A History of Science, Volume 3
Henry Smith Williams

Part 1 out of 6

A History of Science, Volume 3, by Henry Smith Williams

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The work of Johannes Hevelius--Halley and Hevelius--Halley's
observation of the transit of Mercury, and his method
of determining the parallax of the planets--Halley's observation
of meteors--His inability to explain these bodies--The important
work of James Bradley--Lacaille's measurement of the arc of the
meridian--The determination of the question as to the exact shape
of the earth--D'Alembert and his influence upon science-
-Delambre's History of Astronomy--The astronomical work of Euler.


The work of William Herschel--His discovery of Uranus--His
discovery that the stars are suns--His conception
of the universe--His deduction that gravitation has caused
the grouping of the heavenly bodies--The nebula, hypothesis,
--Immanuel Kant's conception of the formation of the
world--Defects in Kant's conception--Laplace's final solution of
the problem--His explanation in detail--Change in the mental
attitude of the world since Bruno--Asteroids and
satellites--Discoveries of Olbers1--The mathematical calculations
of Adams and Leverrier--The discovery of the inner ring of
Saturn--Clerk Maxwell's paper on the stability of Saturn's
rings--Helmholtz's conception of the action of tidal
friction--Professor G. H. Darwin's estimate of the consequences
of tidal action--Comets and meteors--Bredichin's cometary
theory--The final solution of the structure of comets--Newcomb's
estimate of the amount of cometary dust swept up daily by
the earth--The fixed stars--John Herschel's studies
of double stars--Fraunhofer's perfection of the refracting
telescope--Bessel's measurement of the parallax of a
star,--Henderson's measurements--Kirchhoff and Bunsen's
perfection of the spectroscope--Wonderful revelations
of the spectroscope--Lord Kelvin's estimate of the time that
will be required for the earth to become completely cooled--
Alvan Clark's discovery of the companion star of Sirius--
The advent of the photographic film in astronomy--Dr.
Huggins's studies of nebulae--Sir Norman Lockyer's "cosmogonic
guess,"--Croll's pre-nebular theory.


William Smith and fossil shells--His discovery that fossil
rocks are arranged in regular systems--Smith's inquiries
taken up by Cuvier--His Ossements Fossiles containing the
first description of hairy elephant--His contention that fossils
represent extinct species only--Dr. Buckland's studies
of English fossil-beds--Charles Lyell combats catastrophism,
--Elaboration of his ideas with reference to the rotation of
species--The establishment of the doctrine of uniformitarianism,
--Darwin's Origin of Species--Fossil man--Dr. Falconer's visit to
the fossil-beds in the valley of the Somme--Investigations of
Prestwich and Sir John Evans--Discovery of the Neanderthal skull,
--Cuvier's rejection of human fossils--The finding of prehistoric
carving on ivory--The fossil-beds of America--Professor Marsh's
paper on the fossil horses in America--The Warren mastodon,
--The Java fossil, Pithecanthropus Erectus.


James Hutton and the study of the rocks--His theory of the
earth--His belief in volcanic cataclysms in raising and forming
the continents--His famous paper before the Royal Society of
Edinburgh, 1781---His conclusions that all strata of
the earth have their origin at the bottom of the sea---His
deduction that heated and expanded matter caused the elevation
of land above the sea-level--Indifference at first shown this
remarkable paper--Neptunists versus Plutonists--
Scrope's classical work on volcanoes--Final acceptance of
Hutton's explanation of the origin of granites--Lyell and
uniformitarianism--Observations on the gradual elevation
of the coast-lines of Sweden and Patagonia--Observations
on the enormous amount of land erosion constantly taking place,
--Agassiz and the glacial theory--Perraudin the chamois-
hunter, and his explanation of perched bowlders--De Charpentier's
acceptance of Perraudin's explanation--Agassiz's
paper on his Alpine studies--His conclusion that the Alps
were once covered with an ice-sheet--Final acceptance of
the glacial theory--The geological ages--The work
of Murchison and Sedgwick--Formation of the American
continents--Past, present, and future.


Biot's investigations of meteors--The observations of
Brandes and Benzenberg on the velocity of falling stars--
Professor Olmstead's observations on the meteoric shower of 1833-
-Confirmation of Chladni's hypothesis of 1794--The
aurora borealis--Franklin's suggestion that it is of electrical
origin--Its close association with terrestrial
magnetism--Evaporation, cloud-formation, and dew--Dalton's
demonstration that water exists in the air as an independent
gas--Hutton's theory of rain--Luke Howard's paper
on clouds--Observations on dew, by Professor Wilson and
Mr. Six--Dr. Wells's essay on dew--His observations
on several appearances connected with dew--Isotherms
and ocean currents--Humboldt and the-science of comparative
climatology--His studies of ocean currents--
Maury's theory that gravity is the cause of ocean currents--
Dr. Croll on Climate and Time--Cyclones and anti-cyclones,
--Dove's studies in climatology--Professor Ferrel's
mathematical law of the deflection of winds--Tyndall's estimate
of the amount of heat given off by the liberation of a pound
of vapor--Meteorological observations and weather predictions.


Josiah Wedgwood and the clay pyrometer--Count Rumford
and the vibratory theory of heat--His experiments with
boring cannon to determine the nature of heat--Causing
water to boil by the friction of the borer--His final
determination that heat is a form of motion--Thomas Young
and the wave theory of light--His paper on the theory of
light and colors--His exposition of the colors of thin plates--Of
the colors of thick plates, and of striated surfaces, --Arago and
Fresnel champion the wave theory--opposition
to the theory by Biot--The French Academy's tacit
acceptance of the correctness of the theory by its admission of
Fresnel as a member.


Galvani and the beginning of modern electricity--The construction
of the voltaic pile--Nicholson's and Carlisle's discovery
that the galvanic current decomposes water--Decomposition
of various substances by Sir Humphry Davy--His construction of an
arc-light--The deflection of the magnetic needle by electricity
demonstrated by Oersted--Effect of this important
discovery--Ampere creates the science of electro-dynamics--Joseph
Henry's studies of electromagnets--Michael Faraday begins his
studies of electromagnetic induction--His famous paper before the
Royal Society, in 1831, in which he demonstrates electro-magnetic
induction--His explanation of Arago's rotating disk--The
search for a satisfactory method of storing electricity--
Roentgen rays, or X-rays.


Faraday narrowly misses the discovery of the doctrine of
conservation--Carnot's belief that a definite quantity of work
can be transformed into a definite quantity of heat--The work
of James Prescott Joule--Investigations begun by Dr.
Mayer--Mayer's paper of 1842--His statement of the law of the
conservation of energy--Mayer and Helmholtz--Joule's paper of
1843--Joule or Mayer--Lord Kelvin and the dissipation of
energy-The final unification.


James Clerk-Maxwell's conception of ether--Thomas Young
and "Luminiferous ether,"--Young's and Fresnel's conception
of transverse luminiferous undulations--Faraday's experiments
pointing to the existence of ether--Professor
Lodge's suggestion of two ethers--Lord Kelvin's calculation
of the probable density of ether--The vortex theory of
atoms--Helmholtz's calculations in vortex motions
--Professor Tait's apparatus for creating vortex rings in the
air---The ultimate constitution of matter as conceived by
Boscovich--Davy's speculations as to the changes that occur in
the substance of matter at different temperatures--Clausius's
and Maxwell's investigations of the kinetic theory of gases--Lord
Kelvin's estimate of the size of the molecule--
Studies of the potential energy of molecules--Action of
gases at low temperatures.





With the present book we enter the field of the
distinctively modern. There is no precise date
at which we take up each of the successive stories,
but the main sweep of development has to do in each
case with the nineteenth century. We shall see at
once that this is a time both of rapid progress and of
great differentiation. We have heard almost nothing
hitherto of such sciences as paleontology, geology, and
meteorology, each of which now demands full attention.
Meantime, astronomy and what the workers of the
elder day called natural philosophy become wonderfully
diversified and present numerous phases that
would have been startling enough to the star-gazers
and philosophers of the earlier epoch.

Thus, for example, in the field of astronomy, Herschel
is able, thanks to his perfected telescope, to discover
a new planet and then to reach out into the
depths of space and gain such knowledge of stars and
nebulae as hitherto no one had more than dreamed of.
Then, in rapid sequence, a whole coterie of hitherto
unsuspected minor planets is discovered, stellar distances
are measured, some members of the starry
galaxy are timed in their flight, the direction of movement
of the solar system itself is investigated, the
spectroscope reveals the chemical composition even of
suns that are unthinkably distant, and a tangible
theory is grasped of the universal cycle which includes
the birth and death of worlds.

Similarly the new studies of the earth's surface reveal
secrets of planetary formation hitherto quite inscrutable.
It becomes known that the strata of the
earth's surface have been forming throughout untold
ages, and that successive populations differing utterly
from one another have peopled the earth in different
geological epochs. The entire point of view of thoughtful
men becomes changed in contemplating the history
of the world in which we live--albeit the newest
thought harks back to some extent to those days
when the inspired thinkers of early Greece dreamed
out the wonderful theories with which our earlier
chapters have made our readers familiar.

In the region of natural philosophy progress is no
less pronounced and no less striking. It suffices here,
however, by way of anticipation, simply to name the
greatest generalization of the century in physical
science--the doctrine of the conservation of energy.




