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{\Large\bf Edgar Allan Poe's Physical Cosmology}
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{\Large\it Alberto Cappi}
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{Osservatorio Astronomico di Bologna}
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via Zamboni 33, I--40126 Bologna, Italy
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{\rm BAP 11--1993--037--OAB}
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{\em Quarterly Journal of the Royal Astronomical Society}, 1994, {\bf 35}, 177
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\begin{center}
{\bf SUMMARY}
\end{center}

In this paper
I describe the scientific content of {\em Eureka}, the prose poem
written by Edgar Allan Poe in 1848. In that work, starting from
metaphysical assumptions, Poe claims that the Universe is finite
in an infinite Space, and that it was originated
from a primordial Particle, whose fragmentation under the action of a repulsive
force caused a diffusion of atoms in space.
I will show that his subsequently collapsing
universe represents a scientifically acceptable Newtonian model. 
In the framework of his evolving universe, Poe makes use of contemporary 
astronomical knowledge, deriving modern concepts such as a primordial
atomic state of the universe and a common epoch of galaxy formation.
Harrison found in {\em Eureka} the first, qualitative solution of
the Olbers' paradox; I show that Poe also applies in a modern way the
anthropic principle, trying to explain why the Universe is so large.

\newpage

\section{Introduction}

The provocative title of this paper aims at establishing
a relation between 
Edgar Allan Poe (1809--1849) and {\em physical} cosmology.
It is well known that Poe was interested in science,
and that in {\em Eureka}, his ``prose poem" \cite{poe},
he described his original, personal vision of the Universe.
The question is, can we find something {\em scientifically}
relevant in this 
literary work, a bizarre {\em m\'elange} of metaphysics, philosophy, 
and science? Indeed, Harrison \cite{harrison} has already pointed out that
Poe gives in {\em Eureka} a correct solution of the Olbers' paradox.
I will show that this is not a lucky coincidence, and that {\em Eureka}
has other interesting points worthy of attention.

The original premises of {\em Eureka} are metaphysical,
quite na\"{\i}ve, and the more scientific, detailed discussions 
in {\em Eureka} are often vague, and sometimes wrong. 
This is what negative critics have stressed. 
But from his metaphysical speculations Poe reaches the conclusion 
that the Universe is evolving. 
From our point of view, the most interesting part of 
{\em Eureka} concerns the
physical consequences of this conclusion.
And this is why we can find some startling common points between
his cosmology and our modern cosmology.

The idea of a dynamically
evolving universe was accepted
only in the 20th century; Friedmann found that it was a mathematical
consequence of General Relativity, but it gained general consensus
only after the compelling observational evidence presented by Hubble.
Nevertheless, this evolving universe could be conceived before 
general relativity. 

On the 3rd of February, 1848, Edgar Allan Poe 
gave a lecture at the Society Library of New York, entitled 
{\em On the Cosmogony of the Universe}.
{\em Eureka} represented
an extension of that lecture, and was published in the same year.

In a letter to George W.~Eveleth, Poe wrote:

\begin{quotation}
{\small
What I have propounded will (in good time) revolutionize the world of
Physical \& Metaphysical Science. I say this calmly -- but I say it.
\cite{eveleth}
}
\end{quotation}

While {\em Eureka} was appreciated by, among others,
Charles Baudelaire (author of the first french translation
of {\em Eureka}) and Paul Val\'ery, it has never been very popular.

Tipler claims that
{\em Eureka} ``is very much a metaphysical work" \cite{tipler},
and he quotes A.S.Eddington, as defining it
a ``crank-theory" \cite{quinn} (it is ironic that Eddington 
should in his turn propose his {\em Fundamental Theory}).
Indeed, this quotation may be misleading; Eddington expressed also
his appreciation, noting that Poe seemed ``to have had the mind of
a mathematician". Charles O. Olivier, professor of Astronomy at the
University of Pennsylvania, was also favourably impressed \cite{quinn}; 
Carol Hopkins Maddison claimed that {\em Eureka} was a synthesis
of the most advanced thought of the 19th century \cite{maddison}, and
more recently Bruno Bertotti wrote that Poe ``was able to prophesy and 
prefigure modern cosmology" \cite{bertotti}.

Anyway, Harrison has well synthesized the fate of this original work:

\begin{quotation}
{\small
{\em Eureka} failed to revolutionize the world of physics and metaphysics;
its science was too metaphysical and its metaphysics too scientific for
contemporary tastes.
\cite{harrison}
}
\end{quotation}

In particular, a serious source of confusion is represented
by a presumed analogy with 
General Relativity, as suggested by Paul Val\'ery \cite{valery}.
He cites for example the sentence of Poe

\begin{quotation}
{\small
[...] 
{\em each law of Nature is dependent at all points upon all other laws}
}
\end{quotation}

and claims that the definition of the Universe from its intrinsic properties
and the symmetry between the concepts of space, time, matter and gravitation
are the common characteristics of Poe's and Einstein's universes:

\begin{quotation}
{\small
{\em C'est, en effet, une sym\'etrie formelle qui est le caract\`ere essentiel
de la repr\'esentation de l'Univers selon Einstein.} Elle en fait la 
beaut\'e\footnote{It is, in fact, a formal symmetry which constitutes the
essential character of the representation of the Universe according to
Einstein. This symmetry is its beauty.}.
\cite{valery}
}
\end{quotation}

Moreover, there is some reluctance to judge a literary work also from a
scientific point of view. This understandable feeling is
well expressed by Giorello, who writes in his introduction to the Italian 
edition of {\em Eureka}:

\begin{quotation}
{\small
Ma una lettura di {\em Eureka} che, alla luce delle attuali conoscenze
astronomiche, fisiche, ecc., si mettesse a discriminare tra quel che Poe ha
ereditato da un passato che sentiamo come sempre pi\'u remoto e quel che ha 
anticipato di un futuro per lui ancora troppo lontano, ne disperderebbe tutto 
il fascino\footnote{
``But if we should read {\em Eureka} using our present astronomical and physical
knowledge in order to discriminate between Poe's heritage
from a past which is increasingly remote from us, and Poe's
anticipation of a future which was too distant from him, all its
fascination would be lost."}.
\cite{giorello}
}
\end{quotation}

I am aware that {\em Eureka} is a complex literary work;
but it is also clear that Poe attributed
an enormous importance to its content\footnote{
It is curious to read the
comments of Judith Gautier, the daughter of Th\'eophile Gautier, 
who in 1864 (when she was only 15 years old) wrote 
an article in {\em Le Moniteur universel} under the pseudonym of Judith 
Walter about Baudelaire's recent translation of {\em Eureka}:
``On aurait tort de croire qu'Edgar Poe en \'ecrivant Eureka avait seulement
l'id\'ee de faire un po\"eme; il \'etait bien absolument convaincu qu'il
avait d\'ecouvert le grand secret de l'univers, et il employait toute
la force de son talent \` a d\'evelopper son id\'ee"
[It would be wrong to think that Edgar Poe aimed only at composing a poem
when writing Eureka; he was absolutely convinced of having discovered
the big secret of the Universe, and employed all the power of his talent
to develop his idea].

