5. DISCOVERY OF THE TRUE SOLAR SYSTEM—TYCHO BRAHE—KEPLER.
During the period of the intellectual and aesthetic revival, at the
beginning of the sixteenth century, the “spirit of the age” was
fostered by the invention of printing, by the downfall of the Byzantine
Empire, and the scattering of Greek fugitives, carrying the treasures
of literature through Western Europe, by the works of Raphael and
Michael Angelo, by the Reformation, and by the extension of the known
world through the voyages of Spaniards and Portuguese. During that
period there came to the front the founder of accurate observational
astronomy. Tycho Brahe, a Dane, born in 1546 of noble parents, was the
most distinguished, diligent, and accurate observer of the heavens
since the days of Hipparchus, 1,700 years before.
Tycho was devoted entirely to his science from childhood, and the
opposition of his parents only stimulated him in his efforts to
overcome difficulties. He soon grasped the hopelessness of the old
deductive methods of reasoning, and decided that no theories ought to
be indulged in until preparations had been made by the accumulation of
accurate observations. We may claim for him the title of founder of the
inductive method.
For a complete life of this great man the reader is referred to
Dreyer’s _Tycho Brahe_, Edinburgh, 1890, containing a complete
bibliography. The present notice must be limited to noting the work
done, and the qualities of character which enabled him to attain his
scientific aims, and which have been conspicuous in many of his
successors.
He studied in Germany, but King Frederick of Denmark, appreciating his
great talents, invited him to carry out his life’s work in that
country. He granted to him the island of Hveen, gave him a pension, and
made him a canon of the Cathedral of Roskilde. On that island Tycho
Brahe built the splendid observatory which he called Uraniborg, and,
later, a second one for his assistants and students, called
Stjerneborg. These he fitted up with the most perfect instruments, and
never lost a chance of adding to his stock of careful observations.[1]
The account of all these instruments and observations, printed at his
own press on the island, was published by Tycho Brahe himself, and the
admirable and numerous engravings bear witness to the excellence of
design and the stability of his instruments.
His mechanical skill was very great, and in his workmanship he was
satisfied with nothing but the best. He recognised the importance of
rigidity in the instruments, and, whereas these had generally been made
of wood, he designed them in metal. His instruments included armillae
like those which had been used in Alexandria, and other armillae
designed by himself—sextants, mural quadrants, large celestial globes
and various instruments for special purposes. He lived before the days
of telescopes and accurate clocks. He invented the method of
sub-dividing the degrees on the arc of an instrument by transversals
somewhat in the way that Pedro Nunez had proposed.
He originated the true system of observation and reduction of
observations, recognising the fact that the best instrument in the
world is not perfect; and with each of his instruments he set to work
to find out the errors of graduation and the errors of mounting, the
necessary correction being applied to each observation.
When he wanted to point his instrument exactly to a star he was
confronted with precisely the same difficulty as is met in gunnery and
rifle-shooting. The sights and the object aimed at cannot be in focus
together, and a great deal depends on the form of sight. Tycho Brahe
invented, and applied to the pointers of his instruments, an
aperture-sight of variable area, like the iris diaphragm used now in
photography. This enabled him to get the best result with stars of
different brightness. The telescope not having been invented, he could
not use a telescopic-sight as we now do in gunnery. This not only
removes the difficulty of focussing, but makes the minimum visible
angle smaller. Helmholtz has defined the minimum angle measurable with
the naked eye as being one minute of arc. In view of this it is simply
marvellous that, when the positions of Tycho’s standard stars are
compared with the best modern catalogues, his probable error in right
ascension is only ± 24”, 1, and in declination only ± 25”, 9.
Clocks of a sort had been made, but Tycho Brahe found them so
unreliable that he seldom used them, and many of his
position-measurements were made by measuring the angular distances from
known stars.
Taking into consideration the absence of either a telescope or a clock,
and reading his account of the labour he bestowed upon each
observation, we must all agree that Kepler, who inherited these
observations in MS., was justified, under the conditions then existing,
in declaring that there was no hope of anyone ever improving upon them.
In the year 1572, on November 11th, Tycho discovered in Cassiopeia a
new star of great brilliance, and continued to observe it until the end
of January, 1573. So incredible to him was such an event that he
refused to believe his own eyes until he got others to confirm what he
saw. He made accurate observations of its distance from the nine
principal stars in Casseiopeia, and proved that it had no measurable
parallax. Later he employed the same method with the comets of 1577,
1580, 1582, 1585, 1590, 1593, and 1596, and proved that they too had no
measurable parallax and must be very distant.
The startling discovery that stars are not necessarily permanent, that
new stars may appear, and possibly that old ones may disappear, had
upon him exactly the same effect that a similar occurrence had upon
Hipparchus 1,700 years before. He felt it his duty to catalogue all the
principal stars, so that there should be no mistake in the future.
During the construction of his catalogue of 1,000 stars he prepared and
used accurate tables of refraction deduced from his own observations.
Thus he eliminated (so far as naked eye observations required) the
effect of atmospheric refraction which makes the altitude of a star
seem greater than it really is.
Tycho Brahe was able to correct the lunar theory by his observations.
Copernicus had introduced two epicycles on the lunar orbit in the hope
of obtaining a better accordance between theory and observation; and he
was not too ambitious, as his desire was to get the tables accurate to
ten minutes. Tycho Brahe found that the tables of Copernicus were in
error as much as two degrees. He re-discovered the inequality called
“variation” by observing the moon in all phases—a thing which had not
been attended to. [It is remarkable that in the nineteenth century Sir
George Airy established an altazimuth at Greenwich Observatory with
this special object, to get observations of the moon in all phases.] He
also discovered other lunar equalities, and wanted to add another
epicycle to the moon’s orbit, but he feared that these would soon
become unmanageable if further observations showed more new
inequalities.
But, as it turned out, the most fruitful work of Tycho Brahe was on the
motions of the planets, and especially of the planet Mars, for it was
by an examination of these results that Kepler was led to the discovery
of his immortal laws.
After the death of King Frederick the observatories of Tycho Brahe were
not supported. The gigantic power and industry displayed by this
determined man were accompanied, as often happens, by an overbearing
manner, intolerant of obstacles. This led to friction, and eventually
the observatories were dismantled, and Tycho Brahe was received by the
Emperor Rudolph II., who placed a house in Prague at his disposal. Here
he worked for a few years, with Kepler as one of his assistants, and he
died in the year 1601.
It is an interesting fact that Tycho Brahe had a firm conviction that
mundane events could be predicted by astrology, and that this belief
was supported by his own predictions.
