We have yet many phenomena to investigate by the aid of the theory, and
we will develop them in that order which will best exhibit their mutual
dependence. The solar spots have long troubled astronomers, and to this
day no satisfactory solution of the question has been proposed; but we
shall not examine theories. It is sufficient that we can explain them on
the same general principles that we have applied to terrestrial
phenomena. There can be but little doubt about the existence of a solar
atmosphere, and, reasoning from analogy, the constituent elements of the
sun must partake of the nature of other planetary matter. That there are
bodies in our system possessing the same elements as our earth, is
proved by the composition of meteoric masses, which, whether they are
independent bodies of the system, or fragments of an exploded planet, or
projected from lunar volcanoes, is of little consequence; they show that
the same elements are distributed to other bodies of the system,
although not necessarily in the same proportions. The gaseous matter of
the sun's atmosphere may, therefore, be safely considered as vapors
condensable by cold, and the formation of vortices over the surface of
this atmosphere, brings down the ether, and causes it to intermingle
with this atmosphere. But, from the immensely rapid motion of the polar
current of the solar vortex, this ether may be considered to enter the
atmosphere of the sun with the temperature of space.

Sir John Herschel, in commenting on the theory of Mr. Redfield before
the British Association, convened at Newcastle in 1838,[35] suggested an
analogy to terrestrial hurricanes, from a suspected rotation and
progressive motion in these spots. From their rapid formation, change of
shape, and diameter, this view is allowable, and, taken in conjunction
with the action of the ethereal currents, will account for all the
phenomena. The nucleus of the spot is dense, like the nucleus of a storm
on the earth, and surrounded by a penumbon precisely as our storms are
fringed with lighter clouds, permitting the light of the sun to
penetrate. And, it has been observed, that these spots seem to follow
one another in lines on the same parallel of solar latitude (or nearly
the same), exactly as we have determined the action of the vortices on
the surface of the earth from observation. These spots are never found
in very high latitudes--not much above 30° from the solar equator. If we
consider this equator to be but slightly inclined to the plane of the
vortex, this latitude would be the general position of the lateral solar
vortices, and, in fact, be confined principally to a belt on each side
of the equator, between 15° and 30° of solar latitude, rather than at
the equator itself. This, it is needless to say, is actually the case.
But, a more capital feature still has been more recently brought to
light by observation, although previously familiar to the author, who,
in endeavoring to verify the theory, seriously injured his sight, by
observing with inadequate instrumental means. This is the periodicity of
the spots.

We have already observed, that there is reason to suppose that the
action of the inner vortex of the earth is probably greater than that of
the outer vortex, on account of the conflicting currents by which it is
caused. And the full development of this vortex requires, that the
central vortex or mechanical axis of the system shall be nearly
tangential to the surface. In this position, the action of the central
vortex is itself at a maximum; and, when the planets of the system are
so arranged as to produce this result, we may expect the greatest number
of spots. If the axis or central vortex approaches to coincidence with
the axis of the sun, the lateral vortices disappear, and the central
vortex being then perpendicular to the surface, is rendered ineffective.
Under these circumstances, there will be no spots on the sun's disc.
When, on the other hand, all the planets conspire at the same side to
force the sun out from the mechanical centre of the system, the surface
is too distant to be acted on by the central vortex, and the lateral
vortices are also thrown clear of the sun's surface, on account of the
greater velocity of the parts of the vortex, in sweeping past the body
of the sun. In this case, there will be but few spots. The case in which
the axis of the vortex coincides with the axis of the sun, is much more
transient than the first position, and hence, although the interval
between the maxima will be tolerably uniform, there will be an
irregularity between a particular maximum, and the preceding and
subsequent minimum.

The following table exhibits the solar spots, as determined by Schwabe,
of Dessau:

  Year of observation.   Groups of spots observed.   Number of days.
          1826                      118                    277
          1827                      161                    273
          1828                      225                    282
          1829                      199                    244
          1830                      190                    217
          1831                      149                    239
          1832                       84                    270
          1833                       33                    267
          1834                       51                    273
          1835                      173                    244
          1836                      272                    200
          1837                      333                    168
          1838                      282                    202
          1839                      162                    205
          1840                      152                    263
          1841                      102                    283
          1842                       68                    307
          1843                       34                    324

Previous to the publication of this table, the author had inferred the
necessity of admitting the existence of another planet in the solar
system, from the phenomenon of which we are speaking. He found a
sufficient correspondence between the minima of spots to confirm the
explanation given by the theory, and this was still more confirmed by
the more exact determination of Schwabe; yet there was a little
discrepancy in the synchronous values of the ordinates, when the theory
was graphically compared with the table. Previous to the discovery of
Neptune, the theory corresponded much better than afterwards, and as no
doubt could be entertained that the anomalous movements of Uranus were
caused by an exterior planet, he adopted the notion that there were two
planets exterior to Uranus, whose positions at the time were such, that
their mechanical affects on the system were about equal and contrary.
Consequently, when Neptune became known, the existence of another planet
seemed a conclusion necessary to adopt. Accordingly, he calculated the
heliocentric longitudes and true anomalies, and the values of radius
vector, for all the planets during the present century, but not having
any planetary tables, he contented himself with computing for the
nearest degree of true anomaly, and the nearest thousand miles of
distance. Then by a composition and resolution of all the forces, he
deduced the radius vector of the sun, and the longitude of his centre,
for each past year of the century. It was in view of a little
outstanding discrepancy in the times of the minima, as determined by
theory and observation, that he was induced to consider as almost
certain the existence of a theoretical planet, whose longitude, in 1828,
was about 90°, and whose period is from the theory about double that of
Neptune. And for convenience of computation and reference, he has been
in the habit of symbolizing it by a volcano. The following table of the
radii vectores of the sun, and the longitude of his centre, for the
years designated in Schwabe's table, is calculated from the following
data for each planet:

                                                           Long. of
  Planets.    Masses.    Mean distances.  Eccentricities.  Perihelion.
     ♃         1/1648       494.800.000      0.0481           11°
     ♄         1/3310       907.162.000      0.0561           89
     ♅        1/23000      1824.290.000      0.0166          167
     ♆        1/20000      2854.000.000      0.0088            0
     ⊿        1/28000      4464.000.000

                                                       No. of spots in
    Dates.      Rad. vector. Sun's long.  Ordinates.   Schwabe's table.
  Jan. 1, 1826    528,000       320°        +  84           118
     "    1827    480,000       339         +  36           161
     "    1828    432,000       352         -  12 Max.      225 Max.
     "    1829    397,000        38         -  47           199
     "    1830    858,000        71         -  86           190
     "    1831    324,000       104         - 120           149
     "    1832    311,000       144         - 133            84
     "    1833    300,000       183         - 144 Min.       33 Min.
     "    1834    307,000       220         - 137            51
     "    1835    338,000       263         - 106           173
     "    1836    380,000       302         -  55           272
     "    1837    419,000       337         +  25 Max.      333 Max.
     "    1838    488,000         3         +  44           282
     "    1839    651,000        29         + 107           162
     "    1840    632,000        51         + 188           152
     "    1841    680,000        80         + 236           102
     "    1842    730,000       105         + 286            68
     "    1843    160,000       128         + 322            34 Min.
     "    1844    188,000       152         + 339 Min.       52
     "    1845    772,000       174         + 328           114
     "    1846    728,000       196         + 284           157
     "    1847    660,000       218         + 216
     "    1848    563,000       240         + 119       Observed. Max.
     "    1849    447,000       261         +   3 Max.
     "    1850    309,000       283         - 135
     "    1851    170,000       323         - 274
     "    1852     53,000        41         - 391 Min.
     "    1853    167,000       133         - 277
     "    1854    315,000       160         - 129
     "    1855    475,000       183         +  31 Max.
     "    1856    611,000       203         + 167
     "    1857    720,000       225         + 276

It is necessary to observe here, that the values of the numbers in
Schwabe's table are the numbers for the whole year, and, therefore, the
1st of July would have been a better date for the comparison; but, as
the table was calculated before the author was cognizant of the fact,
and being somewhat tedious to calculate, he has left it as it was, viz.,
for January 1st of each year. Hence, the minimum for 1843 appears as
pertaining to 1844. The number of spots ought to be inversely as the
ordinates approximately--these last being derived from the Radii
Vectores minus, the semi-diameter of the sun = 444,000 miles.

In passing judgment on this relation, it must also be borne in mind,
that the recognized masses of the planets cannot be the true masses, if
the theory be true. Both sun and planets are under-estimated, yet, as
they are, probably, all to a certain degree proportionally undervalued,
it will not vitiate the above calculation much.

The spots being considered as solar storms, they ought also to vary in
number at different times of the year, according to the longitude of the
earth and sun, and from their transient character, and the slow rotation
of the sun, they ought, _ceteris paribus_, to be more numerous when the
producing vortex is over a visible portion of the sun's surface.

The difficulty of reconciling the solar spots, and their periodicity to
any known principle of physics, ought to produce a more tolerant spirit
amongst the scientific for speculations even which may afford the
slightest promise of a solution, although emanating from the humblest
inquirer after truth. The hypothesis of an undiscovered planet, exterior
to Neptune, is of a nature to startle the cautions timidity of many;
but, if the general theory be true, this hypothesis becomes extremely
probable. We may not have located it exactly. There may be even two such
planets, whose joint effect shall be equivalent to one in the position
we have assigned. There may even be a comet of great mass, capable of
producing an effect on the position of the sun's centre (although it
follows from the theory that comets have very little mass). Yet, in view
of all these suppositions, there can be but little doubt that the solar
spots are caused by the solar vortices, and these last made effective on
the sun by the positions of the great planets, and, therefore, we have
indicated a new method of determining the existence and position of all
the planets exterior to Neptune. On the supposition that there is only
one more in the system, from its deduced distance and mass, it will
appear only as a star of the eleventh magnitude, and, consequently, will
only be recognizable by its motion, which, at the greatest, will only be
ten or eleven seconds per day.

MASSES OF THE SUN AND PLANETS.

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 inertiæ 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 ⅓, 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 ⅓. 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.

LAW OF DENSITY IN SOLAR VORTEX.

Reverting to the dynamical principle, that the product of every particle
of matter in a fluid vortex, moving around a given axis, by its distance
from the centre and angular velocity, must ever be a constant quantity,
it follows that if the ethereal medium be uniformly dense, the periodic
times of the parts of the vortex will be directly as the distances from
the centre or axis; but the angular velocities being inversely as the
times, the absolute velocities will be equal at all distances from the
centre.

Newton, in examining the doctrine of the Cartesian vortices, supposes
the case of a globe in motion, gradually communicating that motion to
the surrounding fluid, and finds that the periodic times will be in the
duplicate ratio of the distances from the centre of the globe. He and
his successors have always assumed that it was impossible for the
principle of gravity to be true, and a Cartesian plenum also;
consequently, the question has not been fairly treated. It is true that
Descartes sought to explain the motions of the planets, by the
mechanical action of a fluid vortex _solely_; and to Newton belongs the
glorious honor of determining, the existence of a centripetal force,
competent to explain these motions mathematically, (but not physically,)
and rashly rejected an intelligible principle for a miraculous virtue.
If our theory be true, the visible creation depends on the existence of
both working together in harmony, and that a physical medium is
absolutely necessary to the existence of gravitation.