About the idea of a beginning and an end of an expanding and collapsing
universe, she wrote:

``L\`a est l'id\'ee principale d'Eureka, id\'ee tr\`es belle et tr\`es
neuve qui rattache le commencement \`a la fin, marque le point de d\'epart
dans le point d'arriv\'ee, et, si on l'admet, jette beaucoup de clart\'e
dans l'ensemble de l'astronomie" 
[Here is the main idea in Eureka --a very fine and new idea-- which
relates the beginning to the end, marks the starting point in the final point
and, if accepted, represents a significant clarification of the whole of
astronomy]
(reprinted in Edgar Allan Poe, Eureka,
Traduction de C.Baudelaire, Pr\'eface et commentaires de Jean-Louis Schefer,
AGORA, les Classiques, 1990, Paris; p.162--167).}.

He tried to build a ``theory of everything", where
the primordial Unity is at the origin of all things.
In doing so, he adopted some metaphysical assumptions but used the physical
and astronomical knowledge of his time.
Therefore I think that a separate, critical analysis
of the science in {\em Eureka} is justified, and represents a
useful complement to literary and philosophical analysis,
in order to fully appreciate this prose poem in its
complexity.

The purpose of this paper is to give a general description and discussion 
of Poe's cosmology.
I want to stress the following points:

\begin{itemize}
\item the modern universe conceived by Poe is not the result of chance, 
but is the logical consequence of the synthesis between Poe's metaphysical 
principle of the ``Original Unity" of matter
and some of the main astronomical ideas of that epoch;
\item while based on undeniably metaphysical premises,
{\em Eureka} gives us a qualitative, but reasonable, Newtonian
model of the Universe;
\item {\em Eureka} contains not only the correct solution of the 
Olbers' paradox,
but also the first modern application of the anthropic cosmological principle.
\end{itemize}

\section{The Universe of Eureka}

\subsection{The primordial Particle}

An exhaustive analysis of {\em Eureka} and its sources would require a long
and detailed work; here I will deal with those issues which
are most relevant to Poe's physical cosmology.

Poe had a deep interest in science and, particularly, in astronomy.
In 1825, when he was sixteen years old, he began to observe the
moon and the stars with
a small telescope, a present from his step-father John Allan.
According to Poe himself, 
his tale {\em The Unparalleled Adventure of One Hans Pfaall} (1835)
had been inspired by John Herschel's {\em A Treatise in Astronomy}, whose
American edition had been published in 1834.

Poe had also read the popular {\em Views of the Architecture of the Heavens}
(1838) by Rev. Dr John Pringle Nichol, often quoted in {\em Eureka}.
In 1836 Nichol had been appointed
professor of practical astronomy at the University of Glasgow, and
in his {\em Views of the Architecture of the Heavens}
he described and defended the nebular hypothesis of Laplace.

Poe dedicates {\em Eureka} to Alexander von Humboldt, author
of the famous {\em Kosmos, Enkwurf einer physischen Weltbeschreibung},
whose first volume had been translated in English in 1845;
his main references are the works of Kepler, Newton, Laplace and William 
Herschel. Poe synthesizes the ideas
of these great scientists in his cosmology.
Newton's law of gravitation provides him with a
consistent dynamical description of a finite universe; 
the nebular hypothesis of Laplace is generalized by Poe, becoming
the basic and universal process of object formation;
and the observations of Herschel constitute the essential information on 
the present content, structure and distance scale of the Universe.

In {\em Eureka} we find ideas which were well
known, if not always dominant, in 1848 \cite{numbers}.
What makes {\em Eureka} unique is the metaphysical principle assumed
by Poe to explain the origin of the force of gravity
(that {\em Eureka} is the result of
Poe's speculations about the nature of gravity, is shown
clearly by Poe's letter to G.W.Eveleth).

Poe presents his method in the first, satirical pages of 
{\em Eureka}, where his main hero is Kepler.
According to Poe, the process of scientific discovery does not consist in
deduction from arbitrary axioms, or in induction from mere
empirical facts. It is essentially due to {\em intuition}.
And
from his original intuition about the nature of gravity
(the primordial unity of all things), with a minimum of simple assumptions,
Poe wants to derive some logical consequences; in this way he
aims to develop a general theory which can explain the spiritual
and material nature of the Universe, its evolution,
and the form of the fundamental laws.
Such a theory must be in accord with observations, and must be consistent,
because

\begin{quotation}
{\small
{\em A perfect consistency, I repeat, can be nothing but an absolute truth.}
}
\end{quotation}

Poe states that Space is infinite.
On the other hand, he claims that the Universe of Stars, i.e. the material 
content of the Universe, must be finite, both in space and time.
Poe gives philosophical justifications
(later he will add more physical reasons): 
the concepts of an infinite distribution of matter, and 
of a finite extension of space are both unconceivable.
In the following it will be clear that a finite universe
in an infinite space is necessary for 
the consistency of Poe's universe. 

The main metaphysical principle, which implies an evolutionary universe,
is the primordial Unity of Matter.
Poe claims that this principle follows both from reasoning
{\em a priori} and from observing the present state of matter.
The force of gravity, i.e. ``the fact that {\em each
atom attracts each atom}", is considered as a universal tendency of matter
to restore its ``natural" state. Therefore the universality of attraction
implies that this original ``natural" state was the Unity of all matter.

This also implies that the Universe has not always been as we observe it
presently, and that there was an instant when the Universe was created.
What can we say about the state of the Universe at that instant?
We have to assume that it was in its simplest state, and
this simplest state could be nothing else than
a primordial Particle. God created this Particle,
and conferred to matter a repulsive force:
the primordial Particle fragmented into an enormous,
but not infinite, number of atoms.
This Repulsion, which Poe calls Electricity, plays an important
role in his metaphysics; it is the Spiritual Principle:

\begin{quotation}
{\small
To electricity --so, for the present, continuing to call it--
we {\em may} not be wrong in referring the various physical appearances 
of light, heat and magnetism; but far less shall we be liable to err in 
attributing to this strictly spiritual principle the more important 
phaenomena of vitality, consciousness and {\em Thought}.
}
\end{quotation}

This phase of universal repulsion is finite; at the end of this
Action, a Reaction develops: and this Reaction is the force of gravity.