It has already been stated that Tycho Brahe maintained that observation
must precede theory. He did not accept the Copernican theory that the
earth moves, but for a working hypothesis he used a modification of an
old Egyptian theory, mathematically identical with that of Copernicus,
but not involving a stellar parallax. He says (_De Mundi_, _etc_.) that
the Ptolemean system was too complicated, and the new one which that
great man Copernicus had proposed, following in the footsteps of
Aristarchus of Samos, though there was nothing in it contrary to
mathematical principles, was in opposition to those of physics, as the
heavy and sluggish earth is unfit to move, and the system is even
opposed to the authority of Scripture. The absence of annual parallax
further involves an incredible distance between the outermost planet
and the fixed stars.
We are bound to admit that in the circumstances of the case, so long as
there was no question of dynamical forces connecting the members of the
solar system, his reasoning, as we should expect from such a man, is
practical and sound. It is not surprising, then, that astronomers
generally did not readily accept the views of Copernicus, that Luther
(Luther’s _Tischreden_, pp. 22, 60) derided him in his usual pithy
manner, that Melancthon (_Initia doctrinae physicae_) said that
Scripture, and also science, are against the earth’s motion; and that
the men of science whose opinion was asked for by the cardinals (who
wished to know whether Galileo was right or wrong) looked upon
Copernicus as a weaver of fanciful theories.
Johann Kepler is the name of the man whose place, as is generally
agreed, would have been the most difficult to fill among all those who
have contributed to the advance of astronomical knowledge. He was born
at Wiel, in the Duchy of Wurtemberg, in 1571. He held an appointment at
Gratz, in Styria, and went to join Tycho Brahe in Prague, and to assist
in reducing his observations. These came into his possession when Tycho
Brahe died, the Emperor Rudolph entrusting to him the preparation of
new tables (called the Rudolphine tables) founded on the new and
accurate observations. He had the most profound respect for the
knowledge, skill, determination, and perseverance of the man who had
reaped such a harvest of most accurate data; and though Tycho hardly
recognised the transcendent genius of the man who was working as his
assistant, and although there were disagreements between them, Kepler
held to his post, sustained by the conviction that, with these
observations to test any theory, he would be in a position to settle
for ever the problem of the solar system.
[Illustration: PORTRAIT OF JOHANNES KEPLER. By F.
Wanderer, from Reitlinger’s “Johannes Kepler” (original in
Strassburg).]
It has seemed to many that Plato’s demand for uniform circular motion
(linear or angular) was responsible for a loss to astronomy of good
work during fifteen hundred years, for a hundred ill-considered
speculative cosmogonies, for dissatisfaction, amounting to disgust,
with these _à priori_ guesses, and for the relegation of the science to
less intellectual races than Greeks and other Europeans. Nobody seemed
to dare to depart from this fetish of uniform angular motion and
circular orbits until the insight, boldness, and independence of Johann
Kepler opened up a new world of thought and of intellectual delight.
While at work on the Rudolphine tables he used the old epicycles and
deferents and excentrics, but he could not make theory agree with
observation. His instincts told him that these apologists for uniform
motion were a fraud; and he proved it to himself by trying every
possible variation of the elements and finding them fail. The number of
hypotheses which he examined and rejected was almost incredible (for
example, that the planets turn round centres at a little distance from
the sun, that the epicycles have centres at a little distance from the
deferent, and so on). He says that, after using all these devices to
make theory agree with Tycho’s observations, he still found errors
amounting to eight minutes of a degree. Then he said boldly that it was
impossible that so good an observer as Tycho could have made a mistake
of eight minutes, and added: “Out of these eight minutes we will
construct a new theory that will explain the motions of all the
planets.” And he did it, with elliptic orbits having the sun in a focus
of each.[2]
It is often difficult to define the boundaries between fancies,
imagination, hypothesis, and sound theory. This extraordinary genius
was a master in all these modes of attacking a problem. His analogy
between the spaces occupied by the five regular solids and the
distances of the planets from the sun, which filled him with so much
delight, was a display of pure fancy. His demonstration of the three
fundamental laws of planetary motion was the most strict and complete
theory that had ever been attempted.
It has been often suggested that the revival by Copernicus of the
notion of a moving earth was a help to Kepler. No one who reads
Kepler’s great book could hold such an opinion for a moment. In fact,
the excellence of Copernicus’s book helped to prolong the life of the
epicyclical theories in opposition to Kepler’s teaching.
All of the best theories were compared by him with observation. These
were the Ptolemaic, the Copernican, and the Tychonic. The two latter
placed all of the planetary orbits concentric with one another, the sun
being placed a little away from their common centre, and having no
apparent relation to them, and being actually outside the planes in
which they move. Kepler’s first great discovery was that the planes of
all the orbits pass through the sun; his second was that the line of
apses of each planet passes through the sun; both were contradictory to
the Copernican theory.
He proceeds cautiously with his propositions until he arrives at his
great laws, and he concludes his book by comparing observations of
Mars, of all dates, with his theory.
His first law states that the planets describe ellipses with the sun at
a focus of each ellipse.
His second law (a far more difficult one to prove) states that a line
drawn from a planet to the sun sweeps over equal areas in equal times.
These two laws were published in his great work, _Astronomia Nova, sen.
Physica Coelestis tradita commentariis de Motibus Stelloe; Martis_,
Prague, 1609.
It took him nine years more[3] to discover his third law, that the
squares of the periodic times are proportional to the cubes of the mean
distances from the sun.
These three laws contain implicitly the law of universal gravitation.
They are simply an alternative way of expressing that law in dealing
with planets, not particles. Only, the power of the greatest human
intellect is so utterly feeble that the meaning of the words in
Kepler’s three laws could not be understood until expounded by the
logic of Newton’s dynamics.
The joy with which Kepler contemplated the final demonstration of these
laws, the evolution of which had occupied twenty years, can hardly be
imagined by us. He has given some idea of it in a passage in his work
on _Harmonics_, which is not now quoted, only lest someone might say it
was egotistical—a term which is simply grotesque when applied to such a
man with such a life’s work accomplished.
The whole book, _Astronomia Nova_, is a pleasure to read; the mass of
observations that are used, and the ingenuity of the propositions,
contrast strongly with the loose and imperfectly supported explanations
of all his predecessors; and the indulgent reader will excuse the
devotion of a few lines to an example of the ingenuity and beauty of
his methods.
It may seem a hopeless task to find out the true paths of Mars and the
earth (at that time when their shape even was not known) from the
observations giving only the relative direction from night to night.
Now, Kepler had twenty years of observations of Mars to deal with. This
enabled him to use a new method, to find the earth’s orbit. Observe the
date at any time when Mars is in opposition. The earth’s position E at
that date gives the longitude of Mars M. His period is 687 days. Now
choose dates before and after the principal date at intervals of 687
days and its multiples. Mars is in each case in the same position. Now
for any date when Mars is at M and the earth at E3 the date of the year
gives the angle E3SM. And the observation of Tycho gives the direction
of Mars compared with the sun, SE3M. So all the angles of the triangle
SEM in any of these positions of E are known, and also the ratios of
SE1, SE2, SE3, SE4 to SM and to each other.
