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to the circumference beyond, there lie a greater num
ber of atoms than along any other straight line, a
greater number of objects that seek it, the individual
atoms, a greater number of tendencies to unity, a
greater number of satisfactions for its own tendency
to unity, in a word, because in the direction of the
centre lies the utmost possibility of satisfaction, gen
erally, for its own individual appetite. To be brief, the
condition, unity, is all that is really sought; and if

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the atoms seem to seek the centre of the sphere it
is only impliedly, through implication, because such
centre happens to imply, to include, or to involve, the
only essential centre, unity. But on account of this
implication or involution, there is no possibility of
practically separating the tendency to unity in the
abstract from the tendency to the concrete centre.
Thus the tendency of the atoms to the general centre is,
to all practical intents and for all logical purposes, the
tendency each to each ; and the tendency each to each
is the tendency to the centre; and the one tendency
may be assumed as the other; whatever will apply to
the one must be thoroughly applicable to the other;
and, in conclusion, whatever principle will satisfac
torily explain the one cannot be questioned as an ex
planation of the other.

In looking carefully around me for a rational objec
tion to what I have advanced, I am able to discover
nothing; but of that class of objections usually urged
by the doubters for doubt's sake, I very readily per
ceive three; and proceed to dispose of them in
order.

It may be said, first: " That the proof that the force
of irradiation (in the case described) is directly pro
portional to the squares of the distances, depends upon
an unwarranted assumption, that of the number of
atoms in each stratum being the measure of the force
with which they are emitted."

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I reply, not only that I am warranted in such as
sumption, but that I should be utterly unwarranted in
any other. What I assume is, simply, that an effect
is the measure of its cause, that every exercise of the
Divine Will will be proportional to that which de
mands the exertion ; that the means of Omnipotence,
or Omniscience, will be exactly adapted to its purposes.
Neither can a deficiency nor an excess of cause bring
to pass any effect. Had the force which irradiated
any stratum to its position been either more or less
than was needed for the purpose, that is to say, not
directly proportional to the purpose, then to its posi
tion that stratum could not have been irradiated. Had
the force which, with a view to general equability of
distribution, emitted the proper number of atoms for
each stratum been not directly proportional to the
number, then the number would not have been the
number demanded for the equable distribution.

The second supposable objection is somewhat better
entitled to an answer.

It is an admitted principle in dynamics that every
body on receiving an impulse, or disposition to move,
will move onward in a straight line, in the direction
imparted by the impelling force, until deflected, or
stopped, by some other force. How then, it may be
asked, is my first or external stratum of atoms to be
understood as discontinuing their movement at the
circumference of the imaginary glass sphere, when no

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second force, of more than an imaginary character,
appears, to account for the discontinuance ?

I reply that the objection in this case actually does
arise out of " an unwarranted assumption," on the
part of the objector, the assumption of a principle,
in dynamics, at an epoch when no " principles," in
anything, exist. I use the word " principle," of
course, in the objector's understanding of the word.

" In the beginning " we can admit, indeed, we can
comprehend, but one First Cause, the truly ultimate
principle, the volition of God. The primary act, that
of irradiation from unity, must have been independent
of all that which the world now calls " principle,"
because all that we so designate is but a consequence
of the reaction of that primary act : I say " primary"
act; for the creation of the absolute material particle
is more properly to be regarded as a conception than
as an " act " in the ordinary meaning of the term.
Thus, we must regard the primary act as an act for
the establishment of what we now call " principle."
But this primary act itself is to be considered as con
tinuous Volition. The thought of God is to be under
stood as originating the diffusion, as proceeding with it,
as regulating it, and, finally, as being withdrawn from
it upon its completion. Then commences reaction,
and through reaction, " principle," as we employ the
word. It will be advisable, however, to limit the
application of this word to the two immediate results

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of the discontinuance of the Divine Volition, that is,
to the two agents, attraction and repulsion. Every
other natural agent depends, either more or less im
mediately, upon these two, and therefore would be
more conveniently designated as sub-principle.