If gravity were the only force in the Universe, nothing
could exist; this means that atoms must develop a repulsive force to
avoid a premature collapse. Only at the end of the universe,
this tendency to Unity will be completely satisfied (here Poe implicitly
applies the anthropic cosmological principle; in the next section I will 
discuss another, more interesting and explicit application).

Thus Attraction and Repulsion are the two forces 
that make the Universe evolve\footnote{
Critics usually point out that the two terms 
of Attraction and Repulsion were applied to molecular theory
by Ruggero Giuseppe Boscovich (1711--1787), who was a dalmatian Jesuit, 
mathematician and astronomer (founder of the Observatory of Brera, and
member of the Royal Society).
He wrote an influential work about a ``unified" theory;
see for example the synthetic account by J.D.Barrow in
{\em Theories of Everything}, Clarendon Press (Oxford, 1991), p.17.
Nevertheless I don't think it is necessary to see a direct link
with Poe's adoption of the two terms.}.
In his metaphysics Poe's universe is reminiscent of
pre--Socratic cosmologies.
For example, the dialectics between two forces has some analogy with 
the cosmology of Empedocles.
Empedocles, who lived in the Vth century a.C., described in his poem
$\Pi\epsilon\rho\iota$ $\Phi\upsilon\sigma\epsilon\omega\varsigma$
(Peri Physeos) a universe evolving under the action of
two opposing forces on the four elements; these forces are called
$\Phi\iota\lambda o \tau\eta\varsigma$ (Philotes) and
$N\epsilon\iota\kappa o \varsigma$ (Neikos), i.e. Friendship and Hate.
When Friendship dominates, all the matter condenses in one unique
globe, the $\Sigma\phi\alpha\iota\rho o \varsigma$ (Sphairos); 
Hate divides this globe, and gives origin to all
things \cite{empedocles}.
But if it is true that Poe's Attraction and Repulsion play a role
in his metaphysics (they are ``the Body and the Soul"), they are
{\em physical forces}, and one of them, gravitation, is
mathematically well defined.
Indeed the metaphysical nature of Poe's forces
is extrapolated from their physical properties.
On the contrary, Empedocles's universe is a uniquely metaphysical 
construction (a fascinating one, like many of the ideas of pre--Socratic 
philosophers).

Poe argues that, if the original state of matter was Unity, 
and given that the present state of matter is Diffusion,
as implied by the distribution of stars and nebulae, then
matter has been {\em radiated} from the original
primordial Particle. At this point, Poe realizes that there is a problem.
He states that a fundamental property of the Universe is
its globally uniform distribution of matter. It must be so, according to him,
for symmetry and simplicity, and because
{\em observations} show a distribution of stars and nebulae which is
locally irregular, but globally uniform (we would say that observations
suggest an isotropic distribution, thus supporting the
hypothesis that the Universe is homogeneous).
Now, if Matter, under the form of a finite quantity of atoms, had been 
radiated in the same way as light, its surface density should decrease with the 
square of the distance.
In modern terms, the problem Poe has to solve consists in finding
how an expanding universe can conserve homogeneity.
The mere fact that Poe poses this problem is truly remarkable,
but his solution is disappointing.

Poe notes that a constant density in his finite, spherical
universe of matter, implies that the number of atoms
in a shell at a distance $r$ from the centre of
radiation must be proportional to $r^2$.
To obtain this distribution, Poe reasons in the following way.
The repulsive force $F$ acted for a finite lapse of time; at a
given instant it vanished (as a large--scale force; it continued to manifest
itself as Electricity), to be replaced by the force of gravity.
We can suppose that this repulsive force decreased progressively with time.
Now suppose that atoms were radiated from the primordial Particle in successive 
expanding shells, and that the total number $N$ of atoms in each shell
was proportional to the repulsive force $F$ exerted on each atom of the
shell: $F \propto N$. 
Consequently, successive shells had less and less atoms, and were
radiated by a proportionally less intense force, therefore reaching
smaller distances from the centre.
Poe writes that each shell stopped
after reaching a given distance $r$ from the
centre, and that through this process the number of atoms $N$ 
reaching a distance
$r$ from the centre was proportional to $r^2$, thus yielding,
from the proportionality between $F$ and $N$,
the relation $F \propto r^2$. 

In a footnote, Poe suggests that this process was instantaneous:
``Here I describe the whole process as one instantaneous flash";
needless to say, the analogy with the Big Bang has been stressed by several
critics.

The force of gravity appears to Poe as a Reaction to the Repulsive force, and,
as the latter is proportional to $r^2$, the former will be proportional
to $r^{-2}$; the atoms will not tend to their geometrical centre, 
but to their Unity, forming stars and galaxies, and at the same time
pursuing the general collapse.

It is admittedly difficult to find such a symmetry as compelling
as claimed by Poe. Here we are, using his own words, in the ``Cloud-Land
of Metaphysics"!
Moreover, there are serious problems with Poe's mechanism of repulsion.
Poe seems aware that the reader might not be particularly convinced
by his theory, so he answers to three possible objections, all of them quite
natural.

First objection: why should the force of radiation be proportional to the 
number of radiated atoms? Poe explains that this relation
is the only one which could assure
the uniform distribution of the atoms in the sphere.

Second objection: 
if atoms are accelerated by a repulsive force, what should stop them?
Poe says that at that epoch no ``principle" existed, no law of dynamics.
The physical universe, with his laws, began when this repulsive force
stopped.

Third objection: this mechanism of distribution of atoms in the sphere
appears to be a simple (and totally arbitrary)
hypothesis. But, according to Poe, it must be the truth:
he claims that it is the only consistent mechanism which
can explain a radiation from the centre and a uniform distribution.

Unfortunately, his explanations are not convincing.