For the orbit of Mars observations were chosen at intervals of a year,
when the earth was always in the same place.
But Kepler saw much farther than the geometrical facts. He realised
that the orbits are followed owing to a force directed to the sun; and
he guessed that this is the same force as the gravity that makes a
stone fall. He saw the difficulty of gravitation acting through the
void space. He compared universal gravitation to magnetism, and speaks
of the work of Gilbert of Colchester. (Gilbert’s book, _De Mundo Nostro
Sublunari, Philosophia Nova_, Amstelodami, 1651, containing similar
views, was published forty-eight years after Gilbert’s death, and
forty-two years after Kepler’s book and reference. His book _De
Magnete_ was published in 1600.)
A few of Kepler’s views on gravitation, extracted from the Introduction
to his _Astronomia Nova_, may now be mentioned:—
1. Every body at rest remains at rest if outside the attractive power
of other bodies.
2. Gravity is a property of masses mutually attracting in such manner
that the earth attracts a stone much more than a stone attracts the
earth.
3. Bodies are attracted to the earth’s centre, not because it is the
centre of the universe, but because it is the centre of the attracting
particles of the earth.
4. If the earth be not round (but spheroidal?), then bodies at
different latitudes will not be attracted to its centre, but to
different points in the neighbourhood of that centre.
5. If the earth and moon were not retained in their orbits by vital
force (_aut alia aligua aequipollenti_), the earth and moon would come
together.
6. If the earth were to cease to attract its waters, the oceans would
all rise and flow to the moon.
7. He attributes the tides to lunar attraction. Kepler had been
appointed Imperial Astronomer with a handsome salary (on paper), a
fraction of which was doled out to him very irregularly. He was led to
miserable makeshifts to earn enough to keep his family from starvation;
and proceeded to Ratisbon in 1630 to represent his claims to the Diet.
He arrived worn out and debilitated; he failed in his appeal, and died
from fever, contracted under, and fed upon, disappointment and
exhaustion. Those were not the days when men could adopt as a
profession the “research of endowment.”
Before taking leave of Kepler, who was by no means a man of one idea,
it ought to be here recorded that he was the first to suggest that a
telescope made with both lenses convex (not a Galilean telescope) can
have cross wires in the focus, for use as a pointer to fix accurately
the positions of stars. An Englishman, Gascoigne, was the first to use
this in practice.
From the all too brief epitome here given of Kepler’s greatest book, it
must be obvious that he had at that time some inkling of the meaning of
his laws—universal gravitation. From that moment the idea of universal
gravitation was in the air, and hints and guesses were thrown out by
many; and in time the law of gravitation would doubtless have been
discovered, though probably not by the work of one man, even if Newton
had not lived. But, if Kepler had not lived, who else could have
discovered his laws?
FOOTNOTES:
[1] When the writer visited M. D’Arrest, the astronomer, at
Copenhagen, in 1872, he was presented by D’Arrest with one of several
bricks collected from the ruins of Uraniborg. This was one of his most
cherished possessions until, on returning home after a prolonged
absence on astronomical work, he found that his treasure had been
tidied away from his study.
[2] An ellipse is one of the plane, sections of a cone. It is an oval
curve, which may be drawn by fixing two pins in a sheet of paper at S
and H, fastening a string, SPH, to the two pins, and stretching it
with a pencil point at P, and moving the pencil point, while the
string is kept taut, to trace the oval ellipse, APB. S and H are the
_foci_. Kepler found the sun to be in one focus, say S. AB is the
_major axis_. DE is the _minor axis_. C is the _centre_. The direction
of AB is the _line of apses_. The ratio of CS to CA is the
_excentricity_. The position of the planet at A is the _perihelion_
(nearest to the sun). The position of the planet at B is the
_aphelion_ (farthest from the sun). The angle ASP is the _anomaly_
when the planet is at P. CA or a line drawn from S to D is the _mean
distance_ of the planet from the sun.
[3] The ruled logarithmic paper we now use was not then to be had by
going into a stationer’s shop. Else he would have accomplished this in
five minutes.
6. GALILEO AND THE TELESCOPE—NOTIONS OF GRAVITY BY HORROCKS, ETC.
It is now necessary to leave the subject of dynamical astronomy for a
short time in order to give some account of work in a different
direction originated by a contemporary of Kepler’s, his senior in fact
by seven years. Galileo Galilei was born at Pisa in 1564. The most
scientific part of his work dealt with terrestrial dynamics; but one of
those fortunate chances which happen only to really great men put him
in the way of originating a new branch of astronomy.
The laws of motion had not been correctly defined. The only man of
Galileo’s time who seems to have worked successfully in the same
direction as himself was that Admirable Crichton of the Italians,
Leonardo da Vinci. Galileo cleared the ground. It had always been
noticed that things tend to come to rest; a ball rolled on the ground,
a boat moved on the water, a shot fired in the air. Galileo realised
that in all of these cases a resisting force acts to stop the motion,
and he was the first to arrive at the not very obvious law that the
motion of a body will never stop, nor vary its speed, nor change its
direction, except by the action of some force.
It is not very obvious that a light body and a heavy one fall at the
same speed (except for the resistance of the air). Galileo proved this
on paper, but to convince the world he had to experiment from the
leaning tower of Pisa.
At an early age he discovered the principle of isochronism of the
pendulum, which, in the hands of Huyghens in the middle of the
seventeenth century, led to the invention of the pendulum clock,
perhaps the most valuable astronomical instrument ever produced.
These and other discoveries in dynamics may seem very obvious now; but
it is often the most every-day matters which have been found to elude
the inquiries of ordinary minds, and it required a high order of
intellect to unravel the truth and discard the stupid maxims scattered
through the works of Aristotle and accepted on his authority. A blind
worship of scientific authorities has often delayed the progress of
human knowledge, just as too much “instruction” of a youth often ruins
his “education.” Grant, in his history of Physical Astronomy, has well
said that “the sagacity and skill which Galileo displays in resolving
the phenomena of motion into their constituent elements, and hence
deriving the original principles involved in them, will ever assure to
him a distinguished place among those who have extended the domains of
science.”
But it was work of a different kind that established Galileo’s popular
reputation. In 1609 Galileo heard that a Dutch spectacle-maker had
combined a pair of lenses so as to magnify distant objects. Working on
this hint, he solved the same problem, first on paper and then in
practice. So he came to make one of the first telescopes ever used in
astronomy. No sooner had he turned it on the heavenly bodies than he
was rewarded by such a shower of startling discoveries as forthwith
made his name the best known in Europe. He found curious irregular
black spots on the sun, revolving round it in twenty-seven days; hills
and valleys on the moon; the planets showing discs of sensible size,
not points like the fixed stars; Venus showing phases according to her
position in relation to the sun; Jupiter accompanied by four moons;
Saturn with appendages that he could not explain, but unlike the other
planets; the Milky Way composed of a multitude of separate stars.
