BOOK II. THE DYNAMICAL PERIOD

BOOK II. THE DYNAMICAL PERIOD

5. DISCOVERY OF THE TRUE SOLARSYSTEM--TYCHO BRAHE--KEPLER.

During the period of the intellectual andaesthetic revival, at the

beginning of the sixteenth century, the"spirit of the age" was

fostered by the invention of printing, bythe downfall of the

Byzantine Empire, and the scattering ofGreek fugitives, carrying the

treasures of literature through WesternEurope, by the works of

Raphael and Michael Angelo, by theReformation, and by the extension

of the known world through the voyages ofSpaniards and Portuguese.

During that period there came to the frontthe founder of accurate

observational astronomy. Tycho Brahe, aDane, born in 1546 of noble

parents, was the most distinguished,diligent, and accurate observer

of the heavens since the days ofHipparchus, 1,700 years before.

Tycho was devoted entirely to his sciencefrom childhood, and the

opposition of his parents only stimulatedhim in his efforts to

overcome difficulties.  He soon grasped the hopelessness of the old

deductive methods of reasoning, and decidedthat no theories ought to

be indulged in until preparations had beenmade 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 thereader is referred to

Dreyer's _Tycho Brahe_, Edinburgh, 1890,containing a complete

bibliography. The present notice must belimited to noting the work

done, and the qualities of character which enabledhim to attain his

scientific aims, and which have beenconspicuous in many of his

successors.

He studied in Germany, but King Frederickof Denmark, appreciating his

great talents, invited him to carry out hislife's work in that

country. He granted to him the island ofHveen, gave him a pension,

and made him a canon of the Cathedral ofRoskilde. On that island

Tycho Brahe built the splendid observatorywhich he called Uraniborg,

and, later, a second one for his assistantsand students, called

Stjerneborg. These he fitted up with themost perfect instruments, and

never lost a chance of adding to his stockof careful observations.[1]

The account of all these instruments andobservations, printed at his

own press on the island, was published byTycho Brahe himself, and the

admirable and numerous engravings bearwitness to the excellence of

design and the stability of hisinstruments.

His mechanical skill was very great, and inhis workmanship he was

satisfied with nothing but the best. Herecognised the importance of

rigidity in the instruments, and, whereasthese had generally been

made of wood, he designed them in metal.His instruments included

armillae like those which had been used inAlexandria, and other

armillae designed by himself--sextants,mural quadrants, large

celestial globes and various instrumentsfor special purposes. He

lived before the days of telescopes andaccurate clocks. He invented

the method of sub-dividing the degrees onthe arc of an instrument by

transversals somewhat in the way that PedroNunez had proposed.

He originated the true system ofobservation and reduction of

observations, recognising the fact that thebest instrument in the

world is not perfect; and with each of hisinstruments he set to work

to find out the errors of graduation andthe errors of mounting, the

necessary correction being applied to eachobservation.

When he wanted to point his instrumentexactly to a star he was

confronted with precisely the samedifficulty as is met in gunnery and

rifle-shooting. The sights and the objectaimed at cannot be in focus

together, and a great deal depends on theform of sight. Tycho Brahe

invented, and applied to the pointers ofhis instruments, an

aperture-sight of variable area, like theiris diaphragm used now in

photography. This enabled him to get thebest result with stars of

different brightness.  The telescope not having been invented, he

could not use a telescopic-sight as we nowdo in gunnery.  This not

only removes the difficulty of focussing,but makes the minimum

visible angle smaller. Helmholtz hasdefined the minimum angle

measurable with the naked eye as being oneminute of arc. In view of

this it is simply marvellous that, when thepositions of Tycho's

standard stars are compared with the bestmodern 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 TychoBrahe found them so

unreliable that he seldom used them, and manyof his position-measurements

were made by measuring the angulardistances from known stars.

Taking into consideration the absence ofeither a telescope or a

clock, and reading his account of thelabour he bestowed upon each

observation, we must all agree that Kepler,who inherited these

observations in MS., was justified, underthe conditions then

existing, in declaring that there was nohope of anyone ever improving

upon them.

In the year 1572, on November 11th, Tychodiscovered in Cassiopeia a

new star of great brilliance, and continuedto observe it until the

end of January, 1573. So incredible to himwas such an event that he

refused to believe his own eyes until hegot others to confirm what he

saw. He made accurate observations of itsdistance from the nine

principal stars in Casseiopeia, and provedthat it had no measurable

parallax. Later he employed the same methodwith the comets of 1577,

1580, 1582, 1585, 1590, 1593, and 1596, andproved that they too had

no measurable parallax and must be verydistant.

The startling discovery that stars are notnecessarily permanent, that

new stars may appear, and possibly that oldones may disappear, had

upon him exactly the same effect that asimilar occurrence had upon

Hipparchus 1,700 years before. He felt ithis duty to catalogue all

the principal stars, so that there shouldbe no mistake in the

future. During the construction of hiscatalogue of 1,000 stars he

prepared and used accurate tables ofrefraction deduced from his own

observations. Thus he eliminated (so far asnaked eye observations

required) the effect of atmosphericrefraction which makes the

altitude of a star seem greater than itreally is.

Tycho Brahe was able to correct the lunartheory by his observations.

Copernicus had introduced two epicycles onthe lunar orbit in the hope

of obtaining a better accordance betweentheory and observation; and

he was not too ambitious, as his desire wasto get the tables accurate

to ten minutes. Tycho Brahe found that thetables of Copernicus were

in error as much as two degrees. Here-discovered the inequality

called "variation" by observingthe moon in all phases--a thing which

had not been attended to. [It is remarkablethat in the nineteenth

century Sir George Airy established analtazimuth at Greenwich

Observatory with this special object, toget observations of the moon

in all phases.] He also discovered otherlunar equalities, and wanted

to add another epicycle to the moon'sorbit, but he feared that these

would soon become unmanageable if furtherobservations showed more new

inequalities.

But, as it turned out, the most fruitfulwork of Tycho Brahe was on

the motions of the planets, and especiallyof the planet Mars, for it

was by an examination of these results thatKepler was led to the

discovery of his immortal laws.

After the death of King Frederick theobservatories of Tycho Brahe

were not supported. The gigantic power andindustry displayed by this

determined man were accompanied, as oftenhappens, by an overbearing

manner, intolerant of obstacles. This ledto friction, and eventually

the observatories were dismantled, andTycho Brahe was received by the

Emperor Rudolph II., who placed a house inPrague at his disposal.

Here he worked for a few years, with Kepleras one of his assistants,

and he died in the year 1601.

