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Dictionary of the History of Ideas Studies of Selected Pivotal Ideas |
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Dictionary of the History of Ideas | ||
Cosmology as the endeavor to understand the
of the heavenly bodies may well have begun with our
ancestors. In their unceasing efforts to feed on
other animals, and to
avoid being themselves devoured
in turn, they found it advantageous to
themselves with the habits of their prey and predators.
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
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
whereas on others it disappeared altogether. Between
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
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
of cosmic motion. For longer periods the month was
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,
their alternating warmth and cold, rainfall and drought,
and fair weather, further aided mankind to
survive and multiply by
enlarging the food supply
derived from agriculture, fishing, and hunting. The
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,
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
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-
various divinities, which he proceeded to identify
with the natural powers.
Thus the ancient Egyptians
sometimes conceived the sky to be the goddess
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
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
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
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
of this account were developed in religious centers
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
of these conflicting sacerdotal ambitions, Egypt devel-
oped divergent and mutually inconsistent
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
tic Iranian conception of
brilliant light and endless
darkness as the twin primeval forces locked in
combat for control of the cosmos.
An alternative, and presumably earlier, cosmogony
in the Hebrew Scriptures
is affected by a physio-
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
of predictions based on recorded first visibilities of
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,
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
than the sun. Three stars, or striking configurations of
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
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
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
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
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
years were made a month longer than the other twelve,
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
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
or around which turned, an invisible heavenly
canopy bejewelled with the
multitudinous sparkling
stars. The distance between any two of them
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
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
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
preferred to keep the speed steady at one level for
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
to repeat the previous pattern. This discontinuous
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
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
followed by the sun in its annual eastward circuit
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
nearly total solar eclipse is a spectacular event, a minor
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
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
"stray sheep," as the planets visible to the
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.
traveled eastward at a varying speed, stopped at their
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
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
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-
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:
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
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.
constellation was then assigned to one of the twelve
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,
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.
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
who, although they deprived it of its divine status,
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
be turned into darkness, and the moon into blood"
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
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
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
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.
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,
ticed because we mortals have all
heard it from birth.
This was only one indication to the mystically
Pythagorean brotherhood that the cosmos was con-
structed on mathematical lines.
Philolaus, one of the
brethren, held the earth to be a planet, revolving
the others around a central fire, the Hearth of the
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
to the fixed stars. Convinced that the planets could
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
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
study. Plato nevertheless proceeded to con-
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
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
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-
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
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
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
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,
spring, extending from the vernal equinox to the sum-
mer solstice, lasts the longest. Because the sun
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
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
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
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
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
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
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
and simplest hypotheses that would produce results
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
and are born but also whether some of them actually
shift and
move" (Pliny the Elder, Natural History,
24, 95; trans. E.R.). While comparing previous obser-
vations of eclipses with his own, Hipparchus
that a certain star's longitudinal distance from the
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
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
zodiacal, twenty-one northern, and fifteen
southern). Each star was
attached to the universe's
outermost sphere, which completed a daily
from east to west around the poles of the celestial
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
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
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
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.
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
necting the apogee and perigee lay
the earth. On the
apse-line at a distance from the deferent's center
and opposite to the earth's, Ptolemy placed an equant.
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
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
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
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-
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-
or any meaningless and useless thing, is incon-
ceivable" (Ptolemy, Planetary
When viewed abstractly or theoretically, these
neatly designed concentrics,
eccentrics, deferents, and
epicycles were merely indispensable mathematical
in computing and predicting the positions of the cosmic
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
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
let. This absolutely full Ptolemaic
universe devoid of
empty space, or its mathematically equivalent blue-
print, dominated cosmological thought for
centuries (Figure 5).
Arab observers found that in their time the preces-
sion of the equinoxes moved faster than 1° in 100
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
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
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
misappropriated to themselves under the extrane-
ous designation "Old Testament," they professed to
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,
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
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
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
being incorporeal, could not itself move, but
operated like a beloved
object after which the First
Movable, or sphere of the stars, strove and
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
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
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
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
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
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
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
stationary at the center of the earth's orbit. For he
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
whose bulk he calculated as about one-thirtieth of the
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
Copernicus fleshed it out.