His fame flew over Europe like magic, and his discoveries were much
discussed—and there were many who refused to believe. Cosmo de Medici
induced him to migrate to Florence to carry on his observations. He was
received by Paul V., the Pope, at Rome, to whom he explained his
discoveries.
He thought that these discoveries proved the truth of the Copernican
theory of the Earth’s motion; and he urged this view on friends and
foes alike. Although in frequent correspondence with Kepler, he never
alluded to the New Astronomy, and wrote to him extolling the virtue of
epicycles. He loved to argue, never shirked an encounter with any
number of disputants, and laughed as he broke down their arguments.
Through some strange course of events, not easy to follow, the
Copernican theory, whose birth was welcomed by the Church, had now been
taken up by certain anti-clerical agitators, and was opposed by the
cardinals as well as by the dignitaries of the Reformed Church.
Galileo—a good Catholic—got mixed up in these discussions, although on
excellent terms with the Pope and his entourage. At last it came about
that Galileo was summoned to appear at Rome, where he was charged with
holding and teaching heretical opinions about the movement of the
earth; and he then solemnly abjured these opinions. There has been much
exaggeration and misstatement about his trial and punishment, and for a
long time there was a great deal of bitterness shown on both sides. But
the general verdict of the present day seems to be that, although
Galileo himself was treated with consideration, the hostility of the
Church to the views of Copernicus placed it in opposition also to the
true Keplerian system, and this led to unprofitable controversies. From
the time of Galileo onwards, for some time, opponents of religion
included the theory of the Earth’s motion in their disputations, not so
much for the love, or knowledge, of astronomy, as for the pleasure of
putting the Church in the wrong. This created a great deal of
bitterness and intolerance on both sides. Among the sufferers was
Giordano Bruno, a learned speculative philosopher, who was condemned to
be burnt at the stake.
Galileo died on Christmas Day, 1642—the day of Newton’s birth. The
further consideration of the grand field of discovery opened out by
Galileo with his telescopes must be now postponed, to avoid
discontinuity in the history of the intellectual development of this
period, which lay in the direction of dynamical, or physical,
astronomy.
Until the time of Kepler no one seems to have conceived the idea of
universal physical forces controlling terrestrial phenomena, and
equally applicable to the heavenly bodies. The grand discovery by
Kepler of the true relationship of the Sun to the Planets, and the
telescopic discoveries of Galileo and of those who followed him, spread
a spirit of inquiry and philosophic thought throughout Europe, and once
more did astronomy rise in estimation; and the irresistible logic of
its mathematical process of reasoning soon placed it in the position it
has ever since occupied as the foremost of the exact sciences.
The practical application of this process of reasoning was enormously
facilitated by the invention of logarithms by Napier. He was born at
Merchistoun, near Edinburgh, in 1550, and died in 1617. By this system
the tedious arithmetical operations necessary in astronomical
calculations, especially those dealing with the trigonometrical
functions of angles, were so much simplified that Laplace declared that
by this invention the life-work of an astronomer was doubled.
Jeremiah Horrocks (born 1619, died 1641) was an ardent admirer of Tycho
Brahe and Kepler, and was able to improve the Rudolphine tables so much
that he foretold a transit of Venus, in 1639, which these tables failed
to indicate, and was the only observer of it. His life was short, but
he accomplished a great deal, and rightly ascribed the lunar inequality
called _evection_ to variations in the value of the eccentricity and in
the direction of the line of apses, at the same time correctly
assigning _the disturbing force of the Sun_ as the cause. He discovered
the errors in Jupiter’s calculated place, due to what we now know as
the long inequality of Jupiter and Saturn, and measured with
considerable accuracy the acceleration at that date of Jupiter’s mean
motion, and indicated the retardation of Saturn’s mean motion.
Horrocks’ investigations, so far as they could be collected, were
published posthumously in 1672, and seldom, if ever, has a man who
lived only twenty-two years originated so much scientific knowledge.
At this period British science received a lasting impetus by the wise
initiation of a much-abused man, Charles II., who founded the Royal
Society of London, and also the Royal Observatory of Greeenwich, where
he established Flamsteed as first Astronomer Royal, especially for
lunar and stellar observations likely to be useful for navigation. At
the same time the French Academy and the Paris Observatory were
founded. All this within fourteen years, 1662-1675.
Meanwhile gravitation in general terms was being discussed by Hooke,
Wren, Halley, and many others. All of these men felt a repugnance to
accept the idea of a force acting across the empty void of space.
Descartes (1596-1650) proposed an ethereal medium whirling round the
sun with the planets, and having local whirls revolving with the
satellites. As Delambre and Grant have said, this fiction only retarded
the progress of pure science. It had no sort of relation to the more
modern, but equally misleading, “nebular hypothesis.” While many were
talking and guessing, a giant mind was needed at this stage to make
things clear.
7. SIR ISAAC NEWTON—LAW OF UNIVERSAL GRAVITATION.
We now reach the period which is the culminating point of interest in
the history of dynamical astronomy. Isaac Newton was born in 1642.
Pemberton states that Newton, having quitted Cambridge to avoid the
plague, was residing at Wolsthorpe, in Lincolnshire, where he had been
born; that he was sitting one day in the garden, reflecting upon the
force which prevents a planet from flying off at a tangent and which
draws it to the sun, and upon the force which draws the moon to the
earth; and that he saw in the case of the planets that the sun’s force
must clearly be unequal at different distances, for the pull out of the
tangential line in a minute is less for Jupiter than for Mars. He then
saw that the pull of the earth on the moon would be less than for a
nearer object. It is said that while thus meditating he saw an apple
fall from a tree to the ground, and that this fact suggested the
questions: Is the force that pulled that apple from the tree the same
as the force which draws the moon to the earth? Does the attraction for
both of them follow the same law as to distance as is given by the
planetary motions round the sun? It has been stated that in this way
the first conception of universal gravitation arose.[1]
Quite the most important event in the whole history of physical
astronomy was the publication, in 1687, of Newton’s _Principia
(Philosophiae Naturalis Principia Mathematica)_. In this great work
Newton started from the beginning of things, the laws of motion, and
carried his argument, step by step, into every branch of physical
astronomy; giving the physical meaning of Kepler’s three laws, and
explaining, or indicating the explanation of, all the known heavenly
motions and their irregularities; showing that all of these were
included in his simple statement about the law of universal
gravitation; and proceeding to deduce from that law new irregularities
in the motions of the moon which had never been noticed, and to
discover the oblate figure of the earth and the cause of the tides.
These investigations occupied the best part of his life; but he wrote
the whole of his great book in fifteen months.
Having developed and enunciated the true laws of motion, he was able to
show that Kepler’s second law (that equal areas are described by the
line from the planet to the sun in equal times) was only another way of
saying that the centripetal force on a planet is always directed to the
sun. Also that Kepler’s first law (elliptic orbits with the sun in one
focus) was only another way of saying that the force urging a planet to
the sun varies inversely as the square of the distance. Also (if these
two be granted) it follows that Kepler’s third law is only another way
of saying that the sun’s force on different planets (besides depending
as above on distance) is proportional to their masses.