If space be filled with a fluid medium, analogy would teach us that it
is in motion, and that there must be inequalities in the direction and
velocity of that motion, and consequently there must be vortices. And if
we ascend into the history of the past, we shall find ample testimony
that the planetary matter now composing the members of the solar system,
was once one vast nebulous cloud of atoms, partaking of the vorticose
motion of the fluid involving them. Whether the gradual accumulation of
these atoms round a central nucleus from the surrounding space, and thus
having their tangential motion of translation converted into vorticose
motion, first produced the vortex in the ether; or whether the vortex
had previously existed, in consequence of conflicting currents in the
ether, and the scattered atoms of space were drawn into the vortex by
the polar current, thus forming a nucleus at the centre, as a necessary
result of the eddy which would obtain there, is of little consequence.
The ultimate result would be the same. A nucleus, once formed, would
give rise to a central force, tending more and more to counteract the
centripulsive power of the radial stream; and in consequence of this
continually increasing central power, the heaviest atoms would be best
enabled to withstand the radial stream, while the lighter atoms might be
carried away to the outer boundaries of the vortex, to congregate at
leisure, and, after the lapse of a thousand years, to again face the
radial stream in a more condensed mass, and to force a passage to the
very centre of the vortex, in an almost parabolic curve. That space is
filled with isolated atoms or planetary dust, is rendered very probable
by a fact discovered by Struve, that there is a gradual extinction in
the light of the stars, amounting to a loss of 1/107 of the whole, in
the distance which separates Sirius from the sun. According to Struve,
this can be accounted for, "by admitting as very probable that space is
filled with an _ether_, capable of intercepting in some degree the
light." Is it not as probable that this extinction is due to planetary
dust, scattered through the pure ether, whose vibrations convey the
light,--the material atoms of future worlds,--the debris of dilapidated
comets? Does not the Scripture teach the same thing, in asserting that
the heavens are not clean?

The theory of vortices has had many staunch supporters amongst those
deeply versed in the science of the schools. The Bernoullis proposed
several ingenious hypothesis, to free the Cartesian system from the
objections urged against it, viz.: that the velocities of the planets,
in accordance with the three great laws of Kepler, cannot be made to
correspond with the motion of a fluid vortex; but they, and all others,
gave the vantage ground to the defenders of the Newtonian philosophy, by
seeking to refer the principle of gravitation to conditions dependent on
the density and vorticose motion of the ether. When we admit that the
ether is imponderable and yet material, and planetary matter subject to
the law of gravitation, the objections urged against the theory of
vortices become comparatively trivial, and we shall not stop to refute
them, but proceed with the investigation, and consider that the ether is
the original source of the planetary motions and arrangements.

On the supposition that the ether is uniformly dense, we have shown that
the periodic times will be directly as the distances from the axis. If
the density be inversely as the distances, the periodic times will be
equal. If the density be inversely as the square roots of the distances,
the times will be directly in the same ratio. The celebrated J.
Bernoulli assumed this last ratio; but seeking the source of motion in
the rotating central globe, he was led into a hypothesis at variance
with analogy. The ellipticity of the orbit, according to this view,
was caused by the planet oscillating about a mean position,--sinking
first into the dense ether,--then, on account of superior buoyancy,
rising into too light a medium. Even if no other objection could be
urged to this view, the difficulty of explaining why the ether should be
denser near the sun, would still remain. We might make other
suppositions; for whatever ratio of the distances we assume for the
density of the medium, the periodic times will be compounded of those
distances and the assumed ratio. Seeing, therefore, that the periodic
times of the planets observe the direct ses-plicate ratio of the
distances, and that it is consonant to all analogy to suppose the
contiguous parts of the vortex to have the same ratio, we find that the
density of the ethereal medium in the solar vortex, is directly as the
square roots of the distances from the axis.

Against this view, it may be urged that if the inertia of the medium is
so small, as is supposed, and its elasticity so great, there can be no
condensation by centrifugal force of rotation. It is true that when we
say the ether is condensed by this force, we speak incorrectly. If in an
infinite space of imponderable fluid a vortex is generated, the central
parts are rarefied, and the exterior parts are unchanged. But in all
finite vortices there must be a limit, outside of which the motion is
null, or perhaps contrary. In this case there may be a cylindrical ring,
where the medium will be somewhat denser than outside. Just as in water,
every little vortex is surrounded by a circular wave, visible by
reflection. As the density of the planet Neptune appears, from present
indications, to be a little denser than Uranus, and Uranus is denser
than Saturn, we may conceive that there is such a wave in the solar
vortex, near which rides this last magnificent planet, whose ring would
thus be an appropriate emblem of the peculiar position occupied by
Saturn. This may be the case, although the probability is, that the
density of Saturn is much greater than it appears, as we shall presently
explain.

In order to show that there is nothing extravagant in the supposition of
the density of the ether being directly as the square roots of the
distances from the axis, we will take a fluid whose law of density is
known, and calculate the effect of the centrifugal force, considered as
a compressing power. Let us assume our atmosphere to be 47 miles high,
and the compressing power of the earth's gravity to be 289 times greater
than the centrifugal force of the equator, and the periodic time of
rotation necessary to give a centrifugal force at the equator equal to
the gravitating force to be 83 minutes. Now, considering the gravitating
force to be uniform, from the surface of the earth upwards, and knowing
from observation that at 18,000 feet above the surface, the density of
the air is only ½, it follows, (in accordance with the principle that
the density is as the compressing force,) that at 43½ miles high, or
18,000 feet _below_ the surface of the atmosphere, the density is only
1/8000 part of the density at the surface of the earth. Let us
take this density as being near the limit of expansion, and conceive a
hollow tube, reaching from the sun to the orbit of Neptune, and that
this end of the tube is closed, and the end at the sun communicates with
an inexhaustible reservoir of such an attenuated gas as composes the
upper-layer of our atmosphere; and further, that the tube is infinitely
strong to resist pressure, without offering resistance to the passage of
the air within the tube; then we say, that, if the air within the tube
be continually acted on by a force equal to the mean centrifugal force
of the solar vortex, reckoning from the sun to the orbit of Neptune, the
density of the air at that extremity of the tube, would be greater than
the density of a fluid formed by the compression of the ocean into one
single drop. For the centrifugal force of the vortex at 2,300,000 miles
from the centre of the sun, is equal to gravity at the surface of the
earth, and taking the mean centrifugal force of the whole vortex as
one-millionth of this last force; so that at 3,500,000 miles from the
surface of the sun, the density of the air in the tube (supposing it
obstructed at that distance) would be double the density of the
attenuated air in the reservoir. And the air at the extremity of the
tube reaching to the orbit of Neptune, would be as much denser than the
air we breathe, as a number expressed by 273 with 239 ciphers annexed,
is greater than unity. This is on the supposition of infinite
compressibility. Now, in the solar vortex there is no physical barrier
to oppose the passage of the ether from the centre to the circumference,
and the density of the ethereal ocean must be considered uniform, except
in the interior of the stellar vortices, where it will be rarefied; and
the rarefaction will depend on the centrifugal force and the length of
the axis of the vortex. If this axis be very long, and the centrifugal
velocity very great, the polar influx will not be sufficient, and the
central parts will be rarefied. We see, therefore, no reason why the
density of the ether may not be three times greater at Saturn than at
the earth, or as the square roots of the distances directly.

BODES' LAW OF PLANETARY DISTANCES.

Thus, in the solar vortex, there will be two polar currents meeting at
the sun, and thence being deflected at right angles, in planes parallel
to the central plane of the vortex, and strongest in that central plane.
The velocity of expansion must, therefore, diminish from the divergence
of the radii, as the distances increase; but in advancing along these
planes, the ether of the vortex is continually getting more dense,
which operate by absorption or condensation on the radial stream; so
that the velocity is still more diminished, and this in the ratio of the
square roots of the distances directly. By combining these two ratios,
we find that the velocity of the radial stream will be in the
ses-plicate ratio of the distances inversely. But the force of this
stream is not as the velocity, but as the square of the velocity. The
_force_ of the radial stream is consequently as the cubes of the
distances inversely, from the axis of the vortex, reckoned in the same
plane. If the ether, however, loses in velocity by the increasing
density of the medium, it becomes also more dense; therefore the true
force of the radial stream will be as its density and the square of its
velocity, or directly as the square roots of the distances, and
inversely as the cubes of the distances, or as the 2.5 power of the
distances inversely.

If we consider the central plane of the vortex as coincident with the
plane of the ecliptic, and the planetary orbits, also, in the same
plane; and had the force of the radial stream been inversely as the
square of the distances, there could be no disturbance produced by the
action of the radial stream. It would only counteract the gravitation of
the central body by a certain amount, and would be exactly proportioned
at all distances. As it is, there is an outstanding force as a
disturbing force, which is in the inverse ratio of the square roots of
the distances from the sun; and to this is, no doubt, owing, in part,
the fact, that the planetary distances are arranged in the inverse order
of their densities.

Suppose two planets to have the same diameter to be placed in the same
orbit, they will only be in equilibrium when their densities are equal.
If their densities are unequal, the lighter planet will continually
enlarge its orbit, until the force of the radial stream becomes
proportional to the planets' resisting energy. This, however, is on the
hypothesis that the planets are not permeable by the radial stream,
which, perhaps, is more consistent with analogy than with the reality.
And it is more probable that the mean atomic weight of a planet's
elements tends more to fix the position of equilibrium for each. Under
the law of gravity, a planet may revolve at any distance from the sun,
but if we superadd a centripulsive force, whose law is not that of
gravity, but yet in some inverse ratio of the distances, and this force
acts only superficially, it would be possible to make up in volume what
is wanted in density, and a lighter planet might thus be found occupying
the position of a dense planet. So the planet Jupiter, respecting only
his resisting surface, is better able to withstand the force of the
radial stream at the earth than the earth itself. To understand this, it
is necessary to bear in mind, that, as far as planetary matter is
concerned, the earth would revolve in Jupiter's orbit in the same
periodic time as Jupiter, under the law of gravity: but that, in
reality, the whole of the gravitating force is not effective, and that
the equilibrium of a planet is due to a nice balance of interfering
forces arising from the planet's physical peculiarities. As in a
refracting body, the density of the ether may be considered inversely as
the refraction, and this as the atomic weight of the refracting
material, so, also, in a planet, the density of the ether will be
inversely in the same ratio of the density of the matter approximately.
Hence, the density of the ether within the planet Jupiter is greater
than that within the earth; and, on this ethereal matter, the sun has no
power to restrain it in its orbit, so that the centrifugal momentum of
Jupiter would be relatively greater than the centrifugal momentum of the
earth, were it also in Jupiter's orbit with the same periodic time.
Hence, to make an equilibrium, the earth should revolve in a medium of
less density, that there may be the same proportion between the external
ether, and the ether within the earth, as there is between the ether
around Jupiter and the ether within; so that the centrifugal tendency of
the dense ether at Jupiter shall counteract the greater momentum of the
dense ether within Jupiter; or, that the lack of centrifugal momentum in
the earth should be rendered equal to the centrifugal momentum of
Jupiter, by the deficiency of the centrifugal momentum of the ether at
the distance of the earth.

