<h3><SPAN name="LAPLACE" id="LAPLACE"></SPAN>LAPLACE.</h3>
<p>The author of the "Mecanique Celeste" was born at Beaumont-en-Auge,
near Honfleur, in 1749, just thirteen years later than his renowned
friend Lagrange. His father was a farmer, but appears to have been
in a position to provide a good education for a son who seemed
promising. Considering the unorthodoxy in religious matters which is
generally said to have characterized Laplace in later years, it is
interesting to note that when he was a boy the subject which first
claimed his attention was theology. He was, however, soon introduced
to the study of mathematics, in which he presently became so
proficient, that while he was still no more than eighteen years old,
he obtained employment as a mathematical teacher in his native town.</p>
<p>Desiring wider opportunities for study and for the acquisition of
fame than could be obtained in the narrow associations of provincial
life, young Laplace started for Paris, being provided with letters of
introduction to D'Alembert, who then occupied the most prominent
position as a mathematician in France, if not in the whole of
Europe. D'Alembert's fame was indeed so brilliant that Catherine the
Great wrote to ask him to undertake the education of her Son, and
promised the splendid income of a hundred thousand francs. He
preferred, however, a quiet life of research in Paris, although there
was but a modest salary attached to his office. The philosopher
accordingly declined the alluring offer to go to Russia, even though
Catherine wrote again to say: "I know that your refusal arises from
your desire to cultivate your studies and your friendships in quiet.
But this is of no consequence: bring all your friends with you, and I
promise you that both you and they shall have every accommodation in
my power." With equal firmness the illustrious mathematician
resisted the manifold attractions with which Frederick the Great
sought to induce him, to take up his residence at Berlin. In reading
of these invitations we cannot but be struck at the extraordinary
respect which was then paid to scientific distinction. It must be
remembered that the discoveries of such a man as D'Alembert were
utterly incapable of being appreciated except by those who possessed
a high degree of mathematical culture. We nevertheless find the
potentates of Russia and Prussia entreating and, as it happens,
vainly entreating, the most distinguished mathematician in France to
accept the positions that they were proud to offer him.</p>
<p>It was to D'Alembert, the profound mathematician, that young Laplace,
the son of the country farmer, presented his letters of
introduction. But those letters seem to have elicited no reply,
whereupon Laplace wrote to D'Alembert submitting a discussion on some
point in Dynamics. This letter instantly produced the desired
effect. D'Alembert thought that such mathematical talent as the
young man displayed was in itself the best of introductions to his
favour. It could not be overlooked, and accordingly he invited
Laplace to come and see him. Laplace, of course, presented himself,
and ere long D'Alembert obtained for the rising philosopher a
professorship of mathematics in the Military School in Paris. This
gave the brilliant young mathematician the opening for which he
sought, and he quickly availed himself of it.</p>
<p>Laplace was twenty-three years old when his first memoir on a
profound mathematical subject appeared in the Memoirs of the Academy
at Turin. From this time onwards we find him publishing one memoir
after another in which he attacks, and in many cases successfully
vanquishes, profound difficulties in the application of the Newtonian
theory of gravitation to the explanation of the solar system. Like
his great contemporary Lagrange, he loftily attempted problems which
demanded consummate analytical skill for their solution. The
attention of the scientific world thus became riveted on the splendid
discoveries which emanated from these two men, each gifted with
extraordinary genius.</p>
<p>Laplace's most famous work is, of course, the "Mecanique Celeste," in
which he essayed a comprehensive attempt to carry out the principles
which Newton had laid down, into much greater detail than Newton had
found practicable. The fact was that Newton had not only to
construct the theory of gravitation, but he had to invent the
mathematical tools, so to speak, by which his theory could be applied
to the explanation of the movements of the heavenly bodies. In the
course of the century which had elapsed between the time of Newton
and the time of Laplace, mathematics had been extensively developed.
