We have alluded to the fact of the radial stream of the sun necessarily
diminishing the sun's power, and, consequently, diminishing his apparent
mass. The radial stream of all the planets will do the same, so that
each planet whose mass is derived from the periodic times of the
satellites, will also appear too small. But, there is also a great
probability that some modification must be made in the wording of the
Newtonian law. The experiments of Newton on the pendulum, with every
variety of substance, was sufficient justification to entitle him to
infer, that inertia was as the weight of matter universally. But, there
was one condition which could not be observed in experimenting on these
substances, viz., the difference of temperature existing between the
interior and surface of a planet.
We have already expressed the idea, that the cause of gravity has no
such mysterious origin as to transcend the power of man to determine it.
But that, on the contrary, we are taught by every analogy around us, as
well as by divine precept, to use the visible things of creation as
stepping stones to the attainment of what is not so apparent. That we
have the volume of nature spread out in tempting characters, inviting us
to read, and, assuredly, it is not so spread in mockery of man's limited
powers. As science advances, strange things, it is true, are brought to
light, but the more _rational_ the queries we propound, in every case
the more satisfactory are the answers. It is only when man consults the
oracle in irrational terms that the response is ambiguous. Alchemy, with
its unnatural transmutations, has long since vanished before the
increasing light. Why should not attraction also? Experience and
experiment, if men would only follow their indications, are consistently
enforcing the necessity of erasing these antiquated chimeras from the
book of knowledge; and inculcating the great truth, that the physical
universe owes all its endless variety to differences in the form, size,
and density of planetary atoms in motion, according to simple mechanical
principles. These, combined with the existence of an all-pervading
medium filling space, between which and planetary matter no bond of
union subsists, other than that which arises from a continual
interchange of motion, are the materials from which the gems of nature
are elaborated. But, simplicity of means is what philosophy has ever
been reluctant to admit, preferring rather the occult and obscure.
If action be equal to reaction, and all nature be vibrating with motion,
these motions must necessarily interfere, and some effect should be
produced. A body radiating its motion on every side into a physical
medium, produces waves. These waves are a mechanical effect, and the
body parts with some of its motion in producing them; but, should
another body be placed in juxtaposition, having the same motion, the
opposing waves neutralize each other, and the bodies lose no motion from
their contiguous sides, and, therefore, the reaction from the opposite
sides acts as a propelling power, and the bodies approach, or tend to
approach each other. If one body be of double the inertia, it moves only
half as far as the first; then, seeing that this atomic motion is
radiated, the law of force must be directly as the mass, and inversely
as the squares of the distances. There may be other atomic vibrations
besides those which we call light, heat, and chemical action, yet the
joint effect of all is infinitesimally small, when we disregard the
united _attraction_ of all the atoms of which the earth is composed. The
_attraction_ of the whole earth at the surface causes bodies to fall 16
feet the first second of time; but, if two spheres of ice of one foot
diameter, were placed in an infinite space, uninfluenced by other
matter, and only 16 feet apart, they would require nearly 10,000 years
to fall together by virtue of their mutual attraction. Our conceptions,
or, rather, our misconceptions, concerning the force of gravity, arises
from our forgetting that every pound of matter on the earth contributes
its share of the force which, in the aggregate, is so powerful. Hence,
the cause we have suggested, is fully adequate to account for the
phenomena. Whether the harmony of vibrations between two bodies may not
have an influence in determining the amount of interference, and,
consequently, produce _some_ difference between the gravitating mass
and its inertia, is a question which, no doubt, will ultimately be
solved; but this harmony of vibrations must depend, in some degree, on
the atomic weight, temperature, and intensity of atomic motion.
That a part of the mass of the earth is _latent_ may be inferred from
certain considerations: 1st, from the discrepancies existing in the
results obtained for the earth's compression by the pendulum and by
actual measurement; and, 2d, from the irregularity of that compression
in particular latitudes and longitudes. The same may also be deduced
from the different values of the moon's mass as derived from different
phenomena, dependent on the law of gravitation. Astronomers have
hitherto covered themselves with the very convenient shield of errors of
observation; but, the perfection of modern instruments now demand a
better account of all outstanding discrepancies. The world requires it
of them.
The mass of the moon comes out much greater by our theory than nutation
gives. The mass deduced from the theory is only dependent on the
relative inertiae of the earth and moon. That given by nutation depends
on gravity. If, then, a part of the mass be latent, nutation will give
too small a value. But, in addition to this, we are justified in
doubting the strict wording of the Newtonian law, deriving our authority
from the very foundation stone of the Newtonian theory.
It is well known that Newton suspected that the moon was retained in her
orbit by the same force which is usually called weight upon the surface,
sixteen years before the fact was confirmed, by finding a correspondence
in the fall of the moon and the fall of bodies on the earth. Usually, in
all elementary works, this problem is considered accurately solved.
Having formed a different idea of the mechanism of nature, this fact
presented itself as a barrier beyond which it was impossible to pass,
until suspicions, derived from other sources, induced the author to
inquire: Whether the phenomenon did exactly accord with the theory? We
are aware that it is easy to place the moon at such a distance, that the
result shall strictly correspond with the fact; but, from the parallax,
as derived from observation (and if this cannot be depended on
certainly, no magnitudes in astronomy can), we find, _that the moon does
not fall from the tangent of her orbit, as much as the theory requires_.