Having further proved the, for that day, wonderful proposition that,
with the law of inverse squares, the attraction by the separate
particles of a sphere of uniform density (or one composed of concentric
spherical shells, each of uniform density) acts as if the whole mass
were collected at the centre, he was able to express the meaning of
Kepler’s laws in propositions which have been summarised as follows:—
The law of universal gravitation.—_Every particle of matter in the
universe attracts every other particle with a force varying inversely
as the square of the distance between them, and directly as the product
of the masses of the two particles_.[2]
But Newton did not commit himself to the law until he had answered that
question about the apple; and the above proposition now enabled him to
deal with the Moon and the apple. Gravity makes a stone fall 16.1 feet
in a second. The moon is 60 times farther from the earth’s centre than
the stone, so it ought to be drawn out of a straight course through
16.1 feet in a minute. Newton found the distance through which she is
actually drawn as a fraction of the earth’s diameter. But when he first
examined this matter he proceeded to use a wrong diameter for the
earth, and he found a serious discrepancy. This, for a time, seemed to
condemn his theory, and regretfully he laid that part of his work
aside. Fortunately, before Newton wrote the _Principia_ the French
astronomer Picard made a new and correct measure of an arc of the
meridian, from which he obtained an accurate value of the earth’s
diameter. Newton applied this value, and found, to his great joy, that
when the distance of the moon is 60 times the radius of the earth she
is attracted out of the straight course 16.1 feet per minute, and that
the force acting on a stone or an apple follows the same law as the
force acting upon the heavenly bodies.[3]
The universality claimed for the law—if not by Newton, at least by his
commentators—was bold, and warranted only by the large number of cases
in which Newton had found it to apply. Its universality has been under
test ever since, and so far it has stood the test. There has often been
a suspicion of a doubt, when some inequality of motion in the heavenly
bodies has, for a time, foiled the astronomers in their attempts to
explain it. But improved mathematical methods have always succeeded in
the end, and so the seeming doubt has been converted into a surer
conviction of the universality of the law.
Having once established the law, Newton proceeded to trace some of its
consequences. He saw that the figure of the earth depends partly on the
mutual gravitation of its parts, and partly on the centrifugal tendency
due to the earth’s rotation, and that these should cause a flattening
of the poles. He invented a mathematical method which he used for
computing the ratio of the polar to the equatorial diameter.
He then noticed that the consequent bulging of matter at the equator
would be attracted by the moon unequally, the nearest parts being most
attracted; and so the moon would tend to tilt the earth when in some
parts of her orbit; and the sun would do this to a less extent, because
of its great distance. Then he proved that the effect ought to be a
rotation of the earth’s axis over a conical surface in space, exactly
as the axis of a top describes a cone, if the top has a sharp point,
and is set spinning and displaced from the vertical. He actually
calculated the amount; and so he explained the cause of the precession
of the equinoxes discovered by Hipparchus about 150 B.C.
One of his grandest discoveries was a method of weighing the heavenly
bodies by their action on each other. By means of this principle he was
able to compare the mass of the sun with the masses of those planets
that have moons, and also to compare the mass of our moon with the mass
of the earth.
Thus Newton, after having established his great principle, devoted his
splendid intellect to the calculation of its consequences. He proved
that if a body be projected with any velocity in free space, subject
only to a central force, varying inversely as the square of the
distance, the body must revolve in a curve which may be any one of the
sections of a cone—a circle, ellipse, parabola, or hyperbola; and he
found that those comets of which he had observations move in parabolae
round the Sun, and are thus subject to the universal law.
Newton realised that, while planets and satellites are chiefly
controlled by the central body about which they revolve, the new law
must involve irregularities, due to their mutual action—such, in fact,
as Horrocks had indicated. He determined to put this to a test in the
case of the moon, and to calculate the sun’s effect, from its mass
compared with that of the earth, and from its distance. He proved that
the average effect upon the plane of the orbit would be to cause the
line in which it cuts the plane of the ecliptic (i.e., the line of
nodes) to revolve in the ecliptic once in about nineteen years. This
had been a known fact from the earliest ages. He also concluded that
the line of apses would revolve in the plane of the lunar orbit also in
about nineteen years; but the observed period is only ten years. For a
long time this was the one weak point in the Newtonian theory. It was
not till 1747 that Clairaut reconciled this with the theory, and showed
why Newton’s calculation was not exact.
Newton proceeded to explain the other inequalities recognised by Tycho
Brahe and older observers, and to calculate their maximum amounts as
indicated by his theory. He further discovered from his calculations
two new inequalities, one of the apogee, the other of the nodes, and
assigned the maximum value. Grant has shown the values of some of these
as given by observation in the tables of Meyer and more modern tables,
and has compared them with the values assigned by Newton from his
theory; and the comparison is very remarkable.
Newton. Modern Tables.
° ’ " ° ’ "
Mean monthly motion of Apses 1.31.28 3.4.0
Mean annual motion of nodes 19.18.1,23 19.21.22,50
Mean value of “variation” 36.10 35.47
Annual equation 11.51 11.14
Inequality of mean motion of apogee 19.43 22.17
Inequality of mean motion of nodes 9.24 9.0
The only serious discrepancy is the first, which has been already
mentioned. Considering that some of these perturbations had never been
discovered, that the cause of none of them had ever been known, and
that he exhibited his results, if he did not also make the discoveries,
by the synthetic methods of geometry, it is simply marvellous that he
reached to such a degree of accuracy. He invented the infinitesimal
calculus which is more suited for such calculations, but had he
expressed his results in that language he would have been
unintelligible to many.
Newton’s method of calculating the precession of the equinoxes, already
referred to, is as beautiful as anything in the _Principia_. He had
already proved the regression of the nodes of a satellite moving in an
orbit inclined to the ecliptic. He now said that the nodes of a ring of
satellites revolving round the earth’s equator would consequently all
regress. And if joined into a solid ring its node would regress; and it
would do so, only more slowly, if encumbered by the spherical part of
the earth’s mass. Therefore the axis of the equatorial belt of the
earth must revolve round the pole of the ecliptic. Then he set to work
and found the amount due to the moon and that due to the sun, and so he
solved the mystery of 2,000 years.
When Newton applied his law of gravitation to an explanation of the
tides he started a new field for the application of mathematics to
physical problems; and there can be little doubt that, if he could have
been furnished with complete tidal observations from different parts of
the world, his extraordinary powers of analysis would have enabled him
to reach a satisfactory theory. He certainly opened up many mines full
of intellectual gems; and his successors have never ceased in their
explorations. This has led to improved mathematical methods, which,
combined with the greater accuracy of observation, have rendered
physical astronomy of to-day the most exact of the sciences.
