years, began to give way. He appeared to rally somewhat in the
summer, but in September he sank rapidly, and died on Sunday, the
23rd of that month.
His remains were borne to the cemetery on Mont Parnasse in a public
funeral. Among his pallbearers were leading men of science, from
other countries as well as France, and the memorial discourses
pronounced at the grave expressed their admiration of his talents and
of the greatness of the services he had rendered to science.
ADAMS.
The illustrious mathematician who, among Englishmen, at all events,
was second only to Newton by his discoveries in theoretical
astronomy, was born on June the 5th, 1819, at the farmhouse of
Lidcot, seven miles from Launceston, in Cornwall. His early
education was imparted under the guidance of the Rev. John Couch
Grylls, a first cousin of his mother. He appears to have received an
education of the ordinary school type in classics and mathematics,
but his leisure hours were largely devoted to studying what
astronomical books he could find in the library of the Mechanics'
Institute at Devonport. He was twenty years old when he entered St.
John's College, Cambridge. His career in the University was one of
almost unparalleled distinction, and it is recorded that his
answering at the Wranglership examination, where he came out at the
head of the list in 1843, was so high that he received more than
double the marks awarded to the Second Wrangler.
Among the papers found after his death was the following memorandum,
dated July the 3rd, 1841: "Formed a design at the beginning of this
week of investigating, as soon as possible after taking my degree,
the irregularities in the motion of Uranus, which are as yet
unaccounted for, in order to find whether they may be attributed to
the action of an undiscovered planet beyond it; and, if possible,
thence to determine the elements of its orbit approximately, which
would lead probably to its discovery."
After he had taken his degree, and had thus obtained a little
relaxation from the lines within which his studies had previously
been necessarily confined, Adams devoted himself to the study of the
perturbations of Uranus, in accordance with the resolve which we have
just seen that he formed while he was still an undergraduate. As a
first attempt he made the supposition that there might be a planet
exterior to Uranus, at a distance which was double that of Uranus
from the sun. Having completed his calculation as to the effect
which such a hypothetical planet might exercise upon the movement of
Uranus, he came to the conclusion that it would be quite possible to
account completely for the unexplained difficulties by the action of
an exterior planet, if only that planet were of adequate size and had
its orbit properly placed. It was necessary, however, to follow up
the problem more precisely, and accordingly an application was made
through Professor Challis, the Director of the Cambridge Observatory,
to the Astronomer Royal, with the object of obtaining from the
observations made at Greenwich Observatory more accurate values for
the disturbances suffered by Uranus. Basing his work on the more
precise materials thus available, Adams undertook his calculations
anew, and at last, with his completed results, he called at Greenwich
Observatory on October the 21st, 1845. He there left for the
Astronomer Royal a paper which contained the results at which he had
arrived for the mass and the mean distance of the hypothetical planet
as well as the other elements necessary for calculating its exact
position.
[PLATE: JOHN COUCH ADAMS.]
As we have seen in the preceding chapter, Le Verrier had been also
investigating the same problem. The place which Le Verrier assigned
to the hypothetical disturbing planet for the beginning of the year
1847, was within a degree of that to which Adams's computations
pointed, and which he had communicated to the Astronomer Royal seven
months before Le Verrier's work appeared. On July the 29th, 1846,
Professor Challis commenced to search for the unknown object with the
Northumberland telescope belonging to the Cambridge Observatory. He
confined his attention to a limited region in the heavens, extending
around that point to which Mr. Adams' calculations pointed. The
relative places of all the stars, or rather star-like objects within
this area, were to be carefully measured. When the same observations
were repeated a week or two later, then the distances of the several
pairs of stars from each other would be found unaltered, but any
planet which happened to lie among the objects measured would
disclose its existence by the alterations in distance due to its
motion in the interval. This method of search, though no doubt it
must ultimately have proved successful, was necessarily a very
tedious one, but to Professor Challis, unfortunately, no other method
was available. Thus it happened that, though Challis commenced his
search at Cambridge two months earlier than Galle at Berlin, yet, as
we have already explained, the possession of accurate star-maps by
Dr. Galle enabled him to discover the planet on the very first night
that he looked for it.