In particular, that potent instrument called the infinitesimal
calculus, which Newton had invented for the investigation of nature,
had become so far perfected that Laplace, when he attempted to
unravel the movements of the heavenly bodies, found himself provided
with a calculus far more efficient than that which had been available
to Newton. The purely geometrical methods which Newton employed,
though they are admirably adapted for demonstrating in a general way
the tendencies of forces and for explaining the more obvious
phenomena by which the movements of the heavenly bodies are
disturbed, are yet quite inadequate for dealing with the more subtle
effects of the Law of Gravitation. The disturbances which one planet
exercises upon the rest can only be fully ascertained by the aid of
long calculation, and for these calculations analytical methods are
required.</p>
<p>With an armament of mathematical methods which had been perfected
since the days of Newton by the labours of two or three generations
of consummate mathematical inventors, Laplace essayed in the
"Mecanique Celeste" to unravel the mysteries of the heavens. It will
hardly be disputed that the book which he has produced is one of the
most difficult books to understand that has ever been written. In
great part, of course, this difficulty arises from the very nature of
the subject, and is so far unavoidable. No one need attempt to read
the "Mecanique Celeste" who has not been naturally endowed with
considerable mathematical aptitude which he has cultivated by years
of assiduous study. The critic will also note that there are grave
defects in Laplace's method of treatment. The style is often
extremely obscure, and the author frequently leaves great gaps in his
argument, to the sad discomfiture of his reader. Nor does it mend
matters to say, as Laplace often does say, that it is "easy to see"
how one step follows from another. Such inferences often present
great difficulties even to excellent mathematicians. Tradition
indeed tells us that when Laplace had occasion to refer to his own
book, it sometimes happened that an argument which he had dismissed
with his usual formula, "Il est facile a voir," cost the illustrious
author himself an hour or two of hard thinking before he could
recover the train of reasoning which had been omitted. But there are
certain parts of this great work which have always received the
enthusiastic admiration of mathematicians. Laplace has, in fact,
created whole tracts of science, some of which have been subsequently
developed with much advantage in the prosecution of the study of
Nature.</p>
<p>Judged by a modern code the gravest defect of Laplace's great work is
rather of a moral than of a mathematical nature. Lagrange and he
advanced together in their study of the mechanics of the heavens, at
one time perhaps along parallel lines, while at other times they
pursued the same problem by almost identical methods. Sometimes the
important result was first reached by Lagrange, sometimes it was
Laplace who had the good fortune to make the discovery. It would
doubtless be a difficult matter to draw the line which should exactly
separate the contributions to astronomy made by one of these
illustrious mathematicians, and the contributions made by the other.
But in his great work Laplace in the loftiest manner disdained to
accord more than the very barest recognition to Lagrange, or to any
of the other mathematicians, Newton alone excepted, who had advanced
our knowledge of the mechanism of the heavens. It would be quite
impossible for a student who confined his reading to the "Mecanique
Celeste" to gather from any indications that it contains whether the
discoveries about which he was reading had been really made by
Laplace himself or whether they had not been made by Lagrange, or by
Euler, or by Clairaut. With our present standard of morality in such
matters, any scientific man who now brought forth a work in which he
presumed to ignore in this wholesale fashion the contributions of
others to the subject on which he was writing, would be justly
censured and bitter controversies would undoubtedly arise. Perhaps
we ought not to judge Laplace by the standard of our own time, and in
any case I do not doubt that Laplace might have made a plausible
defence. It is well known that when two investigators are working at
the same subjects, and constantly publishing their results, it
sometimes becomes difficult for each investigator himself to
distinguish exactly between what he has accomplished and that which
must be credited to his rival. Laplace may probably have said to
himself that he was going to devote his energies to a great work on
the interpretation of Nature, that it would take all his time and all
his faculties, and all the resources of knowledge that he could
command, to deal justly with the mighty problems before him. He
would not allow himself to be distracted by any side issue. He could
not tolerate that pages should be wasted in merely discussing to whom
we owe each formula, and to whom each deduction from such formula is
due. He would rather endeavour to produce as complete a picture as
he possibly could of the celestial mechanics, and whether it were by
means of his mathematics alone, or whether the discoveries of others
may have contributed in any degree to the result, is a matter so
infinitesimally insignificant in comparison with the grandeur of his
subject that he would altogether neglect it. "If Lagrange should
think," Laplace might say, "that his discoveries had been unduly
appropriated, the proper course would be for him to do exactly what I
have done. Let him also write a "Mecanique Celeste," let him employ
those consummate talents which he possesses in developing his noble
subject to the utmost. Let him utilise every result that I or any
other mathematician have arrived at, but not trouble himself unduly
with unimportant historical details as to who discovered this, and
who discovered that; let him produce such a work as he could write,
and I shall heartily welcome it as a splendid contribution to our
science." Certain it is that Laplace and Lagrange continued the best
of friends, and on the death of the latter it was Laplace who was
summoned to deliver the funeral oration at the grave of his great
rival.</p>
<p>The investigations of Laplace are, generally speaking, of too
technical a character to make it possible to set forth any account of
them in such a work as the present. He did publish, however, one
treatise, called the "Systeme du Monde," in which, without
introducing mathematical symbols, he was able to give a general
account of the theories of the celestial movements, and of the
discoveries to which he and others had been led. In this work the
great French astronomer sketched for the first time that remarkable
doctrine by which his name is probably most generally known to those
readers of astronomical books who are not specially mathematicians.