It may be objected, thirdly, that, in general, the
peculiar mode of distribution which I have suggested
for the atoms is " an hypothesis and nothing
more."

Now, I am aware that the word hypothesis is a pon
derous sledge-hammer, grasped immediately, if not
lifted, by all very diminutive thinkers, upon the first
appearance of any proposition wearing, in any par
ticular, the garb of a theory. But " hypothesis " can
not be wielded here to any good purpose, even by those
who succeed in lifting it little men or great.

I maintain, first, that only in the mode described is
it conceivable that matter could have been diffused so
as to fulfil at once the conditions of irradiation and of
generally equable distribution. I maintain, secondly,
that these conditions themselves have been imposed
upon me, as necessities, in a train of ratiocination as
rigorously logical as that which establishes any demon
stration in Euclid ; and I maintain, thirdly, that even
if the charge of " hypothesis " were as fully sustained
as it is, in fact, unsustained and untenable, still the
validity and indisputability of my result would not,
even in the slightest particular, be disturbed.

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To explain: The Newtonian gravity, a law of
nature, a law whose existence as such no one out of
Bedlam questions, a law whose admission as such
enables us to account for nine tenths of the universal
phenomena, a law which, merely because it does so
enable us to account for these phenomena, we are per
fectly willing, without reference to any other consid
erations, to admit, and cannot help admitting, as a
law, a law, nevertheless, of which neither the prin
ciple nor the modus operand! of the principle has ever
yet been traced by the human analysis, a law, in
short, which, neither in its detail nor in its generality,
has been found susceptible of explanation at all, is
at length seen to be at every point thoroughly explic
able, provided we only yield our assent to what ? To
an hypothesis ? Why if an hypothesis, if the merest
hypothesis, if an hypothesis for whose assumption, as
in the case of that pure hypothesis the Newtonian law
itself, no shadow of a priori reason could be assigned;
if an hypothesis, even so absolute as all this implies,
would enable us to perceive a principle for the New
tonian law, would enable us to understand as satisfied
conditions so miraculously, so ineffably complex and
seemingly irreconcilable as those involved in the rela
tions of which gravity tells us, what rational being
could so expose his fatuity as to call even this absolute
hypothesis an hypothesis any longer, unless, indeed, he
were to persist in so calling it, with the understanding

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that he did so, simply for the sake of consistency in
words ?

But what is the true state of our present case ?
What is the fact ? Not only that it is not an hypoth
esis which we are required to adopt in order to admit
the principle at issue explained, but that it is a logical
conclusion which we are requested not to adopt if we
can avoid it, which we are simply invited to deny if we
can, a conclusion of so accurate a logicality that to
dispute it would be the effort to doubt its validity,
beyond our power; a conclusion from which we see
no mode of escape, turn as we will; a result which
confronts us either at the end of an inductive journey
from the phenomena of the very law discussed, or at
the close of a deductive career from the most rigor
ously simple of all conceivable assumptions the
assumption, in a word, of simplicity itself.

And if here, for the mere sake of cavilling, it be
urged that, although my starting-point is, as I assert,
the assumption of absolute simplicity, yet simplicity,
considered merely in itself, is no axiom; and that only
deductions from axioms are indisputable it is thus
that I reply :

Every other science than logic is the science of cer
tain concrete relations. Arithmetic, for example, is
the science of the relations of number; geometry, of
the relations of form ; mathematics in general, of the
relations of quantity in general, of whatever can be

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increased or diminished. Logic, however, is the sci
ence of relation in the abstract, of absolute relation, of
relation considered solely in itself. An axiom in any
particular science other than logic is, thus, merely
a proposition announcing certain concrete relations
which seem to be too obvious for dispute, as when we
say, for instance, that the whole is greater than its
part; and, thus again, the principle of the logical
axiom, in other words, of an axiom in the abstract, is,
simply, obviousness of relation. Now, it is clear, not
only that what is obvious to one mind may not be
obvious to another, but that what is obvious to one
mind at one epoch may be anything but obvious, at
another epoch, to the same mind. It is clear, more
over, that what to-day is obvious even to the majority
of mankind, or to the majority of the best intellects
of mankind, may to-morrow be, to either majority,
more or less obvious, or in no respect obvious at all.
It is seen, then, that the axiomatic principle itself is
susceptible of variation, and of course, that axioms
are susceptible of similar change. Being mutable, the
" truths " which grow out of them are necessarily
mutable too ; or, in other words, are never to be posi
tively depended upon as truths at all, since truth and
immutability are one.