The rival claims of Adams and Le Verrier to the discovery of Neptune,
or rather, we should say, the claims put forward by their respective
champions, for neither of the illustrious investigators themselves
condescended to enter into the personal aspect of the question, need
not be further discussed here. The main points of the controversy
have been long since settled, and we cannot do better than quote the
words of Sir John Herschel when he addressed the Royal Astronomical
Society in 1848:--
"As genius and destiny have joined the names of Le Verrier and Adams,
I shall by no means put them asunder; nor will they ever be
pronounced apart so long as language shall celebrate the triumphs of
science in her sublimest walks. On the great discovery of Neptune,
which may be said to have surpassed, by intelligible and legitimate
means, the wildest pretensions of clairvoyance, it Would now be quite
superfluous for me to dilate. That glorious event and the steps
which led to it, and the various lights in which it has been placed,
are already familiar to every one having the least tincture of
science. I will only add that as there is not, nor henceforth ever
can be, the slightest rivalry on the subject between these two
illustrious men--as they have met as brothers, and as such will, I
trust, ever regard each other--we have made, we could make, no
distinction between then, on this occasion. May they both long adorn
and augment our science, and add to their own fame already so high
and pure, by fresh achievements."
Adams was elected a Fellow of St. John's College, Cambridge, in 1843;
but as he did not take holy orders, his Fellowship, in accordance
with the rules then existing came to an end in 1852. In the
following year he was, however, elected to a Fellowship at Pembroke
College, which he retained until the end of his life. In 1858 he was
appointed Professor of Mathematics in the University of St. Andrews,
but his residence in the north was only a brief one, for in the same
year he was recalled to Cambridge as Lowndean Professor of Astronomy
and Geometry, in succession to Peacock. In 1861 Challis retired from
the Directorship of the Cambridge Observatory, and Adams was
appointed to succeed him.
The discovery of Neptune was a brilliant inauguration of the
astronomical career of Adams. He worked at, and wrote upon, the
theory of the motions of Biela's comet; he made important corrections
to the theory of Saturn; he investigated the mass of Uranus, a
subject in which he was naturally interested from its importance in
the theory of Neptune; he also improved the methods of computing the
orbits of double stars. But all these must be regarded as his minor
labours, for next to the discovery of Neptune the fame of Adams
mainly rests on his researches upon certain movements of the moon,
and upon the November meteors.
The periodic time of the moon is the interval required for one
circuit of its orbit. This interval is known with accuracy at the
present day, and by means of the ancient eclipses the period of the
moon's revolution two thousand years ago can be also ascertained. It
had been discovered by Halley that the period which the moon requires
to accomplish each of its revolutions around the earth has been
steadily, though no doubt slowly, diminishing. The change thus
produced is not appreciable when only small intervals of time are
considered, but it becomes appreciable when we have to deal with
intervals of thousands of years. The actual effect which is produced
by the lunar acceleration, for so this phenomenon is called, may be
thus estimated. If we suppose that the moon had, throughout the
ages, revolved around the earth in precisely the same periodic time
which it has at present, and if from this assumption we calculate
back to find where the moon must have been about two thousand years
ago, we obtain a position which the ancient eclipses show to be
different from that in which the moon was actually situated. The
interval between the position in which the moon would have been found
two thousand years ago if there had been no acceleration, and the
position in which the moon was actually placed, amounts to about a
degree, that is to say, to an arc on the heavens which is twice the
moon's apparent diameter.
If no other bodies save the earth and the moon were present in the
universe, it seems certain that the motion of the moon would never
have exhibited this acceleration. In such a simple case as that
which I have supposed the orbit of the moon would have remained for
ever absolutely unchanged. It is, however, well known that the
presence of the sun exerts a disturbing influence upon the movements
of the moon. In each revolution our satellite is continually drawn
aside by the action of the sun from the place which it would
otherwise have occupied. These irregularities are known as the
perturbations of the lunar orbit, they have long been studied, and
the majority of them have been satisfactorily accounted for. It
seems, however, to those who first investigated the question that the
phenomenon of the lunar acceleration could not be explained as a
consequence of solar perturbation, and, as no other agent competent
to produce such effects was recognised by astronomers, the lunar
acceleration presented an unsolved enigma.
