Great Astronomers - Robert Stawell Ball (the little red hen ebook .TXT) 📗

moon, which has to

be adjusted relatively to the average value of the solar

disturbance, must also be gradually declining. In other words,

the moon must be approaching nearer to the earth in consequence

of the alterations in the eccentricity of the earth’s orbit

produced by the attraction of the other planets. It is true that

the change in the moon’s position thus arising is an extremely

small one, and the consequent effect in accelerating the moon’s

motion is but very slight. It is in fact almost imperceptible,

except when great periods of time are involved. Laplace undertook

a calculation on this subject. He knew what the efficiency of the

planets in altering the dimensions of the earth’s orbit amounted

to; from this he was able to determine the changes that would be

propagated into the motion of the moon. Thus he ascertained, or

at all events thought he had ascertained, that the acceleration of

the moon’s motion, as it had been inferred from the observations

of the ancient eclipses which have been handed down to us, could

be completely accounted for as a consequence of planetary

perturbation. This was regarded as a great scientific triumph.

Our belief in the universality of the law of gravitation would, in

fact, have been seriously challenged unless some explanation of

the lunar acceleration had been forthcoming. For about fifty

years no one questioned the truth of Laplace’s investigation.

When a mathematician of his eminence had rendered an explanation

of the remarkable facts of observation which seemed so complete,

it is not surprising that there should have been but little

temptation to doubt it. On undertaking a new calculation of the

same question, Professor Adams found that Laplace had not pursued

this approximation sufficiently far, and that consequently there

was a considerable error in the result of his analysis. Adams,

it must be observed, did not impugn the value of the lunar

acceleration which Halley had deduced from the observations,

but what he did show was, that the calculation by which Laplace

thought he had provided an explanation of this acceleration was

erroneous. Adams, in fact, proved that the planetary influence

which Laplace had detected only possessed about half the

efficiency which the great French mathematician had attributed to

it. There were not wanting illustrious mathematicians who came

forward to defend the calculations of Laplace. They computed the

question anew and arrived at results practically coincident with

those he had given. On the other hand certain distinguished

mathematicians at home and abroad verified the results of

Adams. The issue was merely a mathematical one. It had only one

correct solution. Gradually it appeared that those who opposed

Adams presented a number of different solutions, all of them

discordant with his, and, usually, discordant with each other.

Adams showed distinctly where each of these investigators had

fallen into error, and at last it became universally admitted that

the Cambridge Professor had corrected Laplace in a very

fundamental point of astronomical theory.

 

Though it was desirable to have learned the truth, yet the breach

between observation and calculation which Laplace was believed to

have closed thus became reopened. Laplace’s investigation, had it

been correct, would have exactly explained the observed facts. It

was, however, now shown that his solution was not correct, and

that the lunar acceleration, when strictly calculated as a

consequence of solar perturbations, only produced about half the

effect which was wanted to explain the ancient eclipses

completely. It now seems certain that there is no means of

accounting for the lunar acceleration as a direct consequence of

the laws of gravitation, if we suppose, as we have been in the

habit of supposing, that the members of the solar system concerned

may be regarded as rigid particles. It has, however, been

suggested that another explanation of a very interesting kind may

be forthcoming, and this we must endeavour to set forth.

 

It will be remembered that we have to explain why the period of

revolution of the moon is now shorter than it used to be. If we

imagine the length of the period to be expressed in terms of days

and fractions of a day, that is to say, in terms of the rotations

of the earth around its axis, then the difficulty encountered is,

that the moon now requires for each of its revolutions around the

earth rather a smaller number of rotations of the earth around its

axis than used formerly to be the case. Of course this may be

explained by the fact that the moon is now moving more swiftly

than of yore, but it is obvious that an explanation of quite a

different kind might be conceivable. The moon may be moving just

at the same pace as ever, but the length of the day may be

increasing. If the length of the day is increasing, then, of

course, a smaller number of days will be required for the moon to

perform each revolution even though the moon’s period was itself

really unchanged. It would, therefore, seem as if the phenomenon

known as the lunar acceleration is the result of the two causes.

The first of these is that discovered by Laplace, though its value

was overestimated by him, in which the perturbations of the earth

by the planets indirectly affect the motion of the moon. The

remaining part of the acceleration of our satellite is apparent

rather than real, it is not that the moon is moving more quickly,

but that our timepiece, the earth, is revolving more slowly, and

is thus actually losing time. It is interesting to note that we

can detect a physical explanation for the apparent checking of the

earth’s motion which is thus manifested. The tides which ebb and

flow on the earth exert a brake-like action on the revolving

globe, and there can be no doubt that they are gradually reducing

its speed, and thus lengthening the day. It has accordingly been

suggested that it is this action of the tides which produces the

supplementary effect necessary to complete the physical

explanation of the lunar acceleration, though it would perhaps be

a little premature to assert that this has been fully

demonstrated.

