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Dictionary of the History of Ideas

Studies of Selected Pivotal Ideas
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Cosmology as the endeavor to understand the motions
of the heavenly bodies may well have begun with our
earliest ancestors. In their unceasing efforts to feed on
other animals, and to avoid being themselves devoured
in turn, they found it advantageous to familiarize
themselves with the habits of their prey and predators.
It was important to know whether these beasts prowled
by day and slept at night, or the reverse. Such knowl-
edge could spell the difference between life and death
for man the hunter and hunted. For this as well as
other reasons he was sternly driven to note carefully
the alternating cycle of day and night, thereby acquir-
ing his first rudimentary concept of the cosmos in

The light that came down to him at night fluctuated
far more conspicuously than daylight. As a cosmic
body, the moon shone bright and full on certain nights,
whereas on others it disappeared altogether. Between
these extremes it displayed a recurring sequence of
changing visible shapes, expanding steadily from the
thin silver of its crescent to the full roundness of its
circular disk, and then shrinking in the opposite order
until it vanished again from view. This striking series
of lunar phases, constituting the synodic month, offered
man another basic cosmological idea. It also provided
him with a second unit of time as the measurement
of cosmic motion. For longer periods the month was
more useful than the day, which was reckoned as the
interval between successive risings, culminations, or
settings of the sun, moon, or stars.

The dark portion of such a day was discovered to
vary in length. The months during which the nights
lasted longer manifestly coincided with a distin-
guishable aspect in the life cycle of edible plants and
animals. Comprehension of the revolving seasons, with
their alternating warmth and cold, rainfall and drought,
storms and fair weather, further aided mankind to
survive and multiply by enlarging the food supply
derived from agriculture, fishing, and hunting. The


accompanying variations in the observed motions of
the sun, mounting higher or lower at noon, shining a
longer or shorter time on any given day, rising and
setting at shifting points on the horizon, provided the
basis for the year as man's third chronological tool in
carving out for himself a more secure place in the
cosmos. The calendar in any of its divergent forms
was an invaluable achievement of early cosmological

After being invisible for a considerable number of
nights, a bright star would reappear briefly at dawn
and then fade out of sight in the more brilliant light
of the sun. But every morning following this heliacal
rising, the star emerged from the eastern horizon ear-
lier and earlier. The heliacal rising of Sirius, the most
conspicuous star in Egypt, coincided with the start of
the Nile's annual flood, on which the livelihood of that
mainly agricultural country depended. Ten days after
Sirius' heliacal rising, another notable star repeated its
performance. Three such individual stars, or readily
recognizable clusters of stars, were grouped together
to form a month, and three sets of four months each
constituted a fairly close approximation to a solar year.
But the principal purpose of these thirty-six decans,
or ten-day groups of stars, was to tell the time by night.
Such a diagonally arranged star clock was employed
in Egypt by 2500 B.C. For daylight a shadow clock
was used a millennium later. The end of the shadow
cast by an upright cross-piece on a horizontal beam
reached a series of parallel marks indicating the prin-
cipal divisions of the day.

The sun, like the other cosmic bodies and forces of
nature, was manifestly much stronger than man's lim-
ited physique. Accordingly his unlimited mind imag-
ined various divinities, which he proceeded to identify
with the natural powers. Thus the ancient Egyptians
sometimes conceived the sky to be the goddess Nut,
whose enormously elongated body overarched the
earth, the tips of her fingers touching the horizon at
one side while her toes rested on the other side. Addi-
tional support was provided in the middle of her torso
by the upstretched arms of her father Shu, the god
of the air, who stood erect with both his feet firmly
planted on the solid earth. As the sun or god Re set,
he was swallowed by Nut's mouth in the west. During
the night he was hidden while passing through Nut's
body, from whose feet he reemerged the following
morning in the east. Alternatively, he traveled in his
night barge through the dark underworld (Dwat),
which extended beneath the earth. The next morning,
on terminating his subterranean sojourn, he transferred
to his day boat.

Re's night barge could traverse Dwat because a great
river ran through the netherworld. In Egyptian cosmo
logical thought, the whole universe originated from
water. In a valley inundated each year by the Nile's
flood, the dry land, which emerged when the waters
subsided, naturally suggested itself as a model for the
imaginary creation of the cosmos. In the beginning
there was nothing but the unlit abyss (Nun). From this
primeval slime arose a hill, on which the god Atum
created himself first, and then by masturbation gener-
ated a pair of divinities. From their sexual union the
rest of creation proceeded stage by stage. Rival versions
of this account were developed in religious centers
which claimed primacy for the local divinity. No single
hierarchical organization was strong enough to sup-
press competing dogmas. Later recensions tended to
subsume their predecessors by absorbing the essential
content and reducing it to a secondary level. As a result
of these conflicting sacerdotal ambitions, Egypt devel-
oped divergent and mutually inconsistent cosmogonical
schemes rather than a single unified view.

In Mesopotamia the Tigris and Euphrates rivers
continually poured their fresh water into the salty brine
of the Persian Gulf. Accordingly, for the local popula-
tion the cosmos commenced with a mingling of salt
water and sweet. These two forms of prime matter
were personified as male and female divinities, from
whose union sprang the rest of creation.

Similarly, in the Hebrew Bible the primordial sub-
stance was water, from which the dry land earth ap-
peared. However, before the sun was created as the
greater light to rule the day, and the moon as the lesser
light to rule the night, the light of day was divided
from the darkness of night. This unexplained pre-solar
light, contrasted with utter darkness, recalls the dualis-
tic Iranian conception of brilliant light and endless
darkness as the twin primeval forces locked in ceaseless
combat for control of the cosmos.

An alternative, and presumably earlier, cosmogony
in the Hebrew Scriptures is affected by a physio-
graphical environment vastly different from irriga-
tional agriculture, with its abundant and sometimes
excessive supply of water. Here the primordial sub-
stance is dry earth without vegetation, since there had
not yet been any rain. The cosmic features mentioned
in this creation story do not include the sea, nor are
fish listed among the species brought to life.

The Hebrews rejected astronomical observations,
systematically performed by “measurers of the heavens
and stargazers who prognosticate each month what
shall be.” The exiled prophet's scornful condemnation
of predictions based on recorded first visibilities of the
lunar crescent was aimed at his Babylonian conquerors.
They had long watched the western sky after sunset
to note precisely when the moon emerged from com-
plete obscuration during its conjunction with the sun,


the phase in which it rose and set nearly simultaneously
with the sun. When the new lunar crescent was seen
thereafter for the first time, the month was officially
declared to have begun. The number of whole days
between any two such successive occurrences was
either twenty-nine or thirty. To know in advance which
of these two lengths of the lunation was applicable
to any particular synodic month was the chief purpose
of the Babylonian observers. In their unremitting
efforts to solve this baffling problem they found it
necessary to “measure the heavens,” that is, to deter-
mine the angular distance between two cosmic bodies.
By contrast, no such measurement of angular separa-
tion is found in indigenous Egyptian documents. In-
stead, there the observer is depicted facing an im-
mobile, seated collaborator (or a life-size model of him)
and identifying the stars near their culmination with
reference to his right elbow, left eye, or other bodily

In Mesopotamia the stars were used as reference
points to locate the moon when, having passed beyond
its crescent phase each month, it set later and later
than the sun. Three stars, or striking configurations of
stars, were assigned to each month. For the needs of
urban life, such as the computation of interest on
business loans, a uniform length of thirty days was
conventionally adopted for the civil month, and twelve
such months for the year. But such a curtailed year,
however convenient for city-dwellers, was unsuitable
for farmers. When the harvest month arrived before
the grain was ripe for cutting, a thirteenth month had
to be intercalated. If no such intercalation had oc-
curred, the purely lunar calendar would soon have been
out of phase with the seasons, as indeed it is today
in Islamic countries, since twelve lunations fall many
days short of a year. On the other hand, thirteen luna-
tions would be excessive.

After centuries of spasmodic intercalations, the
Babylonians recognized a near equation. Nineteen solar
years were almost exactly equal to 235 lunar months.
In this nineteen-year lunisolar cycle, twelve years re-
ceived twelve months each for a subtotal of 144. The
remaining seven years were each assigned thirteen
months, bringing the full total to 235 (91 + 144). By
380 B.C. a definite pattern evolved in which the first,
fourth, seventh, ninth, twelfth, fifteenth, and eighteenth
years were made a month longer than the other twelve,
with the intercalation being inserted after the twelfth
month six times and once after the sixth month (of the
eighteenth year).

Many stars, after traveling along arcs in the sky,
dropped out of sight below the horizon in the west.
By contrast with this disappearance, some northern
stars remained visible above the horizon even at the
lowest point on their nightly curves. These were com-
plete circles, centered at various distances around an
unseen point. This was conceived to be a pivot which
turned, or around which turned, an invisible heavenly
canopy bejewelled with the multitudinous sparkling
stars. The distance between any two of them remained
unchanged night after night, thereby reinforcing the
impression that they were all attached to the imper-
ceptible celestial awning.

Each star always rose at exactly the same point on
the eastern horizon. But its time of rising was somewhat
earlier on successive nights. Gaining a little on the sun
every day, the star overtook it in the course of a year.
This steady advance of the stars with respect to the
sun, those east of it constantly approaching closer to
it, and those west of it steadily withdrawing farther
from it, could be interpreted otherwise. The stars could
be regarded as fixed, and not as slipping westward away
from the sun. Instead, the sun was deemed to be mov-
ing eastward slowly among the fixed stars in a journey
that lasted a whole year, while every day of that year
the sun traveled rapidly westward across the sky.

