No More Learning

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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


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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. By a fortunate
chance he was called to attend the Prince
Consort (Prince George of Denmark), and
in 1705 was made Physician Extraordinary
JOHN ARBUTHNOT
to Queen Anne. If we may believe Swift, the agreeable Scotchman



## p. 723 (#133) ############################################

JOHN ARBUTHNOT
723
at once became her favorite attendant. His position at court was
strengthened by his friendships with the great Tory statesmen.
Arbuthnot's best remembered work is 'The History of John Bull';
not because many people read or will ever read the book itself, but
because it fixed a typical name and a typical character ineffaceably
in the popular fancy and memory. He is credited with having been
the first to use this famous sobriquet for the English nation; he
was certainly the first to make it universal, and the first to make
that burly, choleric, gross-feeding, hard-drinking, blunt-spoken, rather
stupid and decidedly gullible, but honest and straightforward charac-
ter one of the stock types of the world. The book appeared as four
separate pamplets: the first being entitled 'Law is a Bottomless Pit,
Exemplified in the Case of Lord Strutt, John Bull, Nicholas Frog,
and Lewis Baboon, Who Spent All They Had in a Law Suit'; the
second, John Bull in His Senses'; the third, John Bull Still in
His Senses'; and the fourth, Lewis Baboon Turned Honest, and
John Bull Politician. ' Published in 1712, these were at once attrib-
uted to Swift. But Pope says, "Dr. Arbuthnot was the sole writer
of 'John Bull'"; and Swift gives us still more conclusive evidence
by writing, "I hope you read 'John Bull. ' It was a Scotch gentle-
man, a friend of mine, that writ it; but they put it on to me. "
his humorous preface Dr. Arbuthnot says:—
In
"When I was first called to the office of historiographer to John Bull, he
expressed himself to this purpose:- Sir Humphrey Polesworth, I know you
are a plain dealer; it is for that reason I have chosen you for this important
trust; speak the truth, and spare not. ' That I might fulfill those, his honor-
able intentions, I obtained leave to repair to and attend him in his most
secret retirements; and I put the journals of all transactions into a strong
box to be opened at a fitting occasion, after the manner of the histori-
ographers of some Eastern monarchs.
And now, that posterity may
not be ignorant in what age so excellent a history was written (which would
otherwise, no doubt, be the subject of its inquiries), I think it proper to
inform the learned of future times that it was compiled when Louis XIV.
was King of France, and Philip, his grandson, of Spain; when England and
Holland, in conjunction with the Emperor and the allies, entered into a war
against these two princes, which lasted ten years, under the management of
the Duke of Marlborough, and was put to a conclusion by the treaty of
Utrecht under the ministry of the Earl of Oxford, in the year 1713. "
The characters disguised are: "John Bull," the English; "Nicholas
Frog," the Dutch; "Lewis Baboon," the French king; "Lord Strutt,"
the late King of Spain; "Philip Baboon," the Duke of Anjou;
"Esquire South," the King of Spain; "Humphrey Hocus," the Duke
of Marlborough; and "Sir Roger Bold," the Earl of Oxford. The
lawsuit was the War of the Spanish Succession; John Bull's first wife


## p. 724 (#134) ############################################

724
JOHN ARBUTHNOT
was the late ministry; and his second wife the Tory ministry. To
explain the allegory further, John Bull's mother was the Church of
England; his sister Peg, the Scotch nation; and her lover Jack, Pres-
byterianism.
That so witty a work, so strong in typical freehand character-
drawing of permanent validity and remembrance, should be unread.
and its author forgotten except by scholars, is too curious a fact not
to have a deep cause in its own character. The cause is not hard to
find: it is one of the books which try to turn the world's current
backward, and which the world dislikes as offending its ideals of
progress. Stripped of its broad humor, its object, rubbed in with no
great delicacy of touch, was to uphold the most extreme and reac-
tionary Toryism of the time, and to jeer at political liberalism from
the ground up. Its theoretic loyalty is the non-resistant Jacobitism
of the Nonjurors, which it is so hard for us now to distinguish from
abject slavishness; though like the principles of the casuists, one
must not confound theory with practice. It seems the loyalty of a
mujik or a Fiji dressed in cultivated modern clothes, not that of a
conceivable cultivated modern community as a whole; but it would
be very Philistine to pour wholesale contempt on a creed held by
so many large minds and souls. It was of course produced by the
experience of what the reverse tenets had brought on, -a long civil
war, years of military despotism, and immense social and moral dis-
organization. In 'John Bull,' the fidelity of a subject to a king is
made exactly correspondent, both in theory and practice, with the
fidelity of a wife to her husband and her marriage vows; and an
elaborate parallel is worked out to show that advocating the right of
resistance to a bad king is precisely the same, on grounds of either
logic or Scripture, as advocating the right of adultery toward a bad
husband. This is not even good fooling; and, its local use past and
no longer buoyed by personal liking for the author, the book sinks
back into the limbo of partisan polemics with many worse ones and
perhaps some better ones, dragging its real excellences down with it.
In 1714 the famous Scriblerus Club was organized, having for its
members Pope, Swift, Arbuthnot, Gay, Congreve, Lord Oxford, and
Bishop Atterbury. They agreed to write a series of papers ridiculing,
in the words of Pope, "all the false tastes in learning, under the
character of a man of capacity enough, but that had dipped into
every art and science, but injudiciously in each. " The chronicle of
this club was found in 'The Memoirs of the Extraordinary Life,
Works, and Discoveries of Martinus Scriblerus,' which is thought to
have been written entirely by Arbuthnot, and which describes the
education of a learned pedant's son. Its humor may be appreciated
by means of the citation given below. The first book of Scriblerus'