STRANGELY enough, the decade immediately following
Newton was one of comparative barrenness
in scientific progress, the early years of the eighteenth
century not being as productive of great astronomers
as the later years of the seventeenth, or, for
that matter, as the later years of the eighteenth century
itself. Several of the prominent astronomers of
the later seventeenth century lived on into the opening
years of the following century, however, and the
younger generation soon developed a coterie of
astronomers, among whom Euler, Lagrange, Laplace,
and Herschel, as we shall see, were to accomplish great
things in this field before the century closed.

One of the great seventeenth-century astronomers,
who died just before the close of the century, was
Johannes Hevelius (1611-1687), of Dantzig, who advanced
astronomy by his accurate description of the
face and the spots of the moon. But he is remembered
also for having retarded progress by his influence
in refusing to use telescopic sights in his observations,
preferring until his death the plain sights long
before discarded by most other astronomers. The
advantages of these telescope sights have been discussed
under the article treating of Robert Hooke, but
no such advantages were ever recognized by Hevelius.
So great was Hevelius's reputation as an astronomer
that his refusal to recognize the advantage of the telescope
sights caused many astronomers to hesitate before
accepting them as superior to the plain; and even
the famous Halley, of whom we shall speak further in
a moment, was sufficiently in doubt over the matter
to pay the aged astronomer a visit to test his skill in
using the old-style sights. Side by side, Hevelius and
Halley made their observations, Hevelius with his old
instrument and Halley with the new. The results
showed slightly in the younger man's favor, but not
enough to make it an entirely convincing demonstration.
The explanation of this, however, did not lie in
the lack of superiority of the telescopic instrument,
but rather in the marvellous skill of the aged Hevelius,
whose dexterity almost compensated for the defect of
his instrument. What he might have accomplished
could he have been induced to adopt the telescope can
only be surmised.

Halley himself was by no means a tyro in matters
astronomical at that time. As the only son of a
wealthy soap-boiler living near London, he had been
given a liberal education, and even before leaving college
made such novel scientific observations as that of
the change in the variation of the compass. At nineteen
years of age he discovered a new method of determining
the elements of the planetary orbits which
was a distinct improvement over the old. The year
following he sailed for the Island of St, Helena to make
observations of the heavens in the southern hemisphere.

It was while in St. Helena that Halley made his
famous observation of the transit of Mercury over the
sun's disk, this observation being connected, indirectly
at least, with his discovery of a method of determining
the parallax of the planets. By parallax
is meant the apparent change in the position of an object,
due really to a change in the position of the observer.
Thus, if we imagine two astronomers making
observations of the sun from opposite sides of the
earth at the same time, it is obvious that to these
observers the sun will appear to be at two different
points in the sky. Half the angle measuring this difference
would be known as the sun's parallax. This
would depend, then, upon the distance of the earth
from the sun and the length of the earth's radius.
Since the actual length of this radius has been determined,
the parallax of any heavenly body enables
the astronomer to determine its exact distance.

The parallaxes can be determined equally well, however,
if two observers are separated by exactly known
distances, several hundreds or thousands of miles apart.
In the case of a transit of Venus across the sun's disk,
for example, an observer at New York notes the image
of the planet moving across the sun's disk, and notes
also the exact time of this observation. In the same
manner an observer at London makes similar observations.
Knowing the distance between New York
and London, and the different time of the passage, it is
thus possible to calculate the difference of the parallaxes
of the sun and a planet crossing its disk. The
idea of thus determining the parallax of the planets
originated, or at least was developed, by Halley, and
from this phenomenon he thought it possible to conclude
the dimensions of all the planetary orbits. As
we shall see further on, his views were found to be
correct by later astronomers.

In 1721 Halley succeeded Flamsteed as astronomer
royal at the Greenwich Observatory. Although sixty-
four years of age at that time his activity in astronomy
continued unabated for another score of years. At
Greenwich he undertook some tedious observations
of the moon, and during those observations was first
to detect the acceleration of mean motion. He was
unable to explain this, however, and it remained for
Laplace in the closing years of the century to do so,
as we shall see later.

Halley's book, the Synopsis Astronomiae Cometicae,
is one of the most valuable additions to astronomical
literature since the time of Kepler. He was first to
attempt the calculation of the orbit of a comet, having
revived the ancient opinion that comets belong to the
solar system, moving in eccentric orbits round the sun,
and his calculation of the orbit of the comet of 1682 led
him to predict correctly the return of that comet in
1758. Halley's Study of Meteors.

Like other astronomers of his time be was greatly
puzzled over the well-known phenomena of shooting-
stars, or meteors, making many observations himself,
and examining carefully the observations of other
astronomers. In 1714 he gave his views as to the
origin and composition of these mysterious visitors
in the earth's atmosphere. As this subject will be
again referred to in a later chapter, Halley's views,
representing the most advanced views of his age, are
of interest.

"The theory of the air seemeth at present," he says,
"to be perfectly well understood, and the differing
densities thereof at all altitudes; for supposing the
same air to occupy spaces reciprocally proportional to
the quantity of the superior or incumbent air, I have
elsewhere proved that at forty miles high the air is
rarer than at the surface of the earth at three thousand
times; and that the utmost height of the atmosphere,
which reflects light in the Crepusculum, is not fully
forty-five miles, notwithstanding which 'tis still
manifest that some sort of vapors, and those in no
small quantity, arise nearly to that height. An instance
of this may be given in the great light the
society had an account of (vide Transact. Sep., 1676)
from Dr. Wallis, which was seen in very distant counties
almost over all the south part of England. Of
which though the doctor could not get so particular a
relation as was requisite to determine the height thereof,
yet from the distant places it was seen in, it could
not but be very many miles high.

"So likewise that meteor which was seen in 1708, on
the 31st of July, between nine and ten o'clock at night,
was evidently between forty and fifty miles perpendicularly
high, and as near as I can gather, over Shereness
and the buoy on the Nore. For it was seen at London
moving horizontally from east by north to east by
south at least fifty degrees high, and at Redgrove, in
Suffolk, on the Yarmouth road, about twenty miles
from the east coast of England, and at least forty miles
to the eastward of London, it appeared a little to the
westward of the south, suppose south by west, and
was seen about thirty degrees high, sliding obliquely
downward. I was shown in both places the situation
thereof, which was as described, but could wish some
person skilled in astronomical matters bad seen it,
that we might pronounce concerning its height with
more certainty. Yet, as it is, we may securely conclude
that it was not many more miles westerly than Redgrove,
which, as I said before, is about forty miles more
easterly than London. Suppose it, therefore, where
perpendicular, to have been thirty-five miles east from
London, and by the altitude it appeared at in London--
viz., fifty degrees, its tangent will be forty-two miles,
for the height of the meteor above the surface of the
earth; which also is rather of the least, because the
altitude of the place shown me is rather more than
less than fifty degrees; and the like may be concluded
from the altitude it appeared in at Redgrove, near
seventy miles distant. Though at this very great
distance, it appeared to move with an incredible
velocity, darting, in a very few seconds of time, for
about twelve degrees of a great circle from north to
south, being very bright at its first appearance; and
it died away at the east of its course, leaving for some
time a pale whiteness in the place, with some remains
of it in the track where it had gone; but no hissing
sound as it passed, or bounce of an explosion were

"It may deserve the honorable society's thoughts,
how so great a quantity of vapor should be raised to
the top of the atmosphere, and there collected, so
as upon its ascension or otherwise illumination, to
give a light to a circle of above one hundred miles
diameter, not much inferior to the light of the moon;
so as one might see to take a pin from the ground in
the otherwise dark night. 'Tis hard to conceive what
sort of exhalations should rise from the earth, either
by the action of the sun or subterranean heat, so as to
surmount the extreme cold and rareness of the air in
those upper regions: but the fact is indisputable, and
therefore requires a solution."

From this much of the paper it appears that there
was a general belief that this burning mass was
heated vapor thrown off from the earth in some
mysterious manner, yet this is unsatisfactory to Halley,
for after citing various other meteors that
have appeared within his knowledge, he goes on to

"What sort of substance it must be, that could
be so impelled and ignited at the same time; there
being no Vulcano or other Spiraculum of subterraneous
fire in the northeast parts of the world, that
we ever yet heard of, from whence it might be projected.

"I have much considered this appearance, and think
it one of the hardest things to account for that I have
yet met with in the phenomena of meteors, and I am
induced to think that it must be some collection of
matter formed in the aether, as it were, by some
fortuitous concourse of atoms, and that the earth met
with it as it passed along in its orb, then but newly
formed, and before it had conceived any great impetus
of descent towards the sun. For the direction of it
was exactly opposite to that of the earth, which made
an angle with the meridian at that time of sixty-seven
gr., that is, its course was from west southwest to east
northeast, wherefore the meteor seemed to move the
contrary way. And besides falling into the power of
the earth's gravity, and losing its motion from the
opposition of the medium, it seems that it descended
towards the earth, and was extinguished in the
Tyrrhene Sea, to the west southwest of Leghorn. The
great blow being heard upon its first immersion into
the water, and the rattling like the driving of a cart
over stones being what succeeded upon its quenching;
something like this is always heard upon quenching a
very hot iron in water. These facts being past dispute,
I would be glad to have the opinion of the learned thereon,
and what objection can be reasonably made against
the above hypothesis, which I humbly submit to their

These few paragraphs, coming as they do from a
leading eighteenth-century astronomer, convey more
clearly than any comment the actual state of the
meteorological learning at that time. That this ball
of fire, rushing "at a greater velocity than the swiftest
cannon-ball," was simply a mass of heated rock passing
through our atmosphere, did not occur to him, or at
least was not credited. Nor is this surprising when we
reflect that at that time universal gravitation had been
but recently discovered; heat had not as yet been
recognized as simply a form of motion; and thunder
and lightning were unexplained mysteries, not to be
explained for another three-quarters of a century.
In the chapter on meteorology we shall see how the
solution of this mystery that puzzled Halley and his
associates all their lives was finally attained.