The speed of the sun in its annual eastward trek was
discovered to change in a periodic manner. It was
therefore indispensable to grapple with this period,
since the moon's daily withdrawal from the sun was
the basis of the Babylonian lunar calendar. Instead of
assuming that the solar velocity varied continuously
throughout the year, some Mesopotamian astronomers
preferred to keep the speed steady at one level for
about six months, drop it down to a lower constant
level for the rest of the year, and then jump it back
up again to the higher initial level, where it started
to repeat the previous pattern. This discontinuous
treatment of the varying speed, so that it steps up or
down from one straight row of numbers to another,
produces what is termed a “step function.” Alterna-
tively, the sun's eastward velocity was deemed to de-
crease continuously from its maximum to its minimum,
and there alter its direction abruptly, climbing at the
same rate of change back again to the maximum, where
it began the second period of this so-called “linear
zigzag function.” Both step functions and zigzag func-
tions were in use at the same time, the former more
widely because somewhat easier to handle.

These two types of numerical tables made it possible
to predict not only the beginning of the month but
also the lunar eclipse at mid-month. It was noticed that
the moon suffered eclipse, either total or partial, only
when it rose near sunset or set near sunrise. This lunar
phase of opposition to the sun, however, did not always
coincide with an eclipse. This striking phenomenon
occurred only when the moon was near the track
followed by the sun in its annual eastward circuit


through the constellations. This solar path was later
named the “ecliptic,” because the moon was eclipsed
only when its opposition to the sun took place in the
vicinity of the sun's line of march. More often than
not the moon at opposition was not eclipsed, because
it was too far above or below the ecliptic; in other
words, its northern or southern latitude was too great
to permit the effect to occur. However, when the moon
approached one of its nodes, where its path crossed
the sun's, it underwent an eclipse, which would be
followed by another in either five or six months. Con-
tinuous records of lunar oppositions with or without
eclipses revealed a pattern that repeated itself after
approximately eighteen years.

No such cycle was discovered for solar eclipses,
which occur toward the end of the month, when the
sun and moon are in conjunction. While a total or
nearly total solar eclipse is a spectacular event, a minor
partial eclipse of the sun might easily be overlooked
in the daylight, and in any given case might not be
visible to observers in Mesopotamia.

At an early date they distinguished the planet Venus,
which on account of its extraordinary brilliance was
grouped with the sun and moon to constitute a trinity
of celestial divinities. From the day the observers first
saw Venus rise in the east earlier than the sun, they
watched it as a morning star for more than eight
months, until it disappeared from the sky for three
months. Then it reappeared in the west, setting later
than the sun as an evening star. These recurring ap-
pearances and disappearances of Venus were faithfully
recorded. In due course the observers recognized the
remaining “stray sheep,” as the planets visible to the
naked eye were called.

One of them, Mercury, behaved like Venus, which
disappeared twice during each cycle. By contrast, three
other “stray sheep” became invisible only once in each
cycle. The performance of these three (Saturn, Jupiter,
and Mars) was remarkable also in another respect. They
traveled eastward at a varying speed, stopped at their
first stationary point, reversed their direction for a short
while, halted at their second stationary point, and then
resumed their normal eastward or direct motion. These
critical junctures—where the planet stood still, first
appeared, and disappeared—attracted the attention of
the Babylonians. They compiled lists of the dates on
which these transitions occurred. Dividing the planet's
varying velocity into several discontinuous levels, they
treated it either as a periodic step function or as a
linear zigzag function. These functions were often
modified in a variety of ways as different observers
adopted divergent methods of approximating the plan-
et's mean motion. These arithmetical planetary tables
in general resemble those used for the moon. The lunar
tables, however, are far more complicated, containing
as they do supplementary column after column of the
corrections needed to obtain increasingly accurate
predictions of the highly erratic motion of the moon.

Like the other cosmic bodies, the moon was deemed
to be a divinity. Each followed its own course in the
sky, and in so doing gave signs to mankind. In the
remote past the gods had on occasion spoken directly
to this or that man. Now they wrote their will in the
heavens. For those who professed to be skilled in the
art of reading these celestial omens, there was fore-
knowledge of the near future: impending floods and
storms, size of the crops, state of the public health,
outbreaks of civil disorder, length of the ruler's life,
intentions of foreign powers, duration of peace, and
outcome of wars. Such political astrology was espe-
cially prominent in Assyria, whence it spread westward
through the Hittite realm. On the other hand, those
who revered the cosmic bodies were fiercely con-
demned by the monotheistic Hebrew prophet: their
bones shall be spread “before the sun and the moon
and all the host of heaven... whom they have wor-
shipped”; their bones “shall not be gathered, nor be
buried, they shall be for dung upon the face of the
earth” (Jeremiah 8:2).

That oblique portion of the host of heaven within
which the sun, moon, and planets travel was divided
by the Babylonians into configurations resembling to
a greater or lesser extent some terrestrial beast, real
or fanciful, plant, human, or artifact. These imaginative
constellations were later borrowed by the Greeks, who
modified them somewhat and called them in their own
language zodiacal, because their word for a little figure
was zodion. The number of these Babylonian zodiacal
constellations was gradually reduced to twelve. Each
constellation was then assigned to one of the twelve
months during which the sun completes its yearly
course along the ecliptic or “line through the middle
of the zodiac.” To each such twelfth of the zodiac,
or zodiacal sign, 30° of longitude were allotted. The
dividing line between any two neighboring signs was
drawn so that the constellation from which the sign
took its name would fit as well as possible within the
corresponding sign.

A planet could now be located as being at a given
time at a definite degree within a specified zodiacal
sign. This method of pinpointing the position of a
cosmic body was more precise than the previous pro-
cedure of placing it in relation to a constellation, whose
boundaries in the nature of things were bound to be
much more difficult to define.

From the planetary tables it was now possible to
say where each planet was at any given moment, even
if it happened to be in the invisible portion of its orbit.


With the positions of all the planetary divinities known
at the instant of any individual's conception or birth,
it was believed possible to make a long-range predic-
tion of his fate. Two of these deities, Venus and Jupiter,
were regarded as benevolent; two others, Mars and
Saturn, as malevolent; and Mercury as ambivalent.
Their effect on the individual was strengthened or
weakened by their presence in a particular zodiacal
sign and by their aspects, or mutual angular distances
within the zodiac. This kind of horoscopic or geneth-
liacal astrology, based on the locations of the planets
at a supposedly critical juncture and on their imagined
potencies, could profess to read far into the future,
where the planetary tables covered extensive periods
of time. Moreover, the new predictive service was at
the disposal of any person wealthy enough to afford
the fee, and was no longer confined to royalty and other

The nations who worshipped the moon as a deity
might predict its eclipses correctly, but could offer no
physical explanation of them. Nor could the Hebrews
who, although they deprived it of its divine status,
regarded it as a self-luminous body, somewhat less
brilliant than the sun. Their god announced that he
would “show wonders in the heavens.... The sun shall
be turned into darkness, and the moon into blood” (Joel
2:30-31). The copper color of the lunar eclipse was
a product of the divine will, not a natural effect. So
also among the Hindus, the moon was eclipsed because
it was swallowed by a demon; the lunar nodes, the
two points on its orbit where the moon crosses from
north latitude to south and from south to north, were
long called the dragon's head and the dragon's tail.

Anaxagoras, however, who was denounced for impi-
ety and imprisoned in Athens, discovered that the
moon's light is not its own, but comes from the sun.
Hence the eclipses of the moon are caused by its falling
within the shadow of the earth, which comes between
the sun and the moon at that time.

Anaxagoras also recognized that the sun is eclipsed
at new moon, when its dark and opaque bulk is inter-
posed between the earth and the sun. By contrast, in
pre-Hellenic cosmology, which made no effort to as-
certain the earth's distance from the sun and moon,
these bodies, or rather divinities, were regarded as
equally remote. In like manner no attempt had been
made to estimate their size. Anaxagoras, on the other
hand, insisted that the sun was a red-hot rock bigger
than the Peloponnesus. Did he suppose that the large
meteorite which landed during his lifetime fell down
from the sun? In any case he surmised that the moon
is earthy, having mountains, plains, and ravines.

The shape of the earth had puzzled earlier Greek
cosmologists. Thus, to account for its stability, Xeno
phanes had supposed that it extended infinitely down-
ward. But its roundness was proved visually by the
convex shape of the shadow it always casts on the moon
during a lunar eclipse. By the same token, the shadow
thrown by the moon on the sun in a partial solar eclipse
demonstrated ocularly the sphericity of the moon. This
conclusion was confirmed by the lunar phases, with
the half-moon regularly intervening between concave
and convex illuminated segments. Since the moon was
spherical, so were all the other cosmic bodies, and
indeed the universe itself was one big ball. To the under
surface of its exterior shell the stars were attached like
bright studs, whereas the planets were free to roam.

As the planets revolved at various distances from
the center at different speeds, they emitted diverse
tones which blended into a celestial harmony, unno-
ticed because we mortals have all heard it from birth.
This was only one indication to the mystically inclined
Pythagorean brotherhood that the cosmos was con-
structed on mathematical lines. Philolaus, one of the
brethren, held the earth to be a planet, revolving like
the others around a central fire, the Hearth of the
Cosmos. Ecphantus, another brother, maintained that
the earth rotates about its own center from west to
east. “Motion like an auger whirling around the same
place” was attributed by Plato and the Pythagoreans
to the fixed stars. Convinced that the planets could
have no reason to speed up, slow down, stop, and
retrace their steps in loops, the brotherhood asked how
the phenomena seen in the sky could be explained on
the assumption that the cosmic motions were all per-
fectly circular and absolutely uniform.

Although the same question was propounded by
Plato, he insisted that “we shall dispense with the
bodies in the heavens if we propose to obtain a real
understanding of astronomy” (Republic VII, 530C). No
perceptible object could furnish true knowledge, which
comes only from pure reason, not from lowly sight.
Like diagrams in geometry, the visible cosmic bodies
merely furnished illustrations to facilitate a putatively
“higher” study. Plato nevertheless proceeded to con-
coct a creation story, complete with an uncreated
creator god and a divine cosmos animated by a univer-
sal soul. With regard to the three outer planets, he
said that men “neither give them names nor investigate
the measurement of them one against another by nu-
merical calculation” (Timaeus 39C). With all its ob-
scurity and obscurantism, Plato's Timaeus exerted a
pervasive and pernicious influence on subsequent cos-
mological thought. It undertook to combat the specu-
lations advanced by the founders of the atomic theory.
According to them, space is infinite and contains innu-
merable atoms in ceaseless motion. From their colli-
sions unnumbered worlds arise, some expanding, others


collapsing, and still others devoid of moisture. Metro-
dorus, a pupil of the atomist Democritus, maintained
that “a single plant growing in a broad field is just
as absurd as one cosmos in infinite space” (Guthrie,
II, 405; trans. E.R.).

