711 (#121) ############################################
DOMINIQUE FRANÇOIS ARAGO
711
If Newton gave a complete solution of celestial movements
where but two bodies attract each other, he did not even attempt
the infinitely more difficult problem of three.
DOMINIQUE FRANÇOIS ARAGO
711
If Newton gave a complete solution of celestial movements
where but two bodies attract each other, he did not even attempt
the infinitely more difficult problem of three.
Warner - World's Best Literature - v02 - Aqu to Bag
'"
Asked the Caliph, "Dost thou remember what he said? " And
'Adi answered, "Yes. " Rejoined Omar, "Then repeat it;" so
'Adi repeated:-
## p. 702 (#112) ############################################
702
ARABIC LITERATURE
"I saw thee, O thou best of the human race, | Bring out a book
which brought to graceless, grace.
Thou showedst righteous road to men astray | From right, when
darkest wrong had ta'en its place:-
Thou with Islâm didst light the gloomiest way, | Quenching
with proof live coals of frowardness:
I own for Prophet, my Mohammed's self, and men's award
upon his word we base.
Thou madest straight the path that crooked ran | Where in old
days foul growth o'ergrew its face.
Exalt be thou in Joy's empyrean! | And Allah's glory ever grow
apace! "
"And indeed," continued 'Adi, "this Elegy on the Prophet
(Abhak! ) is well known, and to comment on it would be
tedious. "
Quoth Omar, "Who [of the poets] is at the door? " And
quoth 'Adi, "Among them is Omar ibn Rabí'ah, the Korashi;"
whereupon the Caliph cried, "May Allah show him no favor,
neither quicken him! Was it not he who spoke impiously [in
praising his love]? –
'Could I in my clay-bed [the grave] with Ialma repose, | There
to me were better than Heaven or Hell! '
Had he not [continued the Caliph] been the enemy of Allah,
he had wished for her in this world; so that he might, after,
repent and return to righteous dealing. By Allah! he shall not
come in to me! Who is at the door other than he? "
Quoth 'Adi, "Jamil bin Ma'mar al-Uzri is at the door. " And
quoth Omar, "Tis he who saith in one of his love-Elegies:-
'Would Heaven, conjoint we lived! and if I die, | Death only
grant me a grave within her grave!
For I'd no longer deign to live my life | If told, "Upon her head
is laid the pave. ">
Quoth Omar, "Away with him from me! Who is at the door? "
And quoth 'Adi, "Kutthayir 'Azzah": whereupon Omar cried,
"Tis he who saith in one of his [impious] Odes:
'Some talk of faith and creed and nothing else, | And wait for
pains of Hell in prayer-seat;
But did they hear what I from Azzah heard, They'd make
prostration, fearful, at her feet. '
I
## p. 703 (#113) ############################################
ARABIC LITERATURE
703
Leave the mention of him. Who is at the door? " Quoth 'Adi,
"Al-Ahwas al-Ansari. " Cried Omar, "Allah Almighty put him
away, and estrange him from His mercy! Is it not, he who
said, berhyming on a Medinite's slave girl, so that she might
outlive her master:-
-
Allah be judge betwixt me and her lord | Whoever flies with
her and I pursue. '
He
He shall not come in to me! Who is at the door other than
he? " 'Adi replied, "Hammam bin Ghalib al-Farazdak. " And
Omar said, "Tis he who glories in wickedness.
shall not come in to me! Who is at the door other than he? "
'Adi replied, "Al-Akhtal al-Taghlibi. " And Omar said, "He is
the [godless] miscreant who saith in his singing:-
'Ramazan I ne'er fasted in lifetime; nay | I ate flesh in public
at undurn day!
―
Nor chid I the fair, save in word of love, | Nor seek Meccah's
plain in salvation-way:
Nor stand I praying, like rest, who cry, "Hie salvation-
wards! " at the dawn's first ray.
By Allah! he treadeth no carpet of mine. Who is at the door
other than he? " Said 'Adi, "Jarir Ibn al-Khatafah. " And Omar
cried, "Tis he who saith:-
:-
'But for ill-spying glances, had our eyes espied | Eyes of the.
antelope, and ringlets of the Reems!
A Huntress of the eyes, by night-time came; and I cried,
"Turn in peace! No time for visit this, meseems. ">
So 'Adi went
But if it must be, and no help, admit Jarir.
forth and admitted Jarir, who entered saying:-
'Yea, He who sent Mohammed unto men | A just successor of
Islâm assigned.
His ruth and his justice all mankind embrace | To daunt the
bad and stablish well-designed.
Verily now, I look to present good, | for man hath ever tran-
sient weal in mind. '
Quoth Omar, "O Jarir! keep the fear of Allah before thine
eyes, and say naught save the sooth. " And Jarir recited these
Couplets:-
## p. 704 (#114) ############################################
704
DOMINIQUE FRANÇOIS ARAGO
'How many widows loose the hair, in far Yamamah land, |
How many an orphan there abides, feeble of voice and eye,
Since faredst thou, who wast to them instead of father lost |
when they like nestled fledglings were, sans power to creep
or fly.
And now we hope-since broke the clouds their word and
troth with us- -"| Hope from the Caliph's grace to gain a
rain that ne'er shall dry. '
When the Caliph heard this, he said, "By Allah, O Jarir:
Omar possesseth but an hundred dirhams. Ho boy! do thou
give them to him! " Moreover, he gifted Jarir with the orna-
ments of his sword; and Jarir went forth to the other poets,
who asked him, "What is behind thee? " [What is thy news? "]
and he answered, "A man who giveth to the poor, and who
denieth the poets; and with him I am well pleased. "
DOMINIQUE FRANÇOIS ARAGO
(1786-1853)
BY EDWARD S. HOLDEN
D
SOMINIQUE FRANÇOIS ARAGO was born February 26th, 1786, near
Perpignan, in the Eastern Pyrenees, where his father held
the position of Treasurer of the Mint. He entered the École
Polytechnique in Paris after a brilliant examination, and held the first
places throughout the course. In 1806 he was sent to Valencia in
Spain, and to the neighboring island of Iviza, to make the astronom-
ical observations for prolonging the arc of the meridian from Dunkirk
southward, in order to supply the basis for the metric system.
Here begin his extraordinary adventures, which are told with inim-
itable spirit and vigor in his 'Autobiography. ' Arago's work required
him to occupy stations on the summits of the highest peaks in the
mountains of southeastern Spain. The peasants were densely ignor-
ant and hostile to all foreigners, so that an escort of troops was
required in many of his journeys. At some stations he made friends
of the bandits of the neighborhood, and carried on his observations
under their protection, as it were. In 1807 the tribunal of the Inqui-
sition existed in Valencia; and Arago was witness to the trial and
punishment of a pretended sorceress,—and this, as he says, in one
of the principal towns of Spain, the seat of a celebrated university.
Yet the worst criminals lived unmolested in the cathedrals, for the
"right of asylum" was still in force. His geodetic observations were
## p. 705 (#115) ############################################
DOMINIQUE FRANÇOIS ARAGO
705
mysteries to the inhabitants, and his signals on the mountain top.
were believed to be part of the work of a French spy. Just at this
time hostilities broke out between France and Spain, and the astron-
omer was obliged to flee disguised as a Majorcan peasant, carrying
his precious papers with him. His knowledge of the Majorcan lan-
guage saved him, and he reached a Spanish prison with only a slight
wound from a dagger. It is the first recorded instance, he says, of a
fugitive flying to a dungeon for safety. In this prison, under the
care of Spanish officers, Arago found sufficient occupation in calculat-
ing observations which he had made; in reading the accounts in the
Spanish journals of his own execution at Valencia; and in listening.
to rumors that it was proposed (by a Spanish monk) to do away
with the French prisoner by poisoning his food.
The Spanish officer in charge of the prisoners was induced to con-
nive at the escape of Arago and M. Berthémie (an aide-de-camp of
Napoleon); and on the 28th of July, 1808, they stole away from the
coast of Spain in a small boat with three sailors, and arrived at Al-
giers on the 3d of August. Here the French consul procured them
two false passports, which transformed the Frenchmen into strolling
merchants from Schwekat and Leoben. They boarded an Algerian
vessel and set off. Let Arago describe the crew and cargo:-
"The vessel belonged to the Emir of Seca. The commander was a Greek
captain named Spiro Calligero. Among the passengers were five members of
the family superseded by the Bakri as kings of the Jews; two Maroccan
ostrich-feather merchants; Captain Krog from Bergen in Norway; two lions
sent by the Dey of Algiers as presents to the Emperor Napoleon; and a great
number of monkeys. "
As they entered the Golfe du Lion their ship was captured by a
Spanish corsair and taken to Rosas. Worst of all, a former Spanish
servant of Arago's - Pablo - was a sailor in the corsair's crew! At
Rosas the prisoners were brought before an officer for interrogation.
It was now Arago's turn. The officer begins:-
<<<Who are you? '
"A poor traveling merchant. '
«From whence do you come ? >
From a country where you certainly have never been. '
«‹Well — from what country? >
"I feared to answer; for the passports (steeped in vinegar to prevent
infection) were in the officer's hands, and I had entirely forgotten whether I
was from Schwekat or from Leoben. Finally I answered at a chance, 'I am
from Schwekat;' fortunately this answer agreed with the passport.
"You're from Schwekat about as much as I am,' said the officer: 'you're
a Spaniard, and a Spaniard from Valencia to boot, as I can tell by your
accent. >
11-45
## p. 706 (#116) ############################################
706
DOMINIQUE FRANÇOIS ARAGO
«Sir, you are inclined to punish me simply because I have by nature the
gift of languages. I readily learn the dialects of the various countries where
I carry on my trade. For example, I know the dialect of Iviza. '
<<<Well, I will take you at your word. Here is a soldier who comes from
Iviza. Talk to him. '
«Very well; I will even sing the goat-song. '
"The verses of this song (if one may call them verses) are separated by
the imitated bleatings of the goat. I began at once, with an audacity which
even now astonishes me, to intone the song which all the shepherds in Iviza
sing: -
Ah graciada Señora,
Una canzo bouil canta,
Bè bè bè bè.
No sera gaiva pulida,
Nosé si vos agradara,
Bè bè bè bè.
"Upon which my Ivizan avouches, in tears, that I am certainly from
Iviza. The song had affected him as a Switzer is affected by the Ranz des
Vaches. I then said to the officer that if he would bring to me a person
who could speak French, he would find the same embarrassment in this case
also. An emigré of the Bourbon regiment comes forward for the new experi-
ment, and after a few phrases affirms without hesitation that I am surely a
Frenchman. The officer begins to be impatient.
«Have done with these trials: they prove nothing. I require you to tell
me who you are. '
"My foremost desire is to find an answer which will satisfy you.
the son of the innkeeper at Mataro. '
"I know that man: you are not his son. '
«You are right: I told you that I should change my answers till I found
one to suit you. I am a marionette player from Lerida. '
"A huge laugh from the crowd which had listened to the interrogatory
put an end to the questioning. "
I am
Finally it was necessary for Arago to declare outright that he was
French, and to prove it by his old servant Pablo. To supply his
immediate wants he sold his watch; and by a series of misadventures
this watch subsequently fell into the hands of his family, and he was
mourned in France as dead.