Halley was succeeded as astronomer royal by a man
whose useful additions to the science were not to
be recognized or appreciated fully until brought to
light by the Prussian astronomer Bessel early in the
nineteenth century. This was Dr. James Bradley, an
ecclesiastic, who ranks as one of the most eminent
astronomers of the eighteenth century. His most remarkable
discovery was the explanation of a peculiar
motion of the pole-star, first observed, but not explained,
by Picard a century before. For many years a
satisfactory explanation was sought unsuccessfully by
Bradley and his fellow-astronomers, but at last he was
able to demonstrate that the stary Draconis, on which
he was making his observations, described, or appeared
to describe, a small ellipse. If this observation was
correct, it afforded a means of computing the aberration
of any star at all times. The explanation of the
physical cause of this aberration, as Bradley thought,
and afterwards demonstrated, was the result of the
combination of the motion of light with the annual
motion of the earth. Bradley first formulated this
theory in 1728, but it was not until 1748--twenty years
of continuous struggle and observation by him--that he
was prepared to communicate the results of his efforts
to the Royal Society. This remarkable paper is
thought by the Frenchman, Delambre, to entitle its
author to a place in science beside such astronomers as
Hipparcbus and Kepler.

Bradley's studies led him to discover also the libratory
motion of the earth's axis. "As this appearance
of g Draconis. indicated a diminution of the
inclination of the earth's axis to the plane of the
ecliptic," he says; "and as several astronomers have
supposed THAT inclination to diminish regularly; if this
phenomenon depended upon such a cause, and amounted
to 18" in nine years, the obliquity of the ecliptic
would, at that rate, alter a whole minute in thirty
years; which is much faster than any observations,
before made, would allow. I had reason, therefore, to
think that some part of this motion at the least, if not
the whole, was owing to the moon's action upon the
equatorial parts of the earth; which, I conceived, might
cause a libratory motion of the earth's axis. But as I
was unable to judge, from only nine years observations,
whether the axis would entirely recover the same
position that it had in the year 1727, I found it
necessary to continue my observations through a
whole period of the moon's nodes; at the end of
which I had the satisfaction to see, that the stars,
returned into the same position again; as if there had
been no alteration at all in the inclination of the earth's
axis; which fully convinced me that I had guessed
rightly as to the cause of the phenomena. This circumstance
proves likewise, that if there be a gradual
diminution of the obliquity of the ecliptic, it does not
arise only from an alteration in the position of the
earth's axis, but rather from some change in the plane
of the ecliptic itself; because the stars, at the end of the
period of the moon's nodes, appeared in the same
places, with respect to the equator, as they ought to
have done, if the earth's axis had retained the same
inclination to an invariable plane."[2]


Meanwhile, astronomers across the channel were by
no means idle. In France several successful observers
were making many additions to the already long list
of observations of the first astronomer of the Royal
Observatory of Paris, Dominic Cassini (1625-1712),
whose reputation among his contemporaries was
much greater than among succeeding generations of
astronomers. Perhaps the most deserving of these
successors was Nicolas Louis de Lacaille (1713-1762),
a theologian who had been educated at the expense
of the Duke of Bourbon, and who, soon after completing
his clerical studies, came under the patronage
of Cassini, whose attention had been called to the
young man's interest in the sciences. One of Lacaille's
first under-takings was the remeasuring of the French
are of the meridian, which had been incorrectly measured
by his patron in 1684. This was begun in 1739,
and occupied him for two years before successfully
completed. As a reward, however, he was admitted
to the academy and appointed mathematical professor
in Mazarin College.

In 1751 he went to the Cape of Good Hope for the
purpose of determining the sun's parallax by observations
of the parallaxes of Mars and Venus, and incidentally
to make observations on the other southern
hemisphere stars. The results of this undertaking
were most successful, and were given in his Coelum
australe stelligerum, etc., published in 1763. In this he
shows that in the course of a single year he had observed
some ten thousand stars, and computed the
places of one thousand nine hundred and forty-two of
them, measured a degree of the meridian, and made
many observations of the moon--productive industry
seldom equalled in a single year in any field. These
observations were of great service to the astronomers,
as they afforded the opportunity of comparing the stars
of the southern hemisphere with those of the northern,
which were being observed simultaneously by Lelande
at Berlin.

Lacaille's observations followed closely upon the
determination of an absorbing question which occupied
the attention of the astronomers in the
early part of the century. This question was as
to the shape of the earth--whether it was actually
flattened at the poles. To settle this question once
for all the Academy of Sciences decided to make the
actual measurement of the length of two degrees, one
as near the pole as possible, the other at the equator.
Accordingly, three astronomers, Godin, Bouguer, and
La Condamine, made the journey to a spot on the
equator in Peru, while four astronomers, Camus,
Clairaut, Maupertuis, and Lemonnier, made a voyage
to a place selected in Lapland. The result of these
expeditions was the determination that the globe is
oblately spheroidal.

A great contemporary and fellow-countryman of
Lacaille was Jean Le Rond d'Alembert (1717-1783),
who, although not primarily an astronomer, did so much
with his mathematical calculations to aid that science
that his name is closely connected with its progress
during the eighteenth century. D'Alembert, who
became one of the best-known men of science of
his day, and whose services were eagerly sought
by the rulers of Europe, began life as a foundling,
having been exposed in one of the markets of
Paris. The sickly infant was adopted and cared for
in the family of a poor glazier, and treated as a member
of the family. In later years, however, after the
foundling had become famous throughout Europe, his
mother, Madame Tencin, sent for him, and acknowledged
her relationship. It is more than likely that
the great philosopher believed her story, but if so he
did not allow her the satisfaction of knowing his belief,
declaring always that Madame Tencin could "not
be nearer than a step-mother to him, since his mother
was the wife of the glazier."

D'Alembert did much for the cause of science by his
example as well as by his discoveries. By living a
plain but honest life, declining magnificent offers of
positions from royal patrons, at the same time refusing
to grovel before nobility, he set a worthy example to
other philosophers whose cringing and pusillanimous
attitude towards persons of wealth or position had
hitherto earned them the contempt of the upper

His direct additions to astronomy are several, among
others the determination of the mutation of the axis
of the earth. He also determined the ratio of the attractive
forces of the sun and moon, which he found
to be about as seven to three. From this he reached
the conclusion that the earth must be seventy times
greater than the moon. The first two volumes of his
Researches on the Systems of the World, published in
1754, are largely devoted to mathematical and astronomical
problems, many of them of little importance
now, but of great interest to astronomers at that

Another great contemporary of D'Alembert, whose
name is closely associated and frequently confounded
with his, was Jean Baptiste Joseph Delambre (1749-
1822). More fortunate in birth as also in his educational
advantages, Delambre as a youth began his
studies under the celebrated poet Delille. Later he was
obliged to struggle against poverty, supporting himself
for a time by making translations from Latin, Greek,
Italian, and English, and acting as tutor in private
families. The turning-point of his fortune came when
the attention of Lalande was called to the young man
by his remarkable memory, and Lalande soon showed
his admiration by giving Delambre certain difficult
astronomical problems to solve. By performing these
tasks successfully his future as an astronomer became
assured. At that time the planet Uranus had
just been discovered by Herschel, and the Academy
of Sciences offered as the subject for one of
its prizes the determination of the planet's orbit.
Delambre made this determination and won the
prize--a feat that brought him at once into prominence.

By his writings he probably did as much towards
perfecting modern astronomy as any one man. His
History of Astronomy is not merely a narrative of progress
of astronomy but a complete abstract of all the
celebrated works written on the subject. Thus he
became famous as an historian as well as an astronomer.


Still another contemporary of D'Alembert and Delambre,
and somewhat older than either of them, was
Leonard Euler (1707-1783), of Basel, whose fame as a
philosopher equals that of either of the great Frenchmen.
He is of particular interest here in his capacity
of astronomer, but astronomy was only one of the
many fields of science in which he shone. Surely something
out of the ordinary was to be expected of the
man who could "repeat the AEneid of Virgil from the
beginning to the end without hesitation, and indicate
the first and last line of every page of the edition which
he used." Something was expected, and he fulfilled
these expectations.