As this is of vital importance to the integrity of the theory we are
advocating, we have made the computation on Newton's own data, except
such as were necessarily inaccurate at the time he wrote; and we have
done it arithmetically, without logarithmic tables, that, if possible,
no error should creep in to vitiate the result. We take the moon's
elements from no less an authority than Sir John Herschel, as well as
the value of the earth's diameter.
Mass of the moon 1/80
Mean distance in equatorial radii 59.96435
Sidereal period in seconds 2360591
The vibrations of the pendulum give the force of gravity at the surface
of the earth, and it is found to vary in different latitudes. The
intensity in any place being as the squares of the number of vibrations
in a given time. This inequality depends on the centrifugal force of
rotation, and on the spheroidal figure of the earth due to that
rotation. At the equator the fall of a heavy body is found to be
16.045223 feet, per second, and in that latitude the squares of whose
sine is 1/3, it is 16.0697 feet. The effect in this last-named latitude
is the same as if the earth were a perfect sphere. This does not,
however, express the whole force of gravity, as the rotation of the
earth causes a centrifugal tendency which is a maximum at the equator,
and there amounts to 1/289 of the whole gravitating force. In other
latitudes it is diminished in the ratio of the squares of the cosines of
the latitude; it therefore becomes 1/434 in that latitude the square of
whose sine is 1/3. Hence the fall per second becomes 16.1067 feet for
the true gravitating force of the earth, or for that force which retains
the moon in her orbit.
The moon's mean distance is 59.96435 equatorial radii of the earth,
which radius is, according to Sir John Herschel, 20.923.713
feet. Her mean distance as derived from the parallax is not to be
considered the radius vector of the orbit, inasmuch as the earth also
describes a small orbit around the common centre of gravity of the earth
and moon; neither is radius vector to be considered as her distance from
this common centre; for the attracting power is in the centre of the
earth. But the mean distance of the moon moving around a movable centre,
is to the same mean distance when the centre of attraction is fixed, as
the sum of the masses of the two bodies, to the first of two mean
proportionals between this sum and the largest of the two bodies
inversely. (Vid. Prin. Prop. 60 Lib. Prim.) The ratio of the masses
being as above 80 to 1 the mean proportional sought is 80.666 and in
this ratio must the moon's mean distance be diminished to get the force
of gravity at the moon. Therefore as 81 is to 80.666, so is 59.96435 to
59.71657 for the moon's distance in equatorial radii of the earth.
Multiply this last by 20.923,713 to bring the semi-diameter of the lunar
orbit into feet = 1.249.492.373, and this by 6.283185, the ratio of the
circumference to the radius, gives 7.850.791.736 feet, for the mean
circumference of the lunar orbit.
Further, the mean sidereal period of the moon is 2360591 seconds and the
1/2360591th part of 7.850.791.736 is the arc the moon describes in one
second = 3325.77381 feet, the square of which divided by the diameter
of the orbit, gives the fall of the moon from the tangent or versed
size of that arc.
1106771.36876644
= ---------------- = 0.004426106 feet.
2498984746
This fraction is, however, too small, as the ablatitious action of the
sun diminishes the attraction of the earth on the moon, in the ratio of
178 29/40 to 177 29/40. So that we must increase the fall of the moon
in the ratio of 711 to 715, and hence the true fall of the moon from the
tangent of her orbit becomes 0.00451 feet per second.
We have found the fall of a body at the surface of the earth, considered
as a sphere, 16.1067 feet per second, and the force of gravity
diminishes as the squares of the distances increases. The polar diameter
of the earth is set down as 7899.170 miles, and the equatorial diameter
7925.648 miles; therefore, the mean diameter is 7916.189 miles.[36] So
that, reckoning in mean radii of the earth, the moon's distance is
59.787925, which squared, is equal to 3574.595975805625. At one mean
radius distance, that is, at the surface, the force of gravity, or fall
per second, is as above, 16.1067 feet. Divide this by the square of the
distance, it is 16.1067/3574.595975805625 = 0.0045058 feet for the force
of gravity at the moon. But, from the preceding calculation, it appears,
that the moon only falls 0.0044510 feet in a second, showing a
deficiency of 1/82d part of the principal force that retains the moon in
her orbit, being more than double the whole disturbing power of the sun,
which is only 1/178th of the earth's gravity at the moon; yet, on this
1/178th depends the revolution of the lunar apogee and nodes, and all
those variations which clothe the lunar theory with such formidable
difficulties. The moon's mass cannot be less than 1/80, and if we
consider it greater, as it no doubt is, the results obtained will be
still more discrepant. Much of this discrepancy is owing to the
expulsive power of the radial stream of the terral vortex; yet, it may
be suspected that the effect is too great to be attributed to this, and,
for this reason, we have suggested that the fused matter of the moon's
centre may not gravitate with the same force as the exterior parts, and
thus contribute to increase the discrepancy.
As there must be a similar effect produced by the radial stream of every
vortex, the masses of all the planets will appear too small, as derived
from their gravitating force; and the inertia of the sun will also be
greater than his apparent mass; and if, in addition to this, there be a
portion of these masses latent, we shall have an ample explanation of
the connection between the planetary densities and distances. We must
therefore inquire what is the particular law of force which governs the
radial stream of the solar vortex. It will be necessary to enter into
this question a little more in detail than our limits will justify; but
it is the resisting influence of the ether, and its consequences, which
will appear to present a vulnerable point in the present theory, and to
be incompatible with the perfection of astronomical science.