If then, the diameters of all the planets were the same (supposing the
ether to act only superficially), the densities would be as the
distances inversely;[37] for the force due to the radial stream is as
the square roots of the distance inversely, and the force due to the
momentum, if the density of the ether within a planet be inversely as
the square root of a planet's distance, will also be inversely as the
square roots of the distances approximately. We offer these views,
however, only as suggestions to others more competent to grapple with
the question, as promising a satisfactory solution of Bode's empirical
formula.

If there be a wave of denser ether cylindrically disposed around the
vortex at the distance of Saturn, or between Saturn and Uranus, we see
why the law of densities and distances is not continuous. For, if the
law of density changes, it must be owing to such a ring or wave. Inside
this wave, the two forces will be inverse; but outside, one will be
inverse, and the other direct: hence, there should also be a change in
the law of distances. As this change does not take place until we pass
Uranus, it may be suspected that the great disparity in the density of
Saturn may be more apparent than real. The density of a planet is the
relation between its mass and volume or extension, no matter what the
form of the body may be. From certain observations of Sir Wm.
Herschel--the Titan of practical astronomers--the figure of Saturn was
suspected to be that of a square figure, with the corners rounded off,
so as to leave both the equatorial and polar zones flatter than
pertained to a true spheroidal figure. The existence of an unbroken ring
around Saturn, certainly attaches a peculiarity to this planet which
prepares us to meet other departures from the usual order. And when we
reflect on the small density, and rapid rotation, the formation of this
ring, and the figure suspected by Sir Wm. Herschel, it is neither
impossible nor improbable, that there may be a cylindrical vacant space
surrounding the axis of Saturn, or at least, that his solid parts may be
cylindrical, and his globular form be due to elastic gases and vapors,
which effectually conceal his polar openings. And also, by dilating and
contracting at the poles, in consequence of inclination to the radial
stream, (just as the earth's atmosphere is bulged out sufficiently to
affect the barometer at certain hours every day,) give that peculiarity
of form in certain positions of the planet in its orbit. Justice to Sir
Wm. Herschel requires that _his_ observations shall not be attributed to
optical illusions. This view, however, which may be true in the case of
Saturn, would be absurd when applied to the earth, as has been done
within the present century. From these considerations, it is at least
possible, that the density of Saturn may be very little less, or even
greater than the density of Uranus, and be in harmony with the law of
distances.

It is now apparently satisfactorily determined, that Neptune is denser
than Uranus, and the law being changed, we must look for transneptunean
planets at distances corresponding with the new law of arrangement. But
there are other modifying causes which have an influence in fixing the
precise position of equilibrium of a planet. Each planet of the system
possessing rotation, is surrounded by an ethereal vortex, and each
vortex has its own radial stream, the force of which in opposing the
radial stream of the sun, depends on the diameter and density of the
planet, on the velocity of rotation, on the inclination of its axis, and
on the density of the ether at each particular vortex; but the numerical
verification of the position of each planet with the forces we have
mentioned, cannot be made in the present state of the question. There is
one fact worthy of note, as bearing on the theory of vortices in
connection with the rotation of the planets, viz.: that observation has
determined that the axial rotation and sidereal revolution of the
secondaries, are identical; thus showing that they are without vortices,
and are motionless relative to the ether of the vortex to which they
belong. We may also advert to the theory of Doctor Olbers, that the
asteroidal group, are the fragments of a larger planet which once
filled the vacancy between Mars and Jupiter. Although this idea is not
generally received, it is gathering strength every year by the discovery
of other _fragments_, whose number now amounts to twenty-six. If the
idea be just, our theory offers an explanation of the great differences
observable in the mean distances of these bodies, and which would
otherwise form a strong objection against the hypothesis. For if these
little planets be fragments, there will be differences of density
according as they belonged to the central or superficial parts of the
quondam planet, and their mean distances must consequently vary also.

There are some other peculiarities connecting the distances and
densities, to which we shall devote a few words. In the primordial state
of the system, when the nebulous masses agglomerated into spheres, the
diameter of these nebulous spheres would be determined by the relation
existing between the rotation of the mass, and the gravitating force at
the centre; for as long as the centrifugal force at the equator exceeded
the gravitating force, there would be a continual throwing off of matter
from the equator, as fast as it was brought from the poles, until a
balance was produced. It is also extremely probable, (especially if the
elementary components of water are as abundant in other planets as we
have reason to suppose them to be on the earth,) that the condensation
of the gaseous planets into liquids and solids, was effected in a _brief
period of time_,[38] leaving the lighter and more elastic substances as
a nebulous atmosphere around globes of semi-fluid matter, whose
diameters have never been much increased by the subsequent condensation
of their gaseous envelopes. The extent of these atmospheres being (in
the way pointed out) determined by the rotation, their subsequent
condensation has not therefore changed the original rotation of the
central globe by any appreciable quantity. The present rotation of the
planets, is therefore competent to determine the former diameters of the
nebulous planets, _i.e._, the limit where the present central force
would be balanced by the centrifugal force of rotation. If we make the
calculation for the planets, and take for the unit of each planet its
present diameter, we shall find that they have condensed from their
original nebulous state, by a quantity dependent on the distance, from
the centre of the system; and therefore on the original temperature of
the nebulous mass at that particular distance. Let us make the
calculation for Jupiter and the earth, and call the original nebulous
planets the nucleus of the vortex. We find the Equatorial diameter of
Jupiter's nucleus in equatorial diameters of Jupiter = 2.21, and the
equatorial diameter of the earth's nucleus, in equatorial diameters of
the earth = 6.59. Now, if we take the original temperature of the
nebulous planets to be inversely, as the squares of the distances from
the sun, and their volumes directly as the cubes of the diameters in the
unit of each, we find that these cubes are to each other, in the inverse
ratio of the squares of the planet's distances; for,

  2.21³ : 6.59³ :: 1² : 5.2²,

showing that both planets have condensed equally, allowing for the
difference of temperature at the beginning. And we shall find, beginning
at the sun, that the diameters of the nebulous planets, _ceteris
paribus_, diminish outwards, giving for the nebulous sun a diameter of
16,000,000 miles,[39] thus indicating his original great temperature.

That the original nebulous planets did rotate in the same time as they
do at present, is proved by Saturn's ring; for if we make the
calculation, about twice the diameter of Saturn. Now, the diameter of
the planet is about 80,000 miles, which will also be the semi-diameter
of the nebulous planet; and the middle of the outer ring has also a
semi-diameter of 80,000 miles; therefore, the ring is the equatorial
portion of the original nebulous planet, and ought, on this theory, to
rotate in the same time as Saturn. According to Sir John Herschel,
Saturn rotates in 10 hours, 29 minutes, and 17 seconds, and the ring
rotates in 10 hours, 29 minutes, and 17 seconds: yet this is not the
periodic time of a satellite, at the distance of the middle of the ring;
neither ought the rings to rotate in the same time; yet as far as
observation can be trusted, both the inner and outer ring do actually
rotate in the same time. The truth is, the ring rotates too fast, if we
derive its centrifugal force from the analogy of its satellites; but it
is, no doubt, in equilibrium; and the effective mass of Saturn on the
satellites is less than the true mass, in consequence of his radial
stream being immensely increased by the additional force impressed on
the ether, by the centrifugal velocity of the ring. If this be so, the
mass of Saturn, derived from one of the inner satellites, will be less
than the same mass derived from the great satellite, whose orbit is
considerably inclined. The analogy we have mentioned, between the
diameters of the nebulous planets and their distances, does not hold
good in the case of Saturn, for the reason already assigned, viz.: that
the nebulous planet was probably not a globe, but a cylindrical ring,
vacant around the axis, as there is reason to suppose is the case at
present.

And now we have to ask the question, Did the ether involved in the
nebulous planets rotate in the same time? This does not necessarily
follow. The ether will undoubtedly tend to move with increasing velocity
to the very centre of motion, obeying the great dynamical principle when
unresisted. If resisted, the law will perhaps be modified; but in this
case, its motion of translation will be converted into atomic motion or
heat, according to the motion lost by the resistance of atomic matter.
This question has a bearing on many geological phenomena. As regards the
general effect, however, the present velocity of the ether circulating
round the planets, may be considered much greater than the velocities of
the planets themselves.

PERTURBATIONS DUE TO THE ETHER.

In these investigations it is necessary to bear in mind that the whole
resisting power of the ether, in disturbing the planetary movements, is
but small, in comparison with gravitation. We will, however, show that,
in the case of the planets, there is a compensation continually made by
this resistance, which leaves but a very small outstanding balance as a
disturbing power. If we suppose all the planets to move in the central
plane of the vortex in circular orbits, and the force of the radial
stream, (or that portion which is not in accordance with the law of
gravitation,) to be inversely as the square roots of the distances from
the sun, it is evident, from what has been advanced, that an equilibrium
could still obtain, by variations in the densities, distances and
diameter of the planets. Supposing, again, that the planets still move
in the same plane, but in elliptical orbits, and that they are in
equilibrium at their mean distances, under the influence or action of
the tangential current, the radial stream, and the density of the ether;
we see that the force of the radial stream is too great at the
perihelion, and too small at the aphelion. At the perihelion the planet
is urged from the sun and at the aphelion towards the sun. The density
and consequent momentum is also relatively too great at the perihelion,
which also urges the planet from the sun, and at the aphelion,
relatively too small, which urges the planet towards sun; and the law is
the same in both cases, being null at the mean distance of the planet,
at a maximum at the apsides; it is, consequently, as the cosine of the
planet's eccentric anomaly at other distances, and is positive or
negative, according as the planet's distance is above or below the mean.

At the planet's mean distance, the circular velocity of the vortex is
equal to the circular velocity of the planet, and, at different
distances, is inversely in the sub-duplicate ratio of those distances.
But the circular velocity of a planet in the same orbit, is in the
simple ratio of the distances inversely. At the perihelion, the planet
therefore moves faster than the ether of the vortex, and at the
aphelion, slower; and the difference is as the square roots of the
distances; but the force of resistance is as the square of the velocity,
and is therefore in the simple ratio of the distances, as we have
already found for the effect of the radial stream, and centrifugal
momentum of the internal ether. At the perihelion this excess of
tangential velocity creates a resistance, which urges the planet towards
the sun, and at the aphelion, the deficiency of tangential velocity
urges the planet from the sun,--the maximum effect being at the apsides
of the orbit, and null at the mean distances. In other positions it is,
therefore, as the cosines of the eccentric anomaly, as in the former
case; but in this last case it is an addititious force at the
perihelion, and an ablatitious force at the aphelion, whereas the first
disturbing force was an ablatitious force at the perihelion, and an
addititious force at the aphelion; therefore, as we must suppose the
planet to be in equilibrium at its mean distance, it is in equilibrium
at all distances. Hence, a planet moving in the central plane of the
vortex, experiences no disturbance from the resistance of the ether.