After months of captivity the vessel was released, and the prisoner
set out for Marseilles. A fearful tempest drove them to the harbor
of Bougie, an African port a hundred miles east of Algiers. Thence
they made the perilous journey by land to their place of starting,
and finally reached Marseilles eleven months after their voyage
began. Eleven months to make a journey of four days!
The intelligence of the safe arrival, after so many perils, of the
young astronomer, with his packet of precious observations, soon
reached Paris. He was welcomed with effusion. Soon afterward (at
## p. 707 (#117) ############################################
DOMINIQUE FRANÇOIS ARAGO
707
the age of twenty-three years) he was elected a member of the sec-
tion of Astronomy of the Academy of Sciences, and from this time
forth he led the peaceful life of a savant. He was the Director of
the Paris Observatory for many years; the friend of all European
scientists; the ardent patron of young men of talent; a leading physi-
cist; a strong Republican, though the friend of Napoleon; and finally
the Perpetual Secretary of the Academy.
In the latter capacity it was part of his duty to prepare éloges of
deceased Academicians. Of his collected works in fourteen volumes,
'Euvres de François Arago,' published in Paris, 1865, three volumes
are given to these 'Notices Biographiques. ' Here may be found the
biographies of Bailly, Sir William Herschel, Laplace, Joseph Fourier,
Carnot, Malus, Fresnel, Thomas Young, and James Watt; which,
translated rather carelessly into English, have been published under
the title 'Biographies of Distinguished Men,' and can be found in the
larger libraries. The collected works contain biographies also of
Ampère, Condorcet, Volta, Monge, Porson, Gay-Lussac, besides shorter
sketches. They are masterpieces of style and of clear scientific expo-
sition, and full of generous appreciation of others' work. They pre-
sent in a lucid and popular form the achievements of scientific men
whose works have changed the accepted opinion of the world, and
they give general views not found in the original writings them-
selves. Scientific men are usually too much engrossed in advancing
science to spare time for expounding it to popular audiences. The
talent for such exposition is itself a special one. Arago possessed it
to the full, and his own original contributions to astronomy and phys-
ics enabled him to speak as an expert, not merely as an expositor.
The extracts are from his admirable estimate of Laplace, which
he prepared in connection with the proposal, before him and other
members of a State Committee, to publish a new and authoritative
edition of the great astronomer's works. The translation is mainly
that of the 'Biographies of Distinguished Men' cited above, and
much of the felicity of style is necessarily lost in translation; but the
substance of solid and lucid exposition from a master's hand remains.
Arago was a Deputy in 1830, and Minister of War in the Provis-
ional Government of 1848. He died full of honors, October 2d, 1853.
Two of his brothers, Jacques and Étienne, were dramatic authors of
Another, Jean, was a distinguished general in the service of
Mexico. One of his sons, Alfred, is favorably known as a painter;
another, Emmanuel, as a lawyer, deputy, and diplomat.
note.
Edward S. Holden
## p. 708 (#118) ############################################
708
DOMINIQUE FRANÇOIS ARAGO
LAPLACE
THE
HE Marquis de Laplace, peer of France, one of the forty of
the French Academy, member of the Academy of Sciences
and of the Bureau of Longitude, Associate of all the great
Academies or Scientific Societies of Europe, was born at Beau-
mont-en-Auge, of parents belonging to the class of small farmers,
on the 28th of March, 1749; he died on the 5th of March, 1827.
The first and second volumes of the 'Mécanique Céleste' [Mech-
anism of the Heavens] were published in 1799; the third volume
appeared in 1802, the fourth in 1805; part of the fifth volume
was published in 1823, further books in 1824, and the remainder
in 1825. The Théorie des Probabilités was published in 1812.
We shall now present the history of the principal astronomical
discoveries contained in these immortal works.
Astronomy is the science of which the human mind may justly
feel proudest. It owes this pre-eminence to the elevated nature
of its object; to the enormous scale of its operations; to the cer-
tainty, the utility, and the stupendousness of its results. From the
very beginnings of civilization the study of the heavenly bodies
and their movements has attracted the attention of governments
and peoples. The greatest captains, statesmen, philosophers, and
orators of Greece and Rome found it a subject of delight. Yet
astronomy worthy of the name is a modern science: it dates from
the sixteenth century only. Three great, three brilliant phases
have marked its progress. In 1543 the bold and firm hand of
Copernicus overthrew the greater part of the venerable scaffold-
ing which had propped the illusions and the pride of many gen-
erations. The earth ceased to be the centre, the pivot, of celestial
movements. Henceforward it ranged itself modestly among the
other planets, its relative importance as one member of the solar
system reduced almost to that of a grain of sand.
Twenty-eight years had elapsed from the day when the Canon
of Thorn expired while holding in his trembling hands the first
copy of the work which was to glorify the name of Poland, when
Würtemberg witnessed the birth of a man who was destined to
achieve a revolution in science not less fertile in consequences,
and still more difficult to accomplish. This man was Kepler.
Endowed with two qualities which seem incompatible,-a volcanic
imagination, and a dogged pertinacity which the most tedious
calculations could not tire,- Kepler conjectured that celestial
## p. 709 (#119) ############################################
DOMINIQUE FRANÇOIS ARAGO
709
movements must be connected with each other by simple laws;
or, to use his own expression, by harmonic laws. These laws
he undertook to discover. A thousand fruitless attempts — the
errors of calculation inseparable from a colossal undertaking-
did not hinder his resolute advance toward the goal his imagina-
tion descried. Twenty-two years he devoted to it, and still he
was not weary. What are twenty-two years of labor to him who
is about to become the lawgiver of worlds; whose name is to be
ineffaceably inscribed on the frontispiece of an immortal code;
who can exclaim in dithyrambic language, "The die is cast: I
have written my book; it will be read either in the present age
or by posterity, it matters not which; it may well await a reader
since God has waited six thousand years for an interpreter of his
works"?
These celebrated laws, known in astronomy as Kepler's laws,
are three in number. The first law is, that the planets describe
ellipses around the sun, which is placed in their common focus;
the second, that a line joining a planet and the sun sweeps over
equal areas in equal times; the third, that the squares of the
times of revolution of the planets about the sun are proportional
to the cubes of their mean distances from that body. The first
two laws were discovered by Kepler in the course of a laborious
examination of the theory of the planet Mars. A full account of
this inquiry is contained in his famous work, 'De Stella Martis'
[Of the Planet Mars], published in 1609. The discovery of the
third law was announced to the world in his treatise on Har-
monics (1628).
To seek a physical cause adequate to retain the planets in
their closed orbits; to make the stability of the universe depend
on mechanical forces, and not on solid supports like the crys-
talline spheres imagined by our ancestors; to extend to the
heavenly bodies in their courses the laws of earthly mechan-
ics, such were the problems which remained for solution after
Kepler's discoveries had been announced. Traces of these great
problems may be clearly perceived here and there among ancient
and modern writers, from Lucretius and Plutarch down to Kep-
ler, Bouillaud, and Borelli. It is to Newton, however, that we
must award the merit of their solution. This great man, like
several of his predecessors, imagined the celestial bodies to have
a, tendency to approach each other in virtue of some attractive
force, and from the laws of Kepler he deduced the mathematical
――
## p. 710 (#120) ############################################
710
DOMINIQUE FRANÇOIS ARAGO
characteristics of this force. He extended it to all the material
molecules of the solar system; and developed his brilliant dis-
covery in a work which, even at the present day, is regarded as
the supremest product of the human intellect.
The contributions of France to these revolutions in astronom-
ical science consisted, in 1740, in the determination by experi
ment of the spheroidal figure of the earth, and in the discovery
of the local variations of gravity upon the surface of our planet.
These were two great results; but whenever France is not first
in science she has lost her place. This rank, lost for a moment,
was brilliantly regained by the labors of four geometers. When
Newton, giving to his discoveries a generality which the laws of
Kepler did not suggest, imagined that the different planets were
not only attracted by the sun, but that they also attracted each
other, he introduced into the heavens a cause of universal per-
turbation. Astronomers then saw at a glance that in no part of
the universe would the Keplerian laws suffice for the exact repre-
sentation of the phenomena of motion; that the simple regular
movements with which the imaginations of the ancients were
pleased to endow the heavenly bodies must experience numerous,
considerable, perpetually changing perturbations. To discover a
few of these perturbations, and to assign their nature and in
a few rare cases their numerical value, was the object which
Newton proposed to himself in writing his famous book, the
'Principia Mathematica Philosophiæ Naturalis' [Mathematical Prin-
ciples of Natural Philosophy]. Notwithstanding the incomparable
sagacity of its author, the 'Principia' contained merely a rough
outline of planetary perturbations, though not through any lack
of ardor or perseverance.
The efforts of the great philosopher
were always superhuman, and the questions which he did not.
solve were simply incapable of solution in his time.
Five geometers-Clairaut, Euler, D'Alembert, Lagrange, and
Laplace shared between them the world whose existence New-
ton had disclosed. They explored it in all directions, penetrated
into regions hitherto inaccessible, and pointed out phenomena
hitherto undetected. Finally and it is this which constitutes
their imperishable glory-they brought under the domain of a
single principle, a single law, everything that seemed most occult
and mysterious in the celestial movements. Geometry had thus
the hardihood to dispose of the future, while the centuries as
they unroll scrupulously ratify the decisions of science.
- -
## p.
711 (#121) ############################################
DOMINIQUE FRANÇOIS ARAGO
711
If Newton gave a complete solution of celestial movements
where but two bodies attract each other, he did not even attempt
the infinitely more difficult problem of three. The "problem of
three bodies (this is the name by which it has become cele-
brated) the problem of determining the movement of a body
subjected to the attractive influence of two others- was solved
for the first time by our countryman, Clairaut. Though he enu-
merated the various forces which must result from the mutual
action of the planets and satellites of our system, even the great
Newton did not venture to investigate the general nature of
their effects. In the midst of the labyrinth formed by incre-
ments and diminutions of velocity, variations in the forms of
orbits, changes in distances and inclinations, which these forces
must evidently produce, the most learned geometer would fail to
discover a trustworthy guide. Forces so numerous, so variable in
direction, so different in intensity, seemed to be incapable of
maintaining a condition of equilibrium except by a sort of mir-
acle. Newton even suggested that the planetary system did not
contain within itself the elements of indefinite stability. He
was of opinion that a powerful hand must intervene from time
to time to repair the derangements occasioned by the mutual
action of the various bodies. Euler, better instructed than New-
ton in a knowledge of these perturbations, also refused to admit
that the solar system was constituted so as to endure forever.
Never did a greater philosophical question offer itself to the
inquiries of mankind. Laplace attacked it with boldness, persever-
ance, and success. The profound and long-continued researches
of the illustrious geometer completely established the perpetual
variability of the planetary ellipses. He demonstrated that the
extremities of their major axes make the circuit of the heavens;
that independent of oscillation, the planes of their orbits undergo
displacements by which their intersections with the plane of the
terrestrial orbit are each year directed toward different stars.
But in the midst of this apparant chaos, there is one element
which remains constant, or is merely subject to small and peri-
odic changes; namely, the major axis of each orbit, and conse-
quently the time of revolution of each planet. This is the element
which ought to have varied most, on the principles held by New-
ton and Euler. Gravitation, then, suffices to preserve the stability
of the solar system. It maintains the forms and inclinations of
the orbits in an average position, subject to slight oscillations
________________
>>>>
## p. 712 (#122) ############################################
712
DOMINIQUE FRANÇOIS ARAGO
only; variety does not entail disorder; the universe offers an
example of harmonious relations, of a state of perfection which
Newton himself doubted.