In early life he devoted himself to the study of
theology and the Oriental languages, at the request of
his father, but his love of mathematics proved too
strong, and, with his father's consent, he finally gave
up his classical studies and turned to his favorite
study, geometry. In 1727 he was invited by Catharine
I. to reside in St. Petersburg, and on accepting
this invitation he was made an associate of the Academy
of Sciences. A little later he was made professor
of physics, and in 1733 professor of mathematics. In
1735 he solved a problem in three days which some
of the eminent mathematicians would not undertake
under several months. In 1741 Frederick the Great
invited him to Berlin, where he soon became a member
of the Academy of Sciences and professor of mathematics; but in
1766 he returned to St. Petersburg.
Towards the close of his life be became virtually blind,
being obliged to dictate his thoughts, sometimes to
persons entirely ignorant of the subject in hand.
Nevertheless, his remarkable memory, still further
heightened by his blindness, enabled him to carry out
the elaborate computations frequently involved.

Euler's first memoir, transmitted to the Academy of
Sciences of Paris in 1747, was on the planetary perturbations.
This memoir carried off the prize that
had been offered for the analytical theory of the motions
of Jupiter and Saturn. Other memoirs followed,
one in 1749 and another in 1750, with further expansions
of the same subject. As some slight errors were
found in these, such as a mistake in some of the formulae
expressing the secular and periodic inequalities,
the academy proposed the same subject for the prize
of 1752. Euler again competed, and won this prize
also. The contents of this memoir laid the foundation
for the subsequent demonstration of the permanent
stability of the planetary system by Laplace and

It was Euler also who demonstrated that within
certain fixed limits the eccentricities and places of the
aphelia of Saturn and Jupiter are subject to constant
variation, and he calculated that after a lapse of about
thirty thousand years the elements of the orbits of
these two planets recover their original values.



A NEW epoch in astronomy begins with the work
of William Herschel, the Hanoverian, whom England
made hers by adoption. He was a man with a
positive genius for sidereal discovery. At first a mere
amateur in astronomy, he snatched time from his
duties as music-teacher to grind him a telescopic mirror,
and began gazing at the stars. Not content with
his first telescope, he made another and another, and
he had such genius for the work that he soon possessed
a better instrument than was ever made before. His
patience in grinding the curved reflective surface was
monumental. Sometimes for sixteen hours together
he must walk steadily about the mirror, polishing it,
without once removing his hands. Meantime his sister,
always his chief lieutenant, cheered him with her presence,
and from time to time put food into his mouth.
The telescope completed, the astronomer turned night
into day, and from sunset to sunrise, year in and year
out, swept the heavens unceasingly, unless prevented
by clouds or the brightness of the moon. His sister
sat always at his side, recording his observations.
They were in the open air, perched high at the mouth of
the reflector, and sometimes it was so cold that the ink
froze in the bottle in Caroline Herschel's hand; but the
two enthusiasts hardly noticed a thing so common-place as
terrestrial weather. They were living in distant worlds.

The results? What could they be? Such enthusiasm
would move mountains. But, after all, the moving
of mountains seems a liliputian task compared
with what Herschel really did with those wonderful
telescopes. He moved worlds, stars, a universe--
even, if you please, a galaxy of universes; at least he
proved that they move, which seems scarcely less wonderful;
and he expanded the cosmos, as man conceives
it, to thousands of times the dimensions it had before.
As a mere beginning, he doubled the diameter of the
solar system by observing the great outlying planet
which we now call Uranus, but which he christened
Georgium Sidus, in honor of his sovereign, and which
his French contemporaries, not relishing that name,
preferred to call Herschel.

This discovery was but a trifle compared with what
Herschel did later on, but it gave him world-wide reputation
none the less. Comets and moons aside, this
was the first addition to the solar system that had been
made within historic times, and it created a veritable
furor of popular interest and enthusiasm. Incidentally
King George was flattered at having a world named
after him, and he smiled on the astronomer, and came
with his court to have a look at his namesake. The
inspection was highly satisfactory; and presently the
royal favor enabled the astronomer to escape the
thraldom of teaching music and to devote his entire
time to the more congenial task of star-gazing.

Thus relieved from the burden of mundane embarrassments,
he turned with fresh enthusiasm to the skies, and his
discoveries followed one another in bewildering
profusion. He found various hitherto unseen
moons of our sister planets; be made special
studies of Saturn, and proved that this planet, with its
rings, revolves on its axis; he scanned the spots on the
sun, and suggested that they influence the weather of
our earth; in short, he extended the entire field of solar
astronomy. But very soon this field became too small
for him, and his most important researches carried
him out into the regions of space compared with which
the span of our solar system is a mere point. With his
perfected telescopes he entered abysmal vistas which
no human eve ever penetrated before, which no human
mind had hitherto more than vaguely imagined. He
tells us that his forty-foot reflector will bring him light
from a distance of "at least eleven and three-fourths
millions of millions of millions of miles"--light which
left its source two million years ago. The smallest
stars visible to the unaided eye are those of the sixth
magnitude; this telescope, he thinks, has power to
reveal stars of the 1342d magnitude.

But what did Herschel learn regarding these awful
depths of space and the stars that people them? That
was what the world wished to know. Copernicus,
Galileo, Kepler, had given us a solar system, but the
stars had been a mystery. What says the great
reflector--are the stars points of light, as the ancients
taught, and as more than one philosopher of the eighteenth
century has still contended, or are they suns, as
others hold? Herschel answers, they are suns, each
and every one of all the millions--suns, many of them,
larger than the one that is the centre of our tiny system.
Not only so, but they are moving suns. Instead of
being fixed in space, as has been thought, they are
whirling in gigantic orbits about some common centre. Is
our sun that centre? Far from it. Our sun is only a
star like all the rest, circling on with its attendant
satellites--our giant sun a star, no different from
myriad other stars, not even so large as some; a mere
insignificant spark of matter in an infinite shower of

Nor is this all. Looking beyond the few thousand
stars that are visible to the naked eye, Herschel sees
series after series of more distant stars, marshalled in
galaxies of millions; but at last he reaches a distance
beyond which the galaxies no longer increase. And
yet--so he thinks--he has not reached the limits of his
vision. What then? He has come to the bounds of the
sidereal system--seen to the confines of the universe.
He believes that he can outline this system, this universe,
and prove that it has the shape of an irregular
globe, oblately flattened to almost disklike proportions,
and divided at one edge--a bifurcation that is revealed
even to the naked eye in the forking of the Milky Way.

This, then, is our universe as Herschel conceives it--
a vast galaxy of suns, held to one centre, revolving,
poised in space. But even here those marvellous telescopes
do not pause. Far, far out beyond the confines
of our universe, so far that the awful span of our own
system might serve as a unit of measure, are revealed
other systems, other universes, like our own, each composed,
as he thinks, of myriads of suns, clustered like
our galaxy into an isolated system--mere islands of
matter in an infinite ocean of space. So distant from
our universe are these now universes of Herschel's discovery
that their light reaches us only as a dim, nebulous
glow, in most cases invisible to the unaided eye.
About a hundred of these nebulae were known when
Herschel began his studies. Before the close of the
century he had discovered about two thousand more of
them, and many of these had been resolved by his
largest telescopes into clusters of stars. He believed
that the farthest of these nebulae that he could see
was at least three hundred thousand times as distant
from us as the nearest fixed star. Yet that nearest
star--so more recent studies prove--is so remote that
its light, travelling one hundred and eighty thousand
miles a second, requires three and one-half years to
reach our planet.

As if to give the finishing touches to this novel
scheme of cosmology, Herschel, though in the main
very little given to unsustained theorizing, allows himself
the privilege of one belief that he cannot call upon
his telescope to substantiate. He thinks that all the
myriad suns of his numberless systems are instinct with
life in the human sense. Giordano Bruno and a long
line of his followers had held that some of our sister
planets may be inhabited, but Herschel extends the
thought to include the moon, the sun, the stars--all the
heavenly bodies. He believes that he can demonstrate
the habitability of our own sun, and, reasoning from
analogy, he is firmly convinced that all the suns of all
the systems are "well supplied with inhabitants." In
this, as in some other inferences, Herschel is misled by
the faulty physics of his time. Future generations,
working with perfected instruments, may not sustain
him all along the line of his observations, even, let alone
his inferences. But how one's egotism shrivels and
shrinks as one grasps the import of his sweeping

Continuing his observations of the innumerable nebulae,
Herschel is led presently to another curious speculative
inference. He notes that some star groups are
much more thickly clustered than others, and he is led
to infer that such varied clustering tells of varying
ages of the different nebulae. He thinks that at first
all space may have been evenly sprinkled with the
stars and that the grouping has resulted from the
action of gravitation.

"That the Milky Way is a most extensive stratum of
stars of various sizes admits no longer of lasting doubt,"
he declares, "and that our sun is actually one of the
heavenly bodies belonging to it is as evident. I have
now viewed and gauged this shining zone in almost
every direction and find it composed of stars whose
number ... constantly increases and decreases in proportion
to its apparent brightness to the naked eye.

"Let us suppose numberless stars of various sizes,
scattered over an indefinite portion of space in such
a manner as to be almost equally distributed throughout
the whole. The laws of attraction which no doubt
extend to the remotest regions of the fixed stars will
operate in such a manner as most probably to produce
the following effects:

"In the first case, since we have supposed the stars
to be of various sizes, it will happen that a star, being
considerably larger than its neighboring ones, will attract
them more than they will be attracted by others
that are immediately around them; by which means
they will be, in time, as it were, condensed about a
centre, or, in other words, form themselves into a cluster
of stars of almost a globular figure, more or less
regular according to the size and distance of the surrounding

"The next case, which will also happen almost as frequently
as the former, is where a few stars, though not
superior in size to the rest, may chance to be rather
nearer one another than the surrounding ones,... and
this construction admits of the utmost variety of
shapes. . . .