As the eccentricities of the planetary orbits are continually changing
under the influence of the law of gravitation, we must inquire whether,
under these circumstances, such a change would not produce a permanent
derangement by a change in the mean force of the radial stream, so as to
increase or diminish the mean distance of the planet from the sun. The
law of force deduced from the theory for the radial stream is as the 2.5
power of the distances inversely. But, by dividing this ratio, we may
make the investigation easier; for it is equivalent to two forces, one
being as the squares of the distances, and another as the square roots
of the distances. For the former force, we find that in orbits having
the same major axis the mean effect will be as the minor axis of the
ellipse _inversely_, so that two planets moving in different orbits, but
at the same mean distance, experience a less or greater amount of
centripulsive force from this radial stream, according as their orbits
are of less or greater eccentricity, and this in the ratio of the minor
axis. On the other hand, under the influence of a force acting
centripulsively in the inverse ratio of the square roots of the
distances, we find the mean effect to be as the minor axis of the
ellipse _directly_, so that two planets in orbits of different
eccentricity, but having the same major axis, experience a different
amount from the action of this radial stream, the least eccentric orbit
being that which receives the greatest mean effect. By combining these
two results, we get a ratio of equality; and, consequently, the action
of the radial stream will be the same for the same orbit, whatever
change may take place in the eccentricity, and the mean distance of the
planet will be unchanged. A little consideration will also show that the
effect of the centrifugal momentum due to the density of ether will also
be the same by change of eccentricity; for the positive will always
balance the negative effect at the greatest and least distances of the
planet. The same remark applies to the effect of the tangential current,
so that no change can be produced in the major axes of the planetary
orbits by change of eccentricity, as an effect of the resistance of the
ether.

We will now suppose a planet's orbit to be inclined to the central plane
of the vortex, and in this case, also, we find, that the action of the
radial stream tends to increase the inclination in one quadrant as much
as it diminishes it in the next quadrant, so that no change of
inclination will result. But, if the inclination of the orbit be changed
by planetary perturbations, the mean effect of the radial stream will
also be changed, and this will tell on the major axis of the orbit,
enlarging the orbit when the inclination diminishes, and contracting it
when it increases. The change of inclination, however, must be referred
to the central plane of the vortex. Notwithstanding the perfection of
modern analysis, it is confessed that the recession of the moon's nodes
does yet differ from the theory by its 350th part, and a similar
discrepancy is found for the advance of the perigee.[40] This theory is
yet far too imperfect to say that the action of the ethereal medium will
account for these discrepancies; but it certainly wears a promising
aspect, worthy the notice of astronomers. There are other minute
discordancies between theory and observation in many astronomical
phenomena, which theory _is_ competent to remove. Some of these we shall
notice presently; and, it may be remarked, that it is in those minute
quantities which, in astronomy, are usually attributed to errors of
observation, that this theory will eventually find the surest evidence
of its truth.

KEPLER'S THIRD LAW ONLY APPROXIMATELY TRUE.

But it may be asked: If there be a modifying force in astronomy derived
from another source than that of gravitation, why is it that the
elements of the various members of the system derived solely from
gravitation should be so perfect? To this it may be answered, that
although astronomers have endeavored to derive every movement in the
heavens from that great principle, they have but partially succeeded.
Let us not surrender our right of examining Nature to the authority of a
great name, nor call any man master, either in moral or physical
science. It is well known that Kepler's law of the planetary distances
and periods, is a direct consequence of the Newtonian Law of
gravitation, and that the squares of the periodic times ought to be
proportional to the cubes of the mean distances. These times are given
accurately by the planets themselves, by the interval elapsing between
two consecutive passages of the node, and as in the case of the ancient
planets we have observations for more than two thousand years past,
these times are known to the fraction of the second. The determination
of the distances however, depends on the astronomer, and a tyro in the
science might suppose that these distances were actually measured; and
so they are roughly; but the astronomer does not depend on his
instruments, he trusts to _analogy_, and the mathematical perfection of
a law, which in the abstract is true; but which he does not know is
rigidly exact when applied to physical phenomena. From the immense
distance of the planets and the smallness of the earth, man is unable to
command a base line sufficiently long, to make the horizontal parallax a
sensible angle for the more distant planets; and there are difficulties
of no small magnitude to contend with, with those that are the nearest.
In the occasional transit of Venus across the sun, however, he is
presented with a means of measuring on an enlarged scale, from which the
distance of the sun is determined; and by _analogy_ the distance of all
the planets. Even the parallax of the sun itself is only correct, by
supposing that the square of the periodic time of Venus is in the same
proportion to the square of the periodic time of the earth as the cube
of her distance is to the cube of the earth's distance. Our next nearest
planet is Mars, and observations on this planet at its opposition to the
sun, invariably give a larger parallax for the sun--Venus giving 8.5776″
while Mars gives about 10″. It is true that the first is obtained under
more favorable circumstances; but this does not prove the last to be
incorrect. It is well known that the British Nautical Almanac contains a
list of stars lying in the path of the planet Mars about opposition,
(for the very purpose of obtaining a correct parallax,) that minute
differences of declination may be detected by simultaneous observations
in places having great differences of latitude. Yet strange to say, the
result is discredited when not conformable to the parallax given by
Venus. If then, we cannot trust the parallax of Mars, _à fortiori_, how
can we trust the parallax of Jupiter, and say that his mean distance
exactly corresponds to his periodic time? Let us suppose, for instance,
that the radius vector of Jupiter fell short of that indicated by
analogy by 10,000 miles, we say that it would be extremely difficult,
nay, utterly impossible, to detect it by instrumental means. Let not
astronomers, therefore, be too sure that there is not a modifying cause,
independent of gravitation, which they will yet have to recognize. The
moon's distance is about one-fourth of a million of miles, and Neptune's
2854 millions, or in the ratio of 10,000 to 1; yet even the moon's
parallax is not trusted in determining her mass, how then shall we
determine the parallax of Neptune? It is therefore _possible_ that the
effective action of the sun is in some small degree different, on the
different planets, whether due to the action of the ether, to the
similarity or dissimilarity of material elements, to the temperature of
the different bodies, or to all combined, is a question yet to be
considered.

As another evidence of the necessity of modifying the strict wording of
the Newtonian law, it is found that the disturbing action of Jupiter on
different bodies, gives different values for the mass of Jupiter. The
mass deduced from Jupiter's action on his satellites, is different from
that derived from the perturbations of Saturn, and this last does not
correspond with that given by Juno: Vesta also gives a different mass
from the comet of Encke, and both vary from the preceding values.[41]

In the analytical investigation of planetary disturbances, the
disturbing force is usually divided into a radial and tangential force;
the first changing the law of gravitation, to which law the elliptic
form of the orbit is due. The radial disturbing force, therefore, being
directed to or from the centre, can have no influence over the first law
of Kepler, which teaches that the radius vector of each planet having
the sun as the centre, describes equal areas in equal times. If the
radial disturbing force be exterior to the disturbed body, it will
diminish the central force, and cause a progressive motion in the
aphelion point of the orbit. In the case of the moon this motion is very
rapid, the apogee making an entire revolution in 3232 days. Does this,
however, correspond with the law of gravitation? Sir Isaac Newton, in
calculating the effect of the sun's disturbing force on the motion of
the moon's apogee, candidly concludes thus: "Idoque apsis summa singulis
revolutionibus progrediendo conficit 1° 31′ 28″. Apsis lunæ est duplo
velocior circiter." As there was a necessity for reconciling this
stubborn fact with the theory, his followers have made up the deficiency
by resorting to the tangential force, or, as Clairant proposed, by
continuing the approximations to terms of a higher order, or to the
square of the disturbing force.

Now, in a circular orbit, this tangential force will alternately
increase and diminish the velocity of the disturbed body, without
producing any permanent derangement, the same result would obtain in an
elliptical orbit, if the position of the major axis were stationary. In
the case of the moon, the apogee is caused to advance by the disturbing
power of the radial force, and, consequently, an exact compensation is
not effected: there remains a small excess of velocity which geometers
have considered equivalent to a doubling of the radial force, and have
thus obviated the difficulty. To those not imbued with the profound
penetration of the modern analyst, there must ever appear a little
inconsistency in this result. The major axis of a planet's orbit depends
solely on the velocity of the planet at a given distance from the sun,
and the tangential portion of the disturbance due to the sun, and
impressed upon the moon, must necessarily increase and diminish
alternately the velocity of the moon, and interfere with the equable
description of the areas. If, then, there be left outstanding a small
excess of velocity over and above the elliptical velocity of the moon,
at the end of each synodical revolution, in consequence of the motion
impressed on the moon's apogee by the radial force, the _legitimate_
effect would be a small enlargement of the lunar orbit every revolution
in a rapidly-increasing ratio, until the moon would at last be taken
entirely away. In the great inequality of Jupiter and Saturn, this
tangential force is not compensated at each revolution, in consequence
of continual changes in the configuration of the two planets at their
heliocentric conjunctions, with respect to the perihelion of their
orbits, and the near commensurability of their periods; and the effect
of the tangential force is, in this case, legitimately impressed on the
major axes of the orbits. But why (we may ask) should not this also be
expended on the motion of the aphelion as well as in the case of the
moon? Astronomy can make no distinctions between the orbit of a planet
and the orbit of a satellite. And, we might also ask, why the tangential
resistance to the comet of Encke should not also produce a retrograde
motion in the apsides of the orbit, instead of diminishing its period?
To the honor of Newton, be it remembered, that he never resorted to an
explanation of this phenomenon, which would vitiate that fundamental
proposition of his theory, in which the major axis of the orbit is shown
to depend on the velocity at any given distance from the focus.

Some cause, however, exists to double the motion of the apogee, and
that there is an outstanding excess of orbital velocity due to the
tangential force, is also true. This excess may tell in the way
proposed, provided some other arrangement exists to _prevent_ a
permanent dilation of the lunar orbit; and this provision may be found
in the increasing density of the ether, which prevents the moon
overstepping the bounds prescribed by her own density, and the force of
the radial stream of the terral vortex. In the case of Jupiter and
Saturn, their mutual action is much less interfered with by change of
density in the ether in the enlarged or contracted orbit, and,
consequently, the effect is natural. Thus, we have in the law of density
of the ethereal medium a better safeguard to the stability of the
dynamical balance of the system, than in the profound and beautiful
Theorems of La Grange. It will, of course, occur to every one, that we
are not to look for the same law in every vortex, and it will,
therefore, appear as if the satellites of Jupiter, whose theory is so
well known, should render apparent any deviation between their periodic
times and the periodic times of the contiguous parts of the vortex,
which would obtain, if the density of the ether in the Jovian vortex
were not as the square roots of the distances directly. But, we have
shown how there can be a balance preserved, if the tangential resistance
of the vortex shall be equal and contrary at the different distances at
which the satellites are placed; that is, if these two forces shall
follow the same law. These are matters, however, for future
investigation.

LIGHT AND HEAT.

But will not the admission of a vorticose motion of the ethereal medium,
affect the aberration of light? It is well known that the question has
been mooted, whether the velocity of reflected light is the same as that
of direct light. The value of aberration having been considered 20″.25,
from the eclipses of Jupiter's satellites, while later determinations,
from observations on Polaris, give 20″.45. It cannot be doubted that
light, in traversing the central parts of the solar vortex, that is,
having to cross the whole orbit of the earth, should pass this distance
in a portion of time somewhat different to a similar distance outside
the earth's orbit, where the density is greater, and consequently induce
an error in the aberration, determined by the eclipses of Jupiter's
satellites. In the case of Polaris, the circumstances are more equal;
still, a difference ought to be detected between the deduced aberration
in summer and in winter, as, in the first case, the light passes near
the axis of the solar vortex, where (according to the theory) a change
of density occurs. This is an important practical question, and the
suggestion is worthy attention. Now, the question occurs, will light
pass through the rarefied space with greater velocity than through the
denser ether beyond? From recent experiments, first instituted by Arago,
it is determined that light passes with less velocity through water than
through air; and one result of these experiments is the confirmation
they give to the theory of Fresnel, that the medium which conveys the
action of light partly partakes of the motion of the refracting body.
This of itself is a strong confirmation of this theory of an ethereal
medium. It may also be remarked, that every test applied to the
phenomenon of light, adds additional strength to the undulatory theory,
at the expense of the Newtonian theory of emission. As light occupies
time in traversing space, it must follow from the theory that it does
not come from the radiant point exactly in straight lines, inasmuch as
the ether itself is in motion tangentially,--the velocity being in the
sub-duplicate ratio of the distances from the sun inversely.

