ellipses which Kepler has shown to possess such astonishing
astronomical significance. Two pins are stuck through a sheet of
paper on a board, the point of a pencil is inserted in a loop of
string which passes over the pins, and as the pencil is moved round
in such a way as to keep the string stretched, that beautiful curve
known as the ellipse is delineated, while the positions of the pins
indicate the two foci of the curve. If the length of the loop of
string is unchanged then the nearer the pins are together, the
greater will be the resemblance between the ellipse and the circle,
whereas the more the pins are separated the more elongated does the
ellipse become. The orbit of a great planet is, in general, one of
those ellipses which approaches a nearly circular form. It
fortunately happens, however, that the orbit of Mars makes a wider
departure from the circular form than any of the other important
planets. It is, doubtless, to this circumstance that we must
attribute the astonishing success of Kepler in detecting the true
shape of a planetary orbit. Tycho's observations would not have been
sufficiently accurate to have exhibited the elliptic nature of a
planetary orbit which, like that of Venus, differed very little from
a circle.
The more we ponder on this memorable achievement the more striking
will it appear. It must be remembered that in these days we know of
the physical necessity which requires that a planet shall revolve in
an ellipse and not in any other curve. But Kepler had no such
knowledge. Even to the last hour of his life he remained in
ignorance of the existence of any natural cause which ordained that
planets should follow those particular curves which geometers know so
well. Kepler's assignment of the ellipse as the true form of the
planetary orbit is to be regarded as a brilliant guess, the truth of
which Tycho's observations enabled him to verify. Kepler also
succeeded in pointing out the law according to which the velocity of
a planet at different points of its path could be accurately
specified. Here, again, we have to admire the sagacity with which
this marvellously acute astronomer guessed the deep truth of nature.
In this case also he was quite unprovided with any reason for
expecting from physical principles that such a law as he discovered
must be obeyed. It is quite true that Kepler had some slight
knowledge of the existence of what we now know as gravitation. He
had even enunciated the remarkable doctrine that the ebb and flow of
the tide must be attributed to the attraction of the moon on the
waters of the earth. He does not, however, appear to have had any
anticipation of those wonderful discoveries which Newton was destined
to make a little later, in which he demonstrated that the laws
detected by Kepler's marvellous acumen were necessary consequences of
the principle of universal gravitation.
[PLATE: SYMBOLICAL REPRESENTATION OF THE PLANETARY SYSTEM.]
To appreciate the relations of Kepler and Tycho it is necessary to
note the very different way in which these illustrious astronomers
viewed the system of the heavens. It should be observed that
Copernicus had already expounded the true system, which located the
sun at the centre of the planetary system. But in the days of Tycho
Brahe this doctrine had not as yet commanded universal assent. In
fact, the great observer himself did not accept the new views of
Copernicus. It appeared to Tycho that the earth not only appeared to
be the centre of things celestial, but that it actually was the
centre. It is, indeed, not a little remarkable that a student of the
heavens so accurate as Tycho should have deliberately rejected the
Copernican doctrine in favour of the system which now seems so
preposterous. Throughout his great career, Tycho steadily observed
the places of the sun, the moon, and the planets, and as steadily
maintained that all those bodies revolved around the earth fixed in
the centre. Kepler, however, had the advantage of belonging to the
new school. He utilised the observations of Tycho in developing the
great Copernican theory whose teaching Tycho stoutly resisted.
Perhaps a chapter in modern science may illustrate the intellectual
relation of these great men. The revolution produced by Copernicus
in the doctrine of the heavens has often been likened to the
revolution which the Darwinian theory produced in the views held by
biologists as to life on this earth. The Darwinian theory did not at
first command universal assent even among those naturalists whose
lives had been devoted with the greatest success to the study of
organisms. Take, for instance, that great naturalist, Professor
Owen, by whose labours vast extension has been given to our knowledge
of the fossil animals which dwelt on the earth in past ages. Now,
though Owens researches were intimately connected with the great
labours of Darwin, and afforded the latter material for his
epoch-making generalization, yet Owen deliberately refused to accept
the new doctrines. Like Tycho, he kept on rigidly accumulating his
facts under the influence of a set of ideas as to the origin of
living forms which are now universally admitted to be erroneous. If,
therefore, we liken Darwin to Copernicus, and Owen to Tycho, we may
liken the biologists of the present day to Kepler, who interpreted
the results of accurate observation upon sound theoretical
principles.
