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ATOM
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the doctrine of gravitation has been admitted and ex¬
pounded, till it has gradually acquired the character rather
of an ultimate fact than of a fact to be explained.
It seems doubtful whether Lucretius considers gravita¬
tion to be an essential property of matter, as he seems to
assert in the very remarkable lines—
“ Nam si tantundem est in lanse glomere, quantum
Corporis in plumbo est, tantundem pendere par est:
Corporis ofiicium est quoniam premere omnia deorsum.”
—De Rerum Natura, i. 361.
If this is the true opinion of Lucretius, and if the down-
ward flight of the atoms arises, in his view, from their own
gravity, it seems very doubtful whether he attributed the
weight of sensible bodies to the impact of the atoms.
The latter opinion is that of Le Sage, of Geneva, pro¬
pounded in his Lucrece Newtonien, and in his Traite
de Physique Mecanique, published, along with a second
treatise of his own, by Pierre Prevost, of Geneva, in
1818.1 The theory of Le Sage is that the gravitation
of bodies towards each other is caused by the impact of
streams of atoms flying in all directions through space.
These atoms he calls ultramundane corpuscules, because he
conceives them to come in all directions from regions far
beyond that part of the system of the world which is in
any way known to us. He supposes each of them to be so
small that a collision with another ultramundane corpus-
cule is an event of very rare occurrence. It is by striking
against the molecules of gross matter that they discharge
their function of drawing bodies towards each other. A
body placed by itself in free space and exposed to the
impacts of these corpuscules would be bandied about by
them in all directions, but because, on the whole, it
receives as many blows on one side as on another, it cannot
thereby acquire any sensible velocity. But if there are
two bodies in space, each of them will screen the other
from a certain proportion of the corpuscular bombardment,
so that a smaller number of corpuscules will strike either
body on that side which is next the other body, while the
number of corpuscules which strike it in other directions
remains the same.
Each body will therefore be urged towards the other by
the effect of the excess of the impacts it receives on the
side furthest from the other. If we take account of the
impacts of those corpuscules only which come directly from
infinite space, and leave out of consideration those which
have already struck mundane bodies, it is easy to calculate
the result on the two bodies, supposing their dimensions
small compared with the distance between them.
The force of attraction would vary directly as the product
of the areas of the sections of the bodies taken normal to
the distance and inversely as the square of the distance
between them.
Now, the attraction of gravitation varies as the product
of the masses of the bodies between which it acts, and
inversely as the square of the distance between them.
If, then, we can imagine a constitution of bodies such that
the effective areas of the bodies are proportional to their
masses, we shall make the two laws coincide. Here, then,
seems to be a path leading towards an explanation of the
law of gravitation, which, if it can be shown to be in other
respects consistent with facts, may turn out to be a royal
road into the very arcana of science.
Le Sage himself shows that, in order to make the effec¬
tive area of a body, in virtue of which it acts as a screen
to the streams of ultramundane corpuscules, proportional to
the mass of the body, whether the body be large or small,
we must admit that the size of the solid atoms of the body
is exceedingly small compared with the distances between
* See also Constitution de la MoXiere, &c., par le P. Leray, Paris,
them, so that a very small proportion of the corpuscules
are stopped even by the densest and largest bodies. We
may picture to ourselves the streams of corpuscules coming
in every direction, like light from a uniformly illuminated
sky. We may imagine a material body to consist of a con¬
geries of atoms at considerable distances from each other,
and we may represent this by a swarm of insects flying in
the air. To an observer at a distance this swarm will be
visible as a slight darkening of the sky in a certain quarter.
This darkening will represent the action of the material
body in stopping the flight of the corpuscules. Now, if the
proportion of light stopped by the swarm is very small, two
such swarms will stop nearly the same amount of light,
whether they are in a line with the eye or not, but if one
of them stops an appreciable proportion of light, there will
not be so much left to be stopped by the other, and the
effect of two swarms in a line with the eye will be less
than the sum of the two effects separately.
Now, we know that the effect of the attraction of the sun
and earth on the moon is not appreciably different when
the moon is eclipsed than on other occasions when full
moon occurs without an eclipse. This shows that the
number of the corpuscules which are stopped by bodies of
the size and mass of the earth, and even the sun, is very
small compared with the number which pass straight
through the earth or the sun without striking a single
molecule. To the streams of corpuscules the earth and the
sun are mere systems of atoms scattered in space, which
present far more openings than obstacles to their rectilinear
flight.
Such is the ingenious doctrine of Le Sage, by which he
endeavours to explain universal gravitation. Let us try to
form some estimate of this continual bombardment of
ultramundane corpuscules which is being kept up on all
sides of us.
We have seen that the sun stops but a very small frac¬
tion of the corpuscules which enter it. The earth, being a
smaller body, stops a still smaller proportion of them.
The proportion of those which are stopped by a small
body, say a 1 Sb shot, must be smaller still in an enormous
degree, because its thickness is exceedingly small compared
with that of the earth.
Now, the weight of the ball, or its tendency towards the
earth, is produced, according to this theory, by the excess
of the impacts of the corpuscules which come from above
over the impacts of those which come from below, and
have passed through the earth. Either of these quantities
is an exceedingly small fraction of the momentum of the
whole number of corpuscules which pass through the ball
in a second, and their difference is a small fraction of
either, and yet it is equivalent to the weight of a pound.
The velocity of the corpuscules must be enormously greater
than that of any of the heavenly bodies, otherwise, as may
easily be shown, they would act as a resisting medium
opposing the motion of the planets. Now, the energy of a
moving system is half the product of its momentum into its
velocity. Hence the energy of the corpuscules, which by
their impacts on the ball during one second urge it towards
the earth, must be a number of foot-pounds equal to the
number of feet over which a corpuscule travels in a second,
that is to say, not less than thousands of millions. But
this is only a small fraction of the energy of all the impacts
which the atoms of the ball receive from the innumerable
streams of corpuscules which fall upon it in all directions.
Hence the rate at which the energy of the corpuscules
is spent in order to maintain the gravitating property of a
single pound, is at least millions of millions of foot-pounds
per second.
What becomes of this enormous quantity of energy ? If
the corpuscules, after striking the atoms, fly off with a