Poe is rather vague about his mechanism.
If we simply use the second law of dynamics, and we assume that
the repulsive force acted during a fixed interval of time
$\Delta t$, equal for all shells,
his mechanism cannot give a uniform distribution.
It can work with a slight correction.
Suppose for example that atoms are accelerated in the radial direction 
with a constant acceleration $a$ (i.e. a constant
repulsive force $F$; Poe assumes that all atoms have the same mass).
Then $r \propto a$; now we can obtain a homogeneous distribution
if we assume that the force acting on each atom
of a shell is proportional to the {\em square root}
of the number $N$ of atoms in the shell.
At any time we have the relation $r \propto F \propto \sqrt{N}$, 
i.e. the number of
atoms in a shell at a distance $r$ from the centre is proportional
to $r^2$; we have also that at any time the velocity
of each shell is proportional to its distance
$r$ from the centre, $v \propto r$, i.e. the Hubble law.
In both the Newtonian and relativistic cosmologies, the proportionality
between distance and velocity is necessary if we want
the general properties of the Universe, for example the
density, to be the same for all the observers at any time: it is the well known
cosmological principle.
So Poe's {\em ad hoc} mechanism could generate a homogeneous universe.
Of course, in this way we have lost the symmetry between repulsion and 
gravity which is
so important for Poe: the force of gravity cannot be ``explained".

The worst is that, when discussing the second objection, 
Poe claims that no physical law existed during the repulsive phase.
This implies that we cannot apply physical reasonings.
The above discussion about some plausible and simple physical model
which could follow Poe's mechanism is {\em not} what Poe had in mind.
We have to accept that atoms could stop once they reached their
``assigned" position in the sphere.
We can imagine that each shell stopped
where it had to stop, to give a final distribution with $N \propto r^2$.
In this case, Poe's original mechanism ``works"; the drawbacks are
that we have continuous fine tuning, and that the intervention of 
the ``Divine Volition" is heavily required.
Moreover, why should we assume a given relation between the force
of repulsion and the atoms radiated from the centre?
Even though he claims the absence of any general law during the phase of
radiation, Poe implicitly requires Newton's second law
(or at least something equivalent); otherwise, why should we not believe that 
the Divine Volition directly put each atom in its place?

It is quite clear that Poe had a general and vague idea in mind.
He was convinced that matter had been radiated from a primordial
Particle; he had two forces, one repulsive, the other attractive;
the latter was inversely proportional to $r^2$. 
He imagined a mechanism where
Repulsion and Attraction were two symmetric forces
--the result of a metaphysical analogue of the third
Newtonian law, Repulsion being an Action and Attraction a Reaction--
where the force of gravity was a consequence of the structure in the
Universe, and where the form of this force could be predicted!
He did not bother with mathematical or physical ``details". 
He was satisfied with the 
general consistency of his mechanism. He did not realize that it
was quite arbitrary.
Indeed, he was aware --as he states clearly in {\em Eureka}-- 
that the laws of motion would require
the action of a force to stop his atoms; but
probably for a limited ability to {\em apply}
these laws, and also for ``dogmatic" reasons, 
Poe did not realize what appears to us 
--and would have appeared to Newton himself--
the obvious physical implication of his model: the radiated atoms could 
be stopped only by the action of an attractive force, i.e. the force
of gravity.

As concerns the third point, Poe is absolutely convinced of having found the
``theory of everything". It is perhaps this attitude of Poe, and his
obstinacy in explaining not only the physical universe but also the fundamental 
physical laws through his metaphysical speculations, that partly justifies some
negative opinions about {\em Eureka}.

The above discussion was necessary in order to understand why and how
Poe reaches the concept of an evolving, collapsing universe.
Now, my point is that at the end
this na\"{\i}ve metaphysical effort allows Poe to 
achieve a viable cosmological model.
We have seen that, from a primordial particle, atoms are radiated in a sphere 
in such a way that their distribution is uniform: the physical 
cosmological model begins with a static, spherical and uniform
distribution of atoms.

Here is the conclusion of the first part of {\em Eureka}:

\begin{quotation}
{\small
[...] I am fully warranted in announcing that {\em the Law which we call
Gravity exists on account of Matter's having being radiated, at its origin, 
atomically, into a limited sphere of Space, from one, individual, 
unconditional, irrelative, and absolute Particle Proper, by the sole process 
in which it was possible to satisfy, at the same time, the two conditions,
radiation and equable distribution throughout the sphere -- that is to say, 
by a force varying in direct proportion with the squares of the distances 
between the radiated atoms, respectively, and the Particular centre of 
Radiation.}
}
\end{quotation}

\subsection{Poe's evolving universe}

In the previous section I have described how
Poe conceives a universe generated by
a uniform radiation of atoms from a primordial
particle: the force of gravity is responsible for the subsequent collapse
of the Universe, during which 
objects form from the growth of small density fluctuations.
According to Poe, these small fluctuations
originate from the different forms of atoms,
which are initially homogeneously distributed in space.
Hence the famous sentence:

\begin{quotation}
{\small
We thus establish the Universe on a purely {\em geometrical} basis.
}
\end{quotation}

which has clearly no relation with General Relativity\footnote{
Poe writes also `{\em [...] no such things as axioms ever existed or can
possibly exist at all}'; such a philosophical position does not
justify a parallelism with non--euclidean geometries.}.

Nearly a century later, Lema\^{\i}tre wrote:

\begin{quotation}
{\small
Le monde a proc\'ed\'e  du condens\'e au diffus. [...]
L'atome--univers s'est bris\'e en fragments [...]
Nous pouvons concevoir que l'espace a commenc\'e avec l'atome primitif et
que le commencement de l'espace a marqu\'e le commencement du 
temps\footnote{The world has evolved from condensation to diffusion. [...]
The universe--atom has broken into fragments [...]
We can conceive that Space began with the primordial atom,
and that the beginning of space marked the beginning of time.}.
\cite{lemaitre}
}
\end{quotation}

Here Lema\^{\i}tre describes a relativistic universe where space and time
begin with matter, and his primordial atom is not {\em in} space, while
Poe describes a Newtonian universe which is {\em in} an infinite,
pre-existing space.
Poe's choice of a finite content of matter is important:
it makes it possible to have a finite potential in each point of space.
Poe is well aware that an infinite Newtonian universe with constant
density cannot be self--consistent, as we will see later.
According to him, objects begin to form only when the Universe
is collapsing, while we now know that structures can form
during the expansion (otherwise, we would not exist!).

It is important to bear in mind where
Poe's universe differs from
the correct Newtonian counterpart of a Friedmann-Lema\^{\i}tre closed model:
it can be viewed as a collapsing cluster of galaxies, and does not
follow the Hubble law.