This condition of harmony depends on circumstances disclosed
to Laplace by analysis; circumstances which on the surface do
not seem capable of exercising so great an influence. If instead
of planets all revolving in the same direction, in orbits but
slightly eccentric and in planes inclined at but small angles toward
each other, we should substitute different conditions, the stability
of the universe would be jeopardized, and a frightful chaos would
pretty certainly result. The discovery of the actual conditions.
excluded the idea, at least so far as the solar system was con-
cerned, that the Newtonian attraction might be a cause of dis-
order. But might not other forces, combined with the attraction
of gravitation, produce gradually increasing perturbations such as
Newton and Euler feared? Known facts seemed to justify the
apprehension. A comparison of ancient with modern observations
revealed a continual acceleration in the mean motions of the
moon and of Jupiter, and an equally striking diminution of the
mean motion of Saturn. These variations led to a very import-
ant conclusion. In accordance with their presumed cause, to say
that the velocity of a body increased from century to century
was equivalent to asserting that the body continually approached
the centre of motion; on the other hand, when the velocity.
diminished, the body must be receding from the centre. Thus,
by a strange ordering of nature, our planetary system seemed
destined to lose Saturn, its most mysterious ornament; to see the
planet with its ring and seven satellites plunge gradually into
those unknown regions where the eye armed with the most pow-
erful telescope has never penetrated. Jupiter, on the other hand,
the planet compared with which the earth is so insignificant,
appeared to be moving in the opposite direction, so that it would.
ultimately be absorbed into the incandescent matter of the sun.
Finally, it seemed that the moon would one day precipitate itself
upon the earth.
There was nothing doubtful or speculative in these sinister
forebodings. The precise dates of the approaching catastrophes
were alone uncertain. It was known, however, that they were
very distant.
Accordingly, neither the learned dissertations of
men of science nor the animated descriptions of certain poets
produced any impression upon the public mind. . The members
## p. 713 (#123) ############################################
DOMINIQUE FRANÇOIS ARAGO
713
of our scientific societies, however, believed with regret the
approaching destruction of the planetary system. The Academy
of Sciences called the attention of geometers of all countries to
these menacing perturbations. Euler and Lagrange descended
into the arena. Never did their mathematical genius shine with
a brighter lustre. Still the question remained undecided, when
from two obscure corners of the theories of analysis, Laplace,
the author of the 'Mécanique Céleste,' brought the laws of these
great phenomena clearly to light. The variations in velocity of
Jupiter, Saturn, and the moon, were proved to flow from evi-
dent physical causes, and to belong in the category of ordinary
periodic perturbations depending solely on gravitation. These
dreaded variations in orbital dimensions resolved themselves
into simple oscillations included within narrow limits. In a word,
by the powerful instrumentality of mathematical analysis, the
physical universe was again established on a demonstrably firm
foundation.
Having demonstrated the smallness of these periodic oscilla-
tions, Laplace next succeeded in determining the absolute dimen-
sions of the orbits. What is the distance of the sun from the
earth? No scientific question has occupied the attention of man-
kind in a greater degree. Mathematically speaking, nothing is
more simple: it suffices, as in ordinary surveying, to draw visual
lines from the two extremities of a known base line to an inac-
cessible object; the remainder of the process is an elementary
calculation. Unfortunately, in the case of the sun, the distance
is very great and the base lines which can be measured upon
the earth are comparatively very small. In such a case, the
slightest errors in the direction of visual lines exercise an enor-
mous influence upon the results. In the beginning of the last
century, Halley had remarked that certain interpositions of Venus
between the earth and the sun -or to use the common term, the
transits of the planet across the sun's disk—would furnish at each
observing station an indirect means of fixing the position of the
visual ray much superior in accuracy to the most perfect direct
measures. Such was the object of the many scientific expeditions
undertaken in 1761 and 1769, years in which the transits of
Venus occurred. A comparison of observations made in the
Southern Hemisphere with those of Europe gave for the distance
of the sun the result which has since figured in all treatises on
astronomy and navigation. No government hesitated to furnish
## p. 714 (#124) ############################################
714
DOMINIQUE FRANÇOIS ARAGO
scientific academies with the means, however expensive, of estab-
lishing their observers in the most distant regions. We have
already remarked that this determination seemed imperiously to
demand an extensive base, for small bases would have been
totally inadequate. Well, Laplace has solved the problem with-
out a base of any kind whatever; he has deduced the distance of
the sun from observations of the moon made in one and the
same place.
The sun is, with respect to our satellite the moon, the cause
of perturbations which evidently depend on the distance of the
immense luminous globe from the earth. Who does not see that
these perturbations must diminish if the distance increases, and
increase if the distance diminishes, so that the distance determines
the amount of the perturbations? Observation assigns the nu-
merical value of these perturbations; theory, on the other hand,
unfolds the general mathematical relation which connects them with
the solar distance and with other known elements. The deter-
mination of the mean radius of the terrestrial orbit· of the dis-
tance of the sun-then becomes one of the most simple operations
of algebra. Such is the happy combination by the aid of which
Laplace has solved the great, the celebrated problem of parallax.
It is thus that the illustrious geometer found for the mean
distance of the sun from the earth, expressed in radii of the ter-
restrial orbit, a value differing but slightly from that which was
the fruit of so many troublesome and expensive voyages.
The movements of the moon proved a fertile mine of research
to our great geometer. His penetrating intellect discovered in
them unknown treasures. With an ability and a perseverance
equally worthy of admiration, he separated these treasures from
the coverings which had hitherto concealed them from vulgar
eyes. For example, the earth governs the movements of the
moon. The earth is flattened; in other words, its figure is
spheroidal. A spheroidal body does not attract as does a sphere.
There should then exist in the movement - I had almost said in
the countenance-of the moon a sort of impress of the spheroidal
figure of the earth. Such was the idea as it originally occurred
to Laplace. By means of a minutely careful investigation, he
discovered in its motion two well-defined perturbations, each
depending on the spheroidal figure of the earth. When these
were submitted to calculation, each led to the same value of the
ellipticity. It must be recollected that the ellipticity thus derived
## p. 715 (#125) ############################################
DOMINIQUE FRANÇOIS ARAGO
715
from the motions of the moon is not the one corresponding to
such or such a country, to the ellipticity observed in France, in
England, in Italy, in Lapland, in North America, in India, or in
the region of the Cape of Good Hope; for, the earth's crust
having undergone considerable upheavals at different times and
places, the primitive regularity of its curvature has been sensibly
disturbed thereby. The moon (and it is this which renders the
result of such inestimable value) ought to assign, and has in
reality assigned, the general ellipticity of the earth; in other
words, it has indicated a sort of average value of the various
determinations obtained at enormous expense, and with infinite
labor, as the result of long voyages undertaken by astronomers
of all the countries of Europe.
Certain remarks of Laplace himself bring into strong relief
the profound, the unexpected, the almost paradoxical character
of the methods I have attempted to sketch. What are the ele-
ments it has been found necessary to confront with each other
in order to arrive at results expressed with such extreme
precision? On the one hand, mathematical formulæ deduced
from the principle of universal gravitation; on the other, cer-
tain irregularities observed in the returns of the moon to the
meridian. An observing geometer, who from his infancy had
never quitted his study, and who had never viewed the heavens
except through a narrow aperture directed north and south, — to
whom nothing had ever been revealed respecting the bodies
revolving above his head, except that they attract each other
according to the Newtonian law of gravitation,- would still per-
ceive that his narrow abode was situated upon the surface of a
spheroidal body, whose equatorial axis was greater than its polar
by a three hundred and sixth part. In his isolated, fixed position
he could still deduce his true distance from the sun!
-
Laplace's improvement of the lunar tables not only promoted
maritime intercourse between distant countries, but preserved the
lives of mariners. Thanks to an unparalleled sagacity, to a limit-
less perseverance, to an ever youthful and communicable ardor,
Laplace solved the celebrated problem of the longitude with a
precision even greater than the utmost needs of the art of navi-
gation demanded. The ship, the sport of the winds and tem-
pests, no longer fears to lose its way in the immensity of the
ocean. In every place and at every time the pilot reads in the
starry heavens his distance from the meridian of Paris. The
## p. 716 (#126) ############################################
716
DOMINIQUE FRANÇOIS ARAGO
extreme perfection of these tables of the moon places Laplace in
the ranks of the world's benefactors.
In the beginning of the year 1611, Galileo supposed that he
found in the eclipses of Jupiter's satellites a simple and rigorous
solution of the famous problem of the longitude, and attempts
to introduce the new method on board the numerous vessels of
Spain and Holland at once began. They failed because the neces-
sary observations required powerful telescopes, which could not
be employed on a tossing ship. Even the expectations of the
serviceability of Galileo's methods for land calculations proved
premature. The movements of the satellites of Jupiter are far
less simple than the immortal Italian supposed them to be. The
labors of three more generations of astronomers and mathema-
ticians were needed to determine them, and the mathematical
genius of Laplace was needed to complete their labors. At the
present day the nautical ephemerides contain, several years in
advance, the indications of the times of the eclipses and reap-
pearances of Jupiter's satellites. Calculation is as precise as
direct observation.
Influenced by an exaggerated deference, modesty, timidity,
France in the eighteenth century surrendered to England the
exclusive privilege of constructing her astronomical instruments.
Thus, when Herschel was prosecuting his beautiful observations
on the other side of the Channel, we had not even the means of
verifying them. Fortunately for the scientific honor of our
country, mathematical analysis also is a powerful instrument.
The great Laplace, from the retirement of his study, foresaw,
and accurately predicted in advance, what the excellent astrono-
mer of Windsor would soon behold with the largest telescopes
existing. When, in 1610, Galileo directed toward Saturn a lens
of very low power which he had just constructed with his own
hands, although he perceived that the planet was not a globe,
he could not ascertain its real form. The expression "tri-
corporate," by which the illustrious Florentine designated the
appearance of the planet, even implied a totally erroneous ideal
of its structure. At the present day every one knows that
Saturn consists of a globe about nine hundred times greater than
the earth, and of a ring. This ring does not touch the ball of
the planet, being everywhere removed from it to a distance.
of twenty thousand (English) miles. Observation indicates the
breadth of the ring to be fifty-four thousand miles. The thickness
## p. 717 (#127) ############################################
DOMINIQUE FRANÇOIS ARAGO
717
certainly does not exceed two hundred and fifty miles. With the
exception of a black streak which divides the ring throughout its
whole contour into two parts of unequal breadth and of different
brightness, this strange colossal bridge without foundations had
never offered to the most experienced or skillful observers either
spot or protuberance adapted for deciding whether it was immov-
able or endowed with a motion of rotation. Laplace considered.
it to be very improbable, if the ring was stationary, that its con-
stituent parts should be capable of resisting by mere cohesion
the continual attraction of the planet. A movement of rotation
occurred to his mind as constituting the principle of stability,
and he deduced the necessary velocity from this consideration.
