directed to the centre of the sun, and the action by which a satellite is retained in its orbit is directed to the centre of the planet to which it belongs. On the other hand, the intensity of all such actions varies only with the distance of the planet from the sun, and of the satellite from the planet. Whence we conclude that the actions which we attribute to these bodies are really their own.
Now, if such great bodies as the sun, the earth, and all the planets act thus in a sphere, it is manifest that every particle of matter in their mass acts in a sphere. For the action of the whole mass, being only a resultant of the particular actions of all the component elements, cannot but follow the nature of its components; and therefore, from the fact that the action of the whole mass is directed in a sphere, and has equal intensity at equal distances, we must conclude that all the component actions are similarly directed, and have equal intensities at equal distances. Hence every element of matter has a sphere of action, and acts all around itself with equal actions on all other elements equally distant from it.
This conclusion applies to all matter. For we have proved, on the one hand, that matter cannot act except at a distance, and, on [pg 590] the other, we can show by a general argument that the actions themselves must be equal at equal distances around each centre of activity. It is evident, in fact, that the actions of any material element on any other must be equal when the local relation between the elements is the same. But whatever be the position in space of the element acted on, its local relation to the other element remains the same whenever the distance between them is not altered; for so long as we consider two elements only, no other local relation can be conceived to exist between them than that of distance; and therefore a change of position in space which does not alter the distance of the two elements leaves them in the same relation with one another, however much it may alter their relation to other surrounding matter. Since, then, the elements which are arranged spherically around a given element are all equally distant from it, they are all equally related to it, and are all acted on in the same manner. And therefore all material element acts with equal intensity on all other elements equally distant from it.
The truth of this proposition being very generally acknowledged by astronomers and physicists, we need not dwell on it any longer. We must, however, mention and solve two objections which have been advanced against it. The first is, that the cohesion of the molecules in a certain number of bodies is more energetic in some directions than in others; as in crystals, which are cleavable only in definite planes. This would tend to show that material elements do not always act in a sphere. The second objection is, that the action of the sun and of the planets, on which the demonstration of our proposition is grounded, can be denied. Some modern physicists, in fact, hold that what we persist in calling “universal attraction” is not attraction, but only an ethereal pressure exercised on the celestial bodies; and if this be the real case, the action of matter in a sphere will be out of the question.
In answer to the first objection, we say that elements of matter and molecules of bodies are not to be confounded. The molecule is capable of internal movements, as we have already remarked; and therefore every molecule consists of a number of primitive elements having a distinct and independent existence in space. Hence the action of a molecule is not a simple action, but is the resultant of the actions proceeding from those distinct elements; and it is plain that, if such elements are made to approach the centre of the molecule in one direction more than in another, the resultant of their actions will be greater in one direction than in another, and the neighboring molecules will adhere to each other more firmly in one direction than in another. This inequality of molecular actions does not, however, extend beyond the limits of molecular distances; for, when the distance is great (and we can call great those distances in comparison with which the diameter of a molecule is of no account), all the distinct centres of elementary action may be admitted to coincide with the centre of the molecule, and all their spheres to coalesce into one sphere. And thus at such greater distances all molecules, no less than all primitive elements, act in a sphere.
The second objection rests on the [pg 591] singular assumption that the universal ether, owing to the centrifugal force called into existence by the rotation of the celestial bodies, is reduced, around each of them, to a density directly proportional to the distance from the centre of the rotation. Hence they suppose that the ether which surrounds and presses the earth must be denser on the hemisphere where there is night than on that where there is day, because the former is more distant from the sun than the latter; and they infer that on the former hemisphere the pressure of the ether must be greater than on the latter; which brings them to the conclusion that the earth must move towards the sun with a velocity proportional to the difference between the two pressures. Such is the theory by which some modern thinkers tried to supplant universal attraction. We need not go far to show the utter absurdity of this rash conception, as the most common phenomena and the most elementary principles of mechanics supply us with abundant proofs of its falsity. Centrifugal force is necessarily perpendicular to the axis of the rotation, and is proportional to the radius of the circle described. Hence its intensity, which is a maximum on the equator of the revolving body, diminishes from the equator to the poles, where it becomes = 0. If, then, the ether surrounding the earth (or any other celestial body) acquires by centrifugal force a greater density at a greater distance from the earth, the effect must be greater at the equator than in any latitude from the equator to the poles, and bodies must accordingly have a greater weight, and fall with greater impetus, at the equator than in any latitude. Moreover, all bodies should fall in the direction of the pressure—that is, perpendicularly to the axis of rotation, and not perpendicularly to the horizon. Then, also, the pressure of the ether being proportional to the surface of the falling body, of two equal masses having different surfaces, the one whose surface is greater should fall with a greater impetus. Now, all this is contrary to fact.