In reading the works of Kepler in the light of our modern knowledge
we are often struck by the extent to which his perception of the
sublimest truths in nature was associated with the most extravagant
errors and absurdities. But, of course, it must be remembered that
he wrote in an age in which even the rudiments of science, as we now
understand it, were almost entirely unknown.
It may well be doubted whether any joy experienced by mortals is more
genuine than that which rewards the successful searcher after natural
truths. Every science-worker, be his efforts ever so humble, will be
able to sympathise with the enthusiastic delight of Kepler when at
last, after years of toil, the glorious light broke forth, and that
which he considered to be the greatest of his astonishing laws first
dawned upon him. Kepler rightly judged that the number of days which
a planet required to perform its voyage round the sun must be
connected in some manner with the distance from the planet to the
sun; that is to say, with the radius of the planet's orbit, inasmuch
as we may for our present object regard the planet's orbit as
circular.
Here, again, in his search for the unknown law, Kepler had no
accurate dynamical principles to guide his steps. Of course, we now
know not only what the connection between the planet's distance and
the planet's periodic time actually is, but we also know that it is a
necessary consequence of the law of universal gravitation. Kepler,
it is true, was not without certain surmises on the subject, but they
were of the most fanciful description. His notions of the planets,
accurate as they were in certain important respects, were mixed up
with vague ideas as to the properties of metals and the geometrical
relations of the regular solids. Above all, his reasoning was
penetrated by the supposed astrological influences of the stars and
their significant relation to human fate. Under the influence of
such a farrago of notions, Kepler resolved to make all sorts of
trials in his search for the connection between the distance of a
planet from the sun and the time in which the revolution of that
planet was accomplished.
It was quite easily demonstrated that the greater the distance of the
planet from the sun the longer was the time required for its
journey. It might have been thought that the time would be directly
proportional to the distance. It was, however, easy to show that
this supposition did not agree with the fact. Finding that this
simple relation would not do, Kepler undertook a vast series of
calculations to find out the true method of expressing the
connection. At last, after many vain attempts, he found, to his
indescribable joy, that the square of the time in which a planet
revolves around the sun was proportional to the cube of the average
distance of the planet from that body.
The extraordinary way in which Kepler's views on celestial matters
were associated with the wildest speculations, is well illustrated in
the work in which he propounded his splendid discovery just referred
to. The announcement of the law connecting the distances of the
planets from the sun with their periodic times, was then mixed up
with a preposterous conception about the properties of the different
planets. They were supposed to be associated with some profound
music of the spheres inaudible to human ears, and performed only for
the benefit of that being whose soul formed the animating spirit of
the sun.
Kepler was also the first astronomer who ever ventured to predict the
occurrence of that remarkable phenomenon, the transit of a planet in
front of the sun's disc. He published, in 1629, a notice to the
curious in things celestial, in which he announced that both of the
planets, Mercury and Venus, were to make a transit across the sun on
specified days in the winter of 1631. The transit of Mercury was
duly observed by Gassendi, and the transit of Venus also took place,
though, as we now know, the circumstances were such that it was not
possible for the phenomenon to be witnessed by any European
astronomer.
In addition to Kepler's discoveries already mentioned, with which his
name will be for ever associated, his claim on the gratitude of
astronomers chiefly depends on the publication of his famous
Rudolphine tables. In this remarkable work means are provided for
finding the places of the planets with far greater accuracy than had
previously been attainable.
Kepler, it must be always remembered, was not an astronomical
observer. It was his function to deal with the observations made by
Tycho, and, from close study and comparison of the results, to work
out the movements of the heavenly bodies. It was, in fact, Tycho who
provided as it were the raw material, while it was the genius of
Kepler which wrought that material into a beautiful and serviceable
form. For more than a century the Rudolphine tables were regarded as
a standard astronomical work. In these days we are accustomed to
find the movements of the heavenly bodies set forth with all
desirable exactitude in the NAUTICAL ALMANACK, and the similar
publication issued by foreign Governments. Let it be remembered that
it was Kepler who first imparted the proper impulse in this
direction.
[PLATE: THE COMMEMORATION OF THE RUDOLPHINE TABLES.]