The correct Newtonian approximation was developed only in 1934 by Milne and 
McCrea \cite{milne,milnemccrea}, who showed that it could be
self-consistent; a simple description is found for example in Sciama's 
{\em Modern Cosmology} \cite{sciama}.
In a closed Newtonian Universe, the radius of the Universe obeys
the (Friedmann) equation:

\begin{equation}
\dot{R} = \frac{8}{3} \pi G \rho - k c^2
\end{equation}

where $R(t)$ is the radius (the scale factor in relativity) of the Universe,
$\rho$ is the density, and the constant $k$
is positive; the maximum radius reached
by the Universe before recollapse is then:

\begin{equation}
R_{max} = \frac{8}{3} \pi \frac{G \rho(t_0)}{k}
\end{equation}

In 1955, McCrea wrote:

\begin{quotation}
{\small
Strictly Newtonian analogues of the relativistic cosmological models 
exist but they are bounded, though arbitrarily large, systems.
\cite{mccrea}
}
\end{quotation}

As Ellis notes, ``It is curious that it took so long for these
dynamic models to be discovered after the (more complex) general relativity
models were known" \cite{ellis}.
As I will discuss below, the problem is that the idea of an evolutionary
universe was difficult to accept.

It is important to realize not only that a Newtonian universe can be obtained as
a limiting case of a relativistic one
(thanks to the Birkhoff theorem), but also that the
Newtonian laws before Relativity could allow a consistent cosmology:
it was necessary to accept a non--static, finite universe of 
matter\footnote{This is true
if we assume a globally uniform distribution of matter,
a hypothesis which is shared by both Poe's and modern cosmology. 
Another possible solution is to 
assume a hierarchical, fractal universe (see Harrison's book, chapter 11,
for the history of this concept; it is interesting to note
that in 1848 it was proposed by John Herschel himself).}.
Poe became aware of that, and this seems to me one of 
the most important aspects of {\em Eureka}.

There is another, startling point in common between Poe and Friedmann,
which I point out just as a curiosity.
In a recent biography of Friedmann, we read:

\begin{quotation}
{\small 
[...] His favourite writers were Dostoyevsky, E.T.A.Hoffmann, and Poe;
he read a lot of Merezhkovsky and Fyodor Sologub. Indeed, Friedmann, as it
turns out, was fond of ``the occult" in general; he claimed he could soothe
pain, and once managed to do it.
\cite{tropp}
}
\end{quotation}

Did Friedmann read {\em Eureka}? It would not be serious to push 
this game too far.

Poe's description of the general structure and content of the Universe
is extremely interesting. It is not as original as the first part;
it is derived from the works of the astronomers of his
time, but is more interesting from our point of view, 
being the most strictly scientific part, and
because the astronomical knowledge of the first half of the 19th
century is inserted by Poe in the framework of an evolving
universe. 
This revolutionary and extraordinary synthesis is what gives {\em Eureka}
a modern flavour. This is what I called Poe's physical cosmology.
We can appreciate this legitimate cosmological model, independently of
the various metaphysical reasons which made Poe conceive a collapsing 
universe.

In the eighteenth century, Thomas Wright and Immanuel Kant
maintained the view that nebulae were systems comparable to the Milky Way.
These speculations were supported by the observations
of William Herschel (with his sister Caroline),
who published in 1785 an influential paper entitled
`On the construction of the heavens'
--even if at the end of his life he
should change his mind--. In 1796, Laplace proposed
the mechanism of gravitational contraction from a primordial
rotating cloud (the solar nebula) to explain the formation and the observed 
regularities of the Solar System.
Therefore it is natural that in the first half of the nineteenth
century these ideas were well known, and that Poe could accept and use them
in his work.
Indeed the nebular hypothesis was very popular
in America at that epoch, even if in 1848 it had received serious criticisms
\cite{numbers}, so that Poe felt the need to defend it. Anyway,
what is original in {\em Eureka} is Poe's assumption of the atomic state of 
matter after the primordial expansion. Laplace had considered only the
origin of the solar system; Poe imagines a primordial 
atomic state of the whole Universe.
The part where Poe defends the nebular hypothesis is quite 
interesting.
The problem is the following: Lord Rosse had claimed to have resolved 
some nebulae into stars, so that the nebular hypothesis of Laplace appeared now 
contradicted by observations.
But Poe notices that if one could observe gaseous nebulae, they should be
very nearby. In his evolving universe, the formation of stars and galaxies
is a process which took place in the past, when
the Universe was in an atomic state, and after it had begun to collapse; 
what we presently call the process of galaxy formation
must have stopped a long time ago: now objects are in the same state 
of condensation.
The nebular hypothesis is therefore applicable only to that epoch, and
as a consequence we can now observe only systems of stars.
While Poe, as all the scientists at the time, did not realize that
different objects were classified under the name `nebulae',
it is interesting to see how his evolving model of the Universe allows him
to reach in a natural way the notion of a primordial epoch of object formation.

Poe defines the Universe of Stars as {\em a cluster of clusters}:
in modern terms, we would say that it is a system of galaxies.
For him, ``cluster (of stars)" means ``galaxy", without any doubt:

\begin{quotation}
{\small
The `clusters' of which this Universal `{\em cluster of clusters}' consists
are merely what we have been in the practice of designating `nebulae' and,
of these `nebulae', {\em one} is of paramount interest to mankind. I allude to
the Galaxy, or Milky Way.}

[...]

{\small
We have no reason to suppose the Milky Way {\em really} more extensive than 
the least of these `nebulae'.
}
\end{quotation}

We read also that the form of our galaxy has approximately 
(``a certain general -- {\em very} general resemblance") to the planet 
Saturn: 

\begin{quotation}
{\small
[...]
we must picture to ourselves a lenticular star-island, or collection of 
stars; our Sun lying excentrically --near the shore of the island--
on that side of it which is nearest the constellation of the Cross 
and farthest from that of Cassiopeia.
}
\end{quotation}

And the nearest nebulae are at distances of million of light-years.
Poe quotes the distance estimates made by William Herschel:

\begin{quotation}
{\small
[...]
--yet so far removed from us are some of the `nebulae' that even light, speeding
with this velocity, could not and does not reach us, from those mysterious 
regions, in less than 3 {\em millions of years}.
}
\end{quotation}

On the other hand, Poe does not believe in the rotation of galaxies:
he rejects the hypothesis of M\"adler ``that there exists, in the centre of the
Galaxy, a stupendous globe about which all systems of the cluster revolve".
Poe claims that this hypothesis is in contrast with the observations
of the other `nebulae': quoting John Herschel and Nichol, he remarks
that the form of these `nebulae' is nearly circular, and this fact suggests
that these systems are in a state of collapse, analogously to the Universe
of Stars.