It will now be readily understood that no axiomatic
idea, no idea founded in the fluctuating principle,
obviousness of relation, can possibly be so secure, so

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reliable a basis for any structure erected by the reason,
as that idea (whatever it is, wherever we can find it,
or if it be practicable to find it anywhere) which is
irrelative altogether, which not only presents to the
understanding no obviousness of relation, either
greater or less, to be considered, but subjects the in
tellect not hi the slightest degree to the necessity of
even looking at any relation at all. If such an idea be
not what we too heedlessly term " an axiom," it is at
least preferable, as a logical basis, to any axiom ever
propounded, or to all imaginable axioms combined;
and such, precisely, is the idea with which my deduc
tive process, so thoroughly corroborated by induc
tion, commences. My particle proper is but absolute
irrelation. To sum up what has been advanced : As a
starting-point I have taken it for granted, simply, that
the beginning had nothing behind it or before it, that
it was a beginning in fact, that it was a beginning and
nothing different from a beginning; in short, that this
beginning was that which it was. If this be a " mere
assumption," then a " mere assumption " let it be.

To conclude this branch of the subject: I am fully
warranted in announcing that the law which we have
been in the habit of calling gravity exists on account
of matter's having been irradiated, at its origin, atomi-
cally, into a limited r sphere of space, from one, indi-

1 " Limited sphere " a sphere is necessarily limited. I prefer tautology
to a chance of misconception.

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vidual, unconditional, irrelative, and absolute particle
proper, by the sole process in which it was possible to
satisfy, at the same time, the two conditions, irradia
tion, and generally equable distribution throughout the
sphere, that is to say, by a force varying in direct pro
portion with the squares of the distances between the
irradiated atoms, respectively, and the particular centre
of irradiation.

I have already given my reasons for presuming mat
ter to have been diffused by a determinate rather than
by a continuous or infinitely continued force. Sup
posing a continuous force, we should be unable, in the
first place, to comprehend a reaction at all; and we
should be required, in the second place, to entertain
the impossible conception of an infinite extension of
matter. Not to dwell upon the impossibility of the
conception, the infinite extension of matter is an idea
which, if not positively disproved, is at least not in
any respect warranted by telescopic observation of the
stars, a point to be explained more fully hereafter ; and
this empirical reason for believing in the original finity
of matter is unempirically confirmed. For example :
Admitting, for the moment, the possibility of under
standing space fitted with the irradiated atoms, that is
to say, admitting, as well as we can, for argument's
sake, that the succession of the irradiated atoms had
absolutely no end, then it is abundantly clear that, even
when the volition of God had been withdrawn from

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vidual, unconditional, irrelative, and absolute particle
r , by the sole process in which it was posttble to
% at the same time, the two conditions, irradia
tion, and generally equable distribution throughout the
sphere, that is to say, by a force varying in direct pro
portion with the squares of the distances between the
irradiated atoms, respectively, and the particular centre
of irradiation.