May not that singular phenomenon,--the projection of a star on the
moon's disc, at the time of an occultation,--be due to this curvature of
the path of a ray of light, by considering that the rays from the moon
have less intensity, but more mechanical momentum, and consequently
more power to keep a straight direction? Let us explain: we have urged
that light, as well as heat, is a mechanical effect of atomic motion,
propagated through an elastic medium; that, _ceteris paribus_, the
product of matter by its motion is ever a constant quantity for equal
spaces throughout the universe,--in a word, that it is, and must
necessarily be, a fundamental law of nature. All departures from this
law are consequences of accidental arrangements, which can only be
considered of temporary duration. Our knowledge of planetary matter
requires the admission of differences in the density, form, and size of
ultimate atoms, and, according to the above law, when the atoms are of
uniform temperature or motion, the product of the matter of each by its
motion, when reduced to the same space, will be constant. The momentum
of two different atoms, therefore, we will consider equal, for the sake
of illustration; yet this momentum is made up of two different
elements,--matter and motion. Let us exaggerate the difference, and
assign a ratio of 1000 to 1. Suppose a ball of iron of 1000 lbs.,
resting upon a horizontal plane, should be struck by another ball of 1
lb., having a motion of 1000 feet in a second, and, in a second case,
should be struck by a ball of 1000 lbs., having a velocity of 1 foot per
second, the momentum of each ball is similar; but experience proves that
the motion impressed on the ball at rest is not similar; the ponderous
weight and slow motion is far more effective in displacing this ball,
for the reason that time is essential to the distribution of the motion.
If the body to be struck be small as, for instance, a nail, a greater
motion and less matter is more effective than much matter and little
motion. Hence, we have a _distinction_ applicable to the difference of
momentum of luminous and calorific rays. The velocity of a wave of sound
through the atmosphere, is the same for the deep-toned thunder and the
shrillest whistle,--being dependent on the density of the medium, and
not on the source from which it emanates. So it is in the ethereal
medium.

This view is in accordance with the experiments of M. Delaroche and
Melloni, on the transmission of light and heat through diaphanous
bodies--the more calorific rays feeling more and more the influence of
thickness, showing that more motion was imparted to the particles of the
diaphanous substance by the rays possessing more material momentum, and
still more when the temperature of the radiating body was low, evidently
analogous to the illustration we have cited. Light may therefore be
regarded as the effect of the vibration of atoms having little mass, and
as this mass increases, the rays become more calorific, and finally the
calorific effect is the only evidence of their existence; as towards the
extreme red end of the spectrum they cease to be visible, owing to their
inability to impart their vibrations to the optic nerve. This may also
influence the law of gravitation. In this we have also an explanation of
the dispersion of light. The rays proceeding from atoms of small mass
having less material momentum, are the most refrangible, and those
possessing greater material momentum, are the least refrangible; so that
instead of presenting a difficulty in the undulatory theory of light,
this dispersion is a necessary consequence of its first principles.

It is inferred from the experiments cited, and the facts ascertained by
them, viz.: that the velocity of light in water is less than its
velocity in air; that the density of the ether is greater in the first
case; but this by no means follows. We have advocated the idea, that the
ethereal medium is less dense within a refracting body than without. We
regard it as a fundamental principle. Taking the free ether of heaven;
the vibrations in the denser ether will no doubt be slowest; but within
a refracting body we must consider there is motion lost, or _light
absorbed_, and the time of the transmission is thus increased.

There has been a phenomenon observed in transits of Mercury and Venus
across the sun, of which no explanation has been rendered by
astronomers. When these planets are visible on the solar disc, they are
seen surrounded by rings, as if the light was intercepted and increased
alternately. This is no doubt due to a small effect of interference,
caused by change of velocity in passing through the rarefied nucleus of
these planetary vortices, near the body of the planet, and through the
denser ether beyond, acting first as a concave, and secondly as a convex
refracting body; always considering that the ray will deviate _towards_
the side of least insistence, and thus interfere.

That heat is simply atomic motion, and altogether mechanical, is a
doctrine which ought never to have been questioned. The interest excited
by the bold experiments of Ericson, has caused the scientific to
_suspect_, that heat can be converted into motion, and motion into
heat--a fact which the author has considered too palpable to deny for
the last twenty years. He has ever regarded matter and motion as the two
great principles of nature, ever inseparable, yet variously combined;
and that without these two elements, we could have no conception of
anything existing.

It may be thought by some, who are afraid to follow truth up the rugged
precipices of the hill of knowledge, that this theory of an
interplanetary plenum leads to materialism; forgetting, that He who made
the world, formed it of matter, and pronounced it "very good." We may
consider ethereal matter, in one sense, _purer_ than planetary matter,
because unaffected by chemical laws. Whether still purer matter exists,
it is not for us to aver or deny. The Scriptures teach us that "there is
a natural body and there is a spiritual body." Beyond this we know
nothing. We, however, believe that the _invisible_ world of matter, can
only be comprehended by the indications of that which is visible; yet
while humbly endeavoring to connect by one common tie, the various
phenomena of matter and motion, we protest against those doctrines which
teach the eternal duration of the present order of things, as being
incompatible with the analogies of the past, as well as with the
revelations of the future.

FOOTNOTES:

[35] Silliman's Journal, vol xxxv., page 283.

[36] The real diameter of the earth in that latitude, whose sine is
one-third, is a little greater than this; but the true mean is more
favorable for the Newtonian law.

[37] This is, perhaps, the nearest ratio of the densities and distances.

[38] This is an important consideration, as bearing on the geology of
the earth.

[39] It is not as likely that the condensation of the sun was so sudden
as that of the planets, and therefore in this case this distance is only
approximate.

[40] Mechanique Celeste. Theory of the Moon.

[41] Mechanique Celeste. Masses of the planets.

SECTION FIFTH.

COMETARY PHENOMENA.

The planetary arrangements of the solar system are all _à priori_
indications of the theory of vortices, not only by the uniform direction
of the motions, the circular orbits in which these motions are
performed, the near coincidence of the planes of these orbits, and the
uniform direction of the rotation of the planets themselves; but, also,
by the law of densities and distances, which we have already attempted
to explain. In the motions of comets we find no such agreement. These
bodies move in planes at all possible inclinations in orbits extremely
eccentrical and without any general direction--as many moving contrary
to the direction of the planets as in the opposite direction; and when
we consider their great volume, and their want of mass, it appears, at
first sight, that comets do present a serious objection to the theory.
We shall point out, however, a number of _facts_ which tend to
invalidate this objection, and which will ultimately give the
preponderance to the opposite argument.

Every fact indicative of the nature of comets proves that the nuclei are
masses of material gases, similar, perhaps (at least in the case of the
short-period comets), to the elementary gases of our own planet, and,
consequently, these masses must be but small. In the nascent state of
the system, the radial stream of the vortex would operate as a fan,
purging the planetary materials of the least ponderable atoms, and, as
it were, separating the wheat from the chaff. It is thus we conceive
that the average atomic density of each planet has been first determined
by the radial stream, and, subsequently, that the solidification of the
nebulous planets has, by their atomic density, assigned to each its
position in the system, from the consequent relation which it
established between the density of the ether within the planet, and the
density of the ether external to it, so that, according to this view, a
single isolated atom of the same density as the mean atomic density of
the earth could (_ceteris paribus_) revolve in an orbit at the distance
of the earth, and in the same periodic time. This, however, is only
advanced by way of illustration.

The expulsive force of the radial stream would thus drive off this
cometary dust to distances in some inverse ratio of the density of the
atoms; but, a limit would ultimately be reached, when gravitation would
be relatively the strongest--the last force diminishing only as the
squares of the distances, and the first diminishing in the compound
ratio of the squares and the square roots of the distances. At the
extreme verge of the system, this cometary matter would accumulate, and,
by accumulation, would still further gather up the scattered atoms--the
sweepings of the inner space--and, in this condensed form, would again
visit the sun in an extremely elongated ellipse. It does not, however,
follow, that all comets are composed of such unsubstantial materials.
There may be comets moving in parabolas, or even in hyperbolas--bodies
which may have been accumulating for ages in the unknown regions of
space, far removed from the sun and stars, drifting on the mighty
currents of the great ethereal ocean, and thus brought within the sphere
of the sun's attraction; and these bodies may have no analogy to the
periodical comets of our system, which last are those with which we are
more immediately concerned.

The periodical comets known are clearly arranged into two distinct
classes--one having a mean distance between Saturn and Uranus, with a
period of about seventy-five years, and another class, whose mean
distance assigns their position between the smaller planets and Jupiter,
having periods of about six years. These last may be considered the
siftings of the smaller planets, and the first the refuse of the
Saturnian system. In this light we may look for comets having a mean
distance corresponding to the intervals of the planets, rather than to
the distances of the planets themselves. One remarkable fact, however,
to be observed in these bodies is, that all their motions are in the
same direction as the planets, and, with one exception, there is no
periodical comet positively known whose motion is retrograde.

The exception we have mentioned is the celebrated comet of Halley, whose
period is also about seventy-five years. In reasoning on the resistance
of the ether, we must consider that the case can have very little
analogy with the theory of projectiles in air; nor can we estimate the
inertia of an infinitely divisible fluid, from its resisting influence
on atomic matter, by a comparison of the resistance of an atomic fluid
on an atomic solid. Analogy will only justify comparisons of like with
like. The tangent of a comet's orbit, also, can only be tangential to
the circular motion of the ether at and near perihelion, which is a very
small portion of its period of revolution. As far as the tangential
resistance is concerned, therefore, it matters little whether its motion
be direct or retrograde. If a retrograde comet, of short period and
small eccentricity, were discovered moving also near the central plane
of the vortex, it would present a very serious objection, as being
indicative of contrary motions in the nascent state of the system. There
is no such case known. So, also, with the inclinations of the orbits; if
these be great, it matters little whether the comet moves in one way or
the other, as far as the tangential current of the vortex is concerned.
Yet, when we consider the average inclination of the orbit, and not of
its plane, we find that the major axes of nearly all known cometary
orbits are very little inclined to the plane of the ecliptic.