It is an interesting fact that Tycho Brahehad a firm conviction that

mundane events could be predicted byastrology, and that this belief

was supported by his own predictions.

It has already been stated that Tycho Brahemaintained that

observation must precede theory. He did notaccept the Copernican

theory that the earth moves, but for aworking hypothesis he used a

modification of an old Egyptian theory,mathematically identical with

that of Copernicus, but not involving astellar parallax.  He says

(_De Mundi_, etc.) that

  thePtolemean 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

  theheavy 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 thecircumstances of the case, so long

as there was no question of dynamicalforces connecting the members of

the solar system, his reasoning, as weshould expect from such a man,

is practical and sound. It is notsurprising, then, that astronomers

generally did not readily accept the viewsof Copernicus, that Luther

(Luther's _Tischreden_, pp.  22, 60) derided him in his usual pithy

manner, that Melancthon (_Initia doctrinaephysicae_) said that

Scripture, and also science, are againstthe earth's motion; and that

the men of science whose opinion was askedfor by the cardinals (who

wished to know whether Galileo was right orwrong) looked upon

Copernicus as a weaver of fancifultheories.

Johann Kepler is the name of the man whoseplace, as is generally

agreed, would have been the most difficultto fill among all those who

have contributed to the advance ofastronomical knowledge. He was born

at Wiel, in the Duchy of Wurtemberg, in1571. He held an appointment

at Gratz, in Styria, and went to join TychoBrahe in Prague, and to

assist in reducing his observations. Thesecame into his possession

when Tycho Brahe died, the Emperor Rudolphentrusting to him the

preparation of new tables (called theRudolphine tables) founded on

the new and accurate observations. He hadthe most profound respect

for the knowledge, skill, determination, andperseverance of the man

who had reaped such a harvest of mostaccurate data; and though Tycho

hardly recognised the transcendent geniusof the man who was working

as his assistant, and although there weredisagreements between them,

Kepler held to his post, sustained by theconviction that, with these

observations to test any theory, he wouldbe in a position to settle

for ever the problem of the solar system.

[Illustration: PORTRAIT OF JOHANNESKEPLER.  By F. Wanderer, from

Reitlinger's "Johannes Kepler"(original in Strassburg).]

It has seemed to many that Plato's demandfor uniform circular motion

(linear or angular) was responsible for aloss to astronomy of good

work during fifteen hundred years, for ahundred ill-considered

speculative cosmogonies, fordissatisfaction, amounting to disgust,

with these _à priori_ guesses, and for therelegation of the

science to less intellectual races thanGreeks and other Europeans.

Nobody seemed to dare to depart from thisfetish of uniform angular

motion and circular orbits until theinsight, boldness, and

independence of Johann Kepler opened up anew world of thought and of

intellectual delight.

While at work on the Rudolphine tables heused the old epicycles and

deferents and excentrics, but he could notmake theory agree with

observation. His instincts told him thatthese apologists for uniform

motion were a fraud; and he proved it tohimself by trying every

possible variation of the elements andfinding them fail.  The number

of hypotheses which he examined andrejected was almost incredible

(for example, that the planets turn roundcentres at a little distance

from the sun, that the epicycles havecentres at a little distance

from the deferent, and so on). He saysthat, after using all these

devices to make theory agree with Tycho'sobservations, he still found

errors amounting to eight minutes of adegree. Then he said boldly

that it was impossible that so good anobserver as Tycho could have

made a mistake of eight minutes, and added:"Out of these eight

minutes we will construct a new theory thatwill 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 theboundaries between fancies,

imagination, hypothesis, and soundtheory.  This extraordinary genius

was a master in all these modes ofattacking a problem. His analogy

between the spaces occupied by the fiveregular solids and the

distances of the planets from the sun, whichfilled him with so much

delight, was a display of pure fancy. Hisdemonstration of the three

fundamental laws of planetary motion wasthe most strict and complete

theory that had ever been attempted.

It has been often suggested that therevival by Copernicus of the

notion of a moving earth was a help toKepler. No one who reads

Kepler's great book could hold such anopinion for a moment. In fact,

the excellence of Copernicus's book helpedto prolong the life of the

epicyclical theories in opposition toKepler's teaching.

All of the best theories were compared byhim with observation. These

were the Ptolemaic, the Copernican, and theTychonic. The two latter

placed all of the planetary orbitsconcentric with one another, the

sun being placed a little away from theircommon centre, and having no

apparent relation to them, and beingactually outside the planes in

which they move.  Kepler's first great discovery was that theplanes

of all the orbits pass through the sun; hissecond was that the line

of apses of each planet passes through thesun; both were

contradictory to the Copernican theory.

He proceeds cautiously with hispropositions until he arrives at his

great laws, and he concludes his book bycomparing observations of

Mars, of all dates, with his theory.

His first law states that the planetsdescribe ellipses with the sun

at a focus of each ellipse.

His second law (a far more difficult one toprove) states that a line

drawn from a planet to the sun sweeps overequal areas in equal

times. These two laws were published in hisgreat work, _Astronomia

Nova, sen.  Physica Coelestis tradita commentariis deMotibus Stelloe;

Martis_, Prague, 1609.

It took him nine years more[3] to discoverhis third law, that the

squares of the periodic times areproportional to the cubes of the

mean distances from the sun.

These three laws contain implicitly the lawof universal

gravitation. They are simply an alternativeway of expressing that law

in dealing with planets, not particles.Only, the power of the

greatest human intellect is so utterlyfeeble that the meaning of the

words in Kepler's three laws could not beunderstood until expounded

by the logic of Newton's dynamics.

The joy with which Kepler contemplated thefinal demonstration of

these laws, the evolution of which hadoccupied 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 notnow quoted, only lest

someone might say it was egotistical--aterm which is simply grotesque

when applied to such a man with such alife's work accomplished.

The whole book, _Astronomia Nova_, is apleasure to read; the

mass of observations that are used, and theingenuity of the

propositions, contrast strongly with theloose and imperfectly

supported explanations of all hispredecessors; and the indulgent

reader will excuse the devotion of a fewlines to an example of the

ingenuity and beauty of his methods.

It may seem a hopeless task to find out thetrue paths of Mars and the

earth (at that time when their shape evenwas not known) from the

observations giving only the relativedirection from night to

night. Now, Kepler had twenty years ofobservations 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 whenMars is in opposition. The

earth's position E at that date gives thelongitude of Mars M. His

period is 687 days. Now choose dates beforeand after the principal

date at intervals of 687 days and itsmultiples.  Mars is in each case

in the same position. Now for any date whenMars 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 ofMars compared with the

sun, SE₃M. So all the angles of the triangle SEM in any of these

positions of E are known, and also theratios of SE₁,SE₂,SE₃,

SE₄ to SM and to each other.