Laplace only expressed the universal opinion of posterity when he said
that to the _Principia_ is assured “a pre-eminence above all the other
productions of the human intellect.”
The name of Flamsteed, First Astronomer Royal, must here be mentioned
as having supplied Newton with the accurate data required for
completing the theory.
The name of Edmund Halley, Second Astronomer Royal, must ever be held
in repute, not only for his own discoveries, but for the part he played
in urging Newton to commit to writing, and present to the Royal
Society, the results of his investigations. But for his friendly
insistence it is possible that the _Principia_ would never have been
written; and but for his generosity in supplying the means the Royal
Society could not have published the book.
[Illustration: DEATH MASK OF SIR ISAAC NEWTON.
Photographed specially for this work from the original, by kind
permission of the Royal Society, London.]
Sir Isaac Newton died in 1727, at the age of eighty-five. His body lay
in state in the Jerusalem Chamber, and was buried in Westminster Abbey.
FOOTNOTES:
[1] The writer inherited from his father (Professor J. D. Forbes) a
small box containing a bit of wood and a slip of paper, which had been
presented to him by Sir David Brewster. On the paper Sir David had
written these words: “If there be any truth in the story that Newton
was led to the theory of gravitation by the fall of an apple, this bit
of wood is probably a piece of the apple tree from which Newton saw
the apple fall. When I was on a pilgrimage to the house in which
Newton was born, I cut it off an ancient apple tree growing in his
garden.” When lecturing in Glasgow, about 1875, the writer showed it
to his audience. The next morning, when removing his property from the
lecture table, he found that his precious relic had been stolen. It
would be interesting to know who has got it now!
[2] It must be noted that these words, in which the laws of
gravitation are always summarised in histories and text-books, do not
appear in the _Principia_; but, though they must have been composed by
some early commentator, it does not appear that their origin has been
traced. Nor does it appear that Newton ever extended the law beyond
the Solar System, and probably his caution would have led him to avoid
any statement of the kind until it should be proved.
With this exception the above statement of the law of universal
gravitation contains nothing that is not to be found in the
_Principia_; and the nearest approach to that statement occurs in
the Seventh Proposition of Book III.:—
Prop.: That gravitation occurs in all bodies, and that it is
proportional to the quantity of matter in each.
Cor. I.: The total attraction of gravitation on a planet arises,
and is composed, out of the attraction on the separate parts.
Cor. II.: The attraction on separate equal particles of a body is
reciprocally as the square of the distance from the particles.
[3] It is said that, when working out this final result, the
probability of its confirming that part of his theory which he had
reluctantly abandoned years before excited him so keenly that he was
forced to hand over his calculations to a friend, to be completed by
him.
8. NEWTON’S SUCCESSORS—HALLEY, EULER, LAGRANGE, LAPLACE, ETC.
Edmund Halley succeeded Flamsteed as Second Astronomer Royal in 1721.
Although he did not contribute directly to the mathematical proofs of
Newton’s theory, yet his name is closely associated with some of its
greatest successes.
He was the first to detect the acceleration of the moon’s mean motion.
Hipparchus, having compared his own observations with those of more
ancient astronomers, supplied an accurate value of the moon’s mean
motion in his time. Halley similarly deduced a value for modern times,
and found it sensibly greater. He announced this in 1693, but it was
not until 1749 that Dunthorne used modern lunar tables to compute a
lunar eclipse observed in Babylon 721 B.C., another at Alexandria 201
B.C., a solar eclipse observed by Theon 360 A.D., and two later ones up
to the tenth century. He found that to explain these eclipses Halley’s
suggestion must be adopted, the acceleration being 10” in one century.
In 1757 Lalande again fixed it at 10.”
The Paris Academy, in 1770, offered their prize for an investigation to
see if this could be explained by the theory of gravitation. Euler won
the prize, but failed to explain the effect, and said: “It appears to
be established by indisputable evidence that the secular inequality of
the moon’s mean motion cannot be produced by the forces of
gravitation.”
The same subject was again proposed for a prize which was shared by
Lagrange[1] and Euler, neither finding a solution, while the latter
asserted the existence of a resisting medium in space.
Again, in 1774, the Academy submitted the same subject, a third time,
for the prize; and again Lagrange failed to detect a cause in
gravitation.
Laplace[2] now took the matter in hand. He tried the effect of a
non-instantaneous action of gravity, to no purpose. But in 1787 he gave
the true explanation. The principal effect of the sun on the moon’s
orbit is to diminish the earth’s influence, thus lengthening the period
to a new value generally taken as constant. But Laplace’s calculations
showed the new value to depend upon the excentricity of the earth’s
orbit, which, according; to theory, has a periodical variation of
enormous period, and has been continually diminishing for thousands of
years. Thus the solar influence has been diminishing, and the moon’s
mean motion increased. Laplace computed the amount at 10” in one
century, agreeing with observation. (Later on Adams showed that
Laplace’s calculation was wrong, and that the value he found was too
large; so, part of the acceleration is now attributed by some
astronomers to a lengthening of the day by tidal friction.)
Another contribution by Halley to the verification of Newton’s law was
made when he went to St. Helena to catalogue the southern stars. He
measured the change in length of the second’s pendulum in different
latitudes due to the changes in gravity foretold by Newton.
Furthermore, he discovered the long inequality of Jupiter and Saturn,
whose period is 929 years. For an investigation of this also the
Academy of Sciences offered their prize. This led Euler to write a
valuable essay disclosing a new method of computing perturbations,
called the instantaneous ellipse with variable elements. The method was
much developed by Lagrange.
But again it was Laplace who solved the problem of the inequalities of
Jupiter and Saturn by the theory of gravitation, reducing the errors of
the tables from 20’ down to 12”, thus abolishing the use of empirical
corrections to the planetary tables, and providing another glorious
triumph for the law of gravitation. As Laplace justly said: “These
inequalities appeared formerly to be inexplicable by the law of
gravitation—they now form one of its most striking proofs.”
Let us take one more discovery of Halley, furnishing directly a new
triumph for the theory. He noticed that Newton ascribed parabolic
orbits to the comets which he studied, so that they come from infinity,
sweep round the sun, and go off to infinity for ever, after having been
visible a few weeks or months. He collected all the reliable
observations of comets he could find, to the number of twenty-four, and
computed their parabolic orbits by the rules laid down by Newton. His
object was to find out if any of them really travelled in elongated
ellipses, practically undistinguishable, in the visible part of their
paths, from parabolæ, in which case they would be seen more than once.