Poe describes also the fate of the Universe.
The general collapse of the Universe of Stars will cause the final condensation
of all matter in one globe, restoring the original Unity.
Matter then will annihilate.

But at the end of {\em Eureka} Poe suggests that another cycle will follow,
and that this process is `renewed forever'.
Nevertheless Poe himself admits that he is `indulging a hope',
presenting the hypothesis of a cyclic universe.

This is the essential scheme of Edgar Allan Poe's cosmology.
From what I have exposed, I think it is justifiable to claim
that, independently of any metaphysics, the collapsing {\em Newtonian} universe
described by Poe represents a self-consistent pre-relativistic model of 
the Universe.

\subsection{The Olbers' paradox and the Anthropic Cosmological Principle}

I shall briefly discuss two other points,
one concerning the Olbers' paradox, the other the
anthropic principle.

Poe attacks the idea of an infinite Universe of Stars, using
what is presently known as the Olbers' paradox 
(see Harrison's book \cite{harrison}); nevertheless,
he admits that there is a conceivable solution:

\begin{quotation}
{\small
Were the succession of stars endless, then the background of the sky would 
present us an uniform luminosity, like that displayed by the Galaxy 
--since there could be absolutely no point, in all that background, 
at which would not exist a star.
The only mode, therefore, in which, under such a state of affairs, we could
comprehend the {\em voids} which our telescopes find in innumerable directions,
would be by supposing the distance of the invisible background so immense that 
no ray from it has yet been able to reach us at all.
}
\end{quotation}

As Harrison has found, this is a correct solution of 
the Olbers' paradox (the ``finite age solution"). 
Tipler \cite{tipler} has claimed that
Poe's universe is cyclic and of 
infinite age, and that this fact is fatal to the finite age 
solution suggested by Poe himself.
I think this is not the case.

The fundamental point stressed by Poe in {\em Eureka} is that the Universe
of Stars must be finite in an infinite Space.
Poe wants to show that an infinite universe is not consistent;
in the first part of {\em Eureka} he has adduced philosophical
justifications; now he presents physical reasons.
One is the Olbers' paradox, to which Poe finds only one
possible solution.
It is important to realize that Poe discusses
the Olbers' paradox {\em for a static, infinite universe}, and
{\em not} for his universe.

Indeed Poe does not believe in an infinite universe for another
reason: in an infinite universe each particle would undergo the same force 
from each direction, and no motion would be possible.
This is a na\"{\i}ve explanation, but
it is well known that an infinite Newtonian universe is not self-consistent.
In his paper of 1955, McCrea, answering to some criticisms by Layzer
\cite{layzer}, writes:

\begin{quotation}
{\small
We may assert that an unbounded system is newtonian if the infinite integrals
that give the components of newtonian attraction at any point are convergent.
This is the definition most commonly adopted.}

{\small 
According to this definition, a system with uniform density throughout 
euclidean space is not Newtonian. As it is important to recognize, 
this means that, if the gravitational force is to be defined in the present 
manner, then it does not exist in the case of uniform density. Accordingly, 
nothing further can be inferred about this case. In particular, we may not 
proceed to argue, as Layzer does, that the force must be the same at every 
point, and thence that it must be zero. For, in order to prove that a force
takes any value, in particular the value zero, the force has to exist in a 
mathematical sense.}
\end{quotation}

We can conclude that Poe's suggested solution of the 
Olbers' paradox for an infinite universe is correct.   
But Tipler's criticism raises one more question: is the Olbers' paradox 
fatal to {\em Poe's} cyclic universe?  
As I have already mentioned, it is only at the end of {\em Eureka} that Poe
suggests (as a hope) the possibility of a universe
with infinite cycles; this concept is therefore an additional, last hypothesis,
which is not fundamental in his physical universe. 
Anyway, we must recall again that Poe's universe is formed by a {\em finite} 
quantity of matter {\em in an infinite Space}. His Newtonian universe is not
an isolated system: radiation can be diffused into infinite space.
Moreover, matter is created at the beginning
and annihilated at the end of the universe: in this case 
it is more appropriate to
talk about a succession of universes and not about a single cyclic
universe. Therefore the standard arguments used for relativistic cyclic 
universes cannot be applied here.

Tipler suggests it is natural that Poe's universe
is cyclic, because most non--Christian cosmologies of the nineteenth century 
were cyclic to avoid the problems of Creation: but it is quite original the 
fact that Poe admits the Creation of the Universe {\em and}, at the same
time, suggests infinite cycles.

Now, Poe tells us that there is
the Universe of Stars, and all around the infinite, absolute Newtonian Space.
But is this Space completely void? According to Poe, we can
imagine that an infinite number of universes exists in this Space.
If we assume the existence of infinite universes which
follow their cycles eternally, we will apparently face again the same 
problems of a single, infinite universe, for example 
the impossibility to define a potential, or the Olbers' paradox.
But Poe clearly states that these universes do not interact. 
It is the logical consequence of his principle that matter interacts
because of its common origin.
Each universe will have its origin and its laws.
A similar concept of parallel universes is presently found
in quantum mechanics or inflationary cosmology (and, of course,
in science-fiction, of which Poe is one of the three celebrated
founders, together with Jules Verne and H.G.Wells).
This final part of {\em Eureka}, with each universe
with its God at the centre, is the most imaginative.

Another fascinating question posed by Poe is:
why is the Universe so big? 
Why are the distances between ``star and star --between cluster and cluster--"
so large?
Poe writes that Astronomy has no rational explanation; nevertheless, he develops
an interesting argument.
Poe stresses that large distances mean long times:

\begin{quotation}
{\small
[...]