For the orbit of Mars observations werechosen at intervals of a year,

when the earth was always in the sameplace.

[Illustration]

But Kepler saw much farther than thegeometrical facts. He realised

that the orbits are followed owing to aforce directed to the sun; and

he guessed that this is the same force asthe gravity that makes a

stone fall. He saw the difficulty ofgravitation acting through the

void space. He compared universal gravitation to magnetism, and

speaks of the work of Gilbert ofColchester.  (Gilbert's book, _De

Mundo NostroSublunari, Philosophia Nova_, Amstelodami, 1651,

containing similar views, was publishedforty-eight years after

Gilbert's death, and forty-two years afterKepler'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_, maynow be mentioned:--

1. Every body at rest remains at rest ifoutside the attractive power

of other bodies.

2. Gravity is a property of masses mutuallyattracting in such manner

that the earth attracts a stone much morethan a stone attracts the

earth.

3. Bodies are attracted to the earth'scentre, not because it is the

centre of the universe, but because it isthe centre of the attracting

particles of the earth.

4. If the earth be not round (butspheroidal?), then bodies at

different latitudes will not be attractedto its centre, but to

different points in the neighbourhood ofthat centre.

5. If the earth and moon were not retainedin their orbits by vital

force (_aut alia aligua aequipollenti_),the earth and moon would come

together.

6. If the earth were to cease to attractits waters, the oceans would

all rise and flow to the moon.

7. He attributes the tides to lunarattraction.  Kepler had been

appointed Imperial Astronomer with ahandsome salary (on paper), a

fraction of which was doled out to him veryirregularly. He was led to

miserable makeshifts to earn enough to keephis family from

starvation; and proceeded to Ratisbon in1630 to represent his claims

to the Diet. He arrived worn out anddebilitated; he failed in his

appeal, and died from fever, contractedunder, and fed upon,

disappointment and exhaustion. Those werenot the days when men could

adopt as a profession the "research ofendowment."

Before taking leave of Kepler, who was byno means a man of one idea,

it ought to be here recorded that he wasthe first to suggest that a

telescope made with both lenses convex (nota Galilean telescope) can

have cross wires in the focus, for use as apointer 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 givenof Kepler's greatest book,

it must be obvious that he had at that timesome 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 ofgravitation would doubtless

have been discovered, though probably notby the work of one man, even

if Newton had not lived. But, if Kepler hadnot 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 byD'Arrest with one of several

bricks collected from the ruins ofUraniborg. This was one of his most

cherished possessions until, on returninghome after a prolonged

absence on astronomical work, he found thathis 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 twopins in a sheet of paper at S

and H, fastening a string, SPH, to the twopins, and stretching it

with a pencil point at P, and moving thepencil point, while the

string is kept taut, to trace the ovalellipse, APB. S and H are the

_foci_. Kepler found the sun to be in onefocus, say S. AB is the

_major axis_. DE is the _minor axis_. C isthe _centre_. The direction

of AB is the _line of apses_. The ratio ofCS to CA is the

_excentricity_. The position of the planetat A is the _perihelion_

(nearest to the sun). The position of theplanet at B is the

_aphelion_ (farthest from the sun). Theangle ASP is the _anomaly_

when the planet is at P. CA or a line drawnfrom S to D is the _mean

distance_ of the planet from the sun.

[Illustration]

[3] The ruled logarithmic paper we now usewas not then to be had by

going into a stationer's shop. Else hewould have accomplished this in

five minutes.

6. GALILEO AND THE TELESCOPE--NOTIONS OFGRAVITY BY HORROCKS, ETC.

It is now necessary to leave the subject ofdynamical astronomy for a

short time in order to give some account ofwork in a different

direction originated by a contemporary ofKepler's, his senior in fact

by seven years. Galileo Galilei was born atPisa in 1564. The most

scientific part of his work dealt withterrestrial dynamics; but one

of those fortunate chances which happenonly to really great men put

him in the way of originating a new branchof astronomy.

The laws of motion had not been correctlydefined.  The only man of

Galileo's time who seems to have workedsuccessfully in the same

direction as himself was that AdmirableCrichton of the Italians,

Leonardo da Vinci. Galileo cleared theground. It had always been

noticed that things tend to come to rest; aball rolled on the ground,

a boat moved on the water, a shot fired inthe air. Galileo realised

that in all of these cases a resistingforce acts to stop the motion,

and he was the first to arrive at the notvery obvious law that the

motion of a body will never stop, nor varyits speed, nor change its

direction, except by the action of someforce.

It is not very obvious that a light bodyand a heavy one fall at the

same speed (except for the resistance ofthe air). Galileo proved this

on paper, but to convince the world he hadto experiment from the

leaning tower of Pisa.

At an early age he discovered the principleof isochronism of the

pendulum, which, in the hands of Huyghensin the middle of the

seventeenth century, led to the inventionof the pendulum clock,

perhaps the most valuable astronomicalinstrument ever produced.

These and other discoveries in dynamics mayseem very obvious now; but

it is often the most every-day matterswhich have been found to elude

the inquiries of ordinary minds, and itrequired a high order of

intellect to unravel the truth and discardthe stupid maxims scattered

through the works of Aristotle and acceptedon his authority. A blind

worship of scientific authorities has oftendelayed the progress of

human knowledge, just as too much"instruction" of a youth often ruins

his "education." Grant, in hishistory of Physical Astronomy, has well

said that "the sagacity and skillwhich Galileo displays in resolving

the phenomena of motion into theirconstituent elements, and hence

deriving the original principles involvedin them, will ever assure to

him a distinguished place among those whohave extended the domains of

science."

But it was work of a different kind thatestablished Galileo's popular

reputation. In 1609 Galileo heard that aDutch spectacle-maker had

combined a pair of lenses so as to magnifydistant objects. Working on

this hint, he solved the same problem,first on paper and then in

practice. So he came to make one of thefirst telescopes ever used in

astronomy. No sooner had he turned it onthe heavenly bodies than he

was rewarded by such a shower of startlingdiscoveries as forthwith

made his name the best known inEurope.  He found curious irregular

black spots on the sun, revolving round itin twenty-seven days; hills

and valleys on the moon; the planetsshowing discs of sensible size,

not points like the fixed stars; Venusshowing phases according to her

position in relation to the sun; Jupiteraccompanied by four moons;

Saturn with appendages that he could notexplain, but unlike the other

planets; the Milky Way composed of amultitude of separate stars.