At the end of the last century the illustrious French mathematician
Laplace undertook a new investigation of the famous problem, and was
rewarded with a success which for a long time appeared to be quite
complete. Let us suppose that the moon lies directly between the
earth and the sun, then both earth and moon are pulled towards the
sun by the solar attraction; as, however, the moon is the nearer of
the two bodies to the attracting centre it is pulled the more
energetically, and consequently there is an increase in the distance
between the earth and the moon. Similarly when the moon happens to
lie on the other side of the earth, so that the earth is interposed
directly between the moon and the sun, the solar attraction exerted
upon the earth is more powerful than the same influence upon the
moon. Consequently in this case, also, the distance of the moon from
the earth is increased by the solar disturbance. These instances
will illustrate the general truth, that, as one of the consequences
of the disturbing influence exerted by the sun upon the earth-moon
system, there is an increase in the dimensions of the average orbit
which the moon describes around the earth. As the time required by
the moon to accomplish a journey round the earth depends upon its
distance from the earth, it follows that among the influences of the
sun upon the moon there must be an enlargement of the periodic time,
from what it would have been had there been no solar disturbing
action.
This was known long before the time of Laplace, but it did not
directly convey any explanation of the lunar acceleration. It no
doubt amounted to the assertion that the moon's periodic time was
slightly augmented by the disturbance, but it did not give any
grounds for suspecting that there was a continuous change in
progress. It was, however, apparent that the periodic time was
connected with the solar disturbance, so that, if there were any
alteration in the amount of the sun's disturbing effect, there must
be a corresponding alteration in the moon's periodic time. Laplace,
therefore, perceived that, if he could discover any continuous change
in the ability of the sun for disturbing the moon, he would then have
accounted for a continuous change in the moon's periodic time, and
that thus an explanation of the long-vexed question of the lunar
acceleration might be forthcoming.
The capability of the sun for disturbing the earth-moon system is
obviously connected with the distance of the earth from the sun. If
the earth moved in an orbit which underwent no change whatever, then
the efficiency of the sun as a disturbing agent would not undergo any
change of the kind which was sought for. But if there were any
alteration in the shape or size of the earth's orbit, then that might
involve such changes in the distance between the earth and the sun as
would possibly afford the desired agent for producing the observed
lunar effect. It is known that the earth revolves in an orbit which,
though nearly circular, is strictly an ellipse. If the earth were
the only planet revolving around the sun then that ellipse would
remain unaltered from age to age. The earth is, however, only one of
a large number of planets which circulate around the great luminary,
and are guided and controlled by his supreme attracting power. These
planets mutually attract each other, and in consequence of their
mutual attractions the orbits of the planets are disturbed from the
simple elliptic form which they would otherwise possess. The
movement of the earth, for instance, is not, strictly speaking,
performed in an elliptical orbit. We may, however, regard it as
revolving in an ellipse provided we admit that the ellipse is itself
in slow motion.
It is a remarkable characteristic of the disturbing effects of the
planets that the ellipse in which the earth is at any moment moving
always retains the same length; that is to say, its longest diameter
is invariable. In all other respects the ellipse is continually
changing. It alters its position, it changes its plane, and, most
important of all, it changes its eccentricity. Thus, from age to age
the shape of the track which the earth describes may at one time be
growing more nearly a circle, or at another time may be departing
more widely from a circle. These alterations are very small in
amount, and they take place with extreme slowness, but they are in
incessant progress, and their amount admits of being accurately
calculated. At the present time, and for thousands of years past, as
well as for thousands of years to come, the eccentricity of the
earth's orbit is diminishing, and consequently the orbit described by
the earth each year is becoming more nearly circular. We must,
however, remember that under all circumstances the length of the
longest axis of the ellipse is unaltered, and consequently the size
of the track which the earth describes around the sun is gradually
increasing. In other words, it may be said that during the present
ages the average distance between the earth and the sun is waxing
greater in consequence of the perturbations which the earth
experiences from the attraction of the other planets. We have,
however, already seen that the efficiency of the solar attraction for
disturbing the moon's movement depends on the distance between the
earth and the sun. As therefore the average distance between the
earth and the sun is increasing, at all events during the thousands
of years over which our observations extend, it follows that the
ability of the sun for disturbing the moon must be gradually
diminishing.
[PLATE: CAMBRIDGE OBSERVATORY.]
It has been pointed out that, in consequence of the solar
disturbance, the orbit of the moon must be some what enlarged. As it
now appears that the solar disturbance is on the whole declining, it
follows that the orbit of the 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 over-estimated 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 time-piece, 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.