He found two old comets whose orbits, in shape and position, resembled
the orbit of a comet observed by himself in 1682. Apian observed one in
1531; Kepler the other in 1607. The intervals between these appearances
is seventy-five or seventy-six years. He then examined and found old
records of similar appearance in 1456, 1380, and 1305. It is true, he
noticed, that the intervals varied by a year and a-half, and the
inclination of the orbit to the ecliptic diminished with successive
apparitions. But he knew from previous calculations that this might
easily be due to planetary perturbations. Finally, he arrived at the
conclusion that all of these comets were identical, travelling in an
ellipse so elongated that the part where the comet was seen seemed to
be part of a parabolic orbit. He then predicted its return at the end
of 1758 or beginning of 1759, when he should be dead; but, as he said,
“if it should return, according to our prediction, about the year 1758,
impartial posterity will not refuse to acknowledge that this was first
discovered by an Englishman.”[3] [_Synopsis Astronomiae Cometicae_,
1749.]
Once again Halley’s suggestion became an inspiration for the
mathematical astronomer. Clairaut, assisted by Lalande, found that
Saturn would retard the comet 100 days, Jupiter 518 days, and predicted
its return to perihelion on April 13th, 1759. In his communication to
the French Academy, he said that a comet travelling into such distant
regions might be exposed to the influence of forces totally unknown,
and “even of some planet too far removed from the sun to be ever
perceived.”
The excitement of astronomers towards the end of 1758 became intense;
and the honour of first catching sight of the traveller fell to an
amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached
perihelion on March 13th, 1759.
This fact was a startling confirmation of the Newtonian theory, because
it was a new kind of calculation of perturbations, and also it added a
new member to the solar system, and gave a prospect of adding many
more.
When Halley’s comet reappeared in 1835, Pontecoulant’s computations for
the date of perihelion passage were very exact, and afterwards he
showed that, with more exact values of the masses of Jupiter and
Saturn, his prediction was correct within two days, after an invisible
voyage of seventy-five years!
Hind afterwards searched out many old appearances of this comet, going
back to 11 B.C., and most of these have been identified as being really
Halley’s comet by the calculations of Cowell and Cromellin[4] (of
Greenwich Observatory), who have also predicted its next perihelion
passage for April 8th to 16th, 1910, and have traced back its history
still farther, to 240 B.C.
Already, in November, 1907, the Astronomer Royal was trying to catch it
by the aid of photography.
FOOTNOTES:
[1] Born 1736; died 1813.
[2] Born 1749; died 1827.
[3] This sentence does not appear in the original memoir communicated
to the Royal Society, but was first published in a posthumous reprint.
[4] _R. A. S. Monthly Notices_, 1907-8.
9. DISCOVERY OF NEW PLANETS—HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER.
It would be very interesting, but quite impossible in these pages, to
discuss all the exquisite researches of the mathematical astronomers,
and to inspire a reverence for the names connected with these
researches, which for two hundred years have been establishing the
universality of Newton’s law. The lunar and planetary theories, the
beautiful theory of Jupiter’s satellites, the figure of the earth, and
the tides, were mathematically treated by Maclaurin, D’Alembert,
Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly,
Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana,
Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier,
Adams, and others of later date.
By passing over these important developments it is possible to trace
some of the steps in the crowning triumph of the Newtonian theory, by
which the planet Neptune was added to the known members of the solar
system by the independent researches of Professor J.C. Adams and of M.
Le Verrier, in 1846.
It will be best to introduce this subject by relating how the
eighteenth century increased the number of known planets, which was
then only six, including the earth.
On March 13th, 1781, Sir William Herschel was, as usual, engaged on
examining some small stars, and, noticing that one of them appeared to
be larger than the fixed stars, suspected that it might be a comet. To
test this he increased his magnifying power from 227 to 460 and 932,
finding that, unlike the fixed stars near it, its definition was
impaired and its size increased. This convinced him that the object was
a comet, and he was not surprised to find on succeeding nights that the
position was changed, the motion being in the ecliptic. He gave the
observations of five weeks to the Royal Society without a suspicion
that the object was a new planet.
For a long time people could not compute a satisfactory orbit for the
supposed comet, because it seemed to be near the perihelion, and no
comet had ever been observed with a perihelion distance from the sun
greater than four times the earth’s distance. Lexell was the first to
suspect that this was a new planet eighteen times as far from the sun
as the earth is. In January, 1783, Laplace published the elliptic
elements. The discoverer of a planet has a right to name it, so
Herschel called it Georgium Sidus, after the king. But Lalande urged
the adoption of the name Herschel. Bode suggested Uranus, and this was
adopted. The new planet was found to rank in size next to Jupiter and
Saturn, being 4.3 times the diameter of the earth.
In 1787 Herschel discovered two satellites, both revolving in nearly
the same plane, inclined 80° to the ecliptic, and the motion of both
was retrograde.
In 1772, before Herschel’s discovery, Bode[1] had discovered a curious
arbitrary law of planetary distances. Opposite each planet’s name write
the figure 4; and, in succession, add the numbers 0, 3, 6, 12, 24, 48,
96, _etc_., to the 4, always doubling the last numbers. You then get
the planetary distances.
Mercury, dist.-- 4 4 + 0 = 4
Venus " 7 4 + 3 = 7
Earth " 10 4 + 6 = 10
Mars " 15 4 + 12 = 16
-- 4 + 24 = 28
Jupiter dist. 52 4 + 48 = 52
Saturn " 95 4 + 96 = 100
(Uranus) " 192 4 + 192 = 196
-- 4 + 384 = 388
All the five planets, and the earth, fitted this rule, except that
there was a blank between Mars and Jupiter. When Uranus was discovered,
also fitting the rule, the conclusion was irresistible that there is
probably a planet between Mars and Jupiter. An association of
twenty-four astronomers was now formed in Germany to search for the
planet. Almost immediately afterwards the planet was discovered, not by
any member of the association, but by Piazzi, when engaged upon his
great catalogue of stars. On January 1st, 1801, he observed a star
which had changed its place the next night. Its motion was retrograde
till January 11th, direct after the 13th. Piazzi fell ill before he had
enough observations for computing the orbit with certainty, and the
planet disappeared in the sun’s rays. Gauss published an approximate
ephemeris of probable positions when the planet should emerge from the
sun’s light. There was an exciting hunt, and on December 31st (the day
before its birthday) De Zach captured the truant, and Piazzi christened
it Ceres.
The mean distance from the sun was found to be 2.767, agreeing with the
2.8 given by Bode’s law. Its orbit was found to be inclined over 10° to
the ecliptic, and its diameter was only 161 miles.
On March 28th, 1802, Olbers discovered a new seventh magnitude star,
which turned out to be a planet resembling Ceres. It was called Pallas.
Gauss found its orbit to be inclined 35° to the ecliptic, and to cut
the orbit of Ceres; whence Olbers considered that these might be
fragments of a broken-up planet. He then commenced a search for other
fragments. In 1804 Harding discovered Juno, and in 1807 Olbers found
Vesta. The next one was not discovered until 1845, from which date
asteroids, or minor planets (as these small planets are called), have
been found almost every year. They now number about 700.