His fame flew over Europe like magic, andhis discoveries were much

discussed--and there were many who refusedto believe. Cosmo de Medici

induced him to migrate to Florence to carryon his observations.  He

was received by Paul V., the Pope, at Rome,to whom he explained his

discoveries.

He thought that these discoveries provedthe truth of the Copernican

theory of the Earth's motion; and he urgedthis view on friends and

foes alike. Although in frequent correspondence with Kepler, he never

alluded to the New Astronomy, and wrote tohim extolling the virtue of

epicycles. He loved to argue, never shirkedan encounter with any

number of disputants, and laughed as hebroke down their arguments.

Through some strange course of events, noteasy to follow, the

Copernican theory, whose birth was welcomedby the Church, had now

been taken up by certain anti-clericalagitators, and was opposed by

the cardinals as well as by the dignitariesof the Reformed

Church. Galileo--a good Catholic--got mixedup in these discussions,

although on excellent terms with the Popeand his entourage. At last

it came about that Galileo was summoned toappear at Rome, where he

was charged with holding and teachingheretical opinions about the

movement of the earth; and he then solemnlyabjured these

opinions. There has been much exaggerationand misstatement about his

trial and punishment, and for a long timethere was a great deal of

bitterness shown on both sides. But thegeneral verdict of the present

day seems to be that, although Galileohimself was treated with

consideration, the hostility of the Churchto the views of Copernicus

placed it in opposition also to the trueKeplerian system, and this

led to unprofitable controversies.  From the time of Galileo onwards,

for some time, opponents of religionincluded the theory of the

Earth's motion in their disputations, notso much for the love, or

knowledge, of astronomy, as for thepleasure of putting the Church in

the wrong. This created a great deal ofbitterness and intolerance on

both sides. Among the sufferers wasGiordano Bruno, a learned

speculative philosopher, who was condemnedto be burnt at the stake.

Galileo died on Christmas Day, 1642--theday of Newton's birth. The

further consideration of the grand field ofdiscovery opened out by

Galileo with his telescopes must be nowpostponed, to avoid

discontinuity in the history of theintellectual development of this

period, which lay in the direction ofdynamical, or physical,

astronomy.

Until the time of Kepler no one seems tohave conceived the idea of

universal physical forces controllingterrestrial phenomena, and

equally applicable to the heavenly bodies.The grand discovery by

Kepler of the true relationship of the Sunto the Planets, and the

telescopic discoveries of Galileo and ofthose who followed him,

spread a spirit of inquiry and philosophicthought throughout Europe,

and once more did astronomy rise inestimation; and the irresistible

logic of its mathematical process ofreasoning soon placed it in the

position it has ever since occupied as theforemost of the exact

sciences.

The practical application of this processof reasoning was enormously

facilitated by the invention of logarithmsby Napier. He was born at

Merchistoun, near Edinburgh, in 1550, anddied in 1617. By this system

the tedious arithmetical operationsnecessary in astronomical

calculations, especially those dealing withthe trigonometrical

functions of angles, were so muchsimplified that Laplace declared

that by this invention the life-work of anastronomer was doubled.

Jeremiah Horrocks (born 1619, died 1641)was an ardent admirer of

Tycho Brahe and Kepler, and was able toimprove the Rudolphine tables

so much that he foretold a transit ofVenus, in 1639, which these

tables failed to indicate, and was the onlyobserver of it. His life

was short, but he accomplished a greatdeal, and rightly ascribed the

lunar inequality called _evection_ tovariations in the value of

the eccentricity and in the direction ofthe line of apses, at the

same time correctly assigning _thedisturbing force of the Sun_

as the cause. He discovered the errors inJupiter's calculated place,

due to what we now know as the longinequality of Jupiter and Saturn,

and measured with considerable accuracy theacceleration at that date

of Jupiter's mean motion, and indicated theretardation of Saturn's

mean motion.

Horrocks' investigations, so far as theycould be collected, were

published posthumously in 1672, and seldom,if ever, has a man who

lived only twenty-two years originated somuch scientific knowledge.

At this period British science received alasting impetus by the wise

initiation of a much-abused man, CharlesII., who founded the Royal

Society of London, and also the RoyalObservatory of Greeenwich, where

he established Flamsteed as firstAstronomer Royal, especially for

lunar and stellar observations likely to beuseful for navigation. At

the same time the French Academy and theParis Observatory were

founded. All this within fourteen years,1662-1675.

Meanwhile gravitation in general terms wasbeing discussed by Hooke,

Wren, Halley, and many others.  All of these men felt a repugnance to

accept the idea of a force acting acrossthe empty void of space.

Descartes (1596-1650) proposed an etherealmedium whirling round the

sun with the planets, and having localwhirls revolving with the

satellites. As Delambre and Grant havesaid, this fiction only

retarded the progress of pure science. Ithad no sort of relation to

the more modern, but equally misleading,"nebular hypothesis." While

many were talking and guessing, a giantmind was needed at this stage

to make things clear.

7. SIR ISAAC NEWTON--LAW OF UNIVERSALGRAVITATION.

We now reach the period which is theculminating point of interest in

the history of dynamical astronomy.  Isaac Newton was born in

1642. Pemberton states that Newton, havingquitted Cambridge to avoid

the plague, was residing at Wolsthorpe, inLincolnshire, where he had

been born; that he was sitting one day inthe garden, reflecting upon

the force which prevents a planet fromflying off at a tangent and

which draws it to the sun, and upon theforce which draws the moon to

the earth; and that he saw in the case ofthe planets that the sun's

force must clearly be unequal at differentdistances, for the pull out

of the tangential line in a minute is lessfor Jupiter than for

Mars. He then saw that the pull of theearth on the moon would be less

than for a nearer object. It is said thatwhile thus meditating he saw

an apple fall from a tree to the ground,and that this fact suggested

the questions: Is the force that pulledthat apple from the tree the

same as the force which draws the moon tothe earth?  Does the

attraction for both of them follow the samelaw as to distance as is

given by the planetary motions round thesun? It has been stated that

in this way the first conception ofuniversal gravitation arose.[1]

Quite the most important event in the wholehistory of physical

astronomy was the publication, in 1687, ofNewton's _Principia

(Philosophiae Naturalis PrincipiaMathematica)_. In this great work

Newton started from the beginning ofthings, the laws of motion, and

carried his argument, step by step, intoevery branch of physical

astronomy; giving the physical meaning ofKepler's three laws, and

explaining, or indicating the explanationof, all the known heavenly

motions and their irregularities; showingthat all of these were

included in his simple statement about thelaw of universal

gravitation; and proceeding to deduce fromthat law new irregularities

in the motions of the moon which had neverbeen noticed, and to

discover the oblate figure of the earth andthe cause of the

tides. These investigations occupied thebest part of his life; but he

wrote the whole of his great book infifteen months.