## p. 725 (#135) ############################################

JOHN ARBUTHNOT
725
appeared six years after Arbuthnot's death, when it was included in
the second volume of Alexander Pope's works (1741). Pope said that
from the 'Memoirs of Scriblerus' Swift took his idea of 'Gulliver';
and the Dean himself writes to Arbuthnot, July 3d, 1714:-
-
"To talk of Martin' in any hands but Yours is a Folly.
You every day
give better hints than all of us together could do in a twelvemonth.
And to
say the truth, Pope, who first thought of the Hint, has no Genius at all to it,
in my mind; Gay is too young; Parnell has some ideas of it, but is idle; I
could put together, and lard, and strike out well enough, but all that relates
to the Sciences must be from you. "
Swift's opinion that Arbuthnot "has more wit than we all have, and
his humanity is equal to his wit," seems to have been the universal
dictum; and Pope honored him by publishing a dialogue in the 'Pro-
logue to the Satires,' known first as 'The Epistle to Dr. Arbuthnot,'
which contains many affectionate personal allusions. Aitken says, in
his biography:-
"Arbuthnot's attachment to Swift and Pope was of the most intimate
nature, and those who knew them best maintained that he was their equal at
least in gifts. He understood Swift's cynicism, and their correspondence
shows the unequaled sympathy that existed between the two. Gay, Con-
greve, Berkeley, Parnell, were among Arbuthnot's constant friends, and all
of them were indebted to him for kindnesses freely rendered. He was on
terms of intimacy with Bolingbroke and Oxford, Chesterfield, Peterborough,
and Pulteney; and among the ladies with whom he mixed were Lady Mary
Wortley Montagu, Lady Betty Germain, Mrs. Howard, Lady Masham, and
Mrs. Martha Blount. He was, too, the trusted friend and physician of Queen
Anne. Most of the eminent men of science of the time, including some who
were opposed to him in politics, were in frequent intercourse with him; and
it is pleasant to know that at least one of the greatest of the wits who were
most closely allied to the Whig party-Addison - had friendly relations with
him. »
―――
From the letters of Lord Chesterfield we learn that
"His imagination was almost inexhaustible, and whatever subject he
treated, or was consulted upon, he immediately overflowed with all that it
could possibly produce. It was at anybody's service, for as soon as he was
exonerated he did not care what became of it; insomuch that his sons, when
young, have frequently made kites of his scattered papers of hints, which
would have furnished good matter for folios. Not being in the least jealous
of his fame as an author, he would neither take the time nor the trouble of
separating the best from the worst; he worked out the whole mine, which
afterward, in the hands of skillful refiners, produced a rich vein of ore. As
his imagination was always at work, he was frequently absent and inattentive
in company, which made him both say and do a thousand inoffensive absurd-
ities; but which, far from being provoking, as they commonly are, supplied
new matter for conversation, and occasioned wit both in himself and others. »