{\em Space and Duration are One}. That the Universe of Stars might {\em endure}
throughout an aera at all commensurate with the grandeur of its component
material portions and with the high majesty of its spiritual purposes, it was
necessary that the original atomic diffusion be made to so inconceivable
an extent as to be only not infinite. It was required, in a word, that
the stars should be gathered into visibility from invisible nebulosity
--proceed from visibility to consolidation-- and so grow grey in giving 
birth and death to unspeakably numerous and complex variations of vitalic 
development: --it was required that the stars should do all this --should
have time thoroughly to accomplish all these Divine purposes--
{\em during the period} in which all things were effecting their return into 
Unity with a velocity accumulating in the inverse proportion of the squares
of the distances at which lay the inevitable End.
}
\end{quotation}

Compare the above quotation with this one by Barrow:

\begin{quotation}
{\small
[...]
This state of expansion means that the size of the Universe is inextricably 
entwined with its age. The reason that
the Visible Universe is more than 13 billion
light-years in size today is that it is more than 13 billion years old.
A Universe that contained just one galaxy like our own Milky Way, with its 100
billion stars, each perhaps surrounded by planetary systems, might seem 
a reasonable economy if one were in the universal construction business.
But such a universe, with more than a 100 billion fewer galaxies than our own,
could have expanded for little more than a few months. It could have produced 
neither stars nor biological elements. It could contain no astronomers.
\cite{barrow}
}
\end{quotation}

It is interesting how Poe justifies the dimension by using 
the Anthropic Principle (\cite{carter,barrowtipler}). 
He has well understood the link between dimension, age, and life,
which exists in an evolving universe.
Paraphrasing Eddington, we should say that Poe seems to have
had the mind of a cosmologist...

I will stress just a last point about Poe's metaphysics.
In {\em Eureka}, God is the cause of
the origin of the Universe: ``The Universe is a plot of God".
God represents the original Unity, to which all our Spirits will return, 
in a strict parallelism with the matter: ``That God may be
all in all, each must become God".

Here again, we may wonder if
it is Poe's physics which suggests his metaphysics, or the opposite.

\section{The fate of Eureka}

Why has {\em Eureka}'s cosmology so systematically been ignored or forgotten? 
For example, everywhere credit is given to Democritus for his
atoms, to Aristarcus for his heliocentric system, to Kant and Wright
for having considered nebulae as extragalactic systems, and so on,
but nowhere is it given to the modern universe of Poe, except for his solution
of the Olbers' paradox recently pointed out by Harrison.

It is possible to list different reasons.
Harrison has pointed out the main problem: metaphysics.
As I have shown, a number of points in {\em Eureka} are well
posed in rational terms, but Poe did not aim to a simple
scientific cosmology. His assumptions are often arbitrary,
and induce a natural scepticism in the reader.

The diffusion of {\em Eureka} was initially very limited: only 500 copies 
were published (instead of the 50,000 Poe had proposed!).
It was a peculiar work, ``a prose poem" in the tradition of Lucretius' 
{\em De Rerum Natura}. 
The first pages, with an epistemological discussion and a satirical
letter from the future, are quite surprising for the reader.
Some parts of {\em Eureka} could be a good example of a
popular treatise of astronomy of the 19th century; other parts
are devoted to the description of an original metaphysics,
both suggestive and arbitrary; everywhere Poe stresses that what he
says is the absolute Truth.
It is not surprising that it was not immediately appreciated, except for
the enthusiastic Baudelaire
(who had quite a biased vision of Poe anyway\footnote{
French literary critics have been quite severe
with Baudelaire, and in particular point out his erroneous
translation of Poe's {\em consistency} with the french {\em consistance},
and his confusion between {\em Oneness} and {\em Unity}.
}). 

But apart from the above aspects, 
the essential message of {\em Eureka} is that to have a consistent
cosmology we need an evolving universe, with a beginning and an end
(the parallel metaphysical message is that 
the spiritual universe also evolves, from Unity to Multiplicity,
and from Multiplicity to Unity).
The point is that there has always been a resistance to the idea of
an evolving universe;
and surely in 1848, the collapsing universe of Poe would appear quite 
visionary and even if one had believed what Poe claimed,
no observational test would have been possible.

Significantly, most scientists were reluctant to accept 
an evolving universe, after it was predicted by relativistic models but
before the discovery of the Hubble law in 1929.
After all, it is Poe himself who, explaining why John Herschel was reluctant 
to accept the idea of the collapse of the `nebulae', wrote:

\begin{quotation}
{\small
Simply on account of a prejudice; -- merely because the supposition is at war 
with a preconceived and utterly baseless notion -- that of the endlessness -- 
that of the eternal stability of the Universe.
}
\end{quotation}

The above reasons could probably be enough to justify the oblivion of 
{\em Eureka}. Moreover, in the second half of the 19th century
some of the fundamental astronomical ideas on 
which it was based were abandoned.

The change of vision was mainly due to the question of the nature and distance
of nebulae \cite{hoskin}.
By 1846 Lord Rosse could claim to have resolved stars in the Orion nebula,
and this appeared to be fatal to the nebular hypothesis of Laplace.
In the following years, the nebular hypothesis of Laplace was confronted 
with the problem of the distribution of angular momentum in the Solar System:
as a consequence, catastrophist theories prevailed until the 20th century.

In 1864, Huggins could obtain the spectrum of a nebula
and identify three bright emission lines:
he concluded that nebulae were made of gas, and not of stars.
Ironically, this discovery seemed now to be at variance with the
extragalactic nature of nebulae\footnote{I think that the instructive 
history of the problem concerning the nature of the `nebulae', 
essentially due to the assumption that such objects belonged to the
same and unique class, reminds us that the Ockham's Razor can 
be misleading, especially in Cosmology.
Perhaps a modern example is found in the discussion about the nature of
the Dark Matter: after Hot Dark Matter models,
Cold Dark Matter models gained general consensus in the last years.
New data seem now to require mixed models with both Hot and Cold Dark Matter.
Needless to say, this problem is far from a definitive solution.
}.

No wonder that in 1890, in her book {\em The System of the Stars},
Agnes Mary Clerke could write one of the most unfortunate 
and most quoted sentences in the history of astronomy:

\begin{quotation}
{\small
No competent thinker, with the whole of the available evidence before him,
can now, it is safe to say, maintain any single nebula to be a star system
of co-ordinate rank with the Milky Way.
\cite{clerke} 
}
\end{quotation}

As a consequence, for many decades most of the astronomical ideas on which 
{\em Eureka} was based became surpassed. What remained was an original, 
metaphysical work.

With the birth of Modern Cosmology, it became clear that {\em Eureka}
contained some anticipations, but it seems that those who read
this work taking its scientific content seriously, 
were biased in looking for glimpses of General Relativity
while, as I have stressed, Poe's universe was simply the most daring of 
Newtonian cosmologies.

\section{Conclusions}

In this paper I described
Poe's general vision of the Universe 
and why it appears so modern in many aspects.
I have chosen to analyse the ``physical cosmology" of Poe, without
taking into consideration the vague analogies of his metaphysics 
with a modern science he could not foresee.
It is the confusion between some supposedly pseudo-relativistic metaphysics 
(mainly contained in the first part, where Poe describes 
the expanding universe)
and the physical, Newtonian cosmology
(mainly contained in the second part, where Poe describes the collapsing 
universe) which has probably been an obstacle to an objective
analysis of the scientific content of {\em Eureka}.