Having developed and enunciated the truelaws of motion, he was able

to show that Kepler's second law (thatequal areas are described by

the line from the planet to the sun inequal times) was only another

way of saying that the centripetal force ona planet is always

directed to the sun. Also that Kepler'sfirst law (elliptic orbits

with the sun in one focus) was only anotherway of saying that the

force urging a planet to the sun variesinversely as the square of the

distance. Also (if these two be granted) itfollows that Kepler's

third law is only another way of sayingthat the sun's force on

different planets (besides depending asabove on distance) is

proportional to their masses.

Having further proved the, for that day,wonderful proposition that,

with the law of inverse squares, theattraction by the separate

particles of a sphere of uniform density(or one composed of

concentric spherical shells, each ofuniform density) acts as if the

whole mass were collected at the centre, hewas able to express the

meaning of Kepler's laws in propositionswhich have been summarised as

follows:--

The law of universal gravitation.--_Everyparticle of matter in the

universe attracts every other particle witha force varying inversely

as the square of the distance between them,and directly as the

product of the masses of the twoparticles_.[2]

But Newton did not commit himself to the lawuntil he had answered

that question about the apple; and theabove 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 timesfarther from the earth's

centre than the stone, so it ought to bedrawn out of a straight

course through 16.1 feet in a minute.Newton found the distance

through which she is actually drawn as afraction of the earth's

diameter. But when he first examined this matter he proceeded to use

a wrong diameter for the earth, and hefound a serious discrepancy.

This, for a time, seemed to condemn histheory, and regretfully he

laid that part of his work aside.Fortunately, before Newton wrote the

_Principia_ the French astronomer Picardmade a new and correct

measure of an arc of the meridian, fromwhich he obtained an accurate

value of the earth's diameter. Newtonapplied this value, and found,

to his great joy, that when the distance ofthe moon is 60 times the

radius of the earth she is attracted out ofthe straight course 16.1

feet per minute, and that the force actingon a stone or an apple

follows the same law as the force actingupon the heavenly bodies.[3]

The universality claimed for the law--ifnot by Newton, at least by

his commentators--was bold, and warrantedonly by the large number of

cases in which Newton had found it toapply. Its universality has been

under test ever since, and so far it hasstood the test. There has

often been a suspicion of a doubt, whensome inequality of motion in

the heavenly bodies has, for a time, foiledthe astronomers in their

attempts to explain it. But improvedmathematical methods have always

succeeded in the end, and so the seemingdoubt has been converted into

a surer conviction of the universality ofthe law.

Having once established the law, Newtonproceeded to trace some of its

consequences. He saw that the figure of theearth depends partly on

the mutual gravitation of its parts, andpartly on the centrifugal

tendency due to the earth's rotation, andthat these should cause a

flattening of the poles. He invented amathematical method which he

used for computing the ratio of the polarto the equatorial diameter.

He then noticed that the consequent bulgingof matter at the equator

would be attracted by the moon unequally,the nearest parts being most

attracted; and so the moon would tend totilt the earth when in some

parts of her orbit; and the sun would dothis to a less extent,

because of its great distance. Then heproved that the effect ought to

be a rotation of the earth's axis over aconical surface in space,

exactly as the axis of a top describes acone, if the top has a sharp

point, and is set spinning and displacedfrom the vertical. He

actually calculated the amount; and so heexplained the cause of the

precession of the equinoxes discovered byHipparchus about 150 B.C.

One of his grandest discoveries was amethod of weighing the heavenly

bodies by their action on each other. Bymeans of this principle he

was able to compare the mass of the sunwith the masses of those

planets that have moons, and also tocompare the mass of our moon with

the mass of the earth.

Thus Newton, after having established hisgreat principle, devoted his

splendid intellect to the calculation ofits consequences. He proved

that if a body be projected with anyvelocity in free space, subject

only to a central force, varying inverselyas the square of the

distance, the body must revolve in a curvewhich 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 hadobservations move in parabolae

round the Sun, and are thus subject to theuniversal law.

Newton realised that, while planets andsatellites are chiefly

controlled by the central body about whichthey revolve, the new law

must involve irregularities, due to theirmutual action--such, in

fact, as Horrocks had indicated. Hedetermined to put this to a test

in the case of the moon, and to calculatethe sun's effect, from its

mass compared with that of the earth, andfrom its distance. He proved

that the average effect upon the plane ofthe orbit would be to cause

the line in which it cuts the plane of theecliptic (i.e., the line of

nodes) to revolve in the ecliptic once inabout nineteen years. This

had been a known fact from the earliestages. He also concluded that

the line of apses would revolve in theplane of the lunar orbit also

in about nineteen years; but the observedperiod is only ten

years. For a long time this was the oneweak point in the Newtonian

theory. It was not till 1747 that Clairautreconciled this with the

theory, and showed why Newton's calculationwas not exact.

Newton proceeded to explain the otherinequalities recognised by Tycho

Brahe and older observers, and to calculatetheir maximum amounts as

indicated by his theory. He furtherdiscovered from his calculations

two new inequalities, one of the apogee,the other of the nodes, and

assigned the maximum value. Grant has shownthe values of some of

these as given by observation in the tablesof Meyer and more modern

tables, and has compared them with thevalues assigned by Newton from

his theory; and the comparison is veryremarkable.

                                     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 theseperturbations had never been

discovered, that the cause of none of themhad ever been known, and

that he exhibited his results, if he didnot also make the

discoveries, by the synthetic methods ofgeometry, it is simply

marvellous that he reached to such a degreeof accuracy. He invented

the infinitesimal calculus which is moresuited for such calculations,

but had he expressed his results in thatlanguage he would have been

unintelligible to many.

Newton's method of calculating theprecession of the equinoxes,

already referred to, is as beautiful asanything in the _Principia_.

He had already proved the regression of thenodes of a satellite

moving in an orbit inclined to theecliptic. He now said that the

nodes of a ring of satellites revolvinground the earth's equator

would consequently all regress. And ifjoined into a solid ring its

node would regress; and it would do so,only more slowly, if

encumbered by the spherical part of theearth's mass. Therefore the

axis of the equatorial belt of the earthmust revolve round the pole

of the ecliptic. Then he set to work andfound the amount due to the

moon and that due to the sun, and so hesolved the mystery of 2,000

years.