When Kepler was twenty-six he married an heiress from Styria, who,
though only twenty-three years old, had already had some experience
in matrimony. Her first husband had died; and it was after her
second husband had divorced her that she received the addresses of
Kepler. It will not be surprising to hear that his domestic affairs
do not appear to have been particularly happy, and his wife died in
1611. Two years later, undeterred by the want of success in his
first venture, he sought a second partner, and he evidently
determined not to make a mistake this time. Indeed, the methodical
manner in which he made his choice of the lady to whom he should
propose has been duly set forth by him and preserved for our
edification. With some self-assurance he asserts that there were no
fewer than eleven spinsters desirous of sharing his joys and
sorrows. He has carefully estimated and recorded the merits and
demerits of each of these would-be brides. The result of his
deliberations was that he awarded himself to an orphan girl,
destitute even of a portion. Success attended his choice, and his
second marriage seems to have proved a much more suitable union than
his first. He had five children by the first wife and seven by the
second.
The years of Kepler's middle life were sorely distracted by a trouble
which, though not uncommon in those days, is one which we find it
difficult to realise at the present time. His mother, Catherine
Kepler, had attained undesirable notoriety by the suspicion that she
was guilty of witchcraft. Years were spent in legal investigations,
and it was only after unceasing exertions on the part of the
astronomer for upwards of a twelve-month that he was finally able to
procure her acquittal and release from prison.
It is interesting for us to note that at one time there was a
proposal that Kepler should forsake his native country and adopt
England as a home. It arose in this wise. The great man was
distressed throughout the greater part of his life by pecuniary
anxieties. Finding him in a strait of this description, the English
ambassador in Venice, Sir Henry Wotton, in the year 1620, besought
Kepler to come over to England, where he assured him that he would
obtain a favourable reception, and where, he was able to add,
Kepler's great scientific work was already highly esteemed. But his
efforts were unavailing; Kepler would not leave his own country. He
was then forty-nine years of age, and doubtless a home in a foreign
land, where people spoke a strange tongue, had not sufficient
attraction for him, even when accompanied with the substantial
inducements which the ambassador was able to offer. Had Kepler
accepted this invitation, he would, in transferring his home to
England, have anticipated the similar change which took place in the
career of another great astronomer two centuries later. It will be
remembered that Herschel, in his younger days, did transfer himself
to England, and thus gave to England the imperishable fame of
association with his triumphs.
The publication of the Rudolphine tables of the celestial movements
entailed much expense. A considerable part of this was defrayed by
the Government at Venice but the balance occasioned no little trouble
and anxiety to Kepler. No doubt the authorities of those days were
even less willing to spend money on scientific matters than are the
Governments of more recent times. For several years the imperial
Treasury was importuned to relieve him from his anxieties. The
effects of so much worry, and of the long journeys which were
involved, at last broke down Kepler's health completely. As we have
already mentioned, he had never been strong from infancy, and he
finally succumbed to a fever in November, 1630, at the age of
fifty-nine. He was interred at St. Peter's Church at Ratisbon.
Though Kepler had not those personal characteristics which have made
his great predecessor, Tycho Brahe, such a romantic figure, yet a
picturesque element in Kepler's character is not wanting. It was,
however, of an intellectual kind. His imagination, as well as his
reasoning faculties, always worked together. He was incessantly
prompted by the most extraordinary speculations. The great majority
of them were in a high degree wild and chimerical, but every now and
then one of his fancies struck right to the heart of nature, and an
immortal truth was brought to light.
I remember visiting the observatory of one of our greatest modern
astronomers, and in a large desk he showed me a multitude of
photographs which he had attempted but which had not been successful,
and then he showed me the few and rare pictures which had succeeded,
and by which important truths had been revealed. With a felicity of
expression which I have often since thought of, he alluded to the
contents of the desk as the "chips." They were useless, but they
were necessary incidents in the truly successful work. So it is in
all great and good work. Even the most skilful man of science
pursues many a wrong scent. Time after time he goes off on some
track that plays him false. The greater the man's genius and
intellectual resource, the more numerous will be the ventures which
he makes, and the great majority of those ventures are certain to be
fruitless. They are in fact, the "chips." In Kepler's case the
chips were numerous enough. They were of the most extraordinary
variety and structure. But every now and then a sublime discovery
was made of such a character as to make us regard even the most
fantastic of Kepler's chips with the greatest veneration and respect.
ISAAC NEWTON.
It was just a year after the death of Galileo, that an infant came
into the world who was christened Isaac Newton. Even the great fame
of Galileo himself must be relegated to a second place in comparison
with that of the philosopher who first expounded the true theory of
the universe.
Isaac Newton was born on the 25th of December (old style), 1642, at
Woolsthorpe, in Lincolnshire, about a half-mile from Colsterworth,
and eight miles south of Grantham. His father, Mr. Isaac Newton, had
died a few months after his marriage to Harriet Ayscough, the
daughter of Mr. James Ayscough, of Market Overton, in Rutlandshire.