I have already given my reasons for presuming mat
ter to have been diffused by a determinate rather than
by a continuous or infinitely continued force. Sup
posing a continuous force, we should be unable, in the
first plaMfsto GieipHnfc'to<Htfm

should be rwtir 9 kV6^ffiptftf$*tto& entertain
the impossible conception of an infinite extension of
matter. Not to *M pm tkt tepMtfUttty f the
conception, tfc* MM* iMtoMte t flMtttr is an idea
which, if Ml fNMrttftvaty dbprwwi, is at least not in
any respect warranted %y telescopic observation of the
stars, a point to be explained more fully hereafter ; and
this empirical reason for believing in the original finity
of matter is unempirically confirmed. For example :
Admitting, for the moment, the possibility of under
standing space fitted with the irradiated atoms, that is
to say, admitting, as well as we can, for argument's
sake, that the succession of the irradiated atoms had
absolutely no end, then it is abundantly clear that, even
when the volition of God had been withdrawn from

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them, and thus the tendency to return into unity per
mitted (abstractly) to be satisfied, this permission
would have been nugatory and invalid, practically
valueless and of no effect whatever. No reaction could
have taken place; no movement toward unity could
have been made; no law of gravity could have ob
tained.

To explain : Grant the abstract tendency of any one
atom to any one other as the inevitable result of diffu
sion from the normal unity; or, what is the same
thing, admit any given atom as proposing to move in
any given direction, it is clear that, since there is an
infinity of atoms on all sides of the atom proposing to
move, it never can actually move toward the satisfac
tion of its tendency in the direction given, on account
of a precisely equal and counterbalancing tendency in
the direction diametrically opposite. In other words,
exactly as many tendencies to unity are behind the
hesitating atom as before it ; for it is a mere sotticism
to say that one infinite line is longer or shorter than
another infinite line, or that one infinite number is
greater or less than another number that is infinite.
Thus the atom in question must remain stationary
forever. Under the impossible circumstances which
we have been merely endeavoring to conceive for argu
ment's sake, there could have been no aggregate of
matter, no stars, no worlds, nothing but a perpetually
atomic and inconsequential universe. In fact, view



VOL. X. 16.



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it as we will, the whole idea of unlimited matter is not
only untenable, but impossible and preposterous.

With the understanding of a sphere of atoms, how
ever, we perceive at once a satisfiable tendency to
union. The general result of the tendency each to
each being a tendency of all to the centre, the general
process of condensation, or approximation, commences
immediately, by a common and simultaneous move
ment, on withdrawal of the Divine Volition; the
individual approximations, or coalescences not coa
litions of atom with atom, being subject to almost
infinite variations of time, degree, and conditions, on
account of the excessive multiplicity of relation, aris
ing from the differences of form assumed as character
izing the atoms at the moment of their quitting the
particle proper, as well as from the subsequent par
ticular inequidistance, each from each.

What I wish to impress upon the reader is the cer
tainty of there arising, at once (on withdrawal of the
diffusive force, or Divine Volition), out of the condition
of the atoms as described, at innumerable points
throughout the universal sphere, innumerable agglom
erations, characterized by innumerable specific differ
ences of form, size, essential nature, and distance each
from each. The development of repulsion (electricity)
must have commenced, of course, with the very
earliest particular efforts at unity, and must have
proceeded constantly in the ratio of coalescence, that

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is to say, in that of condensation, or, again, of
heterogeneity.

Thus the two principles proper, attraction and re
pulsion, the material and the spiritual, accompany
each other, in the strictest fellowship, forever. Thus
the body and the soul walk hand in hand.

If now, in fancy, we select any one of the agglomera
tions considered as in their primary stages throughout
the universal sphere, and suppose this incipient agglom
eration to be taking place at that point where the
centre of our sun exists, or rather where it did exist
originally, for the sun is perpetually shifting its posi
tion, we shall find ourselves met, and borne onward
for a time at least, by the most magnificent of theories,
by the Nebular Cosmogony of Laplace ; although " cos
mogony " is far too comprehensive a term for what he
really discusses, which is the constitution of our solar
system alone, of one among the myriad of similar
systems which make up the universe proper, that
universal sphere, that all-inclusive and absolute kos-
mos which forms the subject of my present discourse.