When Newton applied his law of gravitationto an explanation of the

tides he started a new field for theapplication of mathematics to

physical problems; and there can be littledoubt that, if he could

have been furnished with complete tidal observationsfrom different

parts of the world, his extraordinarypowers of analysis would have

enabled him to reach a satisfactorytheory.  He certainly opened up

many mines full of intellectual gems; andhis successors have never

ceased in their explorations. This has ledto improved mathematical

methods, which, combined with the greateraccuracy of observation,

have rendered physical astronomy of to-daythe most exact of the

sciences.

Laplace only expressed the universalopinion of posterity when he said

that to the _Principia_ is assured "apre-eminence above all the

other productions of the humanintellect."

The name of Flamsteed, First AstronomerRoyal, must here be mentioned

as having supplied Newton with the accuratedata required for

completing the theory.

The name of Edmund Halley, SecondAstronomer Royal, must ever be held

in repute, not only for his owndiscoveries, but for the part he

played in urging Newton to commit towriting, 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 insupplying the means the

Royal Society could not have published thebook.

[Illustration: DEATH MASK OF SIR ISAACNEWTON.

Photographed specially for this work fromthe original, by kind

permission of the Royal Society, London.]

Sir Isaac Newton died in 1727, at the ageof eighty-five.  His body

lay in state in the Jerusalem Chamber, andwas 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 aslip of paper, which had been

presented to him by Sir David Brewster. Onthe paper Sir David had

written these words: "If there be anytruth in the story that Newton

was led to the theory of gravitation by thefall of an apple, this bit

of wood is probably a piece of the appletree from which Newton saw

the apple fall. When I was on a pilgrimageto the house in which

Newton was born, I cut it off an ancientapple tree growing in his

garden." When lecturing in Glasgow,about 1875, the writer showed it

to his audience. The next morning, whenremoving his property from the

lecture table, he found that his preciousrelic had been stolen. It

would be interesting to know who has got itnow!

[2] It must be noted that these words, inwhich the laws of

gravitation are always summarised inhistories and text-books, do not

appear in the _Principia_; but, though theymust have been composed by

some early commentator, it does not appearthat their origin has been

traced. Nor does it appear that Newton everextended the law beyond

the Solar System, and probably his cautionwould have led him to avoid

any statement of the kind until it shouldbe proved.

With this exception the above statement ofthe law of universal

gravitation contains nothing that is not tobe found in the

_Principia_; and the nearest approach tothat statement occurs in the

Seventh Proposition of Book III.:--

Prop.: That gravitation occurs in allbodies, and that it is

proportional to the quantity of matter ineach.

Cor. I.: The total attraction ofgravitation on a planet arises, and

is composed, out of the attraction on theseparate parts.

Cor. II.: The attraction on separate equalparticles of a body is

reciprocally as the square of the distancefrom the particles.

[3] It is said that, when working out thisfinal result, the

probability of its confirming that part ofhis theory which he had

reluctantly abandoned years before excitedhim so keenly that he was

forced to hand over his calculations to afriend, to be completed by

him.

8. NEWTON'S SUCCESSORS--HALLEY, EULER,LAGRANGE, LAPLACE, ETC.

Edmund Halley succeeded Flamsteed as SecondAstronomer Royal in

1721. Although he did not contributedirectly to the mathematical

proofs of Newton's theory, yet his name isclosely associated with

some of its greatest successes.

He was the first to detect the accelerationof the moon's mean

motion. Hipparchus, having compared his ownobservations with those of

more ancient astronomers, supplied anaccurate value of the moon's

mean motion in his time. Halley similarlydeduced a value for modern

times, and found it sensibly greater.  He announced this in 1693, but

it was not until 1749 that Dunthorne usedmodern lunar tables to

compute a lunar eclipse observed in Babylon721 B.C., another at

Alexandria 201 B.C., a solar eclipseobserved by Theon 360 A.D., and

two later ones up to the tenthcentury.  He found that to explain

these eclipses Halley's suggestion must beadopted, the acceleration

being 10" in one century. In 1757Lalande again fixed it at 10."

The Paris Academy, in 1770, offered theirprize for an investigation

to see if this could be explained by thetheory of gravitation. Euler

won the prize, but failed to explain theeffect, and said: "It appears

to be established by indisputable evidencethat the secular inequality

of the moon's mean motion cannot beproduced by the forces of

gravitation."

The same subject was again proposed for aprize which was shared by

Lagrange [1] and Euler, neither finding asolution, while the latter

asserted the existence of a resistingmedium in space.

Again, in 1774, the Academy submitted thesame subject, a third time,

for the prize; and again Lagrange failed todetect a cause in

gravitation.

Laplace [2] now took the matter in hand. Hetried the effect of a

non-instantaneous action of gravity, to nopurpose. But in 1787 he

gave the true explanation.  The principal effect of the sun on the

moon's orbit is to diminish the earth'sinfluence, thus lengthening

the period to a new value generally takenas constant. But Laplace's

calculations showed the new value to dependupon the excentricity of

the earth's orbit, which, according; totheory, has a periodical

variation of enormous period, and has beencontinually diminishing for

thousands of years. Thus the solarinfluence has been diminishing, and

the moon's mean motion increased. Laplacecomputed the amount at 10"

in one century, agreeing with observation.(Later on Adams showed that

Laplace's calculation was wrong, and thatthe value he found was too

large; so, part of the acceleration is nowattributed by some

astronomers to a lengthening of the day bytidal friction.)

Another contribution by Halley to theverification of Newton's law was

made when he went to St. Helena tocatalogue the southern stars. He

measured the change in length of thesecond's pendulum in different

latitudes due to the changes in gravityforetold by Newton.

Furthermore, he discovered the longinequality of Jupiter and Saturn,

whose period is 929 years. For aninvestigation of this also the

Academy of Sciences offered their prize.This led Euler to write a

valuable essay disclosing a new method ofcomputing perturbations,

called the instantaneous ellipse withvariable elements. The method

was much developed by Lagrange.

But again it was Laplace who solved theproblem of the inequalities of

Jupiter and Saturn by the theory ofgravitation, reducing the errors

of the tables from 20' down to 12",thus abolishing the use of

empirical corrections to the planetarytables, and providing another

glorious triumph for the law ofgravitation.  As Laplace justly said:

"These inequalities appeared formerlyto be inexplicable by the law of

gravitation--they now form one of its moststriking proofs."

