Great Astronomers by Robert Stawell Ball (best ereader for students .txt) 📖

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.

 

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.

 

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.

 

[PLATE: LAPLACE.]

 

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.

 

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.

 

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.

 

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