He was unaware that the followers of the fifth-
century Hindu astronomer Aryabhata "maintain that
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
disagreed, "apparently because he thought that
heavy things are attracted towards the center of the
earth" (Sachau, ed. and trans. I, 372).
Copernicus was equally unaware that in 1377
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.
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
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
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
greater heavens to whirl round with immensely swifter
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
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
speed up, slow down, stop, and reverse their course.
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
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
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."
account for the nonobservation of this phenomenon,
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
of proclaiming it to be infinite, confining himself to
description "similar to the infinite." Unlike the
Buddhists who declared that "the cosmos is neither
finite nor
infinite," Copernicus "left to the philosophers
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
agreed with the ancient Greek expositor Gemi-
nus, who "would not assume that all the stars lie on
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
remote they were, and "the greatest part rest by reason
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
Then the earth could no longer be in the middle of
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
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
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
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
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
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
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-
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
to the remnants of their obsolete metaphysical
prejudices and dogmatic
No such hindrances prevented the intellectual de-
velopment of Brahe's most famous assistant, Johannes
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
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
orbit. The square of the time required by any planet
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.
confirmed the essential truth of the Copernican
system, while revising it
drastically. Gone forever were
the pre-Keplerian eccentrics, deferents, and
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
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
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
of an aster in its proper place and around its own
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
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
(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
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
of the principle of inertia, a term which he added to
vocabulary of the exact sciences. Moreover, he
asserted that the light
radiating spherically from a
point source diminished in intensity with the
of the distance from the source. Then in 1644 G. P.
insisted that "all the parts [of the matter in
the universe]
tend toward one another with unceasing
pressure and mutually attract one
Meanwhile in a magnificent series of discoveries
made with the recently
invented telescope, Galileo
Galilei helped to establish some characteristic
of the emerging cosmology. He revealed that the moon
in lofty mountains and depressed hollows.
Then its surface is no more
perfectly spherical than
is our lowly earth's. Even more irregular was
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
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
principal satellites of Jupiter, Galileo established that
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
of the stars as contrasted with the darkness of the
planets, Galileo settled the age-old controversy once
discussed by
Opinions of intelligent people differ... as to whether the
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
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-
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
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
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
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,
have some other cause, besides the first impressed
that must bend their motion into that curve. And for
performance of this effect I cannot imagine any other
cause besides these two: The first may be from an
density of the medium, through which the planetary
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
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
(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
motion (Figure 6).
The previous assumption that "only a spherical
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
different appearances to observers from Galileo's
time on. Their bafflement
was finally cleared up by
Huygens' discovery of the exterior formation,
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
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
rated in the grand synthesis
accomplished by Isaac
Newton, who admitted that he "stood on the
of giants." His cosmos consisted of discontinuous
ter moving in continuous space and time.
Newton's matter was composed of
solid, massy, hard, impenetrable, movable particles;...
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
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
are resisted" (loc. cit.). By contrast with the
principle of inertia, there were also "active
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
of their orbits; and were it not for the opposition of
contrary force which restrains them to and detains them
their orbits... would fly off in right lines, with a uniform
(Mathematical Principles of Natural
Axioms or Laws of Motion, Law I; Definition
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
(Definition V).
The force which retains the celestial bodies in their orbits
been hitherto called centripetal force; but it being now
made plain that it can be no other than a gravitating
we shall hereafter call it gravity. For the cause of
centripetal force which retains the moon in its orbit
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
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
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
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.
must be caused by an agent acting constantly according
to certain laws, but whether this agent be material or
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
and in a word much like air in all respects, but far
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).
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.
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,
equably without relation to anything external, and by
name is called 'duration.'" Yet "it may be that
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
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
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
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
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
Consequently he suggested that the stars, whose angu-
lar distances from one another had seemed
throughout the ages, wherefore they had traditionally
called the "fixed stars," had their own particular
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
mological thought in a new
direction. Because the stars
of the first three magnitudes are distributed
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
Way. This vast ring, as Democritus had taught, contains
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
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
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
lation) Essay
on the... Mechanical Origin of the
Whole Universe, anonymously,
Kant undertook to set
forth a natural history of the heavens, or evolution
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
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-
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
a rotational motion, Laplace started his cosmos with
"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
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-
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
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
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
74 [1784], 260).