The only cosmos we know was viewed by Eudoxus
as a nest of twenty-seven homocentric spheres. To the
sun, moon, and five known planets he assigned a com-
bination of perfect spheres, each rotating with a con-
stant angular velocity. The cosmic body was attached
to the equator of its innermost sphere. As this carrying
sphere rotated forward, its axis was borne backward
by a second sphere to whose surface its poles were
fixed, the axes of both spheres being inclined to each
other. By adding a third similar sphere for the sun and
moon, and two more for each of the planets, Eudoxus
succeeded in representing the observed motions with
qualitative fidelity, although not with quantitative preci-
sion, especially in the case of Mars.

The seven separate mathematical models of Eudoxus
were later converted into a single physical mechanism
by Aristotle. However, whether merely an abstract
geometrical blueprint or a solid contrivance, no ar-
rangement of concentric spheres could alter the dis-
tance of any planet from the eyes of the observer on
the earth at the middle of the whole system. But Mars
and Venus in particular, and the other planets too, vary
considerably in brightness, and therefore in their dis-
tance from the earth. Moreover, the moon's distance
from the earth also changes, as is shown by central
solar eclipses, in some of which the sun's disk is entirely
obscured, whereas in the annular eclipses a bright ring
surrounds the moon's shadow.

These two fatal defects in the theory of homocentrics
were overcome by removing the earth from the center
of the cosmic body's uniform circular motion in its
orbit. The displacement of the earth from the orbital
center made the distance from the revolving cosmic
body to the terrestrial observer a variable quantity. At
its perigee, or closest approach to the earth, the body
was seen to move more rapidly than at its apogee, or
greatest distance from the earth (Figure 1).

Such an “eccentric” pattern fits the sun's annual
journey. This solar orbit is divided into four equal
quadrants by the solstices and equinoxes, which mark
the four seasons of the year. But the sun traverses these
equal arcs in unequal times. Of the four seasons, the
spring, extending from the vernal equinox to the sum-
mer solstice, lasts the longest. Because the sun travels
most slowly then, it crosses its apogee. By the same
token it passes through its perigee in the autumn, the
shortest of the four seasons.

This simple eccentric scheme had to be modified in
the case of Mars. When this planet culminates at mid-
night it is at its brightest, and therefore closest to the
earth. At that same time it is in opposition to the sun.
Mars' opposition, however, does not always occur at
the same point of the zodiac. On the contrary, the
opposition may take place anywhere along Mars' orbit.
To permit the opposition to shift in this way, Mars'
eccentric was provided with a moving, instead of a
fixed, center. This center, always aligned with the sun,
revolved around the earth in the course of a year. A
similar moving eccentric suited the other two planets,
Jupiter and Saturn, which are found at any angular
distance, or elongation, from the sun (Figure 2).

In the case of Venus and Mercury, however, the
circle described by the eccentric's center would have
to exceed the eccentric itself in size. This arrangement
would be tantamount to each of these planets riding
on a small epicycle whose center traversed a large
deferent. This moving center could be identified with


the sun, since Venus and Mercury are never seen very
far away from that luminary, their greatest elongations
from it being quite moderate. Moreover, they are
sometimes east of it, and at other times west of it. This
alternate crisscrossing and perpetual proximity sug-
gested the inference that Venus and Mercury revolved
around the sun like satellites, while at the same time
the sun executed its annual orbit around the earth.

The epicycles of Venus and Mercury had a material
body, the sun, for their moving center. If this became
an immaterial point, revolving around an earth-
centered deferent, the planet-bearing epicycle pro-
duced the same visual effect for a terrestrial observer
as an eccentric with a fixed center. The radii of the
eccentric and deferent were equal and parallel to each
other, while the eccentricity was equal to the radius
of the epicycle. The kinematic equivalence of these
two simple schemes was demonstrated by Apollonius.
The introduction of eccentrics and epicycles in place
of geocentric spheres gave mathematical cosmology a
new freedom to choose any center of rotation outside
the earth and at any suitable distance from it. In every
case the accepted procedure was to adopt the fewest
and simplest hypotheses that would produce results
conforming as closely as possible to the observed
phenomena, or “save the phenomena,” as the Greeks
liked to say.

A startling phenomenon, either a nova or a comet,
impelled Hipparchus to compile for posterity the first
catalogue of fixed stars, “indicating the position and
magnitude of each, so that from this catalogue it could
be readily determined not only whether stars perish
and are born but also whether some of them actually
shift and move” (Pliny the Elder, Natural History, II,
24, 95; trans. E.R.). While comparing previous obser-
vations of eclipses with his own, Hipparchus noticed
that a certain star's longitudinal distance from the
nearby equinoctial point had decreased somewhat be-
tween the two observations. He interpreted this de-
crease as a slow westward displacement or precession
of the equinoxes, carrying the equator with them.
Afterwards the alternative explanation prevailed, that
the celestial sphere rotated eastward about the poles
of the ecliptic.

Hipparchus refrained from attempting to construct
theoretical schemes for the five planets because he did
not have at his disposal an adequate supply of accurate
observations. In remedying this deficiency he learned
that the planetary retrograde arcs vary. Building on
the foundations prepared by his highly admired prede-
cessor, Ptolemy was able to complete the edifice of
ancient cosmology.

In the Ptolemaic system the finite spherical cosmos
was bounded by the fixed stars, more than a thousand
of which were catalogued in forty-eight constellations
(twelve zodiacal, twenty-one northern, and fifteen
southern). Each star was attached to the universe's
outermost sphere, which completed a daily rotation
from east to west around the poles of the celestial
equator. This diurnal rotation affected also the sun,
moon, and five planets. Since a planet's apse-lines,
drawn through its apogee and perigee, did not change
their position in the starry sphere, the planets shared
in that outermost sphere's slow eastward rotation
around the poles of the ecliptic in 36,000 years. It was
this rotation which produced the phenomenon still
called the “precession of the equinoxes.”

Below the sphere of the stars three planets—Saturn,
Jupiter, and Mars in that descending order—par-
ticipated in the daily cosmic rotation westward. But
just as passengers may stroll slowly eastward on the
deck of a ship traveling swiftly westward, each of these
three planets at its own speed completed its orbital
revolution in the zodiac. This prevailingly eastward
march slowed down and halted at a first stationary
point, reversed its direction for a time, and after a
second stationary point resumed its direct motion. To
account for these irregular loops Ptolemy had the
planet revolve on an epicycle whose center was in turn
carried around by an eccentric deferent. At a distance
from this deferent's center along the apse-line con-
necting the apogee and perigee lay the earth. On the
apse-line at a distance from the deferent's center equal
and opposite to the earth's, Ptolemy placed an equant.


As measured from this equalizing point, and not from
the deferent's center, the mean angular velocity of the
epicycle's center was uniform (Figure 3).

These three outer planets could be observed at any
elongation from the sun, which revolved around the
earth in a year, either on a simple eccentric or an
epicycle carried by a concentric deferent. In so doing
the sun separated the three outer planets from Venus
and Mercury, which never depart very far from it.
Because Mercury's motion is so irregular, Ptolemy had
to rotate the deferent's center on a circlet.

Below Venus and Mercury (the inner planets) the
moon revolved around the earth. Its motion on an
epicycle carried by a concentric deferent agreed fairly
well with the observations when the moon was in
syzygy, where an eclipse could occur because the moon
was either in opposition to the sun or in conjunction
with it. In quadrature, however, where the half-moon
formed a right angle at the earth with the sun, the
distance moon-earth had to be reduced to conform with
this “evection,” as it was called later. Ptolemy accom-
plished this result by making this distance depend on
a line connecting the epicycle's center with a point
moving around a circlet centered on the earth (Fig-
ure 4).

In the middle of this Ptolemaic cosmos the spherical
earth, or rather terraqueous sphere, rested immovable.
The interval extending outward from the surface of
this sphere to the lunar perigee was filled with air and
elemental fire, in that order. The lunar apogee coin-
cided with the perigee of Mercury, whose apogee was
contiguous with Venus' perigee. This tight fit of apogee
with the next perigee continued all the way out to
the fixed stars on the principle that “in Nature a vac-
uum, or any meaningless and useless thing, is incon-
ceivable” (Ptolemy, Planetary Hypotheses).

When viewed abstractly or theoretically, these
neatly designed concentrics, eccentrics, deferents, and
epicycles were merely indispensable mathematical aids
in computing and predicting the positions of the cosmic
bodies. Alternatively, these constructs were regarded
as physical or material entities. Thus, “like a pearl on
a ring” the spherical body of the planet was affixed
to the equator of its epicycle, which was a solid ball
running in a groove. This channel's lower surface was
formed by the outside or convexity of the planet's
deferent, which was now conceived as a spherical shell
or hollow sphere. The groove's upper surface in like
manner consisted of the interior or concavity of the
next higher planet's deferent. From the stationary earth
to the slowly rotating starry sphere, the celestial bodies,
mounted on their epicycles, each confined within its
own groove, performed their stately and intricate bal-
let. This absolutely full Ptolemaic universe devoid of
empty space, or its mathematically equivalent blue-
print, dominated cosmological thought for fourteen
centuries (Figure 5).