"From the composition and repeated conjunction of
both the foregoing formations, a third may be derived
when many large stars, or combined small ones, are
spread in long, extended, regular, or crooked rows,
streaks, or branches; for they will also draw the surrounding
stars, so as to produce figures of condensed
stars curiously similar to the former which gave rise to
these condensations.

"We may likewise admit still more extensive
combinations; when, at the same time that a cluster of
stars is forming at the one part of space, there may be
another collection in a different but perhaps not far-
distant quarter, which may occasion a mutual approach
towards their own centre of gravity.

"In the last place, as a natural conclusion of the
former cases, there will be formed great cavities or
vacancies by the retreating of the stars towards the
various centres which attract them."[1]

Looking forward, it appears that the time must come
when all the suns of a system will be drawn together
and destroyed by impact at a common centre. Already,
it seems to Herschel, the thickest clusters have
"outlived their usefulness" and are verging towards
their doom.

But again, other nebulae present an appearance suggestive
of an opposite condition. They are not resolvable
into stars, but present an almost uniform appearance
throughout, and are hence believed to be
composed of a shining fluid, which in some instances is
seen to be condensed at the centre into a glowing mass.
In such a nebula Herschel thinks he sees a sun in
process of formation.


Taken together, these two conceptions outline a majestic
cycle of world formation and world destruction--
a broad scheme of cosmogony, such as had been vaguely
adumbrated two centuries before by Kepler and in
more recent times by Wright and Swedenborg. This
so-called "nebular hypothesis" assumes that in the
beginning all space was uniformly filled with cosmic
matter in a state of nebular or "fire-mist" diffusion,
"formless and void." It pictures the condensation--
coagulation, if you will--of portions of this mass to
form segregated masses, and the ultimate development
out of these masses of the sidereal bodies that we see.

Perhaps the first elaborate exposition of this idea
was that given by the great German philosopher Immanuel
Kant (born at Konigsberg in 1724, died in
1804), known to every one as the author of the Critique
of Pure Reason. Let us learn from his own words how
the imaginative philosopher conceived the world to
have come into existence.

"I assume," says Kant, "that all the material of
which the globes belonging to our solar system--all
the planets and comets--consist, at the beginning of
all things was decomposed into its primary elements,
and filled the whole space of the universe in which the
bodies formed out of it now revolve. This state of
nature, when viewed in and by itself without any reference
to a system, seems to be the very simplest that
can follow upon nothing. At that time nothing has
yet been formed. The construction of heavenly bodies
at a distance from one another, their distances regulated
by their attraction, their form arising out of the
equilibrium of their collected matter, exhibit a later
state.... In a region of space filled in this manner, a
universal repose could last only a moment. The elements
have essential forces with which to put each
other in motion, and thus are themselves a source of
life. Matter immediately begins to strive to fashion
itself. The scattered elements of a denser kind, by
means of their attraction, gather from a sphere around
them all the matter of less specific gravity; again, these
elements themselves, together with the material which
they have united with them, collect in those points
where the particles of a still denser kind are found;
these in like manner join still denser particles, and so
on. If we follow in imagination this process by which
nature fashions itself into form through the whole extent
of chaos, we easily perceive that all the results of
the process would consist in the formation of divers
masses which, when their formation was complete,
would by the equality of their attraction be at rest
and be forever unmoved.

"But nature has other forces in store which are
specially exerted when matter is decomposed into fine
particles. They are those forces by which these particles
repel one another, and which, by their conflict
with attractions, bring forth that movement which is,
as it were, the lasting life of nature. This force of repulsion
is manifested in the elasticity of vapors, the
effluences of strong-smelling bodies, and the diffusion
of all spirituous matters. This force is an uncontestable
phenomenon of matter. It is by it that the elements,
which may be falling to the point attracting
them, are turned sideways promiscuously from their
movement in a straight line; and their perpendicular
fall thereby issues in circular movements, which encompass
the centre towards which they were falling.
In order to make the formation of the world more distinctly
conceivable, we will limit our view by withdrawing
it from the infinite universe of nature and directing
it to a particular system, as the one which belongs to
our sun. Having considered the generation of this
system, we shall be able to advance to a similar consideration
of the origin of the great world-systems, and
thus to embrace the infinitude of the whole creation in
one conception.

"From what has been said, it will appear that if a
point is situated in a very large space where the attraction
of the elements there situated acts more strongly
than elsewhere, then the matter of the elementary
particles scattered throughout the whole region will fall
to that point. The first effect of this general fall is
the formation of a body at this centre of attraction,
which, so to speak, grows from an infinitely small
nucleus by rapid strides; and in the proportion in which
this mass increases, it also draws with greater force
the surrounding particles to unite with it. When the
mass of this central body has grown so great that the
velocity with which it draws the particles to itself with
great distances is bent sideways by the feeble degree
of repulsion with which they impede one another, and
when it issues in lateral movements which are capable
by means of the centrifugal force of encompassing the
central body in an orbit, then there are produced
whirls or vortices of particles, each of which by itself
describes a curved line by the composition of the
attracting force and the force of revolution that had been
bent sideways. These kinds of orbits all intersect
one another, for which their great dispersion in this
space gives place. Yet these movements are in many
ways in conflict with one another, and they naturally
tend to bring one another to a uniformity--that is,
into a state in which one movement is as little
obstructive to the other as possible. This happens in
two ways: first by the particles limiting one another's
movement till they all advance in one direction; and,
secondly, in this way, that the particles limit their
vertical movements in virtue of which they are
approaching the centre of attraction, till they all move
horizontally--i. e., in parallel circles round the sun as
their centre, no longer intercept one another, and by
the centrifugal force becoming equal with the falling
force they keep themselves constantly in free circular
orbits at the distance at which they move. The result,
finally, is that only those particles continue to move in
this region of space which have acquired by their fall
a velocity, and through the resistance of the other particles
a direction, by which they can continue to maintain

"The view of the formation of the planets in this system
has the advantage over every other possible theory
in holding that the origin of the movements, and the
position of the orbits in arising at that same point of
time--nay, more, in showing that even the deviations
from the greatest possible exactness in their determinations,
as well as the accordances themselves, become
clear at a glance. The planets are formed out of particles
which, at the distance at which they move, have
exact movements in circular orbits; and therefore the
masses composed out of them will continue the same
movements and at the same rate and in the same direction."[2]

It must be admitted that this explanation leaves a
good deal to be desired. It is the explanation of a
metaphysician rather than that of an experimental
scientist. Such phrases as "matter immediately begins
to strive to fashion itself," for example, have no
place in the reasoning of inductive science. Nevertheless,
the hypothesis of Kant is a remarkable conception;
it attempts to explain along rational lines
something which hitherto had for the most part been
considered altogether inexplicable.

But there are various questions that at once suggest
themselves which the Kantian theory leaves unanswered.
How happens it, for example, that the cosmic
mass which gave birth to our solar system was divided
into several planetary bodies instead of remaining a
single mass? Were the planets struck from the sun by
the chance impact of comets, as Buffon has suggested?
or thrown out by explosive volcanic action, in accordance
with the theory of Dr. Darwin? or do they owe
their origin to some unknown law? In any event, how
chanced it that all were projected in nearly the same
plane as we now find them?


It remained for a mathematical astronomer to solve
these puzzles. The man of all others competent to
take the subject in hand was the French astronomer
Laplace. For a quarter of a century he had devoted
his transcendent mathematical abilities to the solution
of problems of motion of the heavenly bodies.
Working in friendly rivalry with his countryman Lagrange,
his only peer among the mathematicians of the
age, he had taken up and solved one by one the problems
that Newton left obscure. Largely through the
efforts of these two men the last lingering doubts as to
the solidarity of the Newtonian hypothesis of universal
gravitation had been removed. The share of Lagrange
was hardly less than that of his co-worker; but Laplace
will longer be remembered, because he ultimately
brought his completed labors into a system, and,
incorporating with them the labors of his contemporaries,
produced in the Mecanique Celeste the undisputed
mathematical monument of the century, a fitting complement
to the Principia of Newton, which it supplements
and in a sense completes.

In the closing years of the eighteenth century Laplace
took up the nebular hypothesis of cosmogony, to
which we have just referred, and gave it definite
proportions; in fact, made it so thoroughly his own
that posterity will always link it with his name.
Discarding the crude notions of cometary impact
and volcanic eruption, Laplace filled up the gaps in
the hypothesis with the aid of well-known laws of
gravitation and motion. He assumed that the primitive
mass of cosmic matter which was destined to
form our solar system was revolving on its axis
even at a time when it was still nebular in character,
and filled all space to a distance far beyond the
present limits of the system. As this vaporous mass
contracted through loss of heat, it revolved more
and more swiftly, and from time to time, through balance
of forces at its periphery, rings of its substance
were whirled off and left revolving there, subsequently
to become condensed into planets, and in their turn
whirl off minor rings that became moons. The main
body of the original mass remains in the present as the
still contracting and rotating body which we call the

Let us allow Laplace to explain all this in detail:

"In order to explain the prime movements of the
planetary system," he says, "there are the five following
phenomena: The movement of the planets in the
same direction and very nearly in the same plane; the
movement of the satellites in the same direction as
that of the planets; the rotation of these different
bodies and the sun in the same direction as their revolution,
and in nearly the same plane; the slight eccentricity of the
orbits of the planets and of the satellites;
and, finally, the great eccentricity of the orbits of the
comets, as if their inclinations had been left to chance.

