Appendix

Constitutions which I assign to heavy bodies and to the gravitational fluid; followed by a mathematical conception and some remarks to fix the ideas of geometers who desire to follow out for themselves the consequences of this mechanism, and who may desire first to know precisely what are the hypotheses from which I claim all the phenomena to follow necessarily. [158]

The Constitution Of Heavy Bodies

Supposition 1. Their indivisible particles are cages

For example, hollow cubes or octohedra. They are, in other words, skeletons of solids of which there is nothing material except the edges.

Supposition 2. The diameters of the bars of these cages are so small.

This is even if supposed that they are increased by the diameter of the gravitational corpuscles (as they must be in order to conveniently evaluate the portion of the atoms intercepted), relative to the distances between the parallel bars of the same cage. All the particles included in the terrestrial globe intercept not the ten-thousandth part of the corpuscles which present themselves to traverse it.

Supposition 3. These diameters are all equal, or if they are unequal their inequalities sensibly compensate each other.

If, for instance, in the smallest portions of matter separately ponderable (which, it has been stated, may weigh one thirty-second part of a grain) the mean diameter of the bars of the one portion does not differ a tenth part from the mean diameter of the bars of the other, then it would follow that in the greatest ponderable masses the mean diameters do not differ by a ten-thousandth part, for every such great ponderable mass is composed of so large a number of indivisible particles that simple chance suffices to almost perfectly effect a compensation of diameters.

Constitution Of Gravitational Corpuscles

1. Conformably to Supposition 2 above, the diameter of the gravitational corpuscle added even to that of the bars of the indivisible particles is so small relatively to the mutual distance of the parallel bars of a single cage that the weight of celestial bodies does not sensibly vary from the ratio between their masses.

2. The gravitational corpuscles are isolated, so that their progressive movements are necessarily rectilinear.

3. They are so thinly scattered-that is to say, their diameters are so small relative to their mutual mean distance-that there are no more than a few hundreds which encounter one another in the course of a thousand years. Hence the uniformity of their movements is never sensibly disturbed.

4. They move in several thousand of thousands of different directions, even counting as one all those which are parallel to the same line. The distribution of these directions may be conceived as follows: First, imagine all the points conceived to lie in different directions strewn upon a sphere as uniformly as is possible, and consequently separated from one another by less than a second of arc; then imagine a corpuscular path radiating from each of these points.

5. Parallel to each of these directions there moves a stream or torrent of corpuscles. Now, in order to give it no more than the necessary size, the transverse section of this current has the same contour as [159] the orthogonal projection of the visible universe upon the plane of this section.

6. The different parts of a single current are sensibly of equal density, either where contemporary portions of sensible magnitude or successive portions occupying sensible times in traversing a given surface are compared. The densities of different currents are also equal.

7. The mean velocity determined in the same manner as the mean density is also sensibly constant.

8. This velocity is several thousand times as great, relative to the velocities of the planets, as is the gravitation of the planets toward the sun relative to the greatest resistances which secular observations permit us to suppose they experience.

For example, several hundred times greater relative to the velocity of the earth than the gravitation of the earth toward the sun multiplied by the number of times the firmament would contain the disc of the sun is greater than the greatest resistance which the secular differences in the length of the year permit us to suppose the earth experiences from celestial matter.

Concept, Which Facilitates The Application Of Mathematics To Determine The Mutual Influence Of The Heavy Bodies And The Corpuscles.

First. Decompose all heavy bodies into equal masses so small as to allow them to be treated without sensible error as attractive particles are treated in those theories of gravitation in which no hypothesis is made as to its cause. In such a small mass the effects of unequal distance and position of its particles relative to those of the mass which is conceived to attract it, and to be attracted by it, may be neglected. Such masses will have a diameter no more than one one-hundred-thousandth as great as the mutual distance of the two masses under examination. Thus the apparent semi-diameter of one as viewed from the other does not exceed one second.

Second. For the surfaces of this mass, accessible but impermeable to the gravitational fluid, substitute a single spherical surface equal to their sum.

Third. Decompose these first surfaces into facets sufficiently small to be treated as planes without sensible error.

Fourth. Transport all these facets to the spherical surface above mentioned. Each one of the facets should in this transformation occupy that point of the spherical surface at which the tangent plane is parallel to the original position of the facet.

REMARKS.

First. It is not necessary to be very expert to deduce upon these suppositions all the laws of gravitation, both terrestrial and universal (and consequently those of Kepler and some others), with as much of [160] precision and more as the phenomena themselves furnish, for these laws are the inevitable consequences of the constitutions I have supposed.

Second. Although I here present these constitutions crudely and without proof, as if they were gratuitous hypotheses and adventurous fictions, the fair-minded reader will perfectly comprehend that I have at hand some presumptions, at least, in their favour (independent of the perfect accord with all the phenomena), but which I withhold as too extended for development in this place. These suppositions may then be regarded as theorems published without demonstration.

Third. Their number is likely to inspire some opposition at first glance; but the attentive mind will not fail to see that they are but details into which I have wished to enter because of the novelty of this doctrine, and that they will be readily understood when it shall have become sufficiently well known that its students may attend under favourable circumstances to the details. If the authors who have written upon hydrodynamics, aeronautics, or optics had had readers who doubted the existence of water, air, and light, and who consequently indulged no tacit supposition upon equalities or compensations of which no express mention was made, they, too, would be obliged to add a great number of explanations to their definitions which instructed or indulgent readers might well dispense with. We do not accept of hints, and sano sensu, except for propositions which are familiar and in whose favour there is a predisposition.