The velocity thus found was exactly equal to that which Herschel
subsequently derived from a series of extremely delicate observa-
tions. The two parts of the ring, being at different distances
from the planet, could not fail to be given different movements
of precession by the action of the sun. Hence it would seem that
the planes of both rings ought in general to be inclined toward
each other, whereas they appear from observation always to
coincide. It was necessary then that some physical cause capable
of neutralizing the action of the sun should exist. In a memoir
published in February, 1789, Laplace found that this cause
depended on the ellipticity of Saturn produced by a rapid move-
ment of rotation of the planet, a movement whose discovery
Herschel announced in November of the same year.
If we descend from the heavens to the earth, the discoveries
of Laplace will appear not less worthy of his genius. He reduced.
the phenomena of the tides, which an ancient philosopher termed
in despair "the tomb of human curiosity," to an analytical theory
in which the physical conditions of the question figure for the
first time. Consequently, to the immense advantage of coast nav-
igation, calculators now venture to predict in detail the time and
height of the tides several years in advance. Between the phe-
nomena of the ebb and flow, and the attractive forces of the sun
and moon upon the fluid sheet which covers three fourths of the
globe, an intimate and necessary connection exists; a connection
from which Laplace deduced the value of the mass of our satellite
the moon.
Yet so late as the year 1631 the illustrious Galileo,
as appears from his 'Dialogues,' was so far from perceiving
the mathematical relations from which Laplace deduced results
so beautiful, so unequivocal, and so useful, that he taxed with
F
## p. 718 (#128) ############################################
718
DOMINIQUE FRANÇOIS ARAGO
frivolousness the vague idea which Kepler entertained of attribut-
ing to the moon's attraction a certain share in the production of
the diurnal and periodical movements of the waters of the ocean.
Laplace did not confine his genius to the extension and im-
provement of the mathematical theory of the tide. He considered
the phenomenon from an entirely new point of view, and it was
he who first treated of the stability of the ocean. He has estab-
lished its equilibrium, but upon the express condition (which,
however, has been amply proved to exist) that the mean density
of the fluid mass is less than the mean density of the earth.
Everything else remaining the same, if we substituted an ocean.
of quicksilver for the actual ocean, this stability would disappear.
The fluid would frequently overflow its boundaries, to ravage con-
tinents even to the height of the snowy peaks which lose them-
selves in the clouds.
No one was more sagacious than Laplace in discovering inti-
mate relations between phenomena apparently unrelated, or more
skillful in deducing important conclusions from such unexpected
affinities. For example, toward the close of his days, with the
aid of certain lunar observations, with a stroke of his pen he
overthrew the cosmogonic theories of Buffon and Bailly, which
were so long in favor. According to these theories, the earth
was hastening to a state of congelation which was close at hand.
Laplace, never contented with vague statements, sought to deter-
mine in numbers the rate of the rapid cooling of our globe which
Buffon had so eloquently but so gratuitously announced. Noth-
ing could be more simple, better connected, or more conclusive
than the chain of deductions of the celebrated geometer. A body
diminishes in volume when it cools. According to the most ele-
mentary principles of mechanics, a rotating body which contracts
in dimensions must inevitably turn upon its axis with greater and
greater rapidity. The length of the day has been determined in
all ages by the time of the earth's rotation; if the earth is cool-
ing, the length of the day must be continually shortening. Now,
there exists a means of ascertaining whether the length of the
day has undergone any variation; this consists in examining, for
each century, the arc of the celestial sphere described by the
moon during the interval of time which the astronomers of the
existing epoch call a day; in other words, the time required by
the earth to effect a complete rotation on its axis, the velocity of
the moon being in fact independent of the time of the earth's
## p. 719 (#129) ############################################
DOMINIQUE FRANÇOIS ARAGO
719
rotation. Let us now, following Laplace, take from the standard
tables the smallest values, if you choose, of the expansions or
contractions which solid bodies experience from changes of tem-
perature; let us search the annals of Grecian, Arabian, and mod-
ern astronomy for the purpose of finding in them the angular
velocity of the moon: and the great geometer will prove, by
incontrovertible evidence founded upon these data, that during a
period of two thousand years the mean temperature of the earth
has not varied to the extent of the hundredth part of a degree
of the centigrade thermometer. Eloquence cannot resist such
a process of reasoning, or withstand the force of such figures.
Mathematics has ever been the implacable foe of scientific ro-
mances. The constant object of Laplace was the explanation of
the great phenomena of nature according to inflexible principles
of mathematical analysis. No philosopher, no mathematician,
could have guarded himself more cautiously against a propensity
to hasty speculation. No person dreaded more the scientific
errors which cajole the imagination when it passes the boundary
of fact, calculation, and analogy.
Once, and once only, did Laplace launch forward, like Kepler,
like Descartes, like Leibnitz, like Buffon, into the region of con-
jectures. But then his conception was nothing less than a com-
plete cosmogony. All the planets revolve around the sun, from
west to east, and in planes only slightly inclined to each other.
The satellites revolve around their respective primaries in the
same direction. Both planets and satellites, having a rotary mo-
tion, turn also upon their axes from west to east. Finally, the
rotation of the sun also is directed from west to east. Here,
then, is an assemblage of forty-three movements, all operating
alike. By the calculus of probabilities, the odds are four thou-
sand millions to one that this coincidence in direction is not the
effect of accident.
It was Buffon, I think, who first attempted to explain this
singular feature of our solar system. "Wishing, in the explana-
tion of phenomena, to avoid recourse to causes which are not to
be found in nature," the celebrated academician sought for a
physical cause for what is common to the movements of so
many bodies differing as they do in magnitude, in form, and in
their distances from the centre of attraction. He imagined that
he had discovered such a physical cause by making this triple
supposition: a comet fell obliquely upon the sun; it pushed
## p. 720 (#130) ############################################
720
DOMINIQUE FRANÇOIS ARAGO
before it a torrent of fluid matter; this substance, transported to
a greater or less distance from the sun according to its density,
formed by condensation all the known planets. The bold hy-
pothesis is subject to insurmountable difficulties. I proceed to
indicate, in a few words, the cosmogonic system which Laplace
substituted for it.
According to Laplace, the sun was, at a remote epoch, the
central nucleus of an immense nebula, which possessed a very
high temperature, and extended far beyond the region in which
Uranus now revolves. No planet was then in existence. The
solar nebula was endowed with a general movement of rotation
in the direction west to east. As it cooled it could not fail to
experience a gradual condensation, and in consequence to rotate
with greater and greater rapidity. If the nebulous matter ex-
tended originally in the plane of its equator, as far as the limit
where the centrifugal force exactly counterbalanced the attraction
of the nucleus, the molecules situate at this limit ought, during
the process of condensation, to separate from the rest of the
atmospheric matter and to form an equatorial zone, a ring,
revolving separately and with its primitive velocity.
We may
conceive that analogous separations were effected in the remoter
strata of the nebula at different epochs and at different distances
from the nucleus, and that they gave rise to a succession of dis-
tinct rings, all lying in nearly the same plane, and all endowed
with different velocities.
This being once admitted, it is easy to see that the perma-
nent stability of the rings would have required a regularity of
structure throughout their whole contour, which is very improb-
able. Each of them, accordingly, broke in its turn into several
masses, which were obviously endowed with a movement of rota-
tion coinciding in direction with the common movement of revo-
lution, and which, in consequence of their fluidity, assumed
spheroidal forms. In order, next, that one of those spheroids
may absorb all the others belonging to the same ring, it is suffi-
cient to suppose it to have a mass greater than that of any
other spheroid of its group.
Each of the planets, while in this vaporous condition to which
we have just alluded, would manifestly have a central nucleus,
gradually increasing in magnitude and mass, and an atmosphere
offering, at its successive limits, phenomena entirely similar to
those which the solar atmosphere, properly so called, had exhib-
## p. 721 (#131) ############################################
DOMINIQUE FRANÇOIS ARAGO
721
ited. We are here contemplating the birth of satellites and the
birth of the ring of Saturn.
The Nebular Hypothesis, of which I have just given an imper-
fect sketch, has for its object to show how a nebula endowed with
a general movement of rotation must eventually transform itself
into a very luminous central nucleus (a sun), and into a series of
distinct spheroidal planets, situate at considerable distances from
one another, all revolving around the central sun, in the direction
of the original movement of the nebula; how these planets ought
also to have movements of rotation in similar directions; how,
finally, the satellites, when any such are formed, must revolve
upon their axes and around their respective primaries, in the
direction of rotation of the planets and of their movement of
revolution around the sun.
In all that precedes, attention has been concentrated upon the
'Mécanique Céleste. ' The 'Système du Monde' and the 'Théorie
Analytique des Probabilités' also deserve description.
The Exposition of the System of the World is the 'Mécanique
Céleste' divested of that great apparatus of analytical formulæ
which must be attentively perused by every astronomer who, to
use an expression of Plato, wishes to know the numbers which
govern the physical universe. It is from this work that persons
ignorant of mathematics may obtain competent knowledge of the
methods to which physical astronomy owes its astonishing progress.
Written with a noble simplicity of style, an exquisite exactness of
expression, and a scrupulous accuracy, it is universally conceded
to stand among the noblest monuments of French literature.
The labors of all ages to persuade truth from the heavens
are there justly, clearly, and profoundly analyzed.
Genius pre-
sides as the impartial judge of genius. Throughout his work.
Laplace remained at the height of his great mission. It will be
read with respect so long as the torch of science illuminates the
world.
The calculus of probabilities, when confined within just limits,
concerns the mathematician, the experimenter, and the statesman.
From the time when Pascal and Fermat established its first prin-
ciples, it has rendered most important daily services. This it is
which, after suggesting the best form for statistical tables of pop-
ulation and mortality, teaches us to deduce from those numbers,
so often misinterpreted, the most precise and useful conclusions.
This it is which alone regulates with equity insurance premiums,
II-46
## p. 722 (#132) ############################################
722
JOHN ARBUTHNOT
pension funds, annuities, discounts, etc. This it is that has grad-
ually suppressed lotteries, and other shameful snares cunningly
laid for avarice and ignorance. Laplace has treated these ques-
tions with his accustomed superiority: the Analytical Theory of
Probabilities' is worthy of the author of the 'Mécanique Céleste. '
A philosopher whose name is associated with immortal discov-
eries said to his too conservative audience, "Bear in mind, gentle-
men, that in questions of science the authority of a thousand is
not worth the humble reasoning of a single individual. " Two
centuries have passed over these words of Galileo without lessen-
ing their value or impugning their truth. For this reason, it has
been thought better rather to glance briefly at the work of La-
place than to repeat the eulogies of his admirers.
JOHN ARBUTHNOT
(1667-1735)
RBUTHNOT'S place in literature depends as much on his asso-
ciation with the wits of his day as on his own satirical and
humorous productions. Many of these have been published
in the collections of Swift, Gay, Pope, and others, and cannot be
identified. The task of verifying them is rendered more difficult
by the fact that his son repudiated a collection claiming to be his
'Miscellaneous Works,' published in 1750.
John Arbuthnot was born in the manse near Arbuthnot Castle,
Kincardineshire, Scotland, April 29th, 1667. He was the son of a
Scotch Episcopal clergyman, who was soon
to be dispossessed of his parish by the
Presbyterians in the Revolution of 1688.
