Sketch of the life of La Place, author of the “Mécanique
Céleste.”—Newton’s labors.—Halley’s comet.—The importance of
astronomy to navigation.—Comets; Dr. Bowditch translates the
Mécanique Céleste; difficulties attending the undertaking;
objects he had in view; first volume analyzed; Newton’s error
pointed out.
[Sidenote: MÉCANIQUE CÉLESTE.]
In a former part of this story of Dr. Bowditch’s life, you will remember
that I stated that on his last voyage he commenced his notes upon the
“Mécanique Céleste” of La Place. It was on the first day of November,
during his disagreeable voyage homewards, in 1803, that he wrote his
first note to the work which was destined to occupy much of his time from
that moment until his death, thirty-five years afterwards, in Boston.
This work certainly deserves some of our attention, if he thought it
worthy of receiving the attention of so many years of his life. A brief
account of the life of the author of the original work may interest you,
and will serve as an introduction to the book itself.
[Sidenote: LA PLACE.]
[Sidenote: SKETCH OF HIS LIFE.]
Pierre Simon La Place was born on the 23d of March, in the year 1749,
at Beaumont, on the borders of the beautiful and fertile country of
ancient Normandy, situated in the north-western part of France. He was
the son of simple peasants in that country, and from his earliest years
was remarkable for the extraordinary powers of memory, and intense
love of study, with which he was endowed. In early life every branch
of learning was delightful to him. He seemed eager to gain knowledge
merely, without regard to the object of his study. But he soon began to
distinguish himself upon the subject of theology. This pursuit, however,
was soon ended, and by some means, of which no details now remain, his
mind was led to mathematics, and from that moment he was devoted to
them. After spending his youth at his native place, and having taught
mathematics there, he, at the age of eighteen years, went to Paris, to
seek a wider sphere in his pursuit of knowledge. Bearing several letters
of recommendation as a youth of great promise, he presented himself at
the abode of D’Alembert, who at that time was the first mathematician
of France, and contended with Euler, at Berlin, for the honor of being
the first in the world. But the letters upon which the youth depended
so much proved of no use. D’Alembert passed them by in silent neglect,
without even deigning to receive at his own house the bearer of them.
But La Place was fully bent upon success, and relying upon the force of
his own genius as a more powerful recommendation than any letters, he
sent to D’Alembert an essay, written by himself, upon a very abstruse
subject relating to mechanics. The professor, struck with its elegance
and the great learning displayed by it, soon afterwards called upon the
writer, and addressed him in these words: “You see, sir, that I think
recommendations are worth but very little; and for yourself they are
wholly unnecessary. By your own writings you can make yourself better
known than by any other means. They are sufficient. I will do all I
can for you.” In a few days after this conversation, the young man
was appointed professor of mathematics in the public military school
at Paris. From this period until the end of his life he was occupied
upon the science which he was thus called, at this early age, to teach
publicly at the capital of France. He became daily more acquainted with
the great men of the nation, and was himself making additions to the
scientific acquirements of the age, thus giving eminent proofs of his
genius. He was chosen member of the French Academy, a society of learned
men united for the purpose of advancing the cause of learning, and he
stood soon very high amongst them.
[Sidenote: MÉCANIQUE CÉLESTE.]
[Sidenote: GENIUS OF LA PLACE.]
His chief work, the “Celestial Mechanics,”—“_Mécanique Céleste_,”—he
began to publish in 1799, and finished the fourth volume in 1805.[11]
This placed him much above all his contemporaries. In it he had not only
combined many things which he himself had discovered, but likewise gave a
history, as it were, of all that had been done by geometricians from the
time of Sir Isaac Newton until his own day. La Place found many things
detached, but his genius proved that many apparently discordant facts
could be explained by Newton’s theory of universal gravitation. His labor
must have been immense. All Europe rang with the fame of this production,
which was said to be beyond anything ever performed before by man. The
echo of its fame reached America, and Dr. Bowditch obtained the volumes,
as they were successively published. The first two he received in part
payment for his labors on the “Navigator.”
Soon after his arrival home from his fourth voyage, Dr. Bowditch was
taking his accustomed walk towards the lower part of the town of Salem,
and met his old friend, Captain Prince. They entered into conversation,
and Dr. Bowditch remarked that he had, a short time before, received a
book from France, which he had long wished for, having heard that it was
superior to anything ever before written by man, and which very few were
able to comprehend. This work was that to which I have been alluding,
and it now renders Dr. Bowditch’s own name familiarly known among
mathematicians.