It is in the "Systeme du Monde" that Laplace laid down the principles
of the Nebular Theory which, in modern days, has been generally
accepted by those philosophers who are competent to judge, as
substantially a correct expression of a great historical fact.</p>
<p><SPAN name="laplace_ill" id="laplace_ill"></SPAN></p>
<div class="figcenter"> <SPAN href="images/ill_laplace.jpg"> <ANTIMG src="images/ill_laplace_sml.jpg" width-obs="423" height-obs="488" alt="LAPLACE." title="" /></SPAN> <span class="caption">LAPLACE.</span></div>
<p>The Nebular Theory gives a physical account of the origin of the
solar system, consisting of the sun in the centre, with the planets
and their attendant satellites. Laplace perceived the significance
of the fact that all the planets revolved in the same direction
around the sun; he noticed also that the movements of rotation of the
planets on their axes were performed in the same direction as that in
which a planet revolves around the sun; he saw that the orbits of the
satellites, so far at least as he knew them, revolved around their
primaries also in the same direction. Nor did it escape his
attention that the sun itself rotated on its axis in the same sense.
His philosophical mind was led to reflect that such a remarkable
unanimity in the direction of the movements in the solar system
demanded some special explanation. It would have been in the highest
degree improbable that there should have been this unanimity unless
there had been some physical reason to account for it. To appreciate
the argument let us first concentrate our attention on three
particular bodies, namely the earth, the sun, and the moon. First
the earth revolves around the sun in a certain direction, and the
earth also rotates on its axis. The direction in which the earth
turns in accordance with this latter movement might have been that in
which it revolves around the sun, or it might of course have been
opposite thereto. As a matter of fact the two agree. The moon in
its monthly revolution around the earth follows also the same
direction, and our satellite rotates on its axis in the same period
as its monthly revolution, but in doing so is again observing this
same law. We have therefore in the earth and moon four movements,
all taking place in the same direction, and this is also identical
with that in which the sun rotates once every twenty-five days. Such
a coincidence would be very unlikely unless there were some physical
reason for it. Just as unlikely would it be that in tossing a coin
five heads or five tails should follow each other consecutively. If
we toss a coin five times the chances that it will turn up all heads
or all tails is but a small one. The probability of such an event is
only one-sixteenth.</p>
<p>There are, however, in the solar system many other bodies besides the
three just mentioned which are animated by this common movement.