In the following table of all the periodical comets known, the
inclination of the major axis of the orbit is calculated to the nearest
degree; but all cometary orbits with very few exceptions, will be found
to respect the ecliptic, and never to deviate far from that plane:

  +--------------------------------------------------------------------+
  |  Designations  | Periodic  | Inclination | Motion    | Planetary   |
  | of the Comets. |  times.   |    of       | in Orbit. | Intervals.  |
  |                |           | Major Axes  |           |             |
  |--------------------------------------------------------------------|
  |Encke    | 1818 | 3 years.  |      1°     | Direct    |Mars & Ceres.|
  |--------------------------------------------------------------------|
  |De Vico  | 1814 |           |      2      | Direct    |             |
  |Fayo     | 1843 |           |      4      | Direct    |   Ceres     |
  |De Avrest| 1851 |   From    |      1      | Direct    |             |
  |Brorsen  | 1846 |   five    |      7      | Direct    |    and      |
  |Messier  | 1766 |   to      |      0      | Direct    |             |
  |Clausen  | 1743 |   six     |      0      | Direct    |  Jupiter.   |
  |Pigott   | 1783 |   or      |      4      | Direct    |             |
  |Pous     | 1819 |   seven   |      3      | Direct    |             |
  |Biela    | 1826 |   years.  |      9      | Direct    |             |
  |Blaupain | 1819 |           |      2      | Direct    |             |
  |Lexell   | 1770 |           |      1      | Direct    |             |
  |--------------------------------------------------------------------|
  |Pous     | 1812 |           |     17      | Direct    |             |
  |Olbers   | 1816 |   about   |     40      | Direct    |  Saturn     |
  |De Vico  | 1846 |   75      |     13      | Direct    |    and      |
  |Brorsen  | 1847 |   years.  |     12      | Direct    |  Uranus.    |
  |Westphal | 1852 |           |     21      | Direct    |             |
  |Halley   | 1682 |           |     16      | Retrograde|             |
  +--------------------------------------------------------------------+

From which it appears, that the objection arising from the great
inclination of the _planes_ of these orbits is much less important than
at first it appears to be.

Regarding then, that a comet's mean distance depends on its mean atomic
density, as in the case of the planets, the undue enlargement of their
orbits by planetary perturbations is inadmissible. In 1770 Messier
discovered a comet which approached nearer the earth than any comet
known, and it was found to move in a small ellipse with a period of five
and a half years; but although repeatedly sought for, it was the
opinion of many, that it has never been since seen. The cause of this
seeming anomaly is found by astronomers in the disturbing power of
Jupiter,--near which planet the comet must have passed in 1779, but the
comet was not seen in 1776 before it passed near Jupiter, although a
very close search was kept up about this time. Now there are two
suppositions in reference to this body: the comet either moved in a
larger orbit previous to 1767, and was then caused by Jupiter to
diminish its velocity sufficiently to give it a period of five and a
half years, and that after perihelion it recovered a portion of its
velocity in endeavoring to get back into its natural orbit; or if moving
in the natural orbit in 1770, and by passing near Jupiter in 1779 this
orbit was deranged, the comet will ultimately return to that mean
distance although not necessarily having elements even approximating
those of 1770. In 1844, September 15th, the author discovered a comet in
the constellation Cetus, (the same previously discovered by De Vico at
Home,) and from positions _estimated with the naked eye_ approximately
determined the form of its orbit and its periodic time to be very
similar to the lost comet of 1770. These conclusions were published in a
western paper in October 1844, on which occasion he expressed the
conviction, that this was no other than the comet of 1770. As the
question bore strongly on his theory he paid the greater attention to
it, and had, previously to this time, often searched in hopes of finding
that very comet. Since then, M. Le Verrier has examined the question of
identity and given his decision against it; but the author is still
sanguine that the comet of 1844 is the same as that of 1770, once more
settled at its natural distance from the sun. This comet returns to its
perihelion on the 6th of August, 1855, according to Dr. Brünnow, when,
it is hoped, the question of identity will be reconsidered with
reference to the author's principles; and, that when astronomers become
satisfied of this, they will do him the justice of acknowledging that
he was the first who gave publicity to the fact, that the "Lost Comet"
was found.

That comets do experience a resistance, is undeniable; but not in the
way astronomers suppose, if these views be correct. The investigations
of Professor Encke, of Berlin, on the comet which bears his name, has
determined the necessity of a correction, which has been applied for
several returns with apparent success. But there is this peculiarity
about it, which adds strength to our theory: "The Constant of
Resistance" requires a change after perihelion. The necessity for this
change shows the action of the radial stream. From the law of this
force, (reckoning on the central plane of the vortex,) there is an
outstanding portion, acting as a disturbing power, in the sub-duplicate
ratio of the distances inversely. If we only consider the mean or
average effect in orbits nearly circular, this force may be considered
as an ablatitious force at all distances below the mean, counterbalanced
by an opposite effect at all distances above the mean. But when the
orbits become very eccentrical, we must consider this force as
momentarily affecting a comet's velocity, diminishing it as it
approaches the perihelion, and increasing it when leaving the
perihelion. A resolution of this force is also requisite for the comet's
distance above the central plane of the vortex, and a correction,
likewise, for the intensity of the force estimated in that plane. There
is also a correction necessary for the perihelion distance, and another
for the tangential current; but we are only considering here the general
effect. By diminishing the comet's proper velocity in its orbit, if we
consider the attraction of the sun to remain the same, the general
effect _may_ be (for this depends on the tangential portion of the
resolved force preponderating) that the absolute velocity will be
increased, and the periodic time shortened; but after passing the
perihelion, with the velocity of a smaller orbit, there is also
superadded to this already undue velocity, the expulsive power of the
radial stream, adding additional velocity to the comet; the orbit is
therefore enlarged, and the periodic time increased. Hence the necessity
of changing the "Constant of Resistance" after perihelion, and this will
generally be found necessary in all cometary orbits, if this theory be
true. But this question is one which may be emphatically called the most
difficult of dynamical problems, and it may be long before it is fully
understood.

According to the calculations of Professor Encke, the comet's period is
accelerated about 2 hours, 30 minutes, at each return, which he
considers due to a resisting medium. May it not rather be owing to _the
change of inclination of the major axis of the orbit, to the central
plane of the vortex_? Suppose the inclination of the _plane_ of the
orbit to remain unchanged, and the eccentricity of the orbit also, if
the longitude of the perihelion coincides with that of either node, the
major axis of the orbit lies in the ecliptic, and the comet then
experiences the greatest mean effect from the radial stream; its mean
distance is then, _ceteris paribus_, the greatest. When the angle
between the perihelion and the nearest node increases, the mean force of
the radial stream is diminished, and the mean distance is diminished
also. When the angle is 90°, the effect is least, and the mean distance
least. This is supposing the ecliptic the central plane of the vortex.
When Encke's formula was applied to Biela's comet, it was inadequate to
account for a tenth part of the acceleration; and although Biela moves
in a much denser medium, and is of less dense materials, even this taken
into account will not satisfy the observations,--making no other change
in Encke's formula. We must therefore attribute it to changes in the
elements of the orbits of these comets. Now, the effect of resistance
should also have been noticed, as an acceleration of Halley's comet in
1835, yet the period was prolonged. To show, that our theory of the
_cause_ of these anomalies corresponds with facts, we subjoin the
elements in the following tables, taken from Mr. Hind's catalogue:

THE ELEMENTS OF ENCKE'S COMET.

   Date of     Longitude of   Longitude of   Difference of
  Perihelion.  Perihelion.    nearest Node     Longitude.
    1822       157° 11′ 44″   154° 25′  9″     2° 46′ 35″
    1825       157  14  31    154  27  30      2  47   1
    1829       157  17  53    154  29  32      2  48  21
    1832[42]   157  21   1    154  32   9      2  41  52
    1835       157  23  29    154  34  59      2  48  30
    1838       157  27   4    154  36  41      2  50  23
    1842       157  29  27    154  39  10      2  50  17
    1845       157  44  21    154  19  33      3  24  48
    1848       157  47   8    154  22  12      3  24  56
    1852       157  51   2    154  23  21      3  27  41

In this we see a regular increase of the angle, which ought to be
attended with a small acceleration of the comet; but the change of
inclination of the orbit ought also to be taken into consideration, to
get the mean distance of the comet above the plane of the vortex, and,
by this, the mean force of the radial stream.

In the following table, the same comparison is made for Biela's comet:--

ELEMENTS OF BIELA'S COMET.

   Date of     Longitude of   Longitude of    Difference of
  Perihelion.  Perihelion.    nearest Node.    Longitude.
    1772       110° 14′ 54″    74°  0′  1″     36° 14′ 53″
    1806       109  32  23     71  15  15      38  17   8
    1826       109  45  50     71  28  12      38  17  38[43]
    1832       110  55  55     68  15  36      41  45  19
    1846       109   2  20     65  54  39      43   7  41

Between 1832 and 1846, the increase of the angle is twice as great for
Biela as for Encke, and the angle itself throws the major axis of Biela
10° above the ecliptic, whereas the angle made by Encke's major axis, is
only about 1°; the cosine of the first angle, diminishes much faster
therefore, and consequently the same difference of longitude between the
perihelion and node, will cause a greater acceleration of Biela; and
according to Prof. Encke's theory, Biela would require a resisting
medium twenty-five times greater than the comet of Encke to reconcile
observation with the theory. Halley's comet can scarcely be considered
to have had an orbit with perfect elements before 1835. If they were
known accurately for 1759, we should no doubt find, that the angle
between the node and perihelion _diminished_ in the interval between
1750 and 1835, as according to the calculations of M. Rosenberg, the
comet was six days behind its time--a fact fatal to the common ideas of
a resisting medium; but this amount of error must be received as only
approximate.

No comet that has revisited the sun, has given astronomers more trouble
than the great comet of 1843. Various orbits have been tried,
elliptical, parabolic and hyperbolic; yet none will accord with all the
observations. The day before this comet was seen in Europe and the
United States, it was seen close to the body of the sun at Conception,
in South America; yet this observation, combined with those following,
would give an orbital velocity due to a very moderate mean distance.
Subsequent observations best accorded with a hyperbolic orbit; and it
was in view of this anomaly, that the late Sears C. Walker considered
that the comet came into collision with the sun in an elliptical orbit,
and its _debris_ passed off again in a hyperbola. That a concussion
would not add to its velocity is certain, and the departure in a
hyperbolic orbit would be contrary to the law of gravitation. This
principle is thus stated by Newton:--"In parabola velocitas ubiquo
equalis est velocitati corporis revolventis in circulo ad dimidiam
distantiam; in ellipsi minor est in hyperbola major." (Vid. Prin. Lib.
1. Prop. 6 Cor. 7.)

But as regards the _fact_, it is probable that Mr. Walker's views are
correct, so far as the change from an ellipse to an hyperbola is
considered. The Conception observation cannot be summarily set aside,
and Professor Peirce acknowledges, that "If it was made with anything of
the accuracy which might be expected from Captain Ray, it exhibits a
decided anomaly in the nature of the forces to which the comet was
subjected during its perihelion passage." The comet came up to the sun
almost in a straight line against the full force of the radial stream;
its velocity must therefore necessarily have been diminished. After its
perihelion, its path was directly _from_ the sun, and an undue velocity
would be kept up by the auxiliary force impressed upon it by the same
radial stream; and hence, the later observations give orbits much larger
than the early ones, and there can be no chance of identifying this
comet with any of its former appearances, even should its orbit be
elliptical. This unexpected confirmation of the theory by the
observation of Capt. Ray, cannot easily be surmounted.