[Sidenote: SYSTEM OF THE WORLD.]
Later in life, La Place published a work called the “System of the
World.” In this, which, comparatively speaking, is not difficult to be
read by almost any one, he attempts to give a plain and simple statement
of all that is known in regard to those wise and magnificent laws,
whereby this solar system is kept together in perfect harmony, while at
the same time it is sailing onward through fields of space.
[Sidenote: LA PLACE A SENATOR.]
[Sidenote: DR. BOWDITCH’S LABORS.]
La Place, however, was not a truly noble man, because he was not strictly
just. It is said that he was willing to attribute to himself the
discoveries of others. On Napoleon Bonaparte’s becoming first consul in
France, La Place was made one of the ministers of the state; but he was
soon found to be better fitted for study than for the practical duties
of a public office. Accordingly he retired after a few weeks’ service,
but was made a member of the Senate, of which he became president.
After finishing his political career, he published other works of
great moment; but of those I shall not speak. About the year 1827 he
was seized with an acute disorder, which soon terminated his life. His
last words are remarkable, as conveying the same truth that every wise
man has upon his lips at the hour of death. As he reviewed the amount
of his learning, which was in one respect greater than that of any man
living, he exclaimed, “What we know here is very little, but what we are
ignorant of is immense.” Every man is compelled to become silent and
modest as he sees death approach. La Place was like other common men. He
died as a man, and was buried, and the men of science felt sad that one
so learned and of so strong an intellect should have departed. Endowed
by the Almighty with the loftiest powers of intellect, he stood alone,
and commanded the respect, if he did not always gain the love, of his
associates. Dr. Bowditch, though he regarded La Place as the greatest
mathematician that had ever lived, had little real sympathy with his
character.
[Sidenote: LAWS OF GRAVITY.]
[Sidenote: HALLEY’S COMET.]
[Sidenote: GRANDEUR OF MAN.]
[Sidenote: MOON’S MOTIONS.]
We must now try to give you a short account of the “Mécanique Céleste,”
and of Dr. Bowditch’s labors upon it. The original work consists of
five volumes, but Dr. Bowditch lived to finish the translation of and
commentary upon only the first four. There are about fifteen hundred
pages in the original, while there are three thousand eight hundred and
eighteen in the American translation. The object of the original work
may be known from the following introductory remarks by La Place, on
the occasion of printing the first volume, in 1798: “Newton, towards
the end of the last century, published his discovery of the laws of
gravity, or of the power by which the solar system is held together.
Since that period, geometricians have succeeded in bringing under this
law all the known phenomena of the system of the universe. I mean to
bring together those scattered themes and facts upon this subject, so as
to form one whole, which shall embrace all the known results of gravity
upon the motions, forms, &c., of the fluid and solid bodies that compose
our solar system, as well as of those other similar systems that are
spread around in the immensity of space.” You probably all understand
from this quotation the general object of the “Mécanique Céleste.” La
Place likewise informs us that the work is divided into two parts. In the
first he proposes to give the methods for determining the motions of the
heavenly bodies, their forms, the motions of the oceans and seas upon
their surfaces, and finally the movements of rotation of these spheres
about their own axes. In the second part, he promises to apply the rules
which he has given in the first to the planets and the satellites which
move around them, and likewise to the comets. The first part is found in
the first two volumes, the second part occupies the last two. From these
few remarks you will perceive the immense task imposed upon himself
by La Place, and at the same time the grandeur of it. How wonderful,
that a simple man can attempt to mark out the course of the heavenly
bodies, which we see clustering around us at night! But how much more
wonderful does man become, when we find he has the _power_ to foretell
to us the return of comets that have never been seen by any one living
now—comets that have been, during our lives, travelling into the far-off
fields of space! Strange that a simple man can prophesy, to a day, their
return! Many of us now living remember a beautifully bright and clear
comet, which in 1835 appeared, as had been predicted, after an absence
of seventy-six years. It was called Halley’s comet, after its first
discoverer. At first it seemed like a bright speck in the heavens towards
the north; but the next night it was larger. It seemed to approach, with
fearful rapidity, from evening to evening, and, sweeping in majesty
across our western sky, disappeared gradually in its progress towards the
sun, around which it whirled, and again appeared, more faintly visible
than before, just over our eastern horizon, as if to give us one more
glimpse of itself, a strange messenger of the Almighty, before it passed
off on its far-distant journey, not to return until those who were then
young and free as air, are all laid quietly in the grave, or have become
enfeebled and decrepit by the approach of age. Truly, great is God, who
made the comet; but to me man also seems full of grandeur, when I find
him capable of even _foretelling_ the exact passage of such a body.