Among them are, of course, the great planets, Jupiter, Saturn, Mars,
Venus, and Mercury, and the satellites which attend on these
planets. All these planets rotate on their axes in the same
direction as they revolve around the sun, and all their satellites
revolve also in the same way. Confining our attention merely to the
earth, the sun, and the five great planets with which Laplace was
acquainted, we have no fewer than six motions of revolution and seven
motions of rotation, for in the latter we include the rotation of the
sun. We have also sixteen satellites of the planets mentioned whose
revolutions round their primaries are in the same direction. The
rotation of the moon on its axis may also be reckoned, but as to the
rotations of the satellites of the other planets we cannot speak with
any confidence, as they are too far off to be observed with the
necessary accuracy. We have thus thirty circular movements in the
solar system connected with the sun and moon and those great planets
than which no others were known in the days of Laplace. The
significant fact is that all these thirty movements take place in the
same direction. That this should be the case without some physical
reason would be just as unlikely as that in tossing a coin thirty
times it should turn up all heads or all tails every time without
exception.</p>
<p>We can express the argument numerically. Calculation proves that
such an event would not generally happen oftener than once out of
five hundred millions of trials. To a philosopher of Laplace's
penetration, who had made a special study of the theory of
probabilities, it seemed well-nigh inconceivable that there should
have been such unanimity in the celestial movements, unless there had
been some adequate reason to account for it. We might, indeed, add
that if we were to include all the objects which are now known to
belong to the solar system, the argument from probability might be
enormously increased in strength. To Laplace the argument appeared
so conclusive that he sought for some physical cause of the
remarkable phenomenon which the solar system presented. Thus it was
that the famous Nebular Hypothesis took its rise. Laplace devised a
scheme for the origin of the sun and the planetary system, in which
it would be a necessary consequence that all the movements should
take place in the same direction as they are actually observed to do.</p>
<p>Let us suppose that in the beginning there was a gigantic mass of
nebulous material, so highly heated that the iron and other
substances which now enter into the composition of the earth and
planets were then suspended in a state of vapour. There is nothing
unreasonable in such a supposition indeed, we know as a matter of
fact that there are thousands of such nebulae to be discerned at
present through our telescopes. It would be extremely unlikely that
any object could exist without possessing some motion of rotation; we
may in fact assert that for rotation to be entirety absent from the
great primeval nebula would be almost infinitely improbable. As ages
rolled on, the nebula gradually dispersed away by radiation its
original stores of heat, and, in accordance with well-known physical
principles, the materials of which it was formed would tend to
coalesce. The greater part of those materials would become
concentrated in a mighty mass surrounded by outlying uncondensed
vapours. There would, however, also be regions throughout the extent
of the nebula, in which subsidiary centres of condensation would be
found. In its long course of cooling, the nebula would, therefore,
tend ultimately to form a mighty central body with a number of
smaller bodies disposed around it. As the nebula was initially
endowed with a movement of rotation, the central mass into which it
had chiefly condensed would also revolve, and the subsidiary bodies
would be animated by movements of revolution around the central
body. These movements would be all pursued in one common direction,
and it follows, from well-known mechanical principles, that each of
the subsidiary masses, besides participating in the general
revolution around the central body, would also possess a rotation
around its axis, which must likewise be performed in the same
direction. Around the subsidiary bodies other objects still smaller
would be formed, just as they themselves were formed relatively to
the great central mass.</p>
<p>As the ages sped by, and the heat of these bodies became gradually
dissipated, the various objects would coalesce, first into molten
liquid masses, and thence, at a further stage of cooling, they would
assume the appearance of solid masses, thus producing the planetary
bodies such as we now know them. The great central mass, on account
of its preponderating dimensions, would still retain, for further
uncounted ages, a large quantity of its primeval heat, and would thus
display the splendours of a glowing sun. In this way Laplace was
able to account for the remarkable phenomena presented in the
movements of the bodies of the solar system. There are many other
points also in which the nebular theory is known to tally with the
facts of observation. In fact, each advance in science only seems to
make it more certain that the Nebular Hypothesis substantially
represents the way in which our solar system has grown to its present
form.</p>
<p>Not satisfied with a career which should be merely scientific,
Laplace sought to connect himself with public affairs. Napoleon
appreciated his genius, and desired to enlist him in the service of
the State. Accordingly he appointed Laplace to be Minister of the
Interior. The experiment was not successful, for he was not by
nature a statesman. Napoleon was much disappointed at the ineptitude
which the great mathematician showed for official life, and, in
despair of Laplace's capacity as an administrator, declared that he
carried the spirit of his infinitesimal calculus into the management
of business. Indeed, Laplace's political conduct hardly admits of
much defence. While he accepted the honours which Napoleon showered
on him in the time of his prosperity, he seems to have forgotten all
this when Napoleon could no longer render him service. Laplace was
made a Marquis by Louis XVIII., a rank which he transmitted to his
son, who was born in 1789. During the latter part of his life the
philosopher lived in a retired country place at Arcueile. Here he
pursued his studies, and by strict abstemiousness, preserved himself
from many of the infirmities of old age. He died on March the 5th,
1827, in his seventy-eighth year, his last words being, "What we know
is but little, what we do not know is immense."</p>
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