I have shown that Poe has not only suggested a solution of the Olbers'
paradox for an infinite Universe (nevertheless he claims that the Universe of 
Stars must be finite), but that he was also the first
to conceive a Big Bang, and a universe where matter, concentrated 
at the beginning
in one particle, expands under the action of a cosmic repulsion,
generating a uniform spherical distribution of atoms.
Under the action of gravity, this universe collapses, giving birth
to stars, galaxies and life.
According to Poe, gravity is a consequence of the tendency of matter to
come back to the primordial state of Unity; the force of attraction
becomes effective after the phase of repulsion, when the Universe
begins to collapse.
He therefore conceives a definite epoch of galaxy formation
in the past, when matter was in an atomic state.
To justify the enormous size of the Universe,
he makes use of the anthropic principle.

In conclusion, I hope that this article will stimulate others to read
{\em Eureka}.
{\em Eureka} is not a crank nor a scientific theory.
It offers us a fascinating vision of the Universe
by an imaginative mind, which using the science of its time
could conceive the most revolutionary cosmology of the 19th century.
Indeed Poe, who aimed to be a modern
Esiodus or Lucretius, writes in the introduction:

\begin{quotation}
{\small
{\em What I here propound is true}: --therefore it cannot die:--
or if by any means it be now trodden down so that it die, it will
`rise again to the Life Everlasting'.}

{\small
Nevertheless it is as a Poem only that I wish this work to be judged 
after I am dead.
}
\end{quotation}

\section*{Acknowledgements}

I thank Luca Ciotti and Giovanna Stirpe (Osservatorio Astronomico di Bologna) 
and Lauro Moscardini (Dipartimento di Astronomia, Universit\`a di Padova) 
for critically reading the manuscript.

\newpage

\begin{thebibliography}{}

\bibitem{poe} Poe, E.A., 1848. {\em Eureka. A prose poem}, ed George P.Putnam, 
New York; 1976. in {\em The Science Fiction of Edgar Allan Poe}, ed Beaver, H., 
Penguin Books, Harmondsworth.

\bibitem{harrison} Harrison, E., 1987.
{\em Darkness at Night. A Riddle of the Universe}, Harvard University Press,
Cambridge.

\bibitem{eveleth} Poe, E.A., 1966. in
{\em The Letters of Edgar Allan Poe}, p.360, ed Ostron, J.W.,
Gordian Press, New York.

\bibitem{tipler} Tipler, F.J., 1988. (Olbers's Paradox, 
the Beginning of Creation, and Johann M\"adler), 
{\em Journal for the History of Astronomy}, {\bf XIX}, 45.

\bibitem{quinn} Quinn, A.H., 1941, {\em Edgar Allan Poe, A critical
biography}, Appleton--Century--Croft, New York.

\bibitem{maddison} Maddison, C.H., 1960. (Poe's Eureka), p.361, in 
{\em Texas studies in Literature and Language}.

\bibitem{bertotti} Bertotti, B., 1990. in {\em Modern Cosmology in
Retrospect}, p.3, eds Bertotti, B., Balbinot, R., Bergia, S., Messina, A., 
Cambridge University Press, Cambridge.

\bibitem{valery} Val\'ery, P., 1921. (Au sujet d'Eur\^eka),
in {\em Oeuvres Compl\`etes}, p.854--67, Gallimard, Paris. 

\bibitem{giorello} Giorello, G., 1982. Introduction to the italian translation
of {\em Eureka} by G.Giorello \& M.Skey, Edizioni Theoria, Roma.

\bibitem{numbers} Numbers, R.L., 1977. {\em Creation by Natural Law. 
Laplace's Nebular Hypothesis in American Thought}, 
University of Washington Press, Washington.

\bibitem{empedocles} Bollack, J., 1969. {\em Emp\'edocle}, vol.II, Les Origines,
Edition et traduction des fragments et des t\'emoignages,
Gallimard, Paris.

\bibitem{lemaitre} Lema\^{\i}tre, G., 1931. (L'expansion de l'espace),
in 
{\em L'hypoth\`ese de l'atome primitif}, Editions Culture et 
Civilisation, Bruxelles.

\bibitem{milne} Milne, E.A., 1934. (A Newtonian Expanding Universe),
{\em Quart. J. Math.}, {\bf 5}, 64.

\bibitem{milnemccrea} Milne, E.A., McCrea, W.H., 1934.
(Newtonian Universes and the Curvature of Space),
{\em Quart. J. Math.}, {\bf 5}, 73.

\bibitem{sciama} Sciama, D.W., 1971. {\em Modern Cosmology},
Cambridge University Press, Cambridge.

\bibitem{mccrea} McCrea, W.H., 1955. (On the Significance of Newtonian 
Cosmology), {\em Astron.J.}, {\bf 60}, 271.

\bibitem{ellis} Ellis, G.F.R., 1986. (The Expanding Universe: A History
of Cosmology from 1917 to 1960), in {\em Einstein and the History of General
Relativity}, based on the Proceedings of the 1986 Osgood Hill Conference,
p.367, North Andover, Massachussetts.

\bibitem{tropp} Tropp, E.A., Frenkel, V.Ya., Chernin, A.D., 1993.
{\em Alexander A.
Friedmann: the man who made the Universe expand}, 
Cambridge University Press, Cambridge.

\bibitem{layzer} Layzer, D., 1954. (On the significance of Newtonian Cosmology),
{\em Astron.J.}, {\bf 59}, 268.

\bibitem{barrow} Barrow, J.D., 1988. {\em The World within the World},
Clarendon Press, Oxford, p.354.

\bibitem{carter} Carter, B., 1974. (Large Number Coincidences and the Anthropic
Principle in Cosmology), in {\em Confrontation of Cosmological Theories
with Observation}, IAU Symposium no.63, p.291, ed. M.Longair, 
Reidel, Dordrecht.

\bibitem{barrowtipler} Barrow, J.D., Tipler, F.J., 1986.
{\em The Anthropic Cosmological Principle}, Oxford University Press, Oxford.

\bibitem{hoskin} Hoskin, M., 1982. {\em Stellar Astronomy: Historical Studies},
Science Publications Ltd, Chalfont St Giles.

\bibitem{clerke} Clerke, A.M., 1890. {\em The System of the Stars},
Black, London.

\end{thebibliography}
\end{document}