Arab observers found that in their time the preces-
sion of the equinoxes moved faster than 1° in 100 years,
the slightly mistaken figure announced by Ptolemy.
Instead of discarding his value as too slow and accept-
ing their own more rapid rate of 1° in 66 years as
constant, some of them revived an ancient notion that
the precessional speed swung back and forth between
a maximum and a minimum. With this imaginary peri-
odic oscillation or trepidation, they connected another
supposed cyclic variation. This affected the angle at
which the plane of the celestial equator is intersected
by the plane of the ecliptic. This obliquity of the
ecliptic had been somewhat overstated by Ptolemy at
23°51′20″. Putting the maximum at a rounded figure
in this vicinity, the Arabs conceived the obliquity as
oscillating slowly through an arc of about two-fifths
of a degree.

Whereas the Koran was satisfied with only seven
heavens (presumably one each for the moon, sun, and
five planets), these Muslim cosmologists added Ptole-
my's eighth sphere of the fixed stars. To account for
the precession of the equinoxes, they introduced a ninth
sphere, and then a tenth for the trepidation of the
precession. For the related fictive cyclic variation in
the obliquity of the ecliptic an eleventh sphere was
adopted by some Muslims and their Christian followers.


Early Christian writers had denied that the earth
is round, since in that case on the opposite side of the
globe there would be people with their feet upwards
and heads downwards. In the Hebrew Bible, which
they misappropriated to themselves under the extrane-
ous designation “Old Testament,” they professed to find
sacred warrant for their contention that the earth is
the floor of the cosmos. On this flat surface their imagi-
nation erected in the north a high conical mountain,
whose summit created darkness by blocking out the
light of the sun which passed from west to east during
the night. In comparison with the earth, therefore, the
sun was a small object. Its heat, like that of all the
other celestial bodies, would be extinguished, at the
dissolution of the cosmos, by the waters providentially
stored for that purpose above the firmament.

While it still continued to function prior to that
cataclysmic event, each cosmic body was propelled in
its course by a tireless angel. This Christian angel
replaced the pagan soul which Plato and the Neo-
Platonists had assigned to each cosmic body as its
driving force. On the other hand, Aristotle's First
Mover, being incorporeal, could not itself move, but
operated like a beloved object after which the First
Movable, or sphere of the stars, strove and thereby
communicated motion to the remaining cosmic bodies.
They did not receive any impulse from without, ac-
cording to Ptolemy. On the contrary, each of them
had within itself its own vital energy propelling it
forward. Every planet was the source of its own mo
tion, like a living bird. Taken as a whole, the cosmic
bodies flew through space like a flock of birds, each
at its own pace and on its own course. In late antiquity
Johannes Philoponus, a Christian commentator on
Aristotle, early in the sixth century dismissed the angels
who had formerly tugged and strained at the cosmic
bodies. Instead, he had God implant within them at
the time of creation an impetus which kept them going
round and round.

The Christian version of the creation story insisted
that with His unlimited might their God made the
entire universe out of nothing at all. This denial of
the existence of matter prior to creation reinterpreted
the Hebrew Bible's primordial material abyss, and
controverted the ancient atomists' teaching that
“nothing is ever produced by divine action out of
nothing.” Nor, in the Nature of the atomists, is any-
thing reduced to nothing. Instead, it is dissolved into
its component indivisible atoms which, being inde-
structible, are everlasting. Then time itself has no end,
although the several worlds created by Nature may
come into being and pass away. For space is boundless.
If it were confined within the stars, where would a
javelin go when hurled outward from those “flaming
ramparts of the cosmos”?

This was not the kind of question with which
Aristarchus had grappled in the third century B.C.,
when he enormously enlarged the size of the cosmos
without declaring it to be infinite. He ascribed to the
earth a daily rotation about its own axis, so that the
stars remained motionless. He also assigned to the earth
an annual revolution around the sun, which he held
stationary at the center of the earth's orbit. For he
had computed the sun to be some 300 times larger
than the earth in volume, and how could so big a mass
revolve around the smaller earth? Did not the moon,
whose bulk he calculated as about one-thirtieth of the
earth's, revolve around the bigger body?

After lying dormant beneath the ruling geostatic
cosmologies, the Aristarchan geokinetic thinking was
revived early in the sixteenth century of our era by
Nicholas Copernicus. Whereas Aristarchus had pro-
vided only the bare bones of the heliostatic system,
Copernicus fleshed it out.

He was unaware that the followers of the fifth-
century Hindu astronomer Aryabhata “maintain that
the earth moves and heaven rests. People have tried
to refute them by saying that, if such were the case,
stones and trees would fall from the earth.” But
Brahmagupta, Aryabhata's seventh-century successor,
disagreed, “apparently because he thought that all
heavy things are attracted towards the center of the
earth” (Sachau, ed. and trans. I, 372).

Copernicus was equally unaware that in 1377


Nicholas Oresme, while explaining his translation of
Aristotle's Heavens—the earliest rendering in a modern
language—considered many arguments for and against
the daily rotation of the earth. Recognizing that it
benefits from the sun's heat, Oresme reasoned that in
familiar things what “is roasted at a fire receives the
heat of the fire around itself because it is turned and
not because the fire is turned around it” (Le Livre du
ciel et du monde,
eds. A. D. Menut and A. J. Denomy,
Madison [1968], p. 533). Nevertheless Oresme, bishop
of Lisieux, decided in favor of a static earth, on the
basis of biblical passages.

At the same time in the Islamic world Ibn al-Shatir
of Damascus rejected Ptolemy's equant as a violation
of the principle that a cosmic body's orbit must be
compounded from absolutely uniform circular motions.
This Muslim timekeeper at the mosque in Damascus
also introduced a second epicycle into Ptolemy's lunar
theory in order to eliminate its grossly excessive varia-
tion in the length of the moon's apparent diameter.
In these two respects Copernicus' theories resembled
Ibn al Shatir's. But, unlike his Damascene prede-
cessor, Copernicus did not use a second epicycle for
the sun; he retained eccentric orbits; and his numerical
results also differed, being based in part on his own
observations. He knew neither Arabic nor French, and
the relevant writings of Ibn al-Shatir and Oresme had
not been translated into Latin. Copernicus evidently
shared earlier uneasiness with aspects of the Ptolemaic
cosmology. But entirely independently he went back
to Aristarchus' heliostatic cosmos.

One objection thereto was that any motion of the
earth must disrupt it. But, as regards its daily rotation,
the only available alternative required the vastly
greater heavens to whirl round with immensely swifter
speed each day. Would not, Copernicus asked, a more
devastating destruction necessarily be entailed thereby?

Then the daily rising and setting of the sun must
be recognized as a mere appearance, due to the real
axial rotation of the earth. In like manner, the cycle
of the seasons is caused by the earth's annual tilted
orbit. As it carries the observer around, the optical
effect of his motion must be disengaged from the real
revolutions of the planets. These bodies do not actually
speed up, slow down, stop, and reverse their course.
They seem to do so only because they are observed
from that ceaselessly moving observatory which is our
earth. In truth the planets always proceed in the same
direction at a constant speed. So does the earth, which
now took its rightful place in the cosmic order, a planet
like the others.

Copernicus' rearrangement of the cosmic bodies for
the first time clarified certain previously unexplained
coincidences in the Ptolemaic system. The outer plan
ets therein always appeared brightest in opposition;
the radius of the epicycle remained at all times parallel
to the line drawn from the terrestrial observer to the
sun; and the arc of retrogression in the apparent loop
diminished from Mars outward to Saturn. All these
phenomena were now seen to be necessary conse-
quences of the earth's orbital revolution.

In like manner the Ptolemaic system kept Venus and
Mercury within their greatest elongations from the sun
by requiring the line from the earth to the epicycle's
center to be prolonged through the sun. But these two
bodies became true inner planets in Copernicus' cos-
mos, and as seen from the earth they could not exceed
their limited maximum elongations from the sun.
Moreover, by evaluating the distance from Venus to
the sun in terms of terrestrial radii, Copernicus finally
found the way to determine the absolute dimensions
of the planetary system. And he correctly reinterpreted
the precession of the equinoxes as due to a continuous
shift in the direction of the earth's axis of rotation,
instead of to a slow eastward rotation of the sphere
of the stars around the poles of the ecliptic.

In Copernicus' cosmos the earth revolved around the
sun in a huge orbit requiring a whole year to be tra-
versed. Then the direction of any star, as observed at
an interval of six months from two diametrically oppo-
site points on the earth's orbit, should exhibit the dis-
placement known as the “annual stellar parallax.” To
account for the nonobservation of this phenomenon,
Copernicus asserted that the enormous remoteness of
the stars made the diameter of the earth's orbit a
negligible quantity. In other words, Copernicus' uni-
verse became immensely great. But he stopped short
of proclaiming it to be infinite, confining himself to
the description “similar to the infinite.” Unlike the
Buddhists who declared that “the cosmos is neither
finite nor infinite,” Copernicus “left to the philosophers
of nature the question whether the universe is finite
or infinite.”

One philosopher of nature who spoke his mind was
Thomas Digges. In 1576 he declared that the sphere
of the fixed stars reached “up in spherical altitude
without end.” Therefore, although the stars still stayed
within the same sphere, their height varied. Thus
Digges agreed with the ancient Greek expositor Gemi-
nus, who “would not assume that all the stars lie on
a single surface, but rather that some are higher and
others lower, the difference in their height being im-
perceptible because our sight attains [in all directions
only] to an equal distance” (Cohen and Drabkin, p.
118; trans. E. R.). Just as the Roman poet Manilius had
attributed the dimmer brilliance of some stars to their
greater height, so Digges' stars looked smaller the more
remote they were, and “the greatest part rest by reason


of their wonderful distance invisible to us.” Never-
theless the sun and its satellites remained in the middle
of Digges' heliocentric cosmos.

On the other hand, the nonfinite universe preached
by the mystical theologian Nicholas of Cusa had its
circumference nowhere and its center everywhere.
Then the earth could no longer be in the middle of
the cosmos, and it therefore ceased to be the dregs
of the universe. Instead, it became for Cusa a “noble
star,” whose motion was circular albeit not perfectly so.