## p. 726 (#136) ############################################

726
JOHN ARBUTHNOT
Speaking to Boswell of the writers of Queen Anne's time, Dr.
Johnson said, "I think Dr. Arbuthnot the first man among them.
He was the most universal genius, being an excellent physician, a
man of deep learning, and a man of much humor. " He did not,
however, think much of the Scriblerus' papers, and said they were
forgotten because "no man would be the wiser, better, or merrier
for remembering them"; which is hard measure for the wit and
divertingness of some of the travesties. Cowper, reviewing Johnson's
'Lives of the Poets,' declared that "one might search these eight
volumes with a candle to find a man, and not find one, unless per-
haps Arbuthnot were he. " Thackeray, too, called him "one of the
wisest, wittiest, most accomplished, gentlest of mankind. "
Thus fortunate in his sunny spirit, in his genius for friendship, in
his professional eminence, and in his literary capacity, Dr. Arbuthnot
saw his life flow smoothly to its close. He died in London on Feb-
ruary 27th, 1735, at the age of sixty eight, still working and playing
with youthful ardor, and still surrounded with all the good things of
life.
THE TRUE CHARACTERS OF JOHN BULL, NIC. FROG, AND
HOCUS
From The History of John Bull,' Part I.
OR the better understanding the following history, the reader
to know that Bull, in the main, was an honest, plain-
dealing fellow, choleric, bold, and of a very unconstant tem-
per; he dreaded not old Lewis either at backsword, single fal-
chion, or cudgel play; but then he was very apt to quarrel with
his best friends, especially if they pretended to govern him. If
you flattered him, you might lead him like a child. John's tem-
per depended very much upon the air; his spirits rose and fell
with the weather-glass. John was quick and understood his busi-
ness very well; but no man alive was more careless in looking
into his accounts, or more cheated by partners, apprentices, and
servants. This was occasioned by his being a boon companion,
loving his bottle and his diversion; for, to say truth, no man
kept a better house than John, nor spent his money more gener-
ously. By plain and fair dealing John had acquired some plums,
and might have kept them, had it not been for his unhappy law-
suit.
Nic. Frog was a cunning, sly fellow, quite the reverse of
John in many particulars; covetous, frugal, minded domestic


## p. 727 (#137) ############################################

JOHN ARBUTHNOT
727
affairs, would pinch his belly to save his pocket, never lost a
farthing by careless servants or bad debtors. He did not care
much for any sort of diversion, except tricks of High German
artists and legerdemain. No man exceeded Nic. in these; yet
it must be owned that Nic. was a fair dealer, and in that way
acquired immense riches.
Hocus was an old, cunning attorney; and though this was the
first considerable suit that ever he was engaged in, he showed
himself superior in address to most of his profession. He kept
always good clerks, he loved money, was smooth-tongued, gave
good words, and seldom lost his temper. He was not worse than
an infidel, for he provided plentifully for his family, but he loved
himself better than them all. The neighbors reported that he
was henpecked, which was impossible, by such a mild-spirited
woman as his wife was.
HOW THE RELATIONS RECONCILED JOHN AND HIS SISTER
PEG, AND WHAT RETURN PEG MADE TO JOHN'S MESSAGE
From the History of John Bull, Part I.
JOHN
OHN BULL, otherwise a good-natured man, was very hard-
hearted to his sister Peg, chiefly from an aversion he had
conceived in his infancy. While he flourished, kept a warm
house, and drove a plentiful trade, poor Peg was forced to go
hawking and peddling about the streets selling knives, scissors,
and shoe-buckles; now and then carried a basket of fish to the
market; sewed, spun, and knit for a livelihood till her fingers'
ends were sore: and when she could not get bread for her fam-
ily, she was forced to hire them out at journey-work to her neigh-
bors. Yet in these, her poor circumstances, she still preserved
the air and mien of a gentlewoman-a certain decent pride that
extorted respect from the haughtiest of her neighbors. When
she came in to any full assembly, she would not yield the pas to
the best of them. If one asked her, "Are you not related to
John Bull? " "Yes," says she, "he has the honor to be my
brother. " So Peg's affairs went till all the relations cried out
shame upon John for his barbarous usage of his own flesh and
blood; that it was an easy matter for him to put her in a credit-
able way of living, not only without hurt, but with advantage
to himself, seeing she was an industrious person, and might be


## p. 728 (#138) ############################################

728
JOHN ARBUTHNOT
>>
serviceable to him in his way of business. "Hang her, jade,"
quoth John, "I can't endure her as long as she keeps that rascal
Jack's company. They told him the way to reclaim her was to
take her into his house; that by conversation the childish humors.
of their younger days might be worn out.
These arguments were enforced by a certain incident. It
happened that John was at that time about making his will and
entailing his estate, the very same in which Nic. Frog is named
executor. Now, his sister Peg's name being in the entail, he
could not make a thorough settlement without her consent.
There was indeed a malicious story went about, as if John's last
wife had fallen in love with Jack as he was eating custard on
horseback; that she persuaded John to take his sister into the
house the better to drive on the intrigue with Jack, concluding
he would follow his mistress Peg. All I can infer from this
story is that when one has got a bad character in the world,
people will report and believe anything of them, true or false.
But to return to my story.