We must now endeavor to explain the physical peculiarities of comets, in
accordance with the principles laid down. The most prominent phenomenon
of this class is the change of diameter of the visible nebulosity. It is
a most singular circumstance, but well established as a fact, that a
comet contracts in its dimensions on approaching the sun, and expands on
leaving it. In 1829, accurate measures were taken on different days, of
the diameter of Encke's comet, and again in 1838. The comet of 1618 was
also observed by Kepler with this very object, and also the comet of
1807; but without multiplying instances, it may be asserted that it is
one of those facts in cometary phenomena, to which there are no
exceptions. According to all analogy, the very reverse of this ought to
obtain. If a comet is chiefly vaporous, (as this change of volume would
seem to indicate,) its approach to the sun ought to be attended by a
corresponding expansion by increase of temperature. When the contrary is
observed, and invariably so, it ought to be regarded as an index of the
existence of other forces besides gravitation, increasing rapidly in the
neighborhood of the sun; for the disturbing power of the sun's
attraction would be to enlarge the diameter of a comet in proportion to
its proximity. Now, the force of the radial stream, as we have shown, is
as the 2.5th power of the distances inversely. If this alternate
contraction and expansion be due to the action of this force, there
ought to be an approximate correspondence of the law of the effect with
the law of the cause. Arago, in speaking of the comet of 1829, states,
"that between the 28th of October and the 24th of December, the volume
of the comet was reduced as 16000 to 1, the change of distance in the
meantime only varying about 3 to 1." To account for this, a memoir was
published on the subject by M. Valz, in which he supposes an atmosphere
around the sun, whose condensation increases rapidly from superincumbent
pressure; so that the deeper the comet penetrates into this atmosphere
the greater will be the pressure, and the less the volume. In this it is
evident, that the ponderous nature of a resisting medium is not yet
banished from the schools. In commenting on this memoir, Arago justly
observes, that "there would be no difficulty in this if it could be
admitted that the exterior envelope of the nebulosity were not permeable
to the ether; but this difficulty seems insurmountable, and merits our
sincere regret; for M. Valz's ingenious hypothesis has laid down the law
of variation of the bulk of the nebulosity, as well for the short-period
comet as for that of 1618, with a truly wonderful exactness." Now, if we
make the calculation, we shall find that the diameter of the nebulosity
of a comet is inversely as the force of the radial stream. This force is
inversely as the 2.5 power of the distances from the axis, and not from
the sun: it will, therefore, be in the inverse ratio of the cosine of
the comet's heliocentric latitude to radius, and to this ratio the
comet's distance ought to be reduced. But, this will only be correct for
the same plane or for equal distances above the ecliptic plane,
considering this last as approximately the central plane of the vortex.
From the principles already advanced, the radial stream is far more
powerful on the central plane than in more remote planes; therefore, if
a comet, by increase of latitude, approaches near the axis, thus
receiving a larger amount of force from the radial stream in that plane
than pertains to its actual distance from the sun, it will also receive
a less amount of force in that plane than it would in the central plane
at the same distance from the axis. Now, we do not know the difference
of force at different elevations above the central plane of the vortex;
but as the two differences due to elevation are contrary in their
effects and tend to neutralize each other, we shall make the calculation
as if the distances were truly reckoned from the centre of the sun.

The following table is extracted from Arago's tract on Comets, and
represents the variations of the diameter of Encke's comet at different
distances from the sun,--the radius of the orbis magnus being taken as
unity.

  Times of observation,   Distances of the        Real diameters
          1828.          comet from the sun.  in radii of the earth.
       Oct. 28                1.4617                 79.4
       Nov.  7                1.3217                 64.8
       Nov. 30                0.9668                 29.8
       Dec.  7                0.8473                 19.9
       Dec. 14                0.7285                 11.3
       Dec. 24                0.6419                  3.1

In order the better to compare the diameters with the force, we will
reduce them by making the first numbers equal.

  Distances.     Diameters.    The 2.5th power      Reduced
                               of the Distances.   Diameters.
  1.4617            79.4            2.58             2.58
  1.3217            64.8            2.10             2.10
  0.9668            29.8            0.92             0.97
  0.8473            19.9            0.66             0.65
  0.7285            11.3            0.45             0.37
  0.5419             3.1            0.21             0.10

This is a very close approximation, when we consider the difficulty of
micrometric measurement, and the fact, that as the comet gets nearer to
the sun, as at the last date of the table, the diameter is more than
proportionally diminished by the fainter nebulosity becoming invisible.
But, there may be a reality in the discrepancy apparent at the last
date, as the comet was then very near the plane of the ecliptic, and
was, consequently, exposed to the more violent action of the radial
stream.

To attempt to explain the _modus agendi_ is, perhaps, premature. Our
principal aim is to pioneer the way into the labyrinth, and it is
sufficient to connect this seeming anomaly with the same general law we
have deduced from other phenomena. Still, an explanation may be given in
strict accordance with the general principles of the theory.

Admitting the _nucleus_ of a comet to be gaseous, there is no difficulty
about the solution. According to Sir John Herschel, "stars of the
smallest magnitude remain distinctly visible, though covered by what
appears the densest portion of their substances; and since it is an
observed fact, that the large comets which have presented the appearance
of a nucleus, have yet exhibited no phases, though we cannot doubt that
they shine by the reflected solar light, it follows that even these can
only be regarded as great masses of thin vapor." That comets shine
solely by reflected solar light, is a position that we shall presently
question; but that they are masses of vapor is too evident to dispute.
According to the same authority quoted above, "If the earth were reduced
to the one thousandth part of its actual mass, its coercive power over
the atmosphere would be diminished in the same proportion, and in
consequence the latter would expand to a thousand times its actual
_bulk_." If this were so, and comets composed of the elementary gases,
some of them would have very respectable masses, as the nuclei are
frequently not more than 5,000 miles in diameter, and consequently it
becomes important to examine the principle. From all experiments the
density of an elastic fluid is directly as the compressing force; and if
a cylinder reached to the top of our atmosphere, compressed by the
gravitation of the earth, considered equal at each end of the cylinder,
it would represent the actual compressing force to which it owes its
density. If the gravitation of the earth were diminished one thousand
times this atmospheric column would expand one thousand times,[44]
(taking no account of the decrease of gravitation by increase of
distance;) so that the diameter of the aërial globe would be increased
to 108,000 miles, taking the atmosphere at 50 miles. But the mere
increasing the _bulk_ of the atmosphere 1000 times would increase the
diameter to little more than double. Even giving the correct expansion,
a comet's mass must be much greater than is generally supposed, or the
diameters of the nuclei would be greater if composed of any gas lighter
than atmospheric air.

It is very improbable that a comet is composed of only one elementary
gas, and if of many, their specific gravities will vary; the lighter, of
course, occupying the exterior layers. With such a small mass,
therefore, the upper portion of its atmosphere must be very attenuated.
Now let us remember that the density of the ether at a comet's aphelion,
is greater than at the perihelion, in the direct ratio of the square
roots of the distances from the sun nearly. At the aphelion the comet
lingers through half his period, giving ample time for the nucleus to be
permeated by ether proportionally dense with the surrounding ether of
the vortex at that distance. Thus situated, the comet descends to its
perihelion, getting faster and faster into a medium far less dense, and
there must consequently be an escape from the nucleus, or in common
parlance, the comet is positively electric. This escaping ether, in
passing through the attenuated layers composing the surface of the
nucleus, impels the lighter atoms of cometic dust further from the
centre, and as for as this _doubly_ attenuated atmosphere of isolated
particles extends, so far will the escaping ether be rendered luminous.
It may be objected here, that a contrary effect ought to be produced
when the comet is forsaking, its perihelion; but the objection is
premature, as the heat received from the sun will have the same effect
in increasing the elasticity, as change of density, and the comet will
probably part with its internal ether as long as it is visible to the
earth; and not fully regain it perhaps, until after it arrives at its
aphelion. Suppose that we admit that a comet continues to expand in the
same ratio for all distances, as is laid down for the comet of Encke
when near its perihelion; it would follow, that the comet of 1811, would
have a diameter at its aphelion of fifty millions of millions of miles,
that is, its outside would extend one thousand times further from the
sun, at the opposite side to that occupied by the centre of the comet,
than the distance of the comet's centre from the sun, at its enormous
aphelion distance. Such an absurdity shows us that there is a limit of
expansion due to natural causes, and that if there were no radial stream
the volume of a comet would be greatest when nearest the sun.

But while the comet is shortening its distance and hastening to the sun
in the form of a huge globular mass of diffuse light, it is continually
encountering another force, increasing in a far more rapid ratio than
the law of gravitation. At great distances from the sun, the force of
the radial stream was insufficient to detach any portion of the comet's
atmosphere; presently, however, the globular form is changed to an
ellipsoid, the radial stream begins to strip the comet of that doubly
attenuated atmosphere of which we have spoken, and the diameter of the
comet is diminished, merely because the luminosity of the escaping ether
is terminated at the limit of that atmosphere. Meanwhile the mass of the
comet has suffered only an infinitely small diminution; but if the
perihelion distance be small, the force may become powerful enough to
detach the heavier particles of the nucleus, and thus a comet may suffer
in mass by this denudating process. We regard, therefore, the nucleus of
a comet to represent the mass of the comet and the coma, as auroral rays
passing through a very attenuated envelope of detached particles. The
individual gravitating force of these particles to the comet's centre,
may be therefore considered as inversely as the squares of the
distances, and directly as the density of the particles; and this
density will, according to analogical reasoning, be as the distances or
square roots of the distances;--grant the last ratio, and the
gravitating force of the particles composing the exterior envelope of a
comet, becomes inversely as the 2.5th power of the distances from the
comet's centre.[45] This being the law of the radial stream, it follows,
of course, that a comet's diameter is inversely as the force of the
radial stream. It must, however, be borne in mind, that we are speaking
of the atomic density, and not of density by compression; for this
cometary dust, which renders luminous the escaping ether of the nucleus,
must be far too much diffused to merit the name of an elastic fluid. May
not the concentric rings, which were so conspicuous in the comet of
1811, be owing to differences in the gravitating forces of such
particles, sifted, as it were, and thus arranged, according to some
ratio of the distances, by the centripulsive force of the electric coma,
leaving vacant intervals, through which the ether passed without
becoming luminous? This at least is the explanation given by our theory.
We may, indeed, consider it possible that the escaping ether, when very
intense, might be rendered luminous by passing into the surrounding
ether, and, as it became more diffused by radiation, at last become
invisible. In this case, as the law of radiation is as the squares of
the distances from the centre inversely, the rays would be more and more
bent at right angles, or apparently shortened, as the power of the
radial stream increased, and the apparent diameters of the coma would
be diminished faster than the ratio of the 2.5th power of the distances.
But whichever view we adopt, the diameter would again increase in the
same ratio on leaving the sun, if we make allowance for increase of
temperature, as well as for diminution of density, for the ordinary
distance of a comet's visibility. We, however, regard the change of
diameter, as due to both these nodes of action, as best agreeing with
the indications afforded by their tails.