Cusa's loosening of the rigid bounds of the traditional
cosmos made a profound impression on an ill-fated
genius who was publicly burned at the stake by the
Roman Catholic church in 1600. But Giordano Bruno
went far beyond his master Cusa in recognizing our
sun as one of the countless stars in an infinite universe.

In Aristotle's finite universe everything had its natu-
ral place. Whether at rest therein or violently displaced
therefrom, a body capable of motion was in a place
bounded by the inner surface of a stationary nontrans-
portable containing vessel. This Aristotelian concept
of place was rejected by Bernardino Telesio, “the first
of the modern men,” as he was called by Francis Bacon.
Telesio maintained that all bodies are contained in a
single vast emptiness, for which he introduced the term

This universal emptiness was made infinite by
Telesio's contemporary, Francesco Patrizi. His infinite
mathematical space, which he paradoxically described
as an “incorporeal body,” surrounds an inner physical
space, containing the cosmic bodies. Thus Aristotle's
hierarchically ordered set of finite places gave way to
Patrizi's infinite emptiness, which in due course won
acceptance as the concept of absolute space.

The new star of 1572 convinced Tycho Brahe that,
contrary to the long accepted belief in the immuta-
bility of the perfect heavens, changes can occur there.
However, he declined to speculate how the nova came
into existence, although he concluded that it must have
decreased in size.

The great comet of 1577 challenged the traditional
sublunar location of these spectacular bodies. Aristotle
had said that they were ignited below the moon as
dry exhalations rose up from the earth. But a genera-
tion after Peter Apian remarked that a comet's tail
always pointed away from the sun, the comet of 1577
showed no perceptible daily parallax. Therefore it had
to be traveling far beyond the moon. In antiquity
Seneca had said: “We see the comets mingling with
the stars and passing through the higher regions.”

Then the comet's head and tail must collide with
the crystalline spheres carrying the planets. But, Tycho
pointed out, no such collisions between comet and
crystal occurred. The absence of these dreaded catas
trophes demonstrated the entirely imaginary nature of
the spherical machinery which had so long crowded
the heavens before his time. Thereafter the cosmic
bodies moved on their own through the upper regions.

Copernicus' reasoning that five planets revolved
around the sun was accepted by Tycho. But he refused
to believe that the heavy, sluggish earth was capable
of motion, which, moreover, conflicted with the Bible
as he interpreted it. In his own cosmology, therefore,
he kept the earth motionless at the center of the uni-
verse. Around it revolved the sun, which in turn served
as the center for the planets revolving around it. This
Tychonian compromise appealed to those who, while
feeling the force of Copernicus' argumentation, still
clung to the remnants of their obsolete metaphysical
prejudices and dogmatic bibliolatry.

No such hindrances prevented the intellectual de-
velopment of Brahe's most famous assistant, Johannes
Kepler. Inheriting the invaluable treasure of Tycho's
accumulated observations, Kepler tried to fit them to
the orbit of Mars while confining himself to the tradi-
tionally sanctioned cosmological devices. Unable to
find a satisfactory agreement between Tycho's obser-
vations and any conceivable combination of uniform
circular motions, Kepler finally discarded the bimillen-
nial prejudice against all curved tracks save the circu-
lar. An ellipse, departing only slightly from a perfect
circle, turned out to be the true (predictably correct)
path of the planet. Its motion along the ellipse could
be kept uniform by measuring, not the linear velocity,
but the areas swept out in equal intervals of time by
the straight line connecting the moving planet with
the sun, located at one of the two foci of the elliptical
orbit. The square of the time required by any planet
to traverse its ellipse showed the same proportion in
all cases to the cube of the planet's mean distance from
the sun.

These three principles of planetary motion consti-
tuted Kepler's imperishable contribution to cosmology.
They confirmed the essential truth of the Copernican
system, while revising it drastically. Gone forever were
the pre-Keplerian eccentrics, deferents, and epicycles
in their complicated combinations.

Gone too was the conception that a cosmic body
could revolve around a mathematical point not occu-
pied by a physical body. For example, in Copernicus'
cosmos the sun had been near, not at, the universe's
center, which was also the center of the orbit of the
earth. Hence this particular planet still retained a
privileged status in Copernicus' nominally heliocentric
system, wherein the physical sun was separated by a
significant distance from the center of the universe.
Kepler, however, elicited an implication from the
Copernican cosmos which its architect himself had


failed to draw. Since Copernicus' earth was a planet,
then the other planets must be physical bodies like the
earth. But when a physical body traverses an elliptical
orbit, it must have the physical body of the sun present
in one focus of its ellipse. The sun thereby acquired
its rightful special status in the heliocentric system.

Since the planets had now become material bodies
like the earth, some physical cause had to be invoked
to explain their motion. Kepler could no longer accept
Ptolemy's pronouncement that “the power and activity
of an aster in its proper place and around its own
center consist of self-coherent revolution.” For Co-
pernicus, revolution around a center was the motion
natural to a sphere, although in his cosmos two spheres,
the sun and the stars', were motionless. Before Kepler
liberated himself from the grip of traditional notions,
he had believed that the planets were driven around
by “moving souls.” But in the second edition of his
youthful work he wrote:

If you substitute the word “force” for the word “soul,” you
have the very principle on which celestial physics is based
in my Commentaries on Mars.... For previously I used
to believe that the cause responsible for the motion of the
planets was unquestionably a soul. But when I considered
that this moving cause diminishes with distance, and that
the sun's light is also attenuated with the distance from
the sun, I concluded that this force is something corporeal

(Gesammelte Werke, 8, 113; trans. E. R. See also, Mysterium
[2nd ed. 1621], Note 3, Ch. 20).

Copernicus had correctly maintained that the cos-
mos must have more than one gravitational center,
with each planet serving as the collecting core for its
own detached heavy bodies. Accepting this plurality,
Kepler reversed the traditional conception of the fall
of a heavy object. No longer did the freely falling body
seek its natural place as close as possible to its gravita-
tional center. Instead, the gravitational center attracted
to itself its separate parts. But Kepler's earth and moon
were kindred bodies. Therefore they exerted a mutual
attraction on each other. In exercising its gravitational
pull on the earth, the moon helped to produce the ebb
and flow of the oceanic tides on the earth's surface.
So did the sun. And while imagining a flight to the
moon, Kepler attributed to his fictional space vehicle
the property of spontaneously persevering in the mo-
tion initially imparted to it, an incomplete expression
of the principle of inertia, a term which he added to
the vocabulary of the exact sciences. Moreover, he
asserted that the light radiating spherically from a
point source diminished in intensity with the square
of the distance from the source. Then in 1644 G. P.
Roberval insisted that “all the parts [of the matter in
the universe] tend toward one another with unceasing
pressure and mutually attract one another.”

Meanwhile in a magnificent series of discoveries
made with the recently invented telescope, Galileo
Galilei helped to establish some characteristic features
of the emerging cosmology. He revealed that the moon
abounds in lofty mountains and depressed hollows.
Then its surface is no more perfectly spherical than
is our lowly earth's. Even more irregular was Saturn
with its protruding ears, as that planet's rings looked
for a time in Galileo's primitive instrument. Sunspots
impaired the perfection of that luminary, and their
rotation proved that the sun whirls around its own axis,
like Copernicus' earth. Our planet reflects sunlight on
the moon (as Kepler's teacher had publicly announced
in 1596). Venus displayed phases resembling the moon's
and due to the same causes. By detecting the four
principal satellites of Jupiter, Galileo established that
the earth was neither the only planet accompanied by
a satellite nor the only center of a cosmic motion. He
observed numerous stars invisible to the naked eye, and
located them at various altitudes between two spheri-
cal surfaces, the more distant being regarded as con-
cave, and the closer as convex. In the telescope the
stars were not magnified, but remained vividly spar-
kling points. On the other hand, the planets showed
enlarged pale disks. By thus proving the self-luminosity
of the stars as contrasted with the darkness of the
planets, Galileo settled the age-old controversy once
discussed by al-Biruni:

Opinions of intelligent people differ... as to whether the
planets are self-luminous like the sun, or merely illuminated
by the rays of the sun falling on them. Many assert that
light is exclusively the property of the sun, that all the stars
[and planets] are destitute of it.... But others believe that
all the planets are luminous by nature with the exception
of the moon

(The Book of Instruction..., p. 67, ¶156).

Disturbed by the Inquisition's condemnation of
Galileo as a heretic and by his being sentenced to life
imprisonment, René Descartes concealed his adherence
to a cosmology very similar to the Copernican. In his
own cosmos the earth was declared to be at rest, but
only with respect to the celestial matter surrounding
it. While this fluid vortex rotated around the sun, it
pushed the earth along with it, as flowing water affects
an unpropelled boat or a moving vessel transports a
sleeping passenger. Similar whirlpools carried the other
planets around the sun, while smaller eddies bore the
satellites around the earth and Jupiter. Thus in Des-
cartes' cosmos, as in Aristotle's, all action was by direct
contact, and there could be no action at a distance.
Nor could there be a void or empty space, the entire
universe being filled with imperceptibly subtle matter.

Like Descartes, G. A. Borelli avoided assigning any
motion to the earth by professedly confining his cosmo-


logical discussion to Jupiter's satellites. But, following
Kepler, he ascribed to the rotating sun a physical force
that drove the planets along. To explain why they do
not fly off into space, as would a stone being whirled
round in a sling, he attributed to the planets a “natural
instinct” to approach the sun as the center of their
motion. The equilibrium between these two centrifugal
and centripetal motions kept the planets in their orbits,
and their satellites circulating around them.

Whereas in 1666 Borelli attributed to the planets
a natural tendency to approach the sun, that body
attracted the planets and was in turn attracted by
them, according to Robert Hooke's reflections early
in 1665:

I suppose the gravitating power of the Sun in the center
of this part of the Heaven in which we are, hath an attrac-
tive power upon all the bodies of the Planets, and of the
Earth that move about it, and that each of those again have
a respect answerable, whereby they may be said to attract
the Sun in the same manner as the Load-stone hath to Iron,
and the Iron hath to the Load-stone

(R. T. Gunther, Early
Science in Oxford,
Oxford, VIII [1931], 228).