"Buffon is the only man I know who, since the discovery
of the true system of the world, has endeavored
to show the origin of the planets and their satellites.
He supposes that a comet, in falling into the sun, drove
from it a mass of matter which was reassembled at a
distance in the form of various globes more or less
large, and more or less removed from the sun, and that
these globes, becoming opaque and solid, are now the
planets and their satellites.

"This hypothesis satisfies the first of the five preceding
phenomena; for it is clear that all the bodies
thus formed would move very nearly in the plane
which passed through the centre of the sun, and in the
direction of the torrent of matter which was produced;
but the four other phenomena appear to be inexplicable
to me by this means. Indeed, the absolute movement
of the molecules of a planet ought then to be in
the direction of the movement of its centre of gravity;
but it does not at all follow that the motion of the rotation
of the planets should be in the same direction.
Thus the earth should rotate from east to west, but
nevertheless the absolute movement of its molecules
should be from east to west; and this ought also to
apply to the movement of the revolution of the satellites,
in which the direction, according to the hypothesis
which he offers, is not necessarily the same as that
of the progressive movement of the planets.

"A phenomenon not only very difficult to explain
under this hypothesis, but one which is even contrary
to it, is the slight eccentricity of the planetary orbits.
We know, by the theory of central forces, that if a body
moves in a closed orbit around the sun and touches it,
it also always comes back to that point at every revolution;
whence it follows that if the planets were originally
detached from the sun, they would touch it at
each return towards it, and their orbits, far from being
circular, would be very eccentric. It is true that a mass
of matter driven from the sun cannot be exactly compared
to a globe which touches its surface, for the impulse
which the particles of this mass receive from one
another and the reciprocal attractions which they exert
among themselves, could, in changing the direction
of their movements, remove their perihelions from the
sun; but their orbits would be always most eccentric,
or at least they would not have slight eccentricities
except by the most extraordinary chance. Thus we
cannot see, according to the hypothesis of Buffon,
why the orbits of more than a hundred comets already
observed are so elliptical. This hypothesis is therefore
very far from satisfying the preceding phenomena.
Let us see if it is possible to trace them back to their
true cause.

"Whatever may be its ultimate nature, seeing that it
has caused or modified the movements of the planets,
it is necessary that this cause should embrace every
body, and, in view of the enormous distances which
separate them, it could only have been a fluid of immense
extent. In order to have given them an almost
circular movement in the same direction around the
sun, it is necessary that this fluid should have enveloped
the sun as in an atmosphere. The consideration
of the planetary movements leads us then to think
that, on account of excessive heat, the atmosphere of
the sun originally extended beyond the orbits of all
the planets, and that it was successively contracted to
its present limits.

"In the primitive condition in which we suppose the
sun to have been, it resembled a nebula such as the
telescope shows is composed of a nucleus more or less
brilliant, surrounded by a nebulosity which, on condensing
itself towards the centre, forms a star. If it is
conceived by analogy that all the stars were formed in
this manner, it is possible to imagine their previous
condition of nebulosity, itself preceded by other states
in which the nebulous matter was still more diffused,
the nucleus being less and less luminous. By going
back as far as possible, we thus arrive at a nebulosity
so diffused that its existence could hardly be suspected.

"For a long time the peculiar disposition of certain
stars, visible to the unaided eye, has struck philosophical
observers. Mitchell has already remarked
how little probable it is that the stars in the Pleiades,
for example, could have been contracted into the small
space which encloses them by the fortuity of chance
alone, and he has concluded that this group of stars,
and similar groups which the skies present to us, are
the necessary result of the condensation of a nebula,
with several nuclei, and it is evident that a nebula, by
continually contracting, towards these various nuclei,
at length would form a group of stars similar to the
Pleiades. The condensation of a nebula with two
nuclei would form a system of stars close together,
turning one upon the other, such as those double stars
of which we already know the respective movements.

"But how did the solar atmosphere determine the
movements of the rotation and revolution of the planets
and satellites? If these bodies had penetrated very
deeply into this atmosphere, its resistance would have
caused them to fall into the sun. We can therefore
conjecture that the planets were formed at their successive
limits by the condensation of a zone of vapors
which the sun, on cooling, left behind, in the plane of
his equator.

"Let us recall the results which we have given in
a preceding chapter. The atmosphere of the sun could
not have extended indefinitely. Its limit was the point
where the centrifugal force due to its movement of
rotation balanced its weight. But in proportion as
the cooling contracted the atmosphere, and those molecules
which were near to them condensed upon the
surface of the body, the movement of the rotation increased;
for, on account of the Law of Areas, the sum
of the areas described by the vector of each molecule
of the sun and its atmosphere and projected in the
plane of the equator being always the same, the rotation
should increase when these molecules approach the
centre of the sun. The centrifugal force due to this
movement becoming thus larger, the point where the
weight is equal to it is nearer the sun. Supposing,
then, as it is natural to admit, that the atmosphere
extended at some period to its very limits, it should,
on cooling, leave molecules behind at this limit and
at limits successively occasioned by the increased
rotation of the sun. The abandoned molecules would
continue to revolve around this body, since their centrifugal
force was balanced by their weight. But this
equilibrium not arising in regard to the atmospheric
molecules parallel to the solar equator, the latter, on
account of their weight, approached the atmosphere
as they condensed, and did not cease to belong to it
until by this motion they came upon the equator.

"Let us consider now the zones of vapor successively
left behind. These zones ought, according to appearance,
by the condensation and mutual attraction of
their molecules, to form various concentric rings of
vapor revolving around the sun. The mutual gravitational
friction of each ring would accelerate some and
retard others, until they had all acquired the same
angular velocity. Thus the actual velocity of the
molecules most removed from the sun would be the
greatest. The following cause would also operate to
bring about this difference of speed. The molecules
farthest from the sun, and which by the effects of
cooling and condensation approached one another to
form the outer part of the ring, would have always
described areas proportional to the time since the
central force by which they were controlled has been
constantly directed towards this body. But this constancy
of areas necessitates an increase of velocity
proportional to the distance. It is thus seen
that the same cause would diminish the velocity
of the molecules which form the inner part of the

"If all the molecules of the ring of vapor continued
to condense without disuniting, they would at length
form a ring either solid or fluid. But this formation
would necessitate such a regularity in every part of
the ring, and in its cooling, that this phenomenon is
extremely rare; and the solar system affords us, indeed,
but one example--namely, in the ring of Saturn.
In nearly every case the ring of vapor was broken into
several masses, each moving at similar velocities, and
continuing to rotate at the same distance around the
sun. These masses would take a spheroid form with a
rotatory movement in the direction of the revolution,
because their inner molecules had less velocity than
the outer. Thus were formed so many planets in a
condition of vapor. But if one of them were powerful
enough to reunite successively by its attraction all the
others around its centre of gravity, the ring of vapor
would be thus transformed into a single spheroidical
mass of vapor revolving around the sun with a rotation
in the direction of its revolution. The latter case
has been that which is the most common, but nevertheless
the solar system affords us an instance of the
first case in the four small planets which move between
Jupiter and Mars; at least, if we do not suppose,
as does M. Olbers, that they originally formed
a single planet which a mighty explosion broke up
into several portions each moving at different velocities.

"According to our hypothesis, the comets are strangers
to our planetary system. In considering them,
as we have done, as minute nebulosities, wandering
from solar system to solar system, and formed by
the condensation of the nebulous matter everywhere
existent in profusion in the universe, we see that when
they come into that part of the heavens where the sun
is all-powerful, he forces them to describe orbits either
elliptical or hyperbolic, their paths being equally possible
in all directions, and at all inclinations of the
ecliptic, conformably to what has been observed. Thus
the condensation of nebulous matter, by which we
have at first explained the motions of the rotation and
revolution of the planets and their satellites in the same
direction, and in nearly approximate planes, explains
also why the movements of the comets escape this
general law."[3]

The nebular hypothesis thus given detailed completion
by Laplace is a worthy complement of the grand
cosmologic scheme of Herschel. Whether true or false,
the two conceptions stand as the final contributions of
the eighteenth century to the history of man's ceaseless
efforts to solve the mysteries of cosmic origin and cosmic
structure. The world listened eagerly and without
prejudice to the new doctrines; and that attitude tells
of a marvellous intellectual growth of our race. Mark
the transition. In the year 1600, Bruno was burned
at the stake for teaching that our earth is not the centre
of the universe. In 1700, Newton was pronounced
"impious and heretical" by a large school of philosophers
for declaring that the force which holds the planets
in their orbits is universal gravitation. In 1800,
Laplace and Herschel are honored for teaching that
gravitation built up the system which it still controls;
that our universe is but a minor nebula, our sun but
a minor star, our earth a mere atom of matter, our
race only one of myriad races peopling an infinity
of worlds. Doctrines which but the span of two human
lives before would have brought their enunciators
to the stake were now pronounced not impious,
but sublime.