Yet La Place enables any man to prophesy this; and in his “Mécanique
Céleste” we may find all the methods of investigation necessary for this
object. But he likewise tells us the forms of the planets; he enables
us to measure the ring which surrounds the planet Saturn, and enables
us to decide, at least in some degree the form and mass of the sun. In
this same work he treats of those curious phenomena, which, as we see
them daily, we think of little moment—the flow and ebb of the sea, or,
in other words, high and low tides,—and the causes of them. He treats
of the motion of the earth about its centre, and of the same motions in
the moon and planets. These are the chief objects of the first and second
volumes. The third volume, as we have already hinted, contains questions
of great intricacy, and of immense importance; namely, the exact motions
of the planets around the sun, as affected by all the attractions exerted
upon them by the various bodies of the universe; and the still more
important motions of our moon around the earth. I say important, because
the exact knowledge of the course of this body is of the greatest moment
to every sailor who attempts to go from one country to another over the
trackless ocean. By means of observations upon this planet, the seaman
can sail over distant waters for many months, and be able to return,
when he may wish, to his own home in safety. Hence the importance of
the astronomer to the simple navigator of our planet. The history of
Dr. Bowditch is another proof of the truth of this statement. By his
accurate knowledge of astronomy, by his ability to follow La Place in
his investigations of all the motions of the solar system, he was enabled
to produce a work on navigation which is sought for wherever the English
language is spoken, as it combines the best methods of using the results
of pure astronomy in the art of navigation. The “Practical Navigator”
would never have maintained its hold upon the community as it has done,
if Dr. Bowditch had not been as skilful in mathematics and astronomy as
in the details of navigation.
[Sidenote: JUPITER’S SATELLITES.]
[Sidenote: PLANET NEPTUNE.]
But to return to the “Mécanique Céleste.” The fourth volume contains
similar investigations, namely, the motions of the satellites, or moons,
about the other planets. Our moon’s motions about the earth, and the
revolutions of Jupiter’s satellites are the most important. Jupiter has
four satellites. These were the first that the invention of the telescope
by Galileo revealed to man; and by their frequent revolutions around
the planet, they have in their turn shown to us many of the laws which
govern the whole planetary system, besides many curious and interesting
facts in regard to their own forms and masses. From the eclipses or
disappearances of the first satellite, when it passes on the side of the
planet opposite to that at which the observer from the earth is looking,
it has demonstrated the velocity of light. Finally, the author treats of
the seven moons, or satellites, of Saturn, and likewise of those of the
planet Herschel, about which much less is known.[12]
[Sidenote: POWERS ACTING UPON COMETS.]
After attending to these subjects, La Place investigates the powers
which act upon comets, which tend to turn from their courses those
bodies, which, as I have before said, are flying in very many directions
throughout the universe, and which are liable to be moved out of their
direction by the actions of some planets near which they may come. This
was the case with a comet in 1770, whose course was wholly changed by
the planet Jupiter drawing it towards its own body. To investigate the
various laws of these disturbing forces is one subject of this volume.
Some other subjects are treated of, but of these I shall now not speak.
[Sidenote: NOTES ON MÉCANIQUE CÉLESTE.]
From this brief account of the “Mécanique Céleste” you may judge of the
difficulties which the original writer had to overcome in making it, and
of the immense labor requisite. But La Place frequently supposes that
a proposition is perfectly intelligible to his reader because it is so
to him. Having such a powerful mind, he is able to see at a glance that
for which any one else would require a long demonstration, before he
could become thoroughly master of the subject. The consequence of this
is, an obscurity in the work, which has made it doubly difficult of
comprehension. Several years ago, but a long time after Dr. Bowditch
had read and made notes upon the whole work, an English writer said that
there were scarcely twelve men in Europe capable of comprehending it.