While investigating the properties of sunlight, which
Newton had
demonstrated to be composed of differ-
refracted rays related to the colors of the spec-
trum, Herschel found that the various colors are linked
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
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
tion of a more extensive radiation
possessing continuous
In his Dialogue of 1632 Galileo had proposed a
of proving the Copernican thesis that the earth
revolves around the sun.
This orbital motion should
produce the optical effect of a larger annual
in a nearby star than in a distant star situated nearly
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
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
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
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
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
(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
Hercules, a conclusion regarded by astronomers today
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
distance from each other; and, calling this a
stratum, an eye placed somewhere within it will see
the stars in the direction of the planes of the stratum
projected into a great circle, which will appear lucid
account of the accumulation of the stars; while the rest
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-
actions..., 74 [1784],
In the hope of determining the sun's place within
the Milky Way Herschel
introduced a statistical
method in stellar astronomy. Dividing the sky
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
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"
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
remarkable Nebulae which cannot well be less, but are
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,
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
attraction which gives a globular figure to planets, keeps
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"
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
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-
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
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
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
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
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
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
(Grosser, pp. 115-16).
Leverrier's communication reached Galle on 23 Sep-
tember 1846. Two days later Galle replied: "The
whose position you have pointed out actually
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
planet"—Neptune. Further examples of in-
ternational cooperation in the peaceful
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
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
the continuous bright band of color in the solar spec-
trum ranging from red at one end to violet at the
was crossed by many narrow dark lines. These Fraun-
hofer lines, as they were later called, signified that
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
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
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
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
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
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-
it at extremely high velocities was transformed
into a different atomic
nucleus. At the enormous tem-
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
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
wise denied the reality of absolute
space and absolute
time, insisting that all motion is relative, with no
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
Art of Astrology, trans. R. Ramsay Wright (London,
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).
Geminus, see M. R. Cohen and I. E . Drabkin, A
Book in Greek Science (Cambridge, Mass., 1966).
Grosser, The Discovery of Neptune
(Cambridge, Mass.,
1962), pp. 115-16, translating from the French text in
Monthly Notices of the Royal Astronomical Society,
(1910-11), 278-79. W. K. C. Guthrie, A History of Greek
Philosophy, 3 vols. (New
York, 1962, 1965, 1969). T. L.
Heath, Aristarchus of
Samos (Oxford, 1959). M. A. Hoskin,
William Herschel and the Construction of the
(Chicago, 1968). Christiaan Huygens, Oeuvres complètes...
Werke (Munich, 1937—); see also idem, Mysterium cos-
mographicum (1596; 2nd ed., 1621), Note 3, Ch. 20. A.
Koyré, From the Closed World to the Infinite Universe
(Baltimore, 1968); idem, La révolution astronomique (Paris,
1961); idem, Newtonian Studies (Chicago, 1968). B. and J.
Lovell, Discovering the Universe (New York, 1963). Con-
stance A. Lubbock, The Herschel Chronicle (Cambridge,
1933). H. Messel and S. T. Butler, The Universe and its
Origin (New York, 1964). M. K. Munitz, ed., Theories of
the Universe (New York, 1965). O. Neugebauer, Astronomical
Cuneiform Texts (Princeton, 1955); idem, The Exact Sciences
in Antiquity, 2nd ed. (New York, 1969); idem and R. A.
Parker, Egyptian Astronomical Texts (Providence, 1960-68).
Isaac Newton, The Correspondence of Isaac Newton, 4 vols.
(Cambridge, 1959-67). Nicholas Oresme, Le Livre du ciel
et du monde, eds. Menut and Denomy (Madison, 1968).
A. Pannekoek, A History of Astronomy (New York, 1961).
Ptolemy, Planetary Hypotheses, Book I, in Transactions of
the American Philosophical Society, new series, 57 (1967),
Part 4, p. 8. A. Romer, ed., The Discovery of Radioactivity
and Transmutation (New York, 1964). E . Rosen, ed., Three
Copernican Treatises, 3rd ed. (New York, 1971); idem, ed.,
Kepler's Conversation with Galileo's Sidereal Messenger
(New York, 1965); idem, ed., Kepler's Somnium (Madison,
1967). Edward Sachau, Alberuni's India, 2 vols. (Lahore,
1962). H. Shapley, ed., Source Book in Astronomy, 1900-1950
(Cambridge, Mass., 1960). E . T. Whittaker, A History of
the Theories of Aether and Electricity, 2 vols. (New York,
1910; 1960). Wanda Wolska, La topographie chrétienne de
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.]