The first day of the nineteenth century was fittingly
signalized by the discovery of a new world. On the
evening of January 1, 1801, an Italian astronomer,
Piazzi, observed an apparent star of about the eighth
magnitude (hence, of course, quite invisible to the unaided
eye), which later on was seen to have moved,
and was thus shown to be vastly nearer the earth than
any true star. He at first supposed, as Herschel had
done when he first saw Uranus, that the unfamiliar
body was a comet; but later observation proved it a
tiny planet, occupying a position in space between
Mars and Jupiter. It was christened Ceres, after the
tutelary goddess of Sicily.

Though unpremeditated, this discovery was not unexpected,
for astronomers had long surmised the existence
of a planet in the wide gap between Mars and Jupiter.
Indeed, they were even preparing to make concerted
search for it, despite the protests of philosophers,
who argued that the planets could not possibly exceed
the magic number seven, when Piazzi forestalled their
efforts. But a surprise came with the sequel; for the
very next year Dr. Olbers, the wonderful physician-
astronomer of Bremen, while following up the course
of Ceres, happened on another tiny moving star, similarly
located, which soon revealed itself as planetary.
Thus two planets were found where only one was expected.

The existence of the supernumerary was a puzzle, but
Olbers solved it for the moment by suggesting that
Ceres and Pallas, as he called his captive, might be
fragments of a quondam planet, shattered by internal
explosion or by the impact of a comet. Other similar
fragments, he ventured to predict, would be
found when searched for. William Herschel sanctioned
this theory, and suggested the name asteroids
for the tiny planets. The explosion theory was supported
by the discovery of another asteroid, by Harding,
of Lilienthal, in 1804, and it seemed clinched
when Olbers himself found a fourth in 1807. The
new-comers were named Juno and Vesta respectively.

There the case rested till 1845, when a Prussian
amateur astronomer named Hencke found another
asteroid, after long searching, and opened a new epoch
of discovery. From then on the finding of asteroids
became a commonplace. Latterly, with the aid of
photography, the list has been extended to above four
hundred, and as yet there seems no dearth in the supply,
though doubtless all the larger members have been
revealed. Even these are but a few hundreds of miles
in diameter, while the smaller ones are too tiny for
measurement. The combined bulk of these minor
planets is believed to be but a fraction of that of the

Olbers's explosion theory, long accepted by astronomers,
has been proven open to fatal objections. The
minor planets are now believed to represent a ring of
cosmical matter, cast off from the solar nebula like the
rings that went to form the major planets, but prevented
from becoming aggregated into a single body by the
perturbing mass of Jupiter.

The Discovery of Neptune

As we have seen, the discovery of the first asteroid
confirmed a conjecture; the other important planetary
discovery of the nineteenth century fulfilled a prediction.
Neptune was found through scientific prophecy.
No one suspected the existence of a trans-Uranian
planet till Uranus itself, by hair-breadth departures
from its predicted orbit, gave out the secret. No one
saw the disturbing planet till the pencil of the mathematician,
with almost occult divination, had pointed
out its place in the heavens. The general predication
of a trans-Uranian planet was made by Bessel, the great
Konigsberg astronomer, in 1840; the analysis that revealed
its exact location was undertaken, half a decade
later, by two independent workers--John Couch
Adams, just graduated senior wrangler at Cambridge,
England, and U. J. J. Leverrier, the leading French
mathematician of his generation.

Adams's calculation was first begun and first completed.
But it had one radical defect--it was the work
of a young and untried man. So it found lodgment in a
pigeon-hole of the desk of England's Astronomer Royal,
and an opportunity was lost which English astronomers
have never ceased to mourn. Had the search
been made, an actual planet would have been seen
shining there, close to the spot where the pencil of the
mathematician had placed its hypothetical counterpart.
But the search was not made, and while the
prophecy of Adams gathered dust in that regrettable
pigeon-hole, Leverrier's calculation was coming on, his
tentative results meeting full encouragement from
Arago and other French savants. At last the laborious
calculations proved satisfactory, and, confident of
the result, Leverrier sent to the Berlin observatory,
requesting that search be made for the disturber of
Uranus in a particular spot of the heavens. Dr. Galle
received the request September 23, 1846. That very
night he turned his telescope to the indicated region,
and there, within a single degree of the suggested spot,
he saw a seeming star, invisible to the unaided eye,
which proved to be the long-sought planet, henceforth
to be known as Neptune. To the average mind, which
finds something altogether mystifying about abstract
mathematics, this was a feat savoring of the miraculous.

Stimulated by this success, Leverrier calculated an
orbit for an interior planet from perturbations of Mercury,
but though prematurely christened Vulcan, this
hypothetical nursling of the sun still haunts the realm
of the undiscovered, along with certain equally hypothetical
trans-Neptunian planets whose existence has
been suggested by "residual perturbations" of Uranus,
and by the movements of comets. No other veritable
additions of the sun's planetary family have been made
in our century, beyond the finding of seven small moons,
which chiefly attest the advance in telescopic powers.
Of these, the tiny attendants of our Martian neighbor,
discovered by Professor Hall with the great Washington
refractor, are of greatest interest, because of their
small size and extremely rapid flight. One of them is
poised only six thousand miles from Mars, and whirls
about him almost four times as fast as he revolves,
seeming thus, as viewed by the Martian, to rise in the
west and set in the east, and making the month only
one-fourth as long as the day.

The Rings of Saturn

The discovery of the inner or crape ring of Saturn,
made simultaneously in 1850 by William C. Bond, at
the Harvard observatory, in America, and the Rev.
W. R. Dawes in England, was another interesting optical
achievement; but our most important advances
in knowledge of Saturn's unique system are due to the
mathematician. Laplace, like his predecessors, supposed
these rings to be solid, and explained their stability
as due to certain irregularities of contour which
Herschel bad pointed out. But about 1851 Professor
Peirce, of Harvard, showed the untenability of this
conclusion, proving that were the rings such as Laplace
thought them they must fall of their own weight.
Then Professor J. Clerk-Maxwell, of Cambridge, took
the matter in hand, and his analysis reduced the puzzling
rings to a cloud of meteoric particles--a "shower
of brickbats"--each fragment of which circulates exactly
as if it were an independent planet, though of
course perturbed and jostled more or less by its fellows.
Mutual perturbations, and the disturbing pulls
of Saturn's orthodox satellites, as investigated by Maxwell,
explain nearly all the phenomena of the rings in
a manner highly satisfactory.

After elaborate mathematical calculations covering
many pages of his paper entitled "On the Stability
of Saturn's Rings," he summarizes his deductions as

"Let us now gather together the conclusions we
have been able to draw from the mathematical theory
of various kinds of conceivable rings.

"We found that the stability of the motion of a
solid ring depended on so delicate an adjustment, and
at the same time so unsymmetrical a distribution of
mass, that even if the exact conditions were fulfilled, it
could scarcely last long, and, if it did, the immense
preponderance of one side of the ring would be easily
observed, contrary to experience. These considerations,
with others derived from the mechanical structure of
so vast a body, compel us to abandon any theory of
solid rings.

"We next examined the motion of a ring of equal
satellites, and found that if the mass of the planet is
sufficient, any disturbances produced in the arrangement
of the ring will be propagated around it in the
form of waves, and will not introduce dangerous confusion.
If the satellites are unequal, the propagations
of the waves will no longer be regular, but disturbances
of the ring will in this, as in the former case,
produce only waves, and not growing confusion. Supposing
the ring to consist, not of a single row of large
satellites, but a cloud of evenly distributed unconnected
particles, we found that such a cloud must
have a very small density in order to be permanent,
and that this is inconsistent with its outer and inner
parts moving with the same angular velocity. Supposing
the ring to be fluid and continuous, we found that
it will be necessarily broken up into small portions.

"We conclude, therefore, that the rings must consist
of disconnected particles; these must be either
solid or liquid, but they must be independent. The
entire system of rings must, therefore, consist either
of a series of many concentric rings each moving with
its own velocity and having its own system of waves,
or else of a confused multitude of revolving particles
not arranged in rings and continually coming into
collision with one another.

"Taking the first case, we found that in an indefinite
number of possible cases the mutual perturbations of
two rings, stable in themselves, might mount up in
time to a destructive magnitude, and that such cases
must continually occur in an extensive system like
that of Saturn, the only retarding cause being the irregularity
of the rings.

"The result of long-continued disturbance was found
to be the spreading-out of the rings in breadth, the
outer rings pressing outward, while the inner rings
press inward.

"The final result, therefore, of the mechanical
theory is that the only system of rings which can
exist is one composed of an indefinite number of
unconnected particles, revolving around the planet with
different velocities, according to their respective distances.
These particles may be arranged in series of
narrow rings, or they may move through one another
irregularly. In the first case the destruction of the
system will be very slow, in the second case it will be
more rapid, but there may be a tendency towards arrangement
in narrow rings which may retard the

"We are not able to ascertain by observation the
constitution of the two outer divisions of the system
of rings, but the inner ring is certainly transparent,
for the limb of Saturn has been observed through it.
It is also certain that though the space occupied by
the ring is transparent, it is not through the material
parts of it that the limb of Saturn is seen, for his limb
was observed without distortion; which shows that
there was no refraction, and, therefore, that the rays
did not pass through a medium at all, but between the
solar or liquid particles of which the ring is composed.
Here, then, we have an optical argument in favor of
the theory of independent particles as the material of
the rings. The two outer rings may be of the same
nature, but not so exceedingly rare that a ray of light
can pass through their whole thickness without encountering
one of the particles.