Dr. Bowditch, feeling that it was the most valuable work upon astronomy
published in modern times, had undertaken the translation of it, and
had made notes thereupon, for the purpose of “amusing his leisure
hours.” Upon its being known that he had finished the task, the American
Academy offered to publish it. Dr. Bowditch would not allow this, and
reserved the publication until he was able to do so at his own expense.
Let us see, now, what service Dr. Bowditch intended to perform by his
translation and commentary. His first object was to lay before America
the greatest work on the science of astronomy ever published. Secondly,
his aim was to bring that work down to the comprehension of young men,
and students of mathematics, by filling up the places left by La Place
without demonstration. Thirdly, he meant to give the history of the
science of astronomy for the interval between the publication of the
original work and that at which the translation appeared. Fourthly, he
wished to collect together all the discoveries which he had made during
the forty years of his life that he had devoted to science. His first
aim was gained by the translation. His second was completely successful,
for he was assured by correspondents, both in America and Europe, that
he had enabled several to read the immortal work of La Place, who never
would have done so had not Dr. Bowditch published his Commentary. The
royal astronomer at Palermo says, in a printed work published after
the first two volumes of the translation had reached him, “Bowditch’s
Commentary should be translated into Italian;” and Lacroix, a celebrated
French mathematician, advised a young Swiss to read La Place in the
American edition rather than in the original. But what pleased the
commentator more than anything else, were the frequent letters from young
men residing in various parts of America, expressing gratitude for the
benefits they had received from his work. When I think of these, I am
reminded of the epithet bestowed upon Dr. Bowditch since his death, and
by one well capable of judging, namely, “Father of American Mathematics.”
He has given a tone to the study of science which will be long felt.
In regard to the third object, all critics allow that he was eminently
successful in giving the history of science up to the time proposed.
Upon the fourth point, we might refer, first, to the immense increase of
bulk of the work, as a proof, but I prefer to mention a few details; and
in order to this, let us examine the Commentary, and let it speak for
itself. But it must be remembered, that, in making this examination, I
must omit many circumstances, because you would not understand or feel
interested in any greater detail.
[Sidenote: ERRORS IN IT.]
[Sidenote: PERMANENCE OF THE SOLAR SYSTEM.]
[Sidenote: ERROR IN PRINCIPIA.]
In the first volume he points out two errors of La Place, one of which
relates to the motion of the earth; and the other is of much importance.
It relates to the permanency of our solar system, as it is commonly
called. You all doubtless know that the sun is situated in the centre,
and the planets, with our earth, revolve around this luminary, which
gives light and heat to all. Now, these bodies revolve in certain fixed
“nearly circular” directions, and La Place thought that they would always
continue to do so, and that Mercury, Venus, the Earth, Mars, Jupiter,
Saturn, and Herschel would forever continue to wheel around in their
accustomed orbits. Dr. Bowditch proves, however, that though this may
be true of the three larger planets,—Jupiter, Saturn, and Herschel,—it
is not equally certain, _from the proofs given by La Place_, that our
earth, or any of the other smaller planets, may not fly off into regions
far remote from those in which they have been revolving for ages. This
error had been made the subject of a paper to the American Academy at an
earlier period of his life. But it must not be supposed that there is
any proof that the solar system will not continue to exist for many long
ages. On the contrary, there is no doubt that it will last millions of
years. Dr. Bowditch merely wished to assert that La Place’s argument and
calculation did not prove as much as the French mathematician thought
they did. In this volume Dr. Bowditch likewise alludes to a topic which
he had made the subject of a communication, a long time previously, to
the American Academy; I refer to a mistake in Newton’s “Principia,”
which he discovered when quite young, and had sent an account of to the
president of Harvard College. This gentleman referred the question to the
professor of mathematics, who believed the youth was mistaken. Doubtless
he thought it very strange that a simple youth should presume to correct
anything published by so eminent a man as Newton. The error of the
professor will become less singular when you learn that the same mistake
escaped the notice of all the commentators on the “Principia,”—that
is, for more than a century,—and that the cause of the original
communication being made to the Academy was the attempt of Mr. Emerson,
an Englishman, to prove the correctness of the English philosopher. Every
one, I believe, now allows that Dr. Bowditch was correct, and that a
considerable error would result, in calculating the orbit of a comet,
from using Newton’s calculations.