His children, who shared his Jacobite sen-
timents, were forced to leave Scotland; and
John, after finishing his university course
at Aberdeen, and taking his medical de-
gree at St. Andrews, went to London and
taught mathematics. He soon attracted
attention by a keen and satirical Exam-
ination of Dr. Woodward's Account of the
Deluge,' published in 1697.
Asked the Caliph, "Dost thou remember what he said? " And
'Adi answered, "Yes. " Rejoined Omar, "Then repeat it;" so
'Adi repeated:-
## p. 702 (#112) ############################################
702
ARABIC LITERATURE
"I saw thee, O thou best of the human race, | Bring out a book
which brought to graceless, grace.
Thou showedst righteous road to men astray | From right, when
darkest wrong had ta'en its place:-
Thou with Islâm didst light the gloomiest way, | Quenching
with proof live coals of frowardness:
I own for Prophet, my Mohammed's self, and men's award
upon his word we base.
Thou madest straight the path that crooked ran | Where in old
days foul growth o'ergrew its face.
Exalt be thou in Joy's empyrean! | And Allah's glory ever grow
apace! "
"And indeed," continued 'Adi, "this Elegy on the Prophet
(Abhak! ) is well known, and to comment on it would be
tedious. "
Quoth Omar, "Who [of the poets] is at the door? " And
quoth 'Adi, "Among them is Omar ibn Rabí'ah, the Korashi;"
whereupon the Caliph cried, "May Allah show him no favor,
neither quicken him! Was it not he who spoke impiously [in
praising his love]? –
'Could I in my clay-bed [the grave] with Ialma repose, | There
to me were better than Heaven or Hell! '
Had he not [continued the Caliph] been the enemy of Allah,
he had wished for her in this world; so that he might, after,
repent and return to righteous dealing. By Allah! he shall not
come in to me! Who is at the door other than he? "
Quoth 'Adi, "Jamil bin Ma'mar al-Uzri is at the door. " And
quoth Omar, "Tis he who saith in one of his love-Elegies:-
'Would Heaven, conjoint we lived! and if I die, | Death only
grant me a grave within her grave!
For I'd no longer deign to live my life | If told, "Upon her head
is laid the pave. ">
Quoth Omar, "Away with him from me! Who is at the door? "
And quoth 'Adi, "Kutthayir 'Azzah": whereupon Omar cried,
"Tis he who saith in one of his [impious] Odes:
'Some talk of faith and creed and nothing else, | And wait for
pains of Hell in prayer-seat;
But did they hear what I from Azzah heard, They'd make
prostration, fearful, at her feet. '
I
## p. 703 (#113) ############################################
ARABIC LITERATURE
703
Leave the mention of him. Who is at the door? " Quoth 'Adi,
"Al-Ahwas al-Ansari. " Cried Omar, "Allah Almighty put him
away, and estrange him from His mercy! Is it not, he who
said, berhyming on a Medinite's slave girl, so that she might
outlive her master:-
-
Allah be judge betwixt me and her lord | Whoever flies with
her and I pursue. '
He
He shall not come in to me! Who is at the door other than
he? " 'Adi replied, "Hammam bin Ghalib al-Farazdak. " And
Omar said, "Tis he who glories in wickedness.
shall not come in to me! Who is at the door other than he? "
'Adi replied, "Al-Akhtal al-Taghlibi. " And Omar said, "He is
the [godless] miscreant who saith in his singing:-
'Ramazan I ne'er fasted in lifetime; nay | I ate flesh in public
at undurn day!
―
Nor chid I the fair, save in word of love, | Nor seek Meccah's
plain in salvation-way:
Nor stand I praying, like rest, who cry, "Hie salvation-
wards! " at the dawn's first ray.
By Allah! he treadeth no carpet of mine. Who is at the door
other than he? " Said 'Adi, "Jarir Ibn al-Khatafah. " And Omar
cried, "Tis he who saith:-
:-
'But for ill-spying glances, had our eyes espied | Eyes of the.
antelope, and ringlets of the Reems!
A Huntress of the eyes, by night-time came; and I cried,
"Turn in peace! No time for visit this, meseems. ">
So 'Adi went
But if it must be, and no help, admit Jarir.
forth and admitted Jarir, who entered saying:-
'Yea, He who sent Mohammed unto men | A just successor of
Islâm assigned.
His ruth and his justice all mankind embrace | To daunt the
bad and stablish well-designed.
Verily now, I look to present good, | for man hath ever tran-
sient weal in mind. '
Quoth Omar, "O Jarir! keep the fear of Allah before thine
eyes, and say naught save the sooth. " And Jarir recited these
Couplets:-
## p. 704 (#114) ############################################
704
DOMINIQUE FRANÇOIS ARAGO
'How many widows loose the hair, in far Yamamah land, |
How many an orphan there abides, feeble of voice and eye,
Since faredst thou, who wast to them instead of father lost |
when they like nestled fledglings were, sans power to creep
or fly.
And now we hope-since broke the clouds their word and
troth with us- -"| Hope from the Caliph's grace to gain a
rain that ne'er shall dry. '
When the Caliph heard this, he said, "By Allah, O Jarir:
Omar possesseth but an hundred dirhams. Ho boy! do thou
give them to him! " Moreover, he gifted Jarir with the orna-
ments of his sword; and Jarir went forth to the other poets,
who asked him, "What is behind thee? " [What is thy news? "]
and he answered, "A man who giveth to the poor, and who
denieth the poets; and with him I am well pleased. "
DOMINIQUE FRANÇOIS ARAGO
(1786-1853)
BY EDWARD S. HOLDEN
D
SOMINIQUE FRANÇOIS ARAGO was born February 26th, 1786, near
Perpignan, in the Eastern Pyrenees, where his father held
the position of Treasurer of the Mint. He entered the École
Polytechnique in Paris after a brilliant examination, and held the first
places throughout the course. In 1806 he was sent to Valencia in
Spain, and to the neighboring island of Iviza, to make the astronom-
ical observations for prolonging the arc of the meridian from Dunkirk
southward, in order to supply the basis for the metric system.
Here begin his extraordinary adventures, which are told with inim-
itable spirit and vigor in his 'Autobiography. ' Arago's work required
him to occupy stations on the summits of the highest peaks in the
mountains of southeastern Spain. The peasants were densely ignor-
ant and hostile to all foreigners, so that an escort of troops was
required in many of his journeys. At some stations he made friends
of the bandits of the neighborhood, and carried on his observations
under their protection, as it were. In 1807 the tribunal of the Inqui-
sition existed in Valencia; and Arago was witness to the trial and
punishment of a pretended sorceress,—and this, as he says, in one
of the principal towns of Spain, the seat of a celebrated university.
Yet the worst criminals lived unmolested in the cathedrals, for the
"right of asylum" was still in force. His geodetic observations were
## p. 705 (#115) ############################################
DOMINIQUE FRANÇOIS ARAGO
705
mysteries to the inhabitants, and his signals on the mountain top.
were believed to be part of the work of a French spy. Just at this
time hostilities broke out between France and Spain, and the astron-
omer was obliged to flee disguised as a Majorcan peasant, carrying
his precious papers with him. His knowledge of the Majorcan lan-
guage saved him, and he reached a Spanish prison with only a slight
wound from a dagger. It is the first recorded instance, he says, of a
fugitive flying to a dungeon for safety. In this prison, under the
care of Spanish officers, Arago found sufficient occupation in calculat-
ing observations which he had made; in reading the accounts in the
Spanish journals of his own execution at Valencia; and in listening.
to rumors that it was proposed (by a Spanish monk) to do away
with the French prisoner by poisoning his food.
The Spanish officer in charge of the prisoners was induced to con-
nive at the escape of Arago and M. Berthémie (an aide-de-camp of
Napoleon); and on the 28th of July, 1808, they stole away from the
coast of Spain in a small boat with three sailors, and arrived at Al-
giers on the 3d of August. Here the French consul procured them
two false passports, which transformed the Frenchmen into strolling
merchants from Schwekat and Leoben. They boarded an Algerian
vessel and set off. Let Arago describe the crew and cargo:-
"The vessel belonged to the Emir of Seca. The commander was a Greek
captain named Spiro Calligero. Among the passengers were five members of
the family superseded by the Bakri as kings of the Jews; two Maroccan
ostrich-feather merchants; Captain Krog from Bergen in Norway; two lions
sent by the Dey of Algiers as presents to the Emperor Napoleon; and a great
number of monkeys. "
As they entered the Golfe du Lion their ship was captured by a
Spanish corsair and taken to Rosas. Worst of all, a former Spanish
servant of Arago's - Pablo - was a sailor in the corsair's crew! At
Rosas the prisoners were brought before an officer for interrogation.
It was now Arago's turn. The officer begins:-
<<<Who are you? '
"A poor traveling merchant. '
«From whence do you come ? >
From a country where you certainly have never been. '
«‹Well — from what country? >
"I feared to answer; for the passports (steeped in vinegar to prevent
infection) were in the officer's hands, and I had entirely forgotten whether I
was from Schwekat or from Leoben. Finally I answered at a chance, 'I am
from Schwekat;' fortunately this answer agreed with the passport.
"You're from Schwekat about as much as I am,' said the officer: 'you're
a Spaniard, and a Spaniard from Valencia to boot, as I can tell by your
accent. >
11-45
## p. 706 (#116) ############################################
706
DOMINIQUE FRANÇOIS ARAGO
«Sir, you are inclined to punish me simply because I have by nature the
gift of languages. I readily learn the dialects of the various countries where
I carry on my trade. For example, I know the dialect of Iviza. '
<<<Well, I will take you at your word. Here is a soldier who comes from
Iviza. Talk to him. '
«Very well; I will even sing the goat-song. '
"The verses of this song (if one may call them verses) are separated by
the imitated bleatings of the goat. I began at once, with an audacity which
even now astonishes me, to intone the song which all the shepherds in Iviza
sing: -
Ah graciada Señora,
Una canzo bouil canta,
Bè bè bè bè.
No sera gaiva pulida,
Nosé si vos agradara,
Bè bè bè bè.
"Upon which my Ivizan avouches, in tears, that I am certainly from
Iviza. The song had affected him as a Switzer is affected by the Ranz des
Vaches. I then said to the officer that if he would bring to me a person
who could speak French, he would find the same embarrassment in this case
also. An emigré of the Bourbon regiment comes forward for the new experi-
ment, and after a few phrases affirms without hesitation that I am surely a
Frenchman. The officer begins to be impatient.
«Have done with these trials: they prove nothing. I require you to tell
me who you are. '
"My foremost desire is to find an answer which will satisfy you.
the son of the innkeeper at Mataro. '
"I know that man: you are not his son. '
«You are right: I told you that I should change my answers till I found
one to suit you. I am a marionette player from Lerida. '
"A huge laugh from the crowd which had listened to the interrogatory
put an end to the questioning. "
I am
Finally it was necessary for Arago to declare outright that he was
French, and to prove it by his old servant Pablo. To supply his
immediate wants he sold his watch; and by a series of misadventures
this watch subsequently fell into the hands of his family, and he was
mourned in France as dead.
After months of captivity the vessel was released, and the prisoner
set out for Marseilles. A fearful tempest drove them to the harbor
of Bougie, an African port a hundred miles east of Algiers. Thence
they made the perilous journey by land to their place of starting,
and finally reached Marseilles eleven months after their voyage
began. Eleven months to make a journey of four days!