Then on 23 May 1666 Hooke advanced beyond
mutual gravitational attraction between sun and plan-
ets by combining that cause of motion with the princi-
ple of inertia:

I have often wondered, why the planets should move about
the sun according to Copernicus's supposition, being not
included in any solid orbs (which the ancients possibly for
this reason might embrace) nor tied to it, as their centre,
by any visible strings; and neither depart from it beyond
such a degree, nor yet move in a straight line, as all bodies,
that have but one single impulse, ought to do: For a solid
body, moved in a fluid, towards any part... must preserve
[persevere] in its motion in a right line, and neither deflect
this way nor that way from it. But all the celestial bodies,
being regular solid bodies, and moved in a fluid, and yet
moved in circular or elliptical lines, and not straight, must
have some other cause, besides the first impressed impulse,
that must bend their motion into that curve. And for the
performance of this effect I cannot imagine any other likely
cause besides these two: The first may be from an unequal
density of the medium, through which the planetary body
is to be moved.... But the second cause of inflecting a
direct motion into a curve may be from an attractive prop-
erty of the body placed in the centre; whereby it continually
endeavours to attract or draw it to itself. For if such a
principle be supposed, all the phenomena of the planets
seem possible to be explained by the common principle of
mechanic motions; and possibly the prosecuting this specu-
lation may give us a true hypothesis of their motion, and
from some few observations, their motions may be so far
brought to a certainty, that we may be able to calculate
them to the greatest exactness and certainty, that can be

(idem, VI, 265-66).

Hooke's mathematical ability was not great enough
to perform the requisite calculation, but he did proceed
to demonstrate to the Royal Society of London a pen-
dulum whose bob executed a continuous closed curve
in a conical sweep, instead of simply oscillating to and
fro in a vertical plane like the bob of a conventional
pendulum. By imparting to the bob of his conical
pendulum the right impulse in the right direction,
Hooke produced a laboratory replica of planetary
motion (Figure 6).

The previous assumption that “only a spherical
shape” befitted a cosmic body was shattered when
Christiaan Huygens announced anagrammatically in
1656 that with his eyes he had clearly seen Saturn
“surrounded by a thin flat ring not touching it any-
where” (Oeuvres..., XV, 177, 299). Because the ring
is tilted at a considerable constant angle to the plane
in which Saturn revolves around the sun, it presented
quite different appearances to observers from Galileo's
time on. Their bafflement was finally cleared up by
Huygens' discovery of the exterior formation, which
is without any parallel.

Just as the planet Saturn departs from perfect spher-
icity, so does the planet earth. It is flattened at its two
poles, thereby approximating the solid generated by
an ellipse rotating about its minor axis. Then the gravi-
tational pull felt at the earth's equator should be


weaker than at the less distant poles, and Huygens'
pendulum clock should beat time more slowly at lower
latitudes than at higher latitudes on this oblate spheroid
which is our earth.

All the above mentioned partial successes achieved
by Copernicus, Brahe, Digges, Bruno, Galileo, Kepler,
Roberval, Borelli, Hooke, and Huygens were incorpo-
rated in the grand synthesis accomplished by Isaac
Newton, who admitted that he “stood on the shoulders
of giants.” His cosmos consisted of discontinuous mat-
ter moving in continuous space and time.

Newton's matter was composed of

solid, massy, hard, impenetrable, movable particles;...
these primitive particles being solids are incomparably
harder than any porous bodies compounded of them, even
so very hard as never to wear or break in pieces.... The
changes of corporeal things are to be placed only in the
various separations and new associations and motions of
these permanent particles; compound bodies being apt to
break, not in the midst of solid particles, but where those
particles are laid together and only touch in a few points

(Opticks, Book III, Query 31).

Newton's motion comprised the force of inertia or
inactivity, “a passive principle by which bodies persist
in their motion or rest, receive motion in proportion
to the force impressing it, and resist as much as they
are resisted” (loc. cit.). By contrast with the passive
principle of inertia, there were also “active principles,
such as is the cause of gravity, by which planets and
comets keep their motions in their orbs, and bodies
acquire great motion in falling” (loc. cit.).

Every body continues in its state... of uniform motion
in a right [straight] line unless it is compelled to change
that state by forces impressed upon it.... A stone, whirled
about in a sling, endeavors to recede from the hand that
turns it; and by that endeavor distends the sling.... That
force which opposes itself to this endeavor, and by which
the sling continually draws back the stone toward the hand
and retains it in its orbit, because it is directed to the hand
as the center of the orbit, I call the centripetal force. And
the same thing is to be understood of all bodies revolved in
any orbits. They all endeavor to recede from the centers
of their orbits; and were it not for the opposition of a
contrary force which restrains them to and detains them
in their orbits... would fly off in right lines, with a uniform

(Mathematical Principles of Natural Philosophy.
Axioms or Laws of Motion, Law I; Definition V).

In particular, there was a centripetal “... force, what-
ever it is, by which the planets are continually drawn
aside from the rectilinear motions, which otherwise
they would pursue, and made to revolve in curvilinear
orbits” (Definition V).

The force which retains the celestial bodies in their orbits
has been hitherto called centripetal force; but it being now
made plain that it can be no other than a gravitating force,
we shall hereafter call it gravity. For the cause of that
centripetal force which retains the moon in its orbit will
extend itself to all the planets

(idem, Book III, Proposition
5, Theorem 5, Scholium).

In the General Scholium inserted at the end of the
second edition of his Mathematical Principles of Natu-
ral Philosophy,
Newton said:

Hitherto we have explained the phenomena of the heavens
and of our sea by the power of gravity, but have not yet
assigned the cause of this power.... Hitherto I have not
been able to discover the cause of those properties of gravity
from phenomena, and I feign no hypotheses; for whatever
is not deduced from the phenomena is to be called a hy-
pothesis, and hypotheses, whether metaphysical or physical,
whether of occult qualities or mechanical, have no place
in experimental philosophy.... To us it is enough that
gravity does really exist and act according to the laws which
we have explained, and abundantly serves to account for
all the motions of the celestial bodies and of our sea.

To one of his supporters Newton had previously
written: “You sometimes speak of gravity as essential
and inherent to matter. Pray do not ascribe that notion
to me, for the cause of gravity is what I do not pretend
to know” (Correspondence..., III, 240). About a
month later Newton expressed himself even more em-
phatically to the same correspondent:

That gravity should be innate, inherent, and essential to
matter, so that one body may act upon another at a distance
through a vacuum, without the mediation of anything else,
by and through which their action or force may be conveyed
from one to another, is to me so great an absurdity that
I believe no man who has in philosophical matters any
competent faculty of thinking can ever fall into it. Gravity
must be caused by an agent acting constantly according
to certain laws, but whether this agent be material or
immaterial is a question I have left to the consideration
of my readers

(op. cit., III, 254).

In Newton's cosmos there was no vacuum or void,
because, as he told Robert Boyle, “I suppose that there
is diffused through all places an aethereal substance
capable of contraction and dilatation, strongly elastic,
and in a word much like air in all respects, but far
more subtle.”

Newton's subtle aether was universally diffused
through his absolute space, which, “in its own nature,
without relation to anything external, remains always
similar and immovable” (Mathematical Principles...,
Definitions, Scholium II).

No other places are immovable but those that, from infinity
to infinity, do all retain the same given position one to
another, and upon this account must ever remain unmoved
and do thereby constitute immovable space.


Yet he acknowledged that “it may be that there is no
body really at rest to which the places and motions
of others may be referred” (idem, IV).

In like manner Newton's “absolute, true, and math-
ematical time, of itself and from its own nature, flows
equably without relation to anything external, and by
another name is called 'duration.'” Yet “it may be that
there is no such thing as an equable motion whereby
time may be accurately measured. All motions may
be accelerated and retarded, but the flowing of absolute
time is not liable to any change” (idem, I).

In writing about the comet of 1652-53, Giovanni
Domenico Cassini ascribed to those bodies a curved
closed orbit, so that they would return periodically.
That the orbit was nearly parabolic was suggested by
Borelli. On 4 May 1665, Borelli wrote from Pisa to
a private correspondent, requesting him to treat as
confidential “until further attention and events throw
light on the truth,” the idea that

the real movement of the present comet [of 1664-65] can
on no account be along a straight line, but along a curve
so similar to a parabola as to be astonishing, and this is
shown not only by computation but also by a mechanical
contrivance, which I shall demonstrate to you when I arrive
in Florence

(Lettere..., I, 130-31; trans. E. R.).

Then in 1668 parabolic movement was publicly as-
cribed to comets by Hewelke (Hevelius). When the
great comet of 1680 made a very close approach to
the sun, Hewelke's follower, Georg Samuel Dörffel, in
1681 computed a parabolic orbit, with the sun in one
focus. Thereafter Newton showed that the cometary
path was really an ellipse, the visible portion of which
might be indistinguishable from a parabola. Edmond
Halley, without whom Newton's Mathematical Princi-
ples of Natural Philosophy
might never have been
published, then computed the orbits of twenty-four
comets. By scrutinizing earlier descriptions of them,
when they were still regarded as nonrepeating phe-
nomena, he identified periodic returns of the same
body. For instance, the comet observed by Apian in
1531 was identical with that described by Kepler in
1607 and studied by Halley himself in 1682. Thus a
new regular member was added to the family of celes-
tial bodies. Instead of being an unanticipated inter-
loper, the comet was now an orderly constituent of
the cosmos.

Halley discovered that the latitude of three conspic-
uous stars had altered perceptibly since antiquity.
Consequently he suggested that the stars, whose angu-
lar distances from one another had seemed unchanged
throughout the ages, wherefore they had traditionally
been called the “fixed stars,” had their own particular
or proper motions. These were imperceptible or unob
served in the more remote stars, but visible in those
that were largest and nearest to the earth, as Giordano
Bruno had surmised.