"Finally, the two outer rings have been observed for
two hundred years, and it appears, from the careful
analysis of all the observations of M. Struve, that the
second ring is broader than when first observed, and
that its inner edge is nearer the planet than formerly.
The inner ring also is suspected to be approaching
the planet ever since its discovery in 1850. These
appearances seem to indicate the same slow progress of
the rings towards separation which we found to be the
result of theory, and the remark that the inner edge
of the inner ring is more distinct seems to indicate that
the approach towards the planet is less rapid near the
edge, as we had reason to conjecture. As to the apparent
unchangeableness of the exterior diameter of
the outer ring, we must remember that the outer rings
are certainly far more dense than the inner one, and
that a small change in the outer rings must balance a
great change in the inner one. It is possible, however,
that some of the observed changes may be due
to the existence of a resisting medium. If the changes
already suspected should be confirmed by repeated
observations with the same instruments, it will be
worth while to investigate more carefully whether
Saturn's rings are permanent or transitory elements
of the solar system, and whether in that part of the
heavens we see celestial immutability or terrestrial
corruption and generation, and the old order giving
place to the new before our eyes."[4]

Studies of the Moon

But perhaps the most interesting accomplishments
of mathematical astronomy--from a mundane standpoint,
at any rate--are those that refer to the earth's
own satellite. That seemingly staid body was long
ago discovered to have a propensity to gain a little on
the earth, appearing at eclipses an infinitesimal moment
ahead of time. Astronomers were sorely puzzled
by this act of insubordination; but at last Laplace and
Lagrange explained it as due to an oscillatory change
in the earth's orbit, thus fully exonerating the moon,
and seeming to demonstrate the absolute stability of
our planetary system, which the moon's misbehavior
had appeared to threaten.

This highly satisfactory conclusion was an orthodox
belief of celestial mechanics until 1853, when Professor
Adams of Neptunian fame, with whom complex analyses
were a pastime, reviewed Laplace's calculation,
and discovered an error which, when corrected, left
about half the moon's acceleration unaccounted for.
This was a momentous discrepancy, which at first no
one could explain. But presently Professor Helmholtz,
the great German physicist, suggested that a key
might be found in tidal friction, which, acting as a perpetual
brake on the earth's rotation, and affecting not
merely the waters but the entire substance of our
planet, must in the long sweep of time have changed its
rate of rotation. Thus the seeming acceleration of the
moon might be accounted for as actual retardation of
the earth's rotation--a lengthening of the day instead
of a shortening of the month.

Again the earth was shown to be at fault, but this
time the moon could not be exonerated, while the
estimated stability of our system, instead of being
re-established, was quite upset. For the tidal retardation
is not an oscillatory change which will presently
correct itself, like the orbital wobble, but a
perpetual change, acting always in one direction. Unless
fully counteracted by some opposing reaction,
therefore (as it seems not to be), the effect must be
cumulative, the ultimate consequences disastrous.
The exact character of these consequences was first
estimated by Professor G. H. Darwin in 1879. He
showed that tidal friction, in retarding the earth, must
also push the moon out from the parent planet on a
spiral orbit. Plainly, then, the moon must formerly
have been nearer the earth than at present. At some
very remote period it must have actually touched the
earth; must, in other words, have been thrown off from
the then plastic mass of the earth, as a polyp buds out
from its parent polyp. At that time the earth was spinning
about in a day of from two to four hours.

Now the day has been lengthened to twenty-four
hours, and the moon has been thrust out to a distance
of a quarter-million miles; but the end is not yet. The
same progress of events must continue, till, at some remote
period in the future, the day has come to equal
the month, lunar tidal action has ceased, and one face of
the earth looks out always at the moon with that same
fixed stare which even now the moon has been brought
to assume towards her parent orb. Should we choose to
take even greater liberties with the future, it may be
made to appear (though some astronomers dissent
from this prediction) that, as solar tidal action still
continues, the day must finally exceed the month,
and lengthen out little by little towards coincidence
with the year; and that the moon meantime must
pause in its outward flight, and come swinging back
on a descending spiral, until finally, after the lapse
of untold aeons, it ploughs and ricochets along the
surface of the earth, and plunges to catastrophic destruction.

But even though imagination pause far short of this
direful culmination, it still is clear that modern calculations,
based on inexorable tidal friction, suffice to
revolutionize the views formerly current as to the stability
of the planetary system. The eighteenth-century
mathematician looked upon this system as a vast celestial
machine which had been in existence about six
thousand years, and which was destined to run on forever.
The analyst of to-day computes both the past
and the future of this system in millions instead of
thousands of years, yet feels well assured that the solar
system offers no contradiction to those laws of growth
and decay which seem everywhere to represent the
immutable order of nature.


Until the mathematician ferreted out the secret, it
surely never could have been suspected by any one that
the earth's serene attendant,

"That orbed maiden, with white fire laden,
Whom mortals call the moon,"

could be plotting injury to her parent orb. But there
is another inhabitant of the skies whose purposes have
not been similarly free from popular suspicion. Needless
to say I refer to the black sheep of the sidereal
family, that "celestial vagabond" the comet.

Time out of mind these wanderers have been supposed
to presage war, famine, pestilence, perhaps the
destruction of the world. And little wonder. Here is
a body which comes flashing out of boundless space into
our system, shooting out a pyrotechnic tail some hundreds
of millions of miles in length; whirling, perhaps,
through the very atmosphere of the sun at a speed of
three or four hundred miles a second; then darting off
on a hyperbolic orbit that forbids it ever to return, or
an elliptical one that cannot be closed for hundreds or
thousands of years; the tail meantime pointing always
away from the sun, and fading to nothingness as the
weird voyager recedes into the spatial void whence it
came. Not many times need the advent of such an apparition
coincide with the outbreak of a pestilence or
the death of a Caesar to stamp the race of comets as an
ominous clan in the minds of all superstitious generations.

It is true, a hard blow was struck at the prestige of
these alleged supernatural agents when Newton proved
that the great comet of 1680 obeyed Kepler's laws in its
flight about the sun; and an even harder one when the
same visitant came back in 1758, obedient to Halley's
prediction, after its three-quarters of a century of voyaging
but in the abyss of space. Proved thus to bow to
natural law, the celestial messenger could no longer
fully, sustain its role. But long-standing notoriety cannot
be lived down in a day, and the comet, though
proved a "natural" object, was still regarded as a very
menacing one for another hundred years or so. It remained
for the nineteenth century to completely unmask
the pretender and show how egregiously our forebears
had been deceived.

The unmasking began early in the century, when Dr.
Olbers, then the highest authority on the subject, expressed
the opinion that the spectacular tail, which had
all along been the comet's chief stock-in-trade as an
earth-threatener, is in reality composed of the most
filmy vapors, repelled from the cometary body by the
sun, presumably through electrical action, with a velocity
comparable to that of light. This luminous suggestion
was held more or less in abeyance for half a
century. Then it was elaborated by Zollner, and
particularly by Bredichin, of the Moscow observatory, into
what has since been regarded as the most plausible of
cometary theories. It is held that comets and the sun
are similarly electrified, and hence mutually repulsive.
Gravitation vastly outmatches this repulsion in the
body of the comet, but yields to it in the case of gases,
because electrical force varies with the surface, while
gravitation varies only with the mass. From study of
atomic weights and estimates of the velocity of thrust
of cometary tails, Bredichin concluded that the chief
components of the various kinds of tails are hydrogen,
hydrocarbons, and the vapor of iron; and spectroscopic
analysis goes far towards sustaining these

But, theories aside, the unsubstantialness of the
comet's tail has been put to a conclusive test. Twice
during the nineteenth century the earth has actually
plunged directly through one of these threatening
appendages--in 1819, and again in 1861, once being immersed
to a depth of some three hundred thousand
miles in its substance. Yet nothing dreadful happened
to us. There was a peculiar glow in the atmosphere,
so the more imaginative observers thought, and
that was all. After such fiascos the cometary train
could never again pose as a world-destroyer.

But the full measure of the comet's humiliation is not
yet told. The pyrotechnic tail, composed as it is of portions
of the comet's actual substance, is tribute paid the
sun, and can never be recovered. Should the obeisance
to the sun be many times repeated, the train-forming
material will be exhausted, and the comet's chiefest
glory will have departed. Such a fate has actually befallen
a multitude of comets which Jupiter and the
other outlying planets have dragged into our system
and helped the sun to hold captive here. Many of
these tailless comets were known to the eighteenth-
century astronomers, but no one at that time suspected
the true meaning of their condition. It was not even
known how closely some of them are enchained until
the German astronomer Encke, in 1822, showed that
one which he had rediscovered, and which has since
borne his name, was moving in an orbit so contracted
that it must complete its circuit in about three and
a half years. Shortly afterwards another comet, revolving
in a period of about six years, was discovered
by Biela, and given his name. Only two more of these
short-period comets were discovered during the first half
of last century, but latterly they have been shown to be
a numerous family. Nearly twenty are known which
the giant Jupiter holds so close that the utmost reach of
their elliptical tether does not let them go beyond
the orbit of Saturn. These aforetime wanderers have


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