The intelligence of the safe arrival, after so many perils, of the
young astronomer, with his packet of precious observations, soon
reached Paris. He was welcomed with effusion. Soon afterward (at
## p. 707 (#117) ############################################
DOMINIQUE FRANÇOIS ARAGO
707
the age of twenty-three years) he was elected a member of the sec-
tion of Astronomy of the Academy of Sciences, and from this time
forth he led the peaceful life of a savant. He was the Director of
the Paris Observatory for many years; the friend of all European
scientists; the ardent patron of young men of talent; a leading physi-
cist; a strong Republican, though the friend of Napoleon; and finally
the Perpetual Secretary of the Academy.
In the latter capacity it was part of his duty to prepare éloges of
deceased Academicians. Of his collected works in fourteen volumes,
'Euvres de François Arago,' published in Paris, 1865, three volumes
are given to these 'Notices Biographiques. ' Here may be found the
biographies of Bailly, Sir William Herschel, Laplace, Joseph Fourier,
Carnot, Malus, Fresnel, Thomas Young, and James Watt; which,
translated rather carelessly into English, have been published under
the title 'Biographies of Distinguished Men,' and can be found in the
larger libraries. The collected works contain biographies also of
Ampère, Condorcet, Volta, Monge, Porson, Gay-Lussac, besides shorter
sketches. They are masterpieces of style and of clear scientific expo-
sition, and full of generous appreciation of others' work. They pre-
sent in a lucid and popular form the achievements of scientific men
whose works have changed the accepted opinion of the world, and
they give general views not found in the original writings them-
selves. Scientific men are usually too much engrossed in advancing
science to spare time for expounding it to popular audiences. The
talent for such exposition is itself a special one. Arago possessed it
to the full, and his own original contributions to astronomy and phys-
ics enabled him to speak as an expert, not merely as an expositor.
The extracts are from his admirable estimate of Laplace, which
he prepared in connection with the proposal, before him and other
members of a State Committee, to publish a new and authoritative
edition of the great astronomer's works. The translation is mainly
that of the 'Biographies of Distinguished Men' cited above, and
much of the felicity of style is necessarily lost in translation; but the
substance of solid and lucid exposition from a master's hand remains.
Arago was a Deputy in 1830, and Minister of War in the Provis-
ional Government of 1848. He died full of honors, October 2d, 1853.
Two of his brothers, Jacques and Étienne, were dramatic authors of
Another, Jean, was a distinguished general in the service of
Mexico. One of his sons, Alfred, is favorably known as a painter;
another, Emmanuel, as a lawyer, deputy, and diplomat.
note.
Edward S. Holden
## p. 708 (#118) ############################################
708
DOMINIQUE FRANÇOIS ARAGO
LAPLACE
THE
HE Marquis de Laplace, peer of France, one of the forty of
the French Academy, member of the Academy of Sciences
and of the Bureau of Longitude, Associate of all the great
Academies or Scientific Societies of Europe, was born at Beau-
mont-en-Auge, of parents belonging to the class of small farmers,
on the 28th of March, 1749; he died on the 5th of March, 1827.
The first and second volumes of the 'Mécanique Céleste' [Mech-
anism of the Heavens] were published in 1799; the third volume
appeared in 1802, the fourth in 1805; part of the fifth volume
was published in 1823, further books in 1824, and the remainder
in 1825. The Théorie des Probabilités was published in 1812.
We shall now present the history of the principal astronomical
discoveries contained in these immortal works.
Astronomy is the science of which the human mind may justly
feel proudest. It owes this pre-eminence to the elevated nature
of its object; to the enormous scale of its operations; to the cer-
tainty, the utility, and the stupendousness of its results. From the
very beginnings of civilization the study of the heavenly bodies
and their movements has attracted the attention of governments
and peoples. The greatest captains, statesmen, philosophers, and
orators of Greece and Rome found it a subject of delight. Yet
astronomy worthy of the name is a modern science: it dates from
the sixteenth century only. Three great, three brilliant phases
have marked its progress. In 1543 the bold and firm hand of
Copernicus overthrew the greater part of the venerable scaffold-
ing which had propped the illusions and the pride of many gen-
erations. The earth ceased to be the centre, the pivot, of celestial
movements. Henceforward it ranged itself modestly among the
other planets, its relative importance as one member of the solar
system reduced almost to that of a grain of sand.
Twenty-eight years had elapsed from the day when the Canon
of Thorn expired while holding in his trembling hands the first
copy of the work which was to glorify the name of Poland, when
Würtemberg witnessed the birth of a man who was destined to
achieve a revolution in science not less fertile in consequences,
and still more difficult to accomplish. This man was Kepler.
Endowed with two qualities which seem incompatible,-a volcanic
imagination, and a dogged pertinacity which the most tedious
calculations could not tire,- Kepler conjectured that celestial
## p. 709 (#119) ############################################
DOMINIQUE FRANÇOIS ARAGO
709
movements must be connected with each other by simple laws;
or, to use his own expression, by harmonic laws. These laws
he undertook to discover. A thousand fruitless attempts — the
errors of calculation inseparable from a colossal undertaking-
did not hinder his resolute advance toward the goal his imagina-
tion descried. Twenty-two years he devoted to it, and still he
was not weary. What are twenty-two years of labor to him who
is about to become the lawgiver of worlds; whose name is to be
ineffaceably inscribed on the frontispiece of an immortal code;
who can exclaim in dithyrambic language, "The die is cast: I
have written my book; it will be read either in the present age
or by posterity, it matters not which; it may well await a reader
since God has waited six thousand years for an interpreter of his
works"?
These celebrated laws, known in astronomy as Kepler's laws,
are three in number. The first law is, that the planets describe
ellipses around the sun, which is placed in their common focus;
the second, that a line joining a planet and the sun sweeps over
equal areas in equal times; the third, that the squares of the
times of revolution of the planets about the sun are proportional
to the cubes of their mean distances from that body. The first
two laws were discovered by Kepler in the course of a laborious
examination of the theory of the planet Mars. A full account of
this inquiry is contained in his famous work, 'De Stella Martis'
[Of the Planet Mars], published in 1609. The discovery of the
third law was announced to the world in his treatise on Har-
monics (1628).
To seek a physical cause adequate to retain the planets in
their closed orbits; to make the stability of the universe depend
on mechanical forces, and not on solid supports like the crys-
talline spheres imagined by our ancestors; to extend to the
heavenly bodies in their courses the laws of earthly mechan-
ics, such were the problems which remained for solution after
Kepler's discoveries had been announced. Traces of these great
problems may be clearly perceived here and there among ancient
and modern writers, from Lucretius and Plutarch down to Kep-
ler, Bouillaud, and Borelli. It is to Newton, however, that we
must award the merit of their solution. This great man, like
several of his predecessors, imagined the celestial bodies to have
a, tendency to approach each other in virtue of some attractive
force, and from the laws of Kepler he deduced the mathematical
――
## p. 710 (#120) ############################################
710
DOMINIQUE FRANÇOIS ARAGO
characteristics of this force. He extended it to all the material
molecules of the solar system; and developed his brilliant dis-
covery in a work which, even at the present day, is regarded as
the supremest product of the human intellect.
The contributions of France to these revolutions in astronom-
ical science consisted, in 1740, in the determination by experi
ment of the spheroidal figure of the earth, and in the discovery
of the local variations of gravity upon the surface of our planet.
These were two great results; but whenever France is not first
in science she has lost her place. This rank, lost for a moment,
was brilliantly regained by the labors of four geometers. When
Newton, giving to his discoveries a generality which the laws of
Kepler did not suggest, imagined that the different planets were
not only attracted by the sun, but that they also attracted each
other, he introduced into the heavens a cause of universal per-
turbation. Astronomers then saw at a glance that in no part of
the universe would the Keplerian laws suffice for the exact repre-
sentation of the phenomena of motion; that the simple regular
movements with which the imaginations of the ancients were
pleased to endow the heavenly bodies must experience numerous,
considerable, perpetually changing perturbations. To discover a
few of these perturbations, and to assign their nature and in
a few rare cases their numerical value, was the object which
Newton proposed to himself in writing his famous book, the
'Principia Mathematica Philosophiæ Naturalis' [Mathematical Prin-
ciples of Natural Philosophy]. Notwithstanding the incomparable
sagacity of its author, the 'Principia' contained merely a rough
outline of planetary perturbations, though not through any lack
of ardor or perseverance.
The efforts of the great philosopher
were always superhuman, and the questions which he did not.
solve were simply incapable of solution in his time.
Five geometers-Clairaut, Euler, D'Alembert, Lagrange, and
Laplace shared between them the world whose existence New-
ton had disclosed. They explored it in all directions, penetrated
into regions hitherto inaccessible, and pointed out phenomena
hitherto undetected. Finally and it is this which constitutes
their imperishable glory-they brought under the domain of a
single principle, a single law, everything that seemed most occult
and mysterious in the celestial movements. Geometry had thus
the hardihood to dispose of the future, while the centuries as
they unroll scrupulously ratify the decisions of science.
- -
## p.
711 (#121) ############################################
DOMINIQUE FRANÇOIS ARAGO
711
If Newton gave a complete solution of celestial movements
where but two bodies attract each other, he did not even attempt
the infinitely more difficult problem of three. The "problem of
three bodies (this is the name by which it has become cele-
brated) the problem of determining the movement of a body
subjected to the attractive influence of two others- was solved
for the first time by our countryman, Clairaut. Though he enu-
merated the various forces which must result from the mutual
action of the planets and satellites of our system, even the great
Newton did not venture to investigate the general nature of
their effects. In the midst of the labyrinth formed by incre-
ments and diminutions of velocity, variations in the forms of
orbits, changes in distances and inclinations, which these forces
must evidently produce, the most learned geometer would fail to
discover a trustworthy guide. Forces so numerous, so variable in
direction, so different in intensity, seemed to be incapable of
maintaining a condition of equilibrium except by a sort of mir-
acle. Newton even suggested that the planetary system did not
contain within itself the elements of indefinite stability. He
was of opinion that a powerful hand must intervene from time
to time to repair the derangements occasioned by the mutual
action of the various bodies. Euler, better instructed than New-
ton in a knowledge of these perturbations, also refused to admit
that the solar system was constituted so as to endure forever.
Never did a greater philosophical question offer itself to the
inquiries of mankind. Laplace attacked it with boldness, persever-
ance, and success. The profound and long-continued researches
of the illustrious geometer completely established the perpetual
variability of the planetary ellipses. He demonstrated that the
extremities of their major axes make the circuit of the heavens;
that independent of oscillation, the planes of their orbits undergo
displacements by which their intersections with the plane of the
terrestrial orbit are each year directed toward different stars.
But in the midst of this apparant chaos, there is one element
which remains constant, or is merely subject to small and peri-
odic changes; namely, the major axis of each orbit, and conse-
quently the time of revolution of each planet. This is the element
which ought to have varied most, on the principles held by New-
ton and Euler. Gravitation, then, suffices to preserve the stability
of the solar system. It maintains the forms and inclinations of
the orbits in an average position, subject to slight oscillations
________________
>>>>
## p. 712 (#122) ############################################
712
DOMINIQUE FRANÇOIS ARAGO
only; variety does not entail disorder; the universe offers an
example of harmonious relations, of a state of perfection which
Newton himself doubted.