Let us take one more discovery of Halley,furnishing directly a new

triumph for the theory. He noticed thatNewton ascribed parabolic

orbits to the comets which he studied, sothat they come from

infinity, sweep round the sun, and go offto infinity for ever, after

having been visible a few weeks or months.He collected all the

reliable observations of comets he couldfind, to the number of

twenty-four, and computed their parabolicorbits by the rules laid

down by Newton. His object was to find outif any of them really

travelled in elongated ellipses, practicallyundistinguishable, in the

visible part of their paths, from parabolæ,in which case they would

be seen more than once. He found two oldcomets whose orbits, in shape

and position, resembled the orbit of acomet observed by himself in

1682. Apian observed one in 1531; Kepler the other in 1607.  The

intervals between these appearances isseventy-five or seventy-six

years. He then examined and found oldrecords of similar appearance in

1456, 1380, and 1305. It is true, henoticed, that the intervals

varied by a year and a-half, and theinclination of the orbit to the

ecliptic diminished with successiveapparitions.  But he knew from

previous calculations that this mighteasily be due to planetary

perturbations. Finally, he arrived at the conclusionthat all of these

comets were identical, travelling in anellipse so elongated that the

part where the comet was seen seemed to bepart of a parabolic

orbit. He then predicted its return at theend of 1758 or beginning of

1759, when he should be dead; but, as hesaid, "if it should return,

according to our prediction, about the year1758, impartial posterity

will not refuse to acknowledge that thiswas first discovered by an

Englishman."[3] [_Synopsis AstronomiaeCometicae_, 1749.]

Once again Halley's suggestion became aninspiration for the

mathematical astronomer. Clairaut, assistedby Lalande, found that

Saturn would retard the comet 100 days,Jupiter 518 days, and

predicted its return to perihelion on April13th, 1759. In his

communication to the French Academy, hesaid that a comet travelling

into such distant regions might be exposedto the influence of forces

totally unknown, and "even of someplanet too far removed from the sun

to be ever perceived."

The excitement of astronomers towards theend of 1758 became intense;

and the honour of first catching sight ofthe traveller fell to an

amateur in Saxony, George Palitsch, onChristmas Day, 1758. It reached

perihelion on March 13th, 1759.

This fact was a startling confirmation ofthe Newtonian theory,

because it was a new kind of calculation ofperturbations, and also it

added a new member to the solar system, andgave a prospect of adding

many more.

When Halley's comet reappeared in 1835,Pontecoulant's computations

for the date of perihelion passage werevery exact, and afterwards he

showed that, with more exact values of themasses of Jupiter and

Saturn, his prediction was correct withintwo days, after an invisible

voyage of seventy-five years!

Hind afterwards searched out many oldappearances of this comet, going

back to 11 B.C., and most of these havebeen identified as being

really Halley's comet by the calculationsof Cowell and Cromellin[4]

(of Greenwich Observatory), who have alsopredicted 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 AstronomerRoyal 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 theoriginal memoir communicated

to the Royal Society, but was firstpublished 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 quiteimpossible in these pages, to

discuss all the exquisite researches of themathematical astronomers,

and to inspire a reverence for the namesconnected with these

researches, which for two hundred yearshave been establishing the

universality of Newton's law. The lunar andplanetary theories, the

beautiful theory of Jupiter's satellites,the figure of the earth, and

the tides, were mathematically treated byMaclaurin, 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 importantdevelopments it is possible to trace

some of the steps in the crowning triumphof the Newtonian theory, by

which the planet Neptune was added to theknown members of the solar

system by the independent researches of ProfessorJ.C. Adams and of

M. Le Verrier, in 1846.

It will be best to introduce this subjectby relating how the

eighteenth century increased the number ofknown planets, which was

then only six, including the earth.

On March 13th, 1781, Sir William Herschelwas, as usual, engaged on

examining some small stars, and, noticingthat one of them appeared to

be larger than the fixed stars, suspectedthat it might be a comet.

To test this he increased his magnifyingpower from 227 to 460 and

932, finding that, unlike the fixed starsnear it, its definition was

impaired and its size increased.  This convinced him that the object

was a comet, and he was not surprised tofind on succeeding nights

that the position was changed, the motionbeing in the ecliptic. He

gave the observations of five weeks to theRoyal Society without a

suspicion that the object was a new planet.

For a long time people could not compute asatisfactory orbit for the

supposed comet, because it seemed to benear the perihelion, and no

comet had ever been observed with aperihelion distance from the sun

greater than four times the earth'sdistance. Lexell was the first to

suspect that this was a new planet eighteentimes as far from the sun

as the earth is. In January, 1783, Laplacepublished the elliptic

elements. The discoverer of a planet has aright to name it, so

Herschel called it Georgium Sidus, afterthe king.  But Lalande urged

the adoption of the name Herschel.  Bode suggested Uranus, and this

was adopted. The new planet was found torank in size next to Jupiter

and Saturn, being 4.3 times the diameter ofthe earth.

In 1787 Herschel discovered two satellites,both revolving in nearly

the same plane, inclined 80° to theecliptic, 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, addthe numbers 0, 3, 6, 12,

24, 48, 96, etc., to the 4, always doublingthe 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, fittedthis rule, except that

there was a blank between Mars and Jupiter.When Uranus was

discovered, also fitting the rule, theconclusion was irresistible

that there is probably a planet betweenMars and Jupiter. An

association of twenty-four astronomers wasnow formed in Germany to

search for the planet. Almost immediatelyafterwards the planet was

discovered, not by any member of theassociation, but by Piazzi, when

engaged upon his great catalogue of stars.On January 1st, 1801, he

observed a star which had changed its placethe next night. Its motion

was retrograde till January 11th, directafter the 13th.  Piazzi fell

ill before he had enough observations forcomputing the orbit with

certainty, and the planet disappeared inthe sun's rays. Gauss

published an approximate ephemeris ofprobable positions when the

planet should emerge from the sun's light.There was an exciting hunt,

and on December 31st (the day before itsbirthday) De Zach captured

the truant, and Piazzi christened it Ceres.

The mean distance from the sun was found tobe 2.767, agreeing with

the 2.8 given by Bode's law. Its orbit wasfound to be inclined over

10° to the ecliptic, and its diameter wasonly 161 miles.

On March 28th, 1802, Olbers discovered anew seventh magnitude star,

which turned out to be a planet resemblingCeres. It was called

Pallas. Gauss found its orbit to beinclined 35° to the ecliptic, and

to cut the orbit of Ceres; whence Olbersconsidered that these might

be fragments of a broken-up planet. He thencommenced a search for

other fragments. In 1804 Harding discoveredJuno, and in 1807 Olbers

found Vesta. The next one was notdiscovered until 1845, from which

date asteroids, or minor planets (as thesesmall planets are called),

have been found almost every year. They nownumber about 700.

It is impossible to give any idea of theinterest with which the first

additions since prehistoric times to theplanetary system were

received. All of those who showeredcongratulations upon the

discoverers regarded these discoveries inthe light of rewards for

patient and continuous labours, the veryhighest rewards that could be

desired. And yet there remained still themost brilliant triumph of

all, the addition of another planet likeUranus, before it had ever

been seen, when the analysis of Adams and LeVerrier gave a final

proof of the powers of Newton's great lawto explain any planetary

irregularity.