Dictionary of the History of Ideas | ||


text:
If it seemed as if NFL teams have been shedding contracts nearly as fast as signing them in recent weeks that's because it's almost true.
With a shrinking salary cap in a sport with few contracts that are fully guaranteed, teams have spent the weeks leading up to free agency and the first few days of the new league year getting out of deals signed in recent years when there was more money available to spend.
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Whether it was Kansas City getting rid of banged-up and expensive starting offensive tackles Mitchell Schwartz and Eric Fisher, the Raiders cutting ties with Lamarcus Joyner and Tyrell Williams after building their free agent class around them, or Tennessee shedding starting defensive backs Adoree Jackson, Malcolm Butler and Kenny Vaccaro, veterans around the league have been sent to the chopping block.
In all, according to transactions data from SportRadar and contract information from Spotrac and Over The Cap, teams have released players with a combined total of approximately $600 million left on the deals they originally signed between the Super Bowl and the end of the first week of the league year. That figure excludes players who were on rookie or minimum level deals.
The cuts have come after the salary cap was reduced from $198.2 million in 2020 to $182.5 million in 2021 in response to the reduced revenues resulting from mostly empty stadiums last year because of the coronavirus.
The bloodletting could have been even more severe had the league and the NFLPA not agreed to spread those losses over multiple years.
"I think the unprecedented part being, for the first time in modern era, the cap decreases instead of increases," Rams general manager Les Snead said. "But again, I think many people on this planet, not just us in NFL football, have had to make sacrifices, some probably harder than others over the past year."
Cutting high-salaried players is nothing new in the NFL where most free agent contracts have teams often committing to paying lucrative signing bonuses and guaranteed money in the first couple of years of a deal and then deciding whether to keep the player or get rid of him to create salary cap room.
But the rate of it increased substantially this season because of the lowered cap with the total amount of contracts cut in the same time period equaling about $445 million in 2020 and $227 million in 2019.
One of the teams in a cutting mode was the Raiders. Coach Jon Gruden bragged in 2019 about the free agent haul he brought in after trading away stars Khalil Mack and Amari Cooper instead of giving them big extensions.
He said at the owners meeting that year that the Raiders wouldn't have been able to get players such as Antonio Brown, Trent Brown, Williams and Joyner without those deals.
Antonio Brown didn't even last with the team until the opener that season because of run-ins with general manager Mike Mayock and frustration over the type of helmet the league made him wear.
The other three all were sent packing this offseason with Trent Brown traded to New England as part of a 2022 pick swap with two years left on his $66 million, four-year contract, and Williams and Joyner cut this offseason with more than $38 million remaining on their contracts.
The Raiders also cut guard Richie Incognito and brought him back on a cheaper deal, and traded away starting offensive linemen Rodney Hudson and Gabe Jackson for mid-round picks when they refused to take pay cuts.
None of that was part of the original plan.
"If you go back two years and say where was the cap going to be this coming season, the answer would have been plus or minus $225 million," Mayock said. "We're looking at ($182.5 million). It's simple math."
Some players have come out of the situation more than whole. Adoree Jackson got a three-year deal worth a reported $39 million from the Giants after Tennessee refused to pay his $10.24 million fifth-year option.
Guard Kevin Zeitler got cut with $12 million left on his contract with the Giants and promptly signed a three-year, $22.5 million deal with Baltimore that pays him $10 million this season and guarantees him $16 million.
In one of the more curious cases, Miami cut Kyle Van Noy one year into his four-year, $51 million deal, leaving about $36 million unpaid. Van Noy then returned to New England on a two-year, $12 million deal and the Patriots will also get a fourth-round compensation pick in next month's draft based on the deal Van Noy signed last March.
Others such as receivers Alshon Jeffery and Adam Humphries are still looking for work after their contracts were wiped out and will be lucky to get similar deals now that they are back on the market.
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