 

The third of Professor Adams’ most notable achievements was

connected with the great shower of November meteors which

astonished the world in 1866. This splendid display concentrated

the attention of astronomers on the theory of the movements of the

little objects by which the display was produced. For the

definite discovery of the track in which these bodies revolve, we

are indebted to the labours of Professor Adams, who, by a

brilliant piece of mathematical work, completed the edifice whose

foundations had been laid by Professor Newton, of Yale, and other

astronomers.

 

Meteors revolve around the sun in a vast swarm, every individual

member of which pursues an orbit in accordance with the well-known

laws of Kepler. In order to understand the movements of these

objects, to account satisfactorily for their periodic recurrence,

and to predict the times of their appearance, it became necessary

to learn the size and the shape of the track which the swarm

followed, as well as the position which it occupied. Certain

features of the track could no doubt be readily assigned. The

fact that the shower recurs on one particular day of the year,

viz., November 13th, defines one point through which the orbit

must pass. The position on the heavens of the radiant point from

which the meteors appear to diverge, gives another element in the

track. The sun must of course be situated at the focus, so that

only one further piece of information, namely, the periodic time,

will be necessary to complete our knowledge of the movements of

the system. Professor H. Newton, of Yale, had shown that the

choice of possible orbits for the meteoric swarm is limited to

five. There is, first, the great ellipse in which we now know the

meteors revolve once every thirty three and one quarter years.

There is next an orbit of a nearly circular kind in which the

periodic time would be a little more than a year. There is a

similar track in which the periodic time would be a few days short

of a year, while two other smaller orbits would also be

conceivable. Professor Newton had pointed out a test by which it

would be possible to select the true orbit, which we know must be

one or other of these five. The mathematical difficulties which

attended the application of this test were no doubt great, but

they did not baffle Professor Adams.

 

There is a continuous advance in the date of this meteoric shower.

The meteors now cross our track at the point occupied by the

earth on November 13th, but this point is gradually altering.

The only influence known to us which could account for the

continuous change in the plane of the meteor’s orbit arises from

the attraction of the various planets. The problem to be solved

may therefore be attacked in this manner. A specified amount of

change in the plane of the orbit of the meteors is known to

arise, and the changes which ought to result from the attraction

of the planets can be computed for each of the five possible

orbits, in one of which it is certain that the meteors must

revolve. Professor Adams undertook the work. Its difficulty

principally arises from the high eccentricity of the largest of

the orbits, which renders the more ordinary methods of

calculation inapplicable. After some months of arduous labour the

work was completed, and in April, 1867, Adams announced his

solution of the problem. He showed that if the meteors revolved

in the largest of the five orbits, with the periodic time of

thirty three and one quarter years, the perturbations of Jupiter

would account for a change to the extent of twenty minutes of arc

in the point in which the orbit crosses the earth’s track. The

attraction of Saturn would augment this by seven minutes, and

Uranus would add one minute more, while the influence of the Earth

and of the other planets would be inappreciable. The

accumulated effect is thus twenty-eight minutes, which is

practically coincident with the observed value as determined by

Professor Newton from an examination of all the showers of which

there is any historical record. Having thus showed that the great

orbit was a possible path for the meteors, Adams next proved that

no one of the other four orbits would be disturbed in the same

manner. Indeed, it appeared that not half the observed amount of

change could arise in any orbit except in that one with the long

period. Thus was brought to completion the interesting research

which demonstrated the true relation of the meteor swarm to the

solar system.

 

Besides those memorable scientific labours with which his

attention was so largely engaged, Professor Adams found time for

much other study. He occasionally allowed himself to undertake as

a relaxation some pieces of numerical calculation, so tremendously

long that we can only look on them with astonishment. He has

calculated certain important mathematical constants accurately to

more than two hundred places of decimals. He was a diligent

reader of works on history, geology, and botany, and his arduous

labours were often beguiled by novels, of which, like many other

great men, he was very fond. He had also the taste of a

collector, and he brought together about eight hundred volumes of

early printed works, many of considerable rarity and value. As to

his personal character, I may quote the words of Dr. Glaisher when

he says, “Strangers who first met him were invariably struck by

his simple and unaffected manner. He was a delightful companion,

always cheerful and genial, showing in society but few traces of

his really shy and retiring disposition. His nature was

sympathetic and generous, and in few men have the moral and