Halley's discovery of stellar proper motion had a
profound effect on an acute astronomical observer,
Thomas Wright of Durham, who in 1750 turned cos-
mological thought in a new direction. Because the stars
of the first three magnitudes are distributed irregularly
throughout the heavens, Wright contended that the
sun, and the solar system, cannot be located at the
center of the universe. Instead, the sun, its planets, their
satellites, and the comets are situated in the Milky
Way. This vast ring, as Democritus had taught, contains
an immense number of closely packed stars. These lie
between two parallel planes. If we direct our gaze
between these planes, we see the cumulative effect of
the light emanating from the stars in the Milky Way.
On the other hand, the rest of the heavens outside the
Milky Way shows us only scattered constellations. The
Milky Way, however, is only one such aggregation,
other similar formations being visible elsewhere in the
heavens. All the stars, including our sun, move round
some still unknown common center. Wright likened
their movement to that of the innumerable tiny bodies
whirling around Saturn and appearing to us as that
planet's compound ring.

An extensive summary of Wright's novel ideas was
promptly dispatched by an alert German corre-
spondent in London to a Hamburg journal. This report
caught the eye of a young man then unsuccessfully
pursuing the career of a private tutor. Immanuel Kant,
however, went far beyond Wright, who was theolog-
ically oriented. Taking the precaution of publishing his
Allgemeine Naturgeschichte (1755), subtitled (in trans-
lation) Essay on the... Mechanical Origin of the
Whole Universe,
anonymously, Kant undertook to set
forth a natural history of the heavens, or evolution of
the cosmos. He argued, for example, that the moon
is more recent than the earth. In its original state the
moon was fluid. The gravitational attraction exerted
on this lunar fluid by the earth in due course slowed
the moon's axial rotation down to the time required
by the moon to revolve once around the earth. Recip-
rocally, the earth's day is gradually lengthening, and
in the remote future will coincide with the month.
When that condition occurs, only one side of the earth
will always be presented to the moon, and the two
bodies will journey through space face to face, so to

Like the ancient atomists, Kant started his cosmic
history with an initial stage in which primitive vapor-
ous matter was universally dispersed. Through the
operation of Newtonian attraction, heavier particles
attracted lighter, which were deflected from their rec-


tilinear path by mutual repulsion. The resulting whirl-
ing in a disk produced the cosmic bodies, which still
continue to revolve in the same orbit, direction, and
plane. This formation of an orderly system occurred
not only around that center of attraction which is our
sun but also around an infinite number of similar suns
infinitely distant. Yet they all constitute a single system
related to a single center. This process has already gone
on for millions of centuries, and will continue to do
so for myriads of millions of centuries.

The distribution of Kant's cosmogony was delayed
by its publisher's bankruptcy. In any case a rival view
was propounded by the celebrated French astronomer
Pierre Simon de Laplace about half a century later.
Unlike Kant, whose critics objected that his combina-
tion of attraction with repulsion could never produce
a rotational motion, Laplace started his cosmos with
a “protosun” already undergoing a slow axial eastward
rotation. This immense vaporous mass was initially
fiercely hot. Slowly it cooled, contracted, and speeded
up. At its outer edge, when centrifugal force matched
the attraction to the center, a ring around the equator
became detached. This was only the first such product
in a series of such crises. A ring might condense into
a separate planet, which then proceeded to spin off
satellites of its own. Or a ring might disintegrate into
a group of small planets, such as was discovered be-
tween Mars and Jupiter at the turn of the century.
Or a ring might persist in the form discovered by
Huygens in Saturn. Laplace published his nebular hy-
pothesis in four successively developed versions ex-
tending over a period of twenty-eight years

While Laplace's attention was directed principally
to the bodies composing the solar system, the stars were
the chief subject of William Herschel's scrutiny. By
discovering Uranus far beyond Saturn and thereby
making in 1781 the first addition to the family of
planets in historic times, Herschel was enabled to for-
sake music as his means of livelihood and devote his
undivided talents to the advancement of science, pre-
viously his passionate hobby.

Herschel discovered the period of Saturn's axial
rotation with only a minute error. He did the same
for Mars, whose white polar caps he showed were
subject to seasonal fluctuations:

If... we find that the globe we inhabit has its polar regions
frozen and covered with mountains of ice and snow, that
only partly melt when alternately exposed to the sun, I may
well be permitted to surmise that the same causes may
probably have the same effect on the globe of Mars; that
the bright polar spots are owing to the vivid reflection of
light from frozen regions; and that the reduction of those
spots is to be ascribed to their being exposed to the sun

(Philosophical Transactions of the Royal Society of London,
74 [1784], 260).

While investigating the properties of sunlight, which
Newton had demonstrated to be composed of differ-
ently refracted rays related to the colors of the spec-
trum, Herschel found that the various colors are linked
with different heating effects. These increased toward
the red end of the spectrum, but did not stop there.
“The full red falls still short of the maximum of heat;
which perhaps lies even a little beyond visible refrac-
tion. In this case radiant heat will at least partly, if
not chiefly, consist... of invisible light” (op. cit.
[1800], p. 272). Herschel's discovery in 1800 of the
infrared radiation beyond one end of the spectrum was
promptly followed by the finding of chemical reactions
beyond the violet end of the spectrum in 1801. Thus
the spectrum was revealed to be only the visible por-
tion of a more extensive radiation possessing continuous

In his Dialogue of 1632 Galileo had proposed a
method of proving the Copernican thesis that the earth
revolves around the sun. This orbital motion should
produce the optical effect of a larger annual parallax
in a nearby star than in a distant star situated nearly
along the same line of sight. In pursuit of this so-called
differential parallax Herschel undertook to discover
and catalogue such pairs of stars. It had recently been
pointed out that double stars, being too numerous to
be the result of a random scattering throughout the
heavens, must in at least some cases form a physically
connected pair. Herschel reasoned that “as the mutual
gravitation of bodies towards each other is quite suffi-
cient to account for the union of two stars, we are
authorised to ascribe such combinations to that princi-
ple” (op. cit. [1802], p. 485). The effect of Newtonian
gravitational attraction in uniting such binary stars
exemplified the essential unity of the cosmos.

A binary may consist of two components differing
in brightness. As the fainter star passes in front of its
brighter partner, the latter's light diminishes. The first
such periodically variable star was detected in 1596
by Kepler's correspondent, David Fabricius, a minister
who was murdered by an enraged parishioner. Fabric-
ius' Mira Ceti varies in a long period averaging 330
days from its brightest as a star of the second magnitude
down to its minimum of ninth magnitude, invisible to
the naked eye. On the other hand, such a short-period
variable as Algol was known to complete its cycle in
about 69 hours. Herschel found a variable having a
period of about two months, lying in the interval be-
tween a few days and a year, and bringing the variables
into a single class of stars, with which he associated
our sun.


Herschel was convinced “that there is not, in strict-
ness of speaking, one fixed star in the heavens,” and
that our sun too must have its own proper motion
(Armitage, p. 94). As a German contemporary had
pointed out, when we take a walk through the woods,
the trees in front of us seem to move farther apart
as we approach them, while those behind us appear
to close up. By analogy, if the solar system of which
our earth is a part is moving toward some point in
the heavens, which Herschel called the “apex of the
solar motion,” then the stars in that direction should
seem to open out, whereas those in the opposite direc-
tion should appear to come closer together. By analyz-
ing the then known proper motions Herschel located
the apex somewhere near Lambda in the constellation
Hercules, a conclusion regarded by astronomers today
as reasonably close to the truth (Figure 7).

Herschel placed the sun in

the Milky Way, which undoubtedly is nothing but a stratum
of fixed stars.... This... immense starry bed is not of
equal breadth or lustre in every part, nor runs on in one
straight direction, but is curved and even divided into two
streams along a very considerable portion of it.... Suppose
a number of stars arranged between two parallel planes,
indefinitely extended every way, but at a given considerable
distance from each other; and, calling this a sidereal
stratum, an eye placed somewhere within it will see all
the stars in the direction of the planes of the stratum
projected into a great circle, which will appear lucid on
account of the accumulation of the stars; while the rest
of the heavens, at the sides, will only seem to be scattered
over with constellations, more or less crowded, according
to the distance of the planes or number of stars contained
in the thickness or sides of the stratum

(Philosophical Trans-
..., 74 [1784], 442-43).

In the hope of determining the sun's place within
the Milky Way Herschel introduced a statistical
method in stellar astronomy. Dividing the sky into
hundreds of regions, he directed his telescope to each
region in turn, and counted the stars visible therein.
As he thus “gaged the heavens,” he could see many
more stars in some directions than in others. The more
tightly packed they were, the farther out they extended
into space. Herschel surmised that our sun is situated
“very probably not far from the place” of division of
the Milky Way, that “very extensive, branching, com-
pound Congeries of many millions of stars” constituting
a “detached Nebula” or island universe, bounded on
all sides by empty space (op. cit., 75 [1785], 244, 254).
“It may not be amiss to point out some other very
remarkable Nebulae which cannot well be less, but are
probably much larger than our own system,” from
which they are separated by vast distances, no less vast
than those by which they are separated from one an-
other (idem, 258).

In many star clusters Herschel noted “a number of
lucid spots, of equal lustre, scattered over a circular
space, in such a manner as to appear gradually more
compressed towards the middle” (op. cit., 79 [1789],
214). Those clusters showing the greatest density “must
have been the longest exposed to the action of” cen-
tripetal force. Utilizing the implications of Olaus
Römer's demonstration that the transmission of light
is not instantaneous but requires a finite time, Herschel
maintained that

a telescope with a power of penetrating into space... has
also... a power of penetrating into time past.... When
we see an object of the calculated distance at which one
of these very remote nebulae may still be perceived, the
rays of light which convey its image to the eye, must have
been... almost two millions of years on their way; and
... consequently, so many years ago, this object must
already have had an existence in the sidereal heavens, in
order to send out those rays by which we now perceive

(op. cit. [1802], pp. 498-99).

