The Laws of Le Sage

Section 16

The laws of Kepler were necessary consequences of the doctrine that gravitation results from the impulsion of atoms moving in every direction.

This is because Kepler’s laws follow directly from those of Newton.

The first-mentioned laws are the natural consequences of the second.

First Law

The law of areas proportional to times is a necessary consequence of gravitation, always directed toward a single point, is demonstrated by elementary geometry in Proposition 1 of Newton’s Principia.

Second Law

The law of squares of periodic times proportional to the cubes of the distances, for bodies appearing to describe circles, must necessarily follow from a gravitation inversely proportional to the square of the distance constitutes the second part of Corollary 6 to Proposition 4 of Principia.

This may be demonstrated by elementary methods also for regular polygons, which represent more nearly than exact circles the orbits traversed by bodies diverted slightly from their paths by intermittent collisions. [150]

Third Law

The the ellipticity of an orbit is the necessary consequence of gravitation directed toward its focus, and reciprocally proportional to the square of the distance, is the converse of Proposition XI of the same book.

This proposition has been more simply demonstrated as a consequence of the 50th of Book 3 of the conics of Appolonius.

The laws of Kepler are an easy consequence of the system of atoms.

I have not pretended that their application to complex cases readily follows from the slight knowledge of geometry possessed by the ancients.

Fourth Law

Proposition 11 of the Principia once attained it does not appear to me difficult to establish the fiftieth, which extends our second consequences to ellipses.

It proves that in ellipses as well, the squares of the periodic times about an attracting body (placed in one of the foci) are proportional to the cubes of the mean distances.

Section 17

The laws of Galileo may be derived from the hypothesis of the impulsion of the atoms.

The blows of corpuscles, moving with a speed faster than light, upon a body which has fallen three or four seconds, would be sensibly of the same strength as the preceding blows had been on the same body when it had only fallen one or two seconds.[14]

Hence the successive accelerations of the body in equal times must be sensibly equal.

The velocity at any instant must be sensibly proportional to the time elapsed since the beginning of the fall.

From this it follows necessarily that the spaces traversed since the beginning are sensibly proportional to the squares of the total times,[15] and will be sensibly proportional to the successive odd numbers.[151]

Section 18

These synthetic demonstrations of laws of falling bodies by the introduction of mechanism whose existence is only surmised, may perhaps be less philosophical than analytic demonstrations which are based entirely upon observed phenomena.

Still it must be recalled that in cases where direct observation has been difficult and inexact, error has frequently attended deductions of this latter kind.

At all events the former kind of demonstration is much more philosophical than a gratuitous hypothesis, which is, nevertheless, the means of invention employed by Galileo.

Its results are quite as well established as are the laws of Galileo since they are proved by exactly the same means, that is by the sensible accord of their consequences with the phenomena.

Nothing else than this is claimed by Galileo himself and his principal successors.

Section 19

But the atomists would have encountered one very serious objection, to which they were necessarily exposed in common with all physicists who undertake an explanation of gravitation.

A roof has thickness that blocks out hail.

A shield has thickness that blocks out arrows.

Whereas, the weight of all bodies is augmented in direct proportion of their thickness.

So when one removes a heavy body from a shop or dwelling, or reduces it to sheets exposed without protection to material influences (the rain, for example) it receives more than when protected or concentrated so as to present a small surface.

But this has never been found by merchants and artisans who are continually in the habit of weighing, that bodies appear heavier in open air than when under cover.

Gold-beaters have never perceived that the weight of the metal augments in proportion to the increase of its surface.

If the collision of atoms is the cause of heaviness, the weight of bodies ought to be proportional to their surface (or rather to their horizontal projection).

How, then, does it happen that the weight is proportional to the mass!

Do the gravitational atoms then act across the thickest and most compact envelopes of all substances as fully as through the air?

Does not the very sensible weight [152] which they impart to these envelopes demonstrate the contrary, that is that all substances arrest the passage of a great number of corpuscles?

Section 20

The Epicureans would respond that the atoms traverse very freely[16] all heavy bodies just as light passes through diamond and magnetic matter through gold.

This is even if one of these bodies is the hardest and the other the heaviest of all known bodies. This shows that they are less porous than most substances.

Thus the number of atoms which are intercepted by the first layers of a heavy body would be absolutely insensible relatively to the number of those which pass through the last layers.[17]

Nevertheless, the relatively small number intercepted would produce a sensible action upon the body, since they have, in virtue of an immense velocity,[18] the force of impact which they would lack by reason of their small mass.[153]