From the preceding remarks, it results that the density of the particles
producing the nebulous envelope of a comet, renders the variations of
diameter only approximate to the law of the radial stream; a comet's own
electric energy, or the intensity of the escaping ether, may also modify
this expression, and many other causes may be suggested. That the radial
stream is the cause, in the way we have pointed out, is proved by the
positions of the major axis of the short-period comet, making frequently
nearly a right angle with the radius vector of the orbit in 1828. A soap
bubble gently blown aside, without detaching it from the pipe, will
afford a good illustration of the mode, and a confirmation of the cause.
The angles measured by Struve, reckoned from the radius vector,
prolonged towards the sun, are subjoined:

  November 7        99°.7  |  December 7       154°.0
  November 30      145 .3  |  December 14      149 .4

At this last date, the comet was getting pretty close to the sun. When
the angle was greater, as on November 7th, the comet appeared to make
almost a right angle with the radius vector; and in this position of the
earth and comet, the longer axis of the elliptical comet was directed to
the axis of the vortex, as may be verified by experiment. At the later
dates, the comet was more rapidly descending, and, at the same time, the
axis of the comet was getting more directed towards the earth; so that
the angle increased between this axis and the radius vector, and
consequently became more coincident with it. We have now to consider the
luminous appendage of a comet, commonly called a tail.

The various theories hitherto proposed to account for this appendage are
liable to grave objections. That it is not refracted light needs not a
word of comment. Newton supposes the tail to partake of the nature of
vapor, rising from the sun by its extreme levity, as smoke in a chimney,
and rendered visible by the reflected light of the sun. But, how vapor
should rise towards opposition in a vacuum, is utterly inexplicable. In
speaking of the greater number of comets near the sun than on the
opposite side, he observes: "Hinc etiam manifestum est quod cœli
resistentiâ destituuntur."[46] And again, in another place, speaking of
the tail moving with the same velocity of the comet, he says: "Et hinc
rursus colligitur spatia cœlestia vi resistendi destitui; utpote in
quibus non solum solida planetarum et cometarum corpora, sed etiam
rarissimi candarum vapores motus suos velocissimos liberrimè peragunt ac
diutissimè conservant." On what _principle_, therefore, Newton relied to
cause the vapors to ascend, does not appear. Hydrogen rises in our
atmosphere because specifically lighter. If there were no atmosphere,
hydrogen would not rise, but merely expand on all sides. But, a comet's
tail shoots off into space in a straight line of one hundred millions of
miles, and frequently as much as ten millions of miles in a single day,
as in the case of the comet of 1843. Sir John Herschel observes, that
"no rational or even plausible account has yet been rendered of those
immensely luminous appendages which they bear about with them, and which
are known as their tails." Yet, he believes, and astronomers generally
believe, that a comet shines by reflected light. This theory of
reflexion is the incubus which clogs the question with such formidable
difficulties; for, it follows, that the reflecting matter must come
from the comet. But, what wonderful elements must a comet be made of, to
project themselves into space with such immense velocity, and in such
enormous quantities as to exceed in volume the body from which they
emanate many millions of times. This theory may be, therefore, safely
rejected.

From what we have already advanced concerning the coma or nebulosity of
the comet, we pass by an easy path to an explanation of the tail. In the
short-period comets, the density of the elementary atoms is too great to
be detached in the gross from the nucleus, or, rather, the density of
the atoms composing the nucleus is too great to permit the radiating
stream of the comet carrying them to a sufficient distance to be
detached by the radial stream of the sun. Hence, these comets exhibit
but very little tails. We may also conceive, that the continual siftings
which the nucleus undergoes at each successive perihelion passage, have
left but little of those lighter elements in comets whose mean distances
are so small. Yet, again, if by any chance the eccentricity is
increased, there are two causes--the density of the ether, and the heat
of the sun--which may make a comet assume quite an imposing appearance
when apparently reduced to the comparatively passive state above
mentioned.

According to our theory, then, the coma of a comet is due to the
elasticity of the ethereal medium within the nucleus, caused both by the
diminished pressure of the external ether near the sun, and also by the
increased temperature acting on the nucleus, and thus on the involved
ether. The tail, on the contrary, is caused by the lighter particles of
the comet's attenuated atmosphere being blown off by the electric blast
of the radial stream of the solar vortex, in sufficient quantities to
render its passage visible. It is not, therefore, reflected light, but
an ethereal stream rendered luminous by this detached matter still held
in check by the gravitating force of the sun, whose centre each
particle still respects, and endeavors to describe such an orbit as
results from its own atomic density, and the resultant action of both
the acting forces. From the law of density of the ether, the coma ought
to be brightest and the radiating stream of the comet's nucleus
strongest on the side of least pressure: from this cause, and the fact
that the body of the comet affords a certain protection to the particles
immediately behind it, there will be an interval between the comet and
the tail less luminous, as is almost invariably observed. We thus have
an explanation of the fact noticed by Sir John Herschel, "that the
structure of a comet, as seen in section in the direction of its length,
must be that of a hollow envelope of a parabolic form, enclosing near
its vertex the nucleus or head." We have, also, a satisfactory
explanation of the rapid formation of the tail; of its being wider and
fainter at its extremity; of its occasional curvature; and of its
greater length after perihelion than before. But, more especially may we
point to the explanation which this theory gives of the fact, that,
_ceteris paribus_, the long-period comets, when their perihelion
distances are small, have tails of such exaggerated dimensions.

A comet, whose mean distance is considerable, is supposed by the theory
to be composed of elements less dense, and, during its long sojourn at
its aphelion, it may be also supposed that it there receives continual
accessions to its volume from the diffused siftings of the system, and
from the scattered debris of other comets. On approaching the
perihelion, the rapidity of the change in the density of the ether in a
given time, depends on the eccentricity of the orbit, and so does the
change of temperature; so that, from both causes, both the length of the
tail and the brilliancy of the comet measurably depends on the magnitude
of the period and of the eccentricity.

If the nuclei of comets be gaseous as we suppose, and that the smallest
stars are visible through them, it is an outrage on common sense, to
refer that light, which renders a comet visible at noon-day, within six
minutes of space of the sun itself, to the reflected light of the sun.
When a small star has been seen through the nucleus of a comet, without
any perceptible diminution of light, it indicates perfect transparency;
but there can be no reflection from a perfectly transparent body, and
therefore, a comet does not shine by reflected light. It is true that
Arago discovered traces of polarized light in the comet of 1819, and
also in more recent comets, but they are mere traces, and Arago himself
admits, that they do not permit "the conclusion decidedly that these
stars shine only with a borrowed light." But it still does not follow
that a comet (even if independent of reflected light) is in an
incandescent state. The auroral light is not polarized, nor any other
electric light, neither is it owing to a state of incandescence, yet it
is luminous. The intense light of a comet at perihelion is analogous to
the charcoal points of a galvanic battery, caused by a rapid current of
ether from the nucleus, and assisted by the radial stream of the vortex.
This will account for the phenomenon in all its shades of intensity, as
well as for the absence of any perceptible phase. It will also account
for the non-combustion of such comets as those of the years 1680 and
1843. We shall also be at no loss to understand, why there is no
refraction when a ray of light from a star passes through the nebulosity
of a comet; and if, as we may reasonably suppose, the gaseous matter
composing the nucleus be very attenuated, instruments are yet too
imperfect to determine whether these also have any refracting power. On
this point, however, it is safest to suspend our judgment, as there may
be comets not belonging to our system, with even liquid or solid nuclei,
or of matter widely different to those elements composing the members of
the solar system.

In addition to what has been already advanced on this subject of a
comet's light, we may appeal to the well-known fact that the visibility
of a comet is not reciprocally as the squares of the distances from the
earth and sun as it ought to be, if shining by reflected light. In
Mr. Hind's late work on comets, the fact is stated that "Dr. Olbers
found that the comet of 1780 attained its greatest brightness on the 8th
of November, thirteen days subsequent to its discovery, whereas
according to the law of reflected light, it should have become gradually
fainter from the day of its discovery; and supposing the comet
self-luminous, the intensity of light should have increased each day
until November 26th; yet in the interval between the 8th and 26th of
that month, it grew rapidly less." Now this theory teaches, that a comet
is neither self-luminous nor dependent on the sun, but on its distance
from the axis of the vortex, and a certain amount of elapsed time from
the perihelion, varying somewhat in each particular case. This fact is
therefore a very strong argument in favor of our theory.

Amidst the many anomalous peculiarities of comets, it has been noticed
that a short tail is sometimes seen at right angles to the principal
tail, and in a few cases pointing directly towards the sun. Much of this
may be owing to perspective, but granting the reality of the fact, it is
still explicable on the same general principles.

In speaking of the modifying causes which influence the weather, we
mentioned the effect due to the position of the sun with respect to the
axis of the vortex. This will be found to have a sensible effect on the
action of the radial stream. The natural direction of a comet's electric
stream is _towards_ the axis of the vortex, and in the central plane of
the vortex it will be also towards the sun. But this stream is met by
the stronger radial stream from the axis, and as Mr. Hind describes it,
"is driven _backward_ in two streams passing on either side of the head,
and ultimately blending into one to form the tail." Now, if the body of
the sun be situated between the comet and the axis of the vortex, it
will shield the comet from the action of the radial stream, and thus a
tail may really point towards the sun.

In 1744 a brilliant comet exhibited six distinct tails spread out like a
fan, some seven days after its perihelion passage; its distance from
the sun at the time not being more than a third of the earth's distance.
The comet was then rapidly approaching the plane of the ecliptic, and if
we make the calculation for the position of the sun, we shall find that
the body of the sun was on the same side of the axis of the vortex as
the comet, and that the comet was then situated at the boundaries of the
conical space, enclosed by the radial stream in its deflected passage
round the body of the sun. In this position there are numerous cross
currents of the stream, and hence the phenomenon in question. As this
fact rests on the testimony of one individual, and is an occurrence
never recorded before or since, many are disposed to doubt the fact, yet
our theory explains even this peculiarity, and shows that there is no
necessity for impugning the statement of Cheseaux.

Another unexplained phenomenon is the corruscation of the tail. It has
been attempted to explode this fact also, by referring it to conditions
of our own atmosphere; and it is generally considered the argument of
Olbers, founded on the great length of the tail and the velocity of
light, is sufficient to prove that these corruscations are not actually
in the tail. Now, it is undoubtedly true, that as light travels less
than two hundred thousand miles in a second, and a comet's tail is
frequently one hundred millions long, it is impossible to see an
instantaneous motion along the whole line of the tail; but granting that
there are such flickerings in the tail as are described by so many, it
must necessarily be, that these flickerings will be _visible_. It would
be wonderful indeed, if a series of waves passing from the comet to the
extremity of the tail, should have their phases so exactly harmonizing
with their respective distances as to produce a uniform steady light
from a light in rapid motion. The argument, therefore, proves too much,
and as it is in the very nature of electric light thus to corruscate, as
we see frequently in the northern lights, we must be permitted still to
believe that not only the tails, but also the heads of comets do really
corruscate as described.

With respect to the direction of the tail, astronomers have been forced
to abandon the antiquated notion, that the tail always pointed directly
from the sun; yet they still pertinaciously cling to the idea, that
although this is not always the case, the tail only deviates from this
direction _in the plane of the orbit_. As this is a most important
question, it is necessary formally to protest against such a conclusion.
If the earth should happen to be in the plane of the comet's orbit and
the tail appears in that plane, it must of course be in that plane
_really_; but if the earth is not in the plane of the comet's orbit, the
tail is not _necessarily_ in the same plane, whatever its apparent
direction may indicate. It is true there is a tendency of every particle
of the tail, moving under the restraining influence of the sun's
attraction, to continue in the plane of the orbit; and in certain
positions there is no oblique action arising from the force of the
radial stream to cause it to deviate from that plane; yet in other