This condition of harmony depends on circumstances disclosed
to Laplace by analysis; circumstances which on the surface do
not seem capable of exercising so great an influence. If instead
of planets all revolving in the same direction, in orbits but
slightly eccentric and in planes inclined at but small angles toward
each other, we should substitute different conditions, the stability
of the universe would be jeopardized, and a frightful chaos would
pretty certainly result. The discovery of the actual conditions.
excluded the idea, at least so far as the solar system was con-
cerned, that the Newtonian attraction might be a cause of dis-
order. But might not other forces, combined with the attraction
of gravitation, produce gradually increasing perturbations such as
Newton and Euler feared? Known facts seemed to justify the
apprehension. A comparison of ancient with modern observations
revealed a continual acceleration in the mean motions of the
moon and of Jupiter, and an equally striking diminution of the
mean motion of Saturn. These variations led to a very import-
ant conclusion. In accordance with their presumed cause, to say
that the velocity of a body increased from century to century
was equivalent to asserting that the body continually approached
the centre of motion; on the other hand, when the velocity.
diminished, the body must be receding from the centre. Thus,
by a strange ordering of nature, our planetary system seemed
destined to lose Saturn, its most mysterious ornament; to see the
planet with its ring and seven satellites plunge gradually into
those unknown regions where the eye armed with the most pow-
erful telescope has never penetrated. Jupiter, on the other hand,
the planet compared with which the earth is so insignificant,
appeared to be moving in the opposite direction, so that it would.
ultimately be absorbed into the incandescent matter of the sun.
Finally, it seemed that the moon would one day precipitate itself
upon the earth.
There was nothing doubtful or speculative in these sinister
forebodings. The precise dates of the approaching catastrophes
were alone uncertain. It was known, however, that they were
very distant.
Accordingly, neither the learned dissertations of
men of science nor the animated descriptions of certain poets
produced any impression upon the public mind. . The members
## p. 713 (#123) ############################################
DOMINIQUE FRANÇOIS ARAGO
713
of our scientific societies, however, believed with regret the
approaching destruction of the planetary system. The Academy
of Sciences called the attention of geometers of all countries to
these menacing perturbations. Euler and Lagrange descended
into the arena. Never did their mathematical genius shine with
a brighter lustre. Still the question remained undecided, when
from two obscure corners of the theories of analysis, Laplace,
the author of the 'Mécanique Céleste,' brought the laws of these
great phenomena clearly to light. The variations in velocity of
Jupiter, Saturn, and the moon, were proved to flow from evi-
dent physical causes, and to belong in the category of ordinary
periodic perturbations depending solely on gravitation. These
dreaded variations in orbital dimensions resolved themselves
into simple oscillations included within narrow limits. In a word,
by the powerful instrumentality of mathematical analysis, the
physical universe was again established on a demonstrably firm
foundation.
Having demonstrated the smallness of these periodic oscilla-
tions, Laplace next succeeded in determining the absolute dimen-
sions of the orbits. What is the distance of the sun from the
earth? No scientific question has occupied the attention of man-
kind in a greater degree. Mathematically speaking, nothing is
more simple: it suffices, as in ordinary surveying, to draw visual
lines from the two extremities of a known base line to an inac-
cessible object; the remainder of the process is an elementary
calculation. Unfortunately, in the case of the sun, the distance
is very great and the base lines which can be measured upon
the earth are comparatively very small. In such a case, the
slightest errors in the direction of visual lines exercise an enor-
mous influence upon the results. In the beginning of the last
century, Halley had remarked that certain interpositions of Venus
between the earth and the sun -or to use the common term, the
transits of the planet across the sun's disk—would furnish at each
observing station an indirect means of fixing the position of the
visual ray much superior in accuracy to the most perfect direct
measures. Such was the object of the many scientific expeditions
undertaken in 1761 and 1769, years in which the transits of
Venus occurred. A comparison of observations made in the
Southern Hemisphere with those of Europe gave for the distance
of the sun the result which has since figured in all treatises on
astronomy and navigation. No government hesitated to furnish
## p. 714 (#124) ############################################
714
DOMINIQUE FRANÇOIS ARAGO
scientific academies with the means, however expensive, of estab-
lishing their observers in the most distant regions. We have
already remarked that this determination seemed imperiously to
demand an extensive base, for small bases would have been
totally inadequate. Well, Laplace has solved the problem with-
out a base of any kind whatever; he has deduced the distance of
the sun from observations of the moon made in one and the
same place.
The sun is, with respect to our satellite the moon, the cause
of perturbations which evidently depend on the distance of the
immense luminous globe from the earth. Who does not see that
these perturbations must diminish if the distance increases, and
increase if the distance diminishes, so that the distance determines
the amount of the perturbations? Observation assigns the nu-
merical value of these perturbations; theory, on the other hand,
unfolds the general mathematical relation which connects them with
the solar distance and with other known elements. The deter-
mination of the mean radius of the terrestrial orbit· of the dis-
tance of the sun-then becomes one of the most simple operations
of algebra. Such is the happy combination by the aid of which
Laplace has solved the great, the celebrated problem of parallax.
It is thus that the illustrious geometer found for the mean
distance of the sun from the earth, expressed in radii of the ter-
restrial orbit, a value differing but slightly from that which was
the fruit of so many troublesome and expensive voyages.
The movements of the moon proved a fertile mine of research
to our great geometer. His penetrating intellect discovered in
them unknown treasures. With an ability and a perseverance
equally worthy of admiration, he separated these treasures from
the coverings which had hitherto concealed them from vulgar
eyes. For example, the earth governs the movements of the
moon. The earth is flattened; in other words, its figure is
spheroidal. A spheroidal body does not attract as does a sphere.
There should then exist in the movement - I had almost said in
the countenance-of the moon a sort of impress of the spheroidal
figure of the earth. Such was the idea as it originally occurred
to Laplace. By means of a minutely careful investigation, he
discovered in its motion two well-defined perturbations, each
depending on the spheroidal figure of the earth. When these
were submitted to calculation, each led to the same value of the
ellipticity. It must be recollected that the ellipticity thus derived
## p. 715 (#125) ############################################
DOMINIQUE FRANÇOIS ARAGO
715
from the motions of the moon is not the one corresponding to
such or such a country, to the ellipticity observed in France, in
England, in Italy, in Lapland, in North America, in India, or in
the region of the Cape of Good Hope; for, the earth's crust
having undergone considerable upheavals at different times and
places, the primitive regularity of its curvature has been sensibly
disturbed thereby. The moon (and it is this which renders the
result of such inestimable value) ought to assign, and has in
reality assigned, the general ellipticity of the earth; in other
words, it has indicated a sort of average value of the various
determinations obtained at enormous expense, and with infinite
labor, as the result of long voyages undertaken by astronomers
of all the countries of Europe.
Certain remarks of Laplace himself bring into strong relief
the profound, the unexpected, the almost paradoxical character
of the methods I have attempted to sketch. What are the ele-
ments it has been found necessary to confront with each other
in order to arrive at results expressed with such extreme
precision? On the one hand, mathematical formulæ deduced
from the principle of universal gravitation; on the other, cer-
tain irregularities observed in the returns of the moon to the
meridian. An observing geometer, who from his infancy had
never quitted his study, and who had never viewed the heavens
except through a narrow aperture directed north and south, — to
whom nothing had ever been revealed respecting the bodies
revolving above his head, except that they attract each other
according to the Newtonian law of gravitation,- would still per-
ceive that his narrow abode was situated upon the surface of a
spheroidal body, whose equatorial axis was greater than its polar
by a three hundred and sixth part. In his isolated, fixed position
he could still deduce his true distance from the sun!
-
Laplace's improvement of the lunar tables not only promoted
maritime intercourse between distant countries, but preserved the
lives of mariners. Thanks to an unparalleled sagacity, to a limit-
less perseverance, to an ever youthful and communicable ardor,
Laplace solved the celebrated problem of the longitude with a
precision even greater than the utmost needs of the art of navi-
gation demanded. The ship, the sport of the winds and tem-
pests, no longer fears to lose its way in the immensity of the
ocean. In every place and at every time the pilot reads in the
starry heavens his distance from the meridian of Paris. The
## p. 716 (#126) ############################################
716
DOMINIQUE FRANÇOIS ARAGO
extreme perfection of these tables of the moon places Laplace in
the ranks of the world's benefactors.
In the beginning of the year 1611, Galileo supposed that he
found in the eclipses of Jupiter's satellites a simple and rigorous
solution of the famous problem of the longitude, and attempts
to introduce the new method on board the numerous vessels of
Spain and Holland at once began. They failed because the neces-
sary observations required powerful telescopes, which could not
be employed on a tossing ship. Even the expectations of the
serviceability of Galileo's methods for land calculations proved
premature. The movements of the satellites of Jupiter are far
less simple than the immortal Italian supposed them to be. The
labors of three more generations of astronomers and mathema-
ticians were needed to determine them, and the mathematical
genius of Laplace was needed to complete their labors. At the
present day the nautical ephemerides contain, several years in
advance, the indications of the times of the eclipses and reap-
pearances of Jupiter's satellites. Calculation is as precise as
direct observation.
Influenced by an exaggerated deference, modesty, timidity,
France in the eighteenth century surrendered to England the
exclusive privilege of constructing her astronomical instruments.
Thus, when Herschel was prosecuting his beautiful observations
on the other side of the Channel, we had not even the means of
verifying them. Fortunately for the scientific honor of our
country, mathematical analysis also is a powerful instrument.
The great Laplace, from the retirement of his study, foresaw,
and accurately predicted in advance, what the excellent astrono-
mer of Windsor would soon behold with the largest telescopes
existing. When, in 1610, Galileo directed toward Saturn a lens
of very low power which he had just constructed with his own
hands, although he perceived that the planet was not a globe,
he could not ascertain its real form. The expression "tri-
corporate," by which the illustrious Florentine designated the
appearance of the planet, even implied a totally erroneous ideal
of its structure. At the present day every one knows that
Saturn consists of a globe about nine hundred times greater than
the earth, and of a ring. This ring does not touch the ball of
the planet, being everywhere removed from it to a distance.
of twenty thousand (English) miles. Observation indicates the
breadth of the ring to be fifty-four thousand miles. The thickness
## p. 717 (#127) ############################################
DOMINIQUE FRANÇOIS ARAGO
717
certainly does not exceed two hundred and fifty miles. With the
exception of a black streak which divides the ring throughout its
whole contour into two parts of unequal breadth and of different
brightness, this strange colossal bridge without foundations had
never offered to the most experienced or skillful observers either
spot or protuberance adapted for deciding whether it was immov-
able or endowed with a motion of rotation. Laplace considered.
it to be very improbable, if the ring was stationary, that its con-
stituent parts should be capable of resisting by mere cohesion
the continual attraction of the planet. A movement of rotation
occurred to his mind as constituting the principle of stability,
and he deduced the necessary velocity from this consideration.
The velocity thus found was exactly equal to that which Herschel
subsequently derived from a series of extremely delicate observa-
tions. The two parts of the ring, being at different distances
from the planet, could not fail to be given different movements
of precession by the action of the sun. Hence it would seem that
the planes of both rings ought in general to be inclined toward
each other, whereas they appear from observation always to
coincide. It was necessary then that some physical cause capable
of neutralizing the action of the sun should exist. In a memoir
published in February, 1789, Laplace found that this cause
depended on the ellipticity of Saturn produced by a rapid move-
ment of rotation of the planet, a movement whose discovery
Herschel announced in November of the same year.