After Sir William Herschel discoveredUranus, in 1781, it was found

that astronomers had observed it on manyprevious occasions, mistaking

it for a fixed star of the sixth or seventhmagnitude. Altogether,

nineteen observations of Uranus's position,from the time of

Flamsteed, in 1690, had been recorded.

In 1790 Delambre, using all theseobservations, prepared tables for

computing its position. These worked wellenough for a time, but at

last the differences between the calculatedand observed longitudes of

the planet became serious. In 1821 Bouvardundertook a revision of the

tables, but found it impossible toreconcile all the observations of

130 years (the period of revolution ofUranus 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 becameintolerable. In 1835 the error of

longitude was 30"; in 1838, 50";in 1841, 70"; and, by comparing the

errors derived from observations madebefore and after opposition, a

serious error of the distance (radiusvector) became apparent.

In 1843 John Couch Adams came out SeniorWrangler at Cambridge, and

was free to undertake the research which asan undergraduate he had

set himself--to see whether thedisturbances of Uranus could be

explained by assuming a certain orbit, andposition in that orbit, of

a hypothetical planet even more distantthan Uranus.  Such an

explanation had been suggested, but until1843 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 causesof disturbance, using the

latest determinations of the planetarymasses. Still the errors were

nearly as great as ever.  He could now, however, use these errors as

being actually due to the perturbationsproduced by the unknown

planet.

In 1844, assuming a circular orbit, and amean distance agreeing with

Bode's law, he obtained a firstapproximation to the position of the

supposed planet.  He then asked Professor Challis, ofCambridge, to

procure the latest observations of Uranusfrom Greenwich, which Airy

immediately supplied. Then the whole workwas recalculated from the

beginning, with more exactness, andassuming a smaller mean distance.

In September, 1845, he handed to Challisthe elements of the

hypothetical planet, its mass, and itsapparent position for September

30th, 1845. On September 22nd Challis wroteto Airy explaining the

matter, and declaring his belief in Adams'scapabilities. When Adams

called on him Airy was away from home, butat the end of October,

1845, he called again, and left a paperwith full particulars of his

results, which had, for the most part,reduced the discrepancies to

about 1". As a matter of fact, it hassince been found that the

heliocentric place of the new planet thengiven was correct within

about 2°.

Airy wrote expressing his interest, andasked for particulars about

the radius vector. Adams did not thenreply, as the answer to this

question could be seen to be satisfactoryby looking at the data

already supplied.  He was a most unassuming man, and would notpush

himself forward. He may have felt, afterall the work he had done,

that Airy's very natural inquiry showed noproportionate desire to

search for the planet.  Anyway, the matter lay in embryo for nine

months.

Meanwhile, one of the ablest Frenchastronomers, Le Verrier,

experienced in computing perturbations, wasindependently at work,

knowing nothing about Adams. He applied tohis calculations every

possible refinement, and, considering thenovelty of the problem, his

calculation was one of the most brilliantin the records of

astronomy. In criticism it has been saidthat these were exhibitions

of skill rather than helps to a solution ofthe particular problem,

and that, in claiming to find the elementsof the orbit within certain

limits, he was claiming what was, under thecircumstances, impossible,

as the result proved.

In June, 1846, Le Verrier announced, in the_Comptes Rendus de

l'Academie des Sciences_, that thelongitude of the disturbing planet,

for January 1st, 1847, was 325, and thatthe probable error did not

exceed 10°.

This result agreed so well with Adams's(within 1°) that Airy urged

Challis to apply the splendid Northumberlandequatoreal, at Cambridge,

to the search.  Challis, however, had already prepared anexhaustive

plan of attack which must in time settlethe point.  His first work

was to observe, and make a catalogue, orchart, of all stars near

Adams's position.

On August 31st, 1846, Le Verrier publishedthe concluding

part of his labours.

On September 18th, 1846, Le Verriercommunicated his results to the

Astronomers at Berlin, and asked them toassist in searching for the

planet. By good luck Dr. Bremiker had justcompleted a star-chart of

the very part of the heavens including LeVerrier's position; thus

eliminating all of Challis's preliminarywork. The letter was received

in Berlin on September 23rd; and the sameevening Galle found the new

planet, of the eighth magnitude, the sizeof its disc agreeing with Le

Verrier's prediction, and the heliocentriclongitude agreeing within

57'. By this time Challis had recorded,without reduction, the

observations of 3,150 stars, as acommencement for his search.  On

reducing these, he found a star, observedon August 12th, which was

not in the same place on July 30th. Thiswas the planet, and he had

also observed it on August 4th.

The feeling of wonder, admiration, andenthusiasm aroused by this

intellectual triumph was overwhelming.  In the world of astronomy

reminders are met every day of the terriblelimitations of human

reasoning powers; and every success thatenables the mind's eye to see

a little more clearly the meaning of thingshas always been heartily

welcomed by those who have themselves beenengaged in like

researches. But, since the publication ofthe _Principia_, in 1687,

there is probably no analytical successwhich has raised among

astronomers such a feeling of admirationand gratitude as when Adams

and Le Verrier showed the inequalities inUranus's motion to mean that

an unknown planet was in a certain place inthe heavens, where it was

found.

At the time there was an unpleasant displayof international jealousy.

The British people thought that the earlierdate of Adams's work, and

of the observation by Challis, entitled himto at least an equal share

of credit with Le Verrier. The French, onthe other hand, who, on the

announcement of the discovery by Galle,glowed with pride in the new

proof of the great powers of theirastronomer, Le Verrier, whose life

had a long record of successes incalculation, were incredulous on

being told that it had all been alreadydone by a young man whom they

had never heard of.

These displays of jealousy have long sincepassed away, and there is

now universally an _entente cordiale_ thatto each of these great men

belongs equally the merit of having sothoroughly calculated this

inverse problem of perturbations as to leadto the immediate discovery

of the unknown planet, since calledNeptune.

It was soon found that the planet had beenobserved, and its position

recorded as a fixed star by Lalande, on May8th and 10th, 1795.

Mr. Lassel, in the same year, 1846, withhis two-feet reflector,

discovered a satellite, with retrogrademotion, which gave the mass of

the planet about a twentieth of that ofJupiter.

FOOTNOTES:

[1] Bode's law, or something like it, hadalready been fore-shadowed

by Kepler and others, especially Titius(see _Monatliche

Correspondenz_, vol. vii., p. 72).