It is impossible to give any idea of the interest with which the first
additions since prehistoric times to the planetary system were
received. All of those who showered congratulations upon the
discoverers regarded these discoveries in the light of rewards for
patient and continuous labours, the very highest rewards that could be
desired. And yet there remained still the most brilliant triumph of
all, the addition of another planet like Uranus, before it had ever
been seen, when the analysis of Adams and Le Verrier gave a final proof
of the powers of Newton’s great law to explain any planetary
irregularity.
After Sir William Herschel discovered Uranus, in 1781, it was found
that astronomers had observed it on many previous occasions, mistaking
it for a fixed star of the sixth or seventh magnitude. Altogether,
nineteen observations of Uranus’s position, from the time of Flamsteed,
in 1690, had been recorded.
In 1790 Delambre, using all these observations, prepared tables for
computing its position. These worked well enough for a time, but at
last the differences between the calculated and observed longitudes of
the planet became serious. In 1821 Bouvard undertook a revision of the
tables, but found it impossible to reconcile all the observations of
130 years (the period of revolution of Uranus is eighty-four years). So
he deliberately rejected the old ones, expressing the opinion that the
discrepancies might depend upon “some foreign and unperceived cause
which may have been acting upon the planet.” In a few years the errors
even of these tables became intolerable. In 1835 the error of longitude
was 30”; in 1838, 50”; in 1841, 70”; and, by comparing the errors
derived from observations made before and after opposition, a serious
error of the distance (radius vector) became apparent.
In 1843 John Couch Adams came out Senior Wrangler at Cambridge, and was
free to undertake the research which as an undergraduate he had set
himself—to see whether the disturbances of Uranus could be explained by
assuming a certain orbit, and position in that orbit, of a hypothetical
planet even more distant than Uranus. Such an explanation had been
suggested, but until 1843 no one had the boldness to attack the
problem. Bessel had intended to try, but a fatal illness overtook him.
Adams first recalculated all known causes of disturbance, using the
latest determinations of the planetary masses. Still the errors were
nearly as great as ever. He could now, however, use these errors as
being actually due to the perturbations produced by the unknown planet.
In 1844, assuming a circular orbit, and a mean distance agreeing with
Bode’s law, he obtained a first approximation to the position of the
supposed planet. He then asked Professor Challis, of Cambridge, to
procure the latest observations of Uranus from Greenwich, which Airy
immediately supplied. Then the whole work was recalculated from the
beginning, with more exactness, and assuming a smaller mean distance.
In September, 1845, he handed to Challis the elements of the
hypothetical planet, its mass, and its apparent position for September
30th, 1845. On September 22nd Challis wrote to Airy explaining the
matter, and declaring his belief in Adams’s capabilities. When Adams
called on him Airy was away from home, but at the end of October, 1845,
he called again, and left a paper with full particulars of his results,
which had, for the most part, reduced the discrepancies to about 1”. As
a matter of fact, it has since been found that the heliocentric place
of the new planet then given was correct within about 2°.
Airy wrote expressing his interest, and asked for particulars about the
radius vector. Adams did not then reply, as the answer to this question
could be seen to be satisfactory by looking at the data already
supplied. He was a most unassuming man, and would not push himself
forward. He may have felt, after all the work he had done, that Airy’s
very natural inquiry showed no proportionate desire to search for the
planet. Anyway, the matter lay in embryo for nine months.
Meanwhile, one of the ablest French astronomers, Le Verrier,
experienced in computing perturbations, was independently at work,
knowing nothing about Adams. He applied to his calculations every
possible refinement, and, considering the novelty of the problem, his
calculation was one of the most brilliant in the records of astronomy.
In criticism it has been said that these were exhibitions of skill
rather than helps to a solution of the particular problem, and that, in
claiming to find the elements of the orbit within certain limits, he
was claiming what was, under the circumstances, impossible, as the
result proved.
In June, 1846, Le Verrier announced, in the _Comptes Rendus de
l’Academie des Sciences_, that the longitude of the disturbing planet,
for January 1st, 1847, was 325, and that the probable error did not
exceed 10°.
This result agreed so well with Adams’s (within 1°) that Airy urged
Challis to apply the splendid Northumberland equatoreal, at Cambridge,
to the search. Challis, however, had already prepared an exhaustive
plan of attack which must in time settle the point. His first work was
to observe, and make a catalogue, or chart, of all stars near Adams’s
position.
On August 31st, 1846, Le Verrier published the concluding part of his
labours.
On September 18th, 1846, Le Verrier communicated his results to the
Astronomers at Berlin, and asked them to assist in searching for the
planet. By good luck Dr. Bremiker had just completed a star-chart of
the very part of the heavens including Le Verrier’s position; thus
eliminating all of Challis’s preliminary work. The letter was received
in Berlin on September 23rd; and the same evening Galle found the new
planet, of the eighth magnitude, the size of its disc agreeing with Le
Verrier’s prediction, and the heliocentric longitude agreeing within
57’. By this time Challis had recorded, without reduction, the
observations of 3,150 stars, as a commencement for his search. On
reducing these, he found a star, observed on August 12th, which was not
in the same place on July 30th. This was the planet, and he had also
observed it on August 4th.
The feeling of wonder, admiration, and enthusiasm aroused by this
intellectual triumph was overwhelming. In the world of astronomy
reminders are met every day of the terrible limitations of human
reasoning powers; and every success that enables the mind’s eye to see
a little more clearly the meaning of things has always been heartily
welcomed by those who have themselves been engaged in like researches.
But, since the publication of the _Principia_, in 1687, there is
probably no analytical success which has raised among astronomers such
a feeling of admiration and gratitude as when Adams and Le Verrier
showed the inequalities in Uranus’s motion to mean that an unknown
planet was in a certain place in the heavens, where it was found.
At the time there was an unpleasant display of international jealousy.
The British people thought that the earlier date of Adams’s work, and
of the observation by Challis, entitled him to at least an equal share
of credit with Le Verrier. The French, on the other hand, who, on the
announcement of the discovery by Galle, glowed with pride in the new
proof of the great powers of their astronomer, Le Verrier, whose life
had a long record of successes in calculation, were incredulous on
being told that it had all been already done by a young man whom they
had never heard of.
These displays of jealousy have long since passed away, and there is
now universally an _entente cordiale_ that to each of these great men
belongs equally the merit of having so thoroughly calculated this
inverse problem of perturbations as to lead to the immediate discovery
of the unknown planet, since called Neptune.
It was soon found that the planet had been observed, and its position
recorded as a fixed star by Lalande, on May 8th and 10th, 1795.
Mr. Lassel, in the same year, 1846, with his two-feet reflector,
discovered a satellite, with retrograde motion, which gave the mass of
the planet about a twentieth of that of Jupiter.
FOOTNOTES:
[1] Bode’s law, or something like it, had already been fore-shadowed
by Kepler and others, especially Titius (see _Monatliche
Correspondenz_, vol. vii., p. 72).