If we descend from the heavens to the earth, the discoveries
of Laplace will appear not less worthy of his genius. He reduced.
the phenomena of the tides, which an ancient philosopher termed
in despair "the tomb of human curiosity," to an analytical theory
in which the physical conditions of the question figure for the
first time. Consequently, to the immense advantage of coast nav-
igation, calculators now venture to predict in detail the time and
height of the tides several years in advance. Between the phe-
nomena of the ebb and flow, and the attractive forces of the sun
and moon upon the fluid sheet which covers three fourths of the
globe, an intimate and necessary connection exists; a connection
from which Laplace deduced the value of the mass of our satellite
the moon.
Yet so late as the year 1631 the illustrious Galileo,
as appears from his 'Dialogues,' was so far from perceiving
the mathematical relations from which Laplace deduced results
so beautiful, so unequivocal, and so useful, that he taxed with
F
## p. 718 (#128) ############################################
718
DOMINIQUE FRANÇOIS ARAGO
frivolousness the vague idea which Kepler entertained of attribut-
ing to the moon's attraction a certain share in the production of
the diurnal and periodical movements of the waters of the ocean.
Laplace did not confine his genius to the extension and im-
provement of the mathematical theory of the tide. He considered
the phenomenon from an entirely new point of view, and it was
he who first treated of the stability of the ocean. He has estab-
lished its equilibrium, but upon the express condition (which,
however, has been amply proved to exist) that the mean density
of the fluid mass is less than the mean density of the earth.
Everything else remaining the same, if we substituted an ocean.
of quicksilver for the actual ocean, this stability would disappear.
The fluid would frequently overflow its boundaries, to ravage con-
tinents even to the height of the snowy peaks which lose them-
selves in the clouds.
No one was more sagacious than Laplace in discovering inti-
mate relations between phenomena apparently unrelated, or more
skillful in deducing important conclusions from such unexpected
affinities. For example, toward the close of his days, with the
aid of certain lunar observations, with a stroke of his pen he
overthrew the cosmogonic theories of Buffon and Bailly, which
were so long in favor. According to these theories, the earth
was hastening to a state of congelation which was close at hand.
Laplace, never contented with vague statements, sought to deter-
mine in numbers the rate of the rapid cooling of our globe which
Buffon had so eloquently but so gratuitously announced. Noth-
ing could be more simple, better connected, or more conclusive
than the chain of deductions of the celebrated geometer. A body
diminishes in volume when it cools. According to the most ele-
mentary principles of mechanics, a rotating body which contracts
in dimensions must inevitably turn upon its axis with greater and
greater rapidity. The length of the day has been determined in
all ages by the time of the earth's rotation; if the earth is cool-
ing, the length of the day must be continually shortening. Now,
there exists a means of ascertaining whether the length of the
day has undergone any variation; this consists in examining, for
each century, the arc of the celestial sphere described by the
moon during the interval of time which the astronomers of the
existing epoch call a day; in other words, the time required by
the earth to effect a complete rotation on its axis, the velocity of
the moon being in fact independent of the time of the earth's
## p. 719 (#129) ############################################
DOMINIQUE FRANÇOIS ARAGO
719
rotation. Let us now, following Laplace, take from the standard
tables the smallest values, if you choose, of the expansions or
contractions which solid bodies experience from changes of tem-
perature; let us search the annals of Grecian, Arabian, and mod-
ern astronomy for the purpose of finding in them the angular
velocity of the moon: and the great geometer will prove, by
incontrovertible evidence founded upon these data, that during a
period of two thousand years the mean temperature of the earth
has not varied to the extent of the hundredth part of a degree
of the centigrade thermometer. Eloquence cannot resist such
a process of reasoning, or withstand the force of such figures.
Mathematics has ever been the implacable foe of scientific ro-
mances. The constant object of Laplace was the explanation of
the great phenomena of nature according to inflexible principles
of mathematical analysis. No philosopher, no mathematician,
could have guarded himself more cautiously against a propensity
to hasty speculation. No person dreaded more the scientific
errors which cajole the imagination when it passes the boundary
of fact, calculation, and analogy.
Once, and once only, did Laplace launch forward, like Kepler,
like Descartes, like Leibnitz, like Buffon, into the region of con-
jectures. But then his conception was nothing less than a com-
plete cosmogony. All the planets revolve around the sun, from
west to east, and in planes only slightly inclined to each other.
The satellites revolve around their respective primaries in the
same direction. Both planets and satellites, having a rotary mo-
tion, turn also upon their axes from west to east. Finally, the
rotation of the sun also is directed from west to east. Here,
then, is an assemblage of forty-three movements, all operating
alike. By the calculus of probabilities, the odds are four thou-
sand millions to one that this coincidence in direction is not the
effect of accident.
It was Buffon, I think, who first attempted to explain this
singular feature of our solar system. "Wishing, in the explana-
tion of phenomena, to avoid recourse to causes which are not to
be found in nature," the celebrated academician sought for a
physical cause for what is common to the movements of so
many bodies differing as they do in magnitude, in form, and in
their distances from the centre of attraction. He imagined that
he had discovered such a physical cause by making this triple
supposition: a comet fell obliquely upon the sun; it pushed
## p. 720 (#130) ############################################
720
DOMINIQUE FRANÇOIS ARAGO
before it a torrent of fluid matter; this substance, transported to
a greater or less distance from the sun according to its density,
formed by condensation all the known planets. The bold hy-
pothesis is subject to insurmountable difficulties. I proceed to
indicate, in a few words, the cosmogonic system which Laplace
substituted for it.
According to Laplace, the sun was, at a remote epoch, the
central nucleus of an immense nebula, which possessed a very
high temperature, and extended far beyond the region in which
Uranus now revolves. No planet was then in existence. The
solar nebula was endowed with a general movement of rotation
in the direction west to east. As it cooled it could not fail to
experience a gradual condensation, and in consequence to rotate
with greater and greater rapidity. If the nebulous matter ex-
tended originally in the plane of its equator, as far as the limit
where the centrifugal force exactly counterbalanced the attraction
of the nucleus, the molecules situate at this limit ought, during
the process of condensation, to separate from the rest of the
atmospheric matter and to form an equatorial zone, a ring,
revolving separately and with its primitive velocity.
We may
conceive that analogous separations were effected in the remoter
strata of the nebula at different epochs and at different distances
from the nucleus, and that they gave rise to a succession of dis-
tinct rings, all lying in nearly the same plane, and all endowed
with different velocities.
This being once admitted, it is easy to see that the perma-
nent stability of the rings would have required a regularity of
structure throughout their whole contour, which is very improb-
able. Each of them, accordingly, broke in its turn into several
masses, which were obviously endowed with a movement of rota-
tion coinciding in direction with the common movement of revo-
lution, and which, in consequence of their fluidity, assumed
spheroidal forms. In order, next, that one of those spheroids
may absorb all the others belonging to the same ring, it is suffi-
cient to suppose it to have a mass greater than that of any
other spheroid of its group.
Each of the planets, while in this vaporous condition to which
we have just alluded, would manifestly have a central nucleus,
gradually increasing in magnitude and mass, and an atmosphere
offering, at its successive limits, phenomena entirely similar to
those which the solar atmosphere, properly so called, had exhib-
## p. 721 (#131) ############################################
DOMINIQUE FRANÇOIS ARAGO
721
ited. We are here contemplating the birth of satellites and the
birth of the ring of Saturn.
The Nebular Hypothesis, of which I have just given an imper-
fect sketch, has for its object to show how a nebula endowed with
a general movement of rotation must eventually transform itself
into a very luminous central nucleus (a sun), and into a series of
distinct spheroidal planets, situate at considerable distances from
one another, all revolving around the central sun, in the direction
of the original movement of the nebula; how these planets ought
also to have movements of rotation in similar directions; how,
finally, the satellites, when any such are formed, must revolve
upon their axes and around their respective primaries, in the
direction of rotation of the planets and of their movement of
revolution around the sun.
In all that precedes, attention has been concentrated upon the
'Mécanique Céleste. ' The 'Système du Monde' and the 'Théorie
Analytique des Probabilités' also deserve description.
The Exposition of the System of the World is the 'Mécanique
Céleste' divested of that great apparatus of analytical formulæ
which must be attentively perused by every astronomer who, to
use an expression of Plato, wishes to know the numbers which
govern the physical universe. It is from this work that persons
ignorant of mathematics may obtain competent knowledge of the
methods to which physical astronomy owes its astonishing progress.
Written with a noble simplicity of style, an exquisite exactness of
expression, and a scrupulous accuracy, it is universally conceded
to stand among the noblest monuments of French literature.
The labors of all ages to persuade truth from the heavens
are there justly, clearly, and profoundly analyzed.
Genius pre-
sides as the impartial judge of genius. Throughout his work.
Laplace remained at the height of his great mission. It will be
read with respect so long as the torch of science illuminates the
world.
The calculus of probabilities, when confined within just limits,
concerns the mathematician, the experimenter, and the statesman.
From the time when Pascal and Fermat established its first prin-
ciples, it has rendered most important daily services. This it is
which, after suggesting the best form for statistical tables of pop-
ulation and mortality, teaches us to deduce from those numbers,
so often misinterpreted, the most precise and useful conclusions.
This it is which alone regulates with equity insurance premiums,
II-46
## p. 722 (#132) ############################################
722
JOHN ARBUTHNOT
pension funds, annuities, discounts, etc. This it is that has grad-
ually suppressed lotteries, and other shameful snares cunningly
laid for avarice and ignorance. Laplace has treated these ques-
tions with his accustomed superiority: the Analytical Theory of
Probabilities' is worthy of the author of the 'Mécanique Céleste. '
A philosopher whose name is associated with immortal discov-
eries said to his too conservative audience, "Bear in mind, gentle-
men, that in questions of science the authority of a thousand is
not worth the humble reasoning of a single individual. " Two
centuries have passed over these words of Galileo without lessen-
ing their value or impugning their truth. For this reason, it has
been thought better rather to glance briefly at the work of La-
place than to repeat the eulogies of his admirers.
JOHN ARBUTHNOT
(1667-1735)
RBUTHNOT'S place in literature depends as much on his asso-
ciation with the wits of his day as on his own satirical and
humorous productions. Many of these have been published
in the collections of Swift, Gay, Pope, and others, and cannot be
identified. The task of verifying them is rendered more difficult
by the fact that his son repudiated a collection claiming to be his
'Miscellaneous Works,' published in 1750.
John Arbuthnot was born in the manse near Arbuthnot Castle,
Kincardineshire, Scotland, April 29th, 1667. He was the son of a
Scotch Episcopal clergyman, who was soon
to be dispossessed of his parish by the
Presbyterians in the Revolution of 1688.
His children, who shared his Jacobite sen-
timents, were forced to leave Scotland; and
John, after finishing his university course
at Aberdeen, and taking his medical de-
gree at St. Andrews, went to London and
taught mathematics. He soon attracted
attention by a keen and satirical Exam-
ination of Dr. Woodward's Account of the
Deluge,' published in 1697.