Herschel became convinced that not every nebulos-
ity could be resolved by increased telescopic power
into an aggregation of stars. In the middle of some
nebulae he saw a somewhat greater brightness, which
could serve as “a seat of attraction” for the formation
of stars.


Since we are already acquainted with the centripetal force
of attraction which gives a globular figure to planets, keeps
them from flying out of their orbits in tangents, and makes
one star revolve around another, why should we not look
up to the universal gravitation of matter as the cause of
every condensation, accumulation, compression, and con-
centration of the nebulous matter?

(op. cit. [1811], p. 284).

For “what might be called the growth of stars” “mil-
lions of years perhaps are but moments.” “We have
an eternity of past duration to recur to.”

For cosmologists the nineteenth century opened
most auspiciously with the discovery of an asteroid on
the very first evening of the new century. The succes-
sive distances of the planets from the sun had showed
a disproportionately wide gap between Mars and
Jupiter. In that gap the relatively tiny asteroids (as this
class of cosmic bodies was constituted and christened
by Herschel) have been found in great numbers. Since
their brightness fluctuates considerably, their shape
may be irregular rather than round. Writing to
Herschel on 17 June 1802, Wilhelm Olbers, the dis-
coverer of the second asteroid, suggested that the two
known asteroids might be “just a pair of fragments, of
portions of a once greater planet which at one time
occupied its proper place between Mars and Jupiter,
and was in size more analogous to the other planets,
and perhaps millions of years ago, had, either through
the impact of a comet, or from an internal explosion,
burst into pieces” (Lubbock, p. 273).

An alternative origin of the asteroids was proposed
about a century later by two American scientists. Con-
vinced that the technical defects in the nebular hy-
pothesis could not be overcome, they imagined that
in the remote past while our sun still had no planets,
it was approached by another star closely enough to
raise huge tides upon it. Where the matter ejected by
the sun was dominated by a nucleus, a planet was
formed. But the asteroids or planetoids occupy a region
in which no dominating nucleus existed to assemble
them as a single planet.

Herschel's discovery of the planet Uranus led to a
search for earlier determinations of its position, which
had often been noted under the mistaken impression
that it was a star. When these prior observations were
compared with those made after Herschel's discovery,
it was found that the two sets of data could not be
combined into a unified theory of the motions of
Uranus. Moreover, the computed tables of the planet's
places increasingly diverged from fresh observations.
Hence the suspicion grew that Herschel's planet was
subject to perturbations caused by an unknown cosmic
body. Could the position of this trans-Uranian planet
at a given time be mathematically deduced from its
disturbing effect on Uranus? A young French mathe
matician, U. J. J. Leverrier, wrote to Johann Gottfried
Galle, an assistant at the Berlin Observatory, the two
countries not being at war:

I would like to find a persistent observer who would be
willing to devote some time to an examination of a part
of the sky in which there may be a planet to discover. I
have been led to this conclusion by the theory of Uranus.
... I demonstrate that it is impossible to satisfy the obser-
vations of Uranus without introducing the action of a new
planet, thus far unknown; and remarkably, there is only one
single position in the ecliptic where this perturbing planet
can be located.... The mass of the planet allows us to
conclude that its apparent diameter is more than 3″ [three
seconds] of arc

(Grosser, pp. 115-16).

Leverrier's communication reached Galle on 23 Sep-
tember 1846. Two days later Galle replied: “The planet
whose position you have pointed out actually exists.
The same day that I received your letter, I found a
star of the eighth magnitude.... The observations
made the following day determined that this was the
sought-for planet”—Neptune. Further examples of in-
ternational cooperation in the peaceful investigation
of our cosmos were provided by corrections of Lever-
rier's computations by John Couch Adams in England
and Benjamin Peirce at Harvard.

Later unexplained perturbations of Uranus as well
as irregularities in the motion of Neptune led to a
search in the twentieth century for a trans-Neptunian
planet. Pluto was found in 1930 by an American farmer
and amateur astronomer, Clyde W. Tombaugh, who
detected in photographic plates exposed two days apart
a shift in an image of the fifteenth magnitude. This
most recently discovered satellite of our sun turned
out to be much less of a giant than its four closest

The art of photography, invented in the nineteenth
century, proved to be of inestimable value to the cos-
mologist. It provided him with a precise, impersonal,
and permanent record of the object or field he was
investigating. It could make faint objects or details
visible by prolonging the exposure, since the action
of light on the sensitive plate is cumulative.

At least equally valuable is spectroscopy. When
sunlight was passed through a narrow slit and then
dispersed by a prism, Joseph Fraunhofer noticed that
the continuous bright band of color in the solar spec-
trum ranging from red at one end to violet at the other
was crossed by many narrow dark lines. These Fraun-
hofer lines, as they were later called, signified that some
constituents were missing from sunlight. Laboratory
investigations subsequently showed that every chemical
substance, when heated to incandescence, gives off its
own characteristic line spectrum. When light from a
hotter source passes through a cooler gas, the latter


absorbs and does not transmit those components of the
source's light that correspond to the bright lines in the
spectrum of the gas. Bright lines in the spectra of some
common chemical elements were shown by Gustav
Kirchhoff to coincide with dark lines in the solar spec-
trum. He therefore concluded that these elements were
present in the atmosphere of the sun. Then that body
consists of an intensely hot core surrounded by layers
of somewhat cooler gases containing in incandescent
form chemical elements found on the earth. The spec-
tra of the other stars likewise reveal the presence in
them of known terrestrial chemical elements. In one
case, helium was first detected spectroscopically in the
sun before its existence on the earth was discovered,
and its lightness and noninflammability utilized in bal-
loons. Spectroscopy has proved that the cosmos is built
up of the same elements throughout its enormous

When a chemical element is heated to incandescence
in the laboratory, its line spectrum coincides with that
derived from its counterpart in a distant star. A dis-
placement of the corresponding lines may indicate that
the two sources are not at rest with respect to each
other. If they are in relative motion, a displacement
toward the violet end of the spectrum indicates a
lessening of the distance between them. On the other
hand, a displacement toward the red end of the spec-
trum signifies an increase of the distance between them.
This principle was formulated by Christian Doppler
in 1842. Since then the spectra of remote nebulae have
exhibited a shift toward the red. Regarded as a
“Doppler effect,” this red shift indicates that these
nebulae are receding into space at speeds proportional
to their distances from us, with important implications
for the history of the cosmos.

Whereas it had always been assumed that the atom
as the ultimate constituent of matter was indivisible,
in 1896 Henri Becquerel discovered that uranium and
its compounds in their natural state spontaneously gave
off an invisible radiation capable of affecting a photo-
graphic plate. When similar radioactivity was found
in other heavy chemical elements, their atoms were
regarded as breaking down into lighter atoms, while
the process of disintegration was marked by the emis-
sion of charged particles. The rate at which this trans-
formation proceeds can be computed and used to form
an estimate of the age of the earth.

Such release of energy stored up within the atom
was soon accomplished artificially by man-made de-
vices. An atomic nucleus bombarded by particles pen-
etrating it at extremely high velocities was transformed
into a different atomic nucleus. At the enormous tem-
peratures prevailing in the interior of the sun thermo-
nuclear reactions could convert hydrogen into helium
with an accompanying output of energy approximating
the present radiation of the sun. The other stars may
be considered to be similar atomic furnaces at various
stages of development.

On the basis of the different kinds of spectra which
they exhibit the stars have been grouped into a number
of classes capable of being arranged in a single se-
quence. These various types have been viewed as suc-
cessive chronological stages in the evolution of the
stars, some of which are giants while others are dwarfs.
Variable stars of a certain variety have been regarded
as gaseous spheres alternately expanding and contract-
ing rhythmically in response to balanced opposing
forces of gravitational attraction and internal pressure.
When the latter crosses a critical threshold, the result-
ing explosion produces a nova. After it subsides, in its
defunct state the former nova resembles the so-called
planetary nebula.

Ingenious measurements of the velocity of light on
the surface of the earth showed that this velocity was
unaffected by the direction. Whether the beam of light
traveled in the direction of the earth's orbital motion
or in the opposite direction, the speed remained the
same. This experimental result was combined by Albert
Einstein with his own theoretical analysis to yield the
postulate that the velocity of light is a constant of
nature. Accordingly he dismissed as superfluous the
supposed existence of a luminiferous aether, widely
accepted throughout the nineteenth century. He like-
wise denied the reality of absolute space and absolute
time, insisting that all motion is relative, with no sys-
tem of coordinates possessing any privileged status.
Thus the fundamental underpinning of the Newtonian
synthesis was removed to make way for the sweeping
rival speculative cosmologies of the twentieth century.


Al-Biruni, The Book of Instruction in the Elements of the
Art of Astrology,
trans. R. Ramsay Wright (London, 1934).
A. Armitage, A Century of Astronomy (London, 1950); idem,
William Herschel (New York, 1962). For G. A. Borelli, see
Lettere indeite di uomini illustri, ed. Angelo Fabroni, 2 vols.
(Florence, 1773-75). S. G. F. Brandon, Creation Legends of
the Ancient Near East
(Mystic, Conn., 1963). David R. Dicks,
Early Greek Astronomy to Aristotle (London, 1970). For
Geminus, see M. R. Cohen and I. E. Drabkin, A Source
Book in Greek Science
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(Chicago, 1968). Christiaan Huygens, Oeuvres complètes...


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et du monde,
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the American Philosophical Society,
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Copernican Treatises,
3rd ed. (New York, 1971); idem, ed.,
Kepler's Conversation with Galileo's Sidereal Messenger
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Cosmas Indicopleustès
(Paris, 1962).

Translations identified as E. R. are by the author of this


[See also Astrology; Atomism; Cosmic Fall; Cosmic Images;
Cosmic Voyages; Islamic Conception; Pythagorean Har-
mony; Relativity;
Space; Time and Measurement.]