Confining himself to an obviously limited region,
that of our solar system with its comparatively imme
diate vicinity, and merely assuming, that is to say,
assuming without any basis whatever, either deductive
or inductive, much of what I have been just endeavor
ing to place upon a more stable basis than assumption ;
assuming, for example, matter as diffused (without

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pretending to account for the diffusion) throughout,
and somewhat beyond, the space occupied by our
system, diffused in a state of heterogenous nebulosity
and obedient to that omniprevalent law of gravity at
whose principle he ventured to make no guess,
assuming all this (which is quite true, although he had
no logical right to its assumption), Laplace has shown,
dynamically and mathematically, that the results in
such case necessarily ensuing are those and those
alone which we find manifested in the actually existing
condition of the system itself.

To explain : Let us conceive that particular agglom
eration of which we have just spoken, the one at the
point designated by our sun's centre, to have so far
proceeded that a vast quantity of nebulous matter
has here assumed a roughly globular form, its centre
being, of course, coincident with what is now, or rather
was originally, the centre of our sun, and its periph
ery extending out beyond the orbit of Neptune, the
most remote of our planets ; in other words, let us sup
pose the diameter of this rough sphere to be some six
thousand millions of miles. For ages, this mass of mat
ter has been undergoing condensation, until at length
it has become reduced into the bulk we imagine;
having proceeded gradually, of course, from its atomic
and imperceptible state into what we understand of
visible, palpable, or otherwise appreciable nebulosity.

Now, the condition of this mass implies a rotation
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about an imaginary axis, a rotation which, commenc
ing with the absolute incipiency of the aggregation,
has been ever since acquiring velocity. The very first
two atoms which met, approaching each other from
points not diametrically opposite, would, in rushing
partially past each other, form a nucleus for the rotary
movement described. How this would increase in
velocity is readily seen. The two atoms are joined by
others, an aggregation is formed. The mass con
tinues to rotate while condensing. But any atom at
the circumference has, of course, a more rapid motion
than one nearer the centre. The outer atom, how
ever, with its superior velocity, approaches the centre,
carrying this superior velocity with it as it goes. Thus
every atom, proceeding inwardly, and finally attach
ing itself to the condensed centre, adds something to
the original velocity of that centre, that is to say, in
creases the rotary movement of the mass.

Let us now suppose this mass so far condensed that
it occupies precisely the space circumscribed by the
orbit of Neptune, and that the velocity with which the
surface of the mass moves, in the general rotation, is
precisely that velocity with which Neptune now re
volves about the sun. At this epoch, then, we are to
understand that the constantly increasing centrifugal
force, having gotten the better of the non-increasing
centripetal, loosened and separated the exterior and
least condensed strata, at the equator of the sphere,

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where the tangential velocity predominated; so that
these strata formed about the main body an indepen
dent ring encircling the equatorial regions; just as
the exterior portion thrown off by excessive velocity of
rotation, from a grindstone, would form a ring about
the grindstone but for the solidity of the superficial
material; were this caoutchouc, or anything similar
in consistency, precisely the phenomenon I describe
would be presented.

The ring thus whirled from the nebulous mass, re
volved, of course, as a separate ring, with just that
velocity with which, while the surface of the mass, it
rotated. In the meantime, condensation still pro
ceeding, the interval between the discharged ring and
the main body continued to increase until the former
was left at a vast distance from the latter.

Now, admitting the ring to have possessed, by some
seemingly accidental arrangement of its heterogeneous
materials, a constitution nearly uniform, then this
ring, as such, would never have ceased revolving about
its primary; but, as might have been anticipated,
there appears to have been enough irregularity in the
disposition of the materials to make them cluster about
centres of superior solidity ; and thus the annular form
was destroyed. 1 No doubt the band was soon broken

1 Laplace assumed his nebulosity heterogeneous, merely that he might be
thus enabled to account for the breaking up of the rings; for had the nebu
losity been homogeneous, they would not have broken. I reach the same
result, heterogeneity of the secondary masses immediately resulting from the
atoms purely from an a priori consideration of their general design relation.

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up into several portions, and one of these portions,
predominating in mass, absorbed the others into itself,
the whole settling, spherically, into a planet. That
this latter, as a planet, continued the revolutionary
movement which characterized it while a ring is
sufficiently clear; and that it took upon itself, also,


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