The little Isaac was at first so excessively frail and weakly that
his life was despaired of. The watchful mother, however, tended her
delicate child with such success that he seems to have thriven better
than might have been expected from the circumstances of his infancy,
and he ultimately acquired a frame strong enough to outlast the
ordinary span of human life.
For three years they continued to live at Woolsthorpe, the widow's
means of livelihood being supplemented by the income from another
small estate at Sewstern, in a neighbouring part of Leicestershire.
[PLATE: WOOLSTHORPE MANOR.
Showing solar dial made by Newton when a boy.]
In 1645, Mrs. Newton took as a second husband the Rev. Barnabas
Smith, and on moving to her new home, about a mile from Woolsthorpe,
she entrusted little Isaac to her mother, Mrs. Ayscough. In due
time we find that the boy was sent to the public school at Grantham,
the name of the master being Stokes. For the purpose of being near
his work, the embryo philosopher was boarded at the house of Mr.
Clark, an apothecary at Grantham. We learn from Newton himself that
at first he had a very low place in the class lists of the school,
and was by no means one of those model school-boys who find favour in
the eyes of the school-master by attention to Latin grammar. Isaac's
first incentive to diligent study seems to have been derived from the
circumstance that he was severely kicked by one of the boys who was
above him in the class. This indignity had the effect of stimulating
young Newton's activity to such an extent that he not only attained
the desired object of passing over the head of the boy who had
maltreated him, but continued to rise until he became the head of the
school.
The play-hours of the great philosopher were devoted to pursuits very
different from those of most school-boys. His chief amusement was
found in making mechanical toys and various ingenious contrivances.
He watched day by day with great interest the workmen engaged in
constructing a windmill in the neighbourhood of the school, the
result of which was that the boy made a working model of the windmill
and of its machinery, which seems to have been much admired, as
indicating his aptitude for mechanics. We are told that Isaac also
indulged in somewhat higher flights of mechanical enterprise. He
constructed a carriage, the wheels of which were to be driven by the
hands of the occupant, while the first philosophical instrument he
made was a clock, which was actuated by water. He also devoted much
attention to the construction of paper kites, and his skill in this
respect was highly appreciated by his school-fellows. Like a true
philosopher, even at this stage he experimented on the best methods
of attaching the string, and on the proportions which the tail ought
to have. He also made lanthorns of paper to provide himself with
light as he walked to school in the dark winter mornings.
The only love affair in Newton's life appears to have commenced while
he was still of tender years. The incidents are thus described in
Brewster's "Life of Newton," a work to which I am much indebted in
this chapter.
"In the house where he lodged there were some female inmates, in
whose company he appears to have taken much pleasure. One of these,
a Miss Storey, sister to Dr. Storey, a physician at Buckminster, near
Colsterworth, was two or three years younger than Newton and to great
personal attractions she seems to have added more than the usual
allotment of female talent. The society of this young lady and her
companions was always preferred to that of his own school-fellows,
and it was one of his most agreeable occupations to construct for
them little tables and cupboards, and other utensils for holding
their dolls and their trinkets. He had lived nearly six years in the
same house with Miss Storey, and there is reason to believe that
their youthful friendship gradually rose to a higher passion; but the
smallness of her portion, and the inadequacy of his own fortune,
appear to have prevented the consummation of their happiness. Miss
Storey was afterwards twice married, and under the name of Mrs.
Vincent, Dr. Stukeley visited her at Grantham in 1727, at the age of
eighty-two, and obtained from her many particulars respecting the
early history of our author. Newton's esteem for her continued
unabated during his life. He regularly visited her when he went to
Lincolnshire, and never failed to relieve her from little pecuniary
difficulties which seem to have beset her family."
The schoolboy at Grantham was only fourteen years of age when his
mother became a widow for the second time. She then returned to the
old family home at Woolsthorpe, bringing with her the three children
of her second marriage. Her means appear to have been somewhat
scanty, and it was consequently thought necessary to recall Isaac
from the school. His recently-born industry had been such that he
had already made good progress in his studies, and his mother hoped
that he would now lay aside his books, and those silent meditations
to which, even at this early age, he had become addicted. It was
expected that, instead of such pursuits, which were deemed quite
useless, the boy would enter busily into the duties of the farm and
the details of a country life. But before long it became manifest
that the study of nature and the pursuit of knowledge had such a
fascination for the youth that he could give little attention to
aught else. It was plain that he would make but an indifferent
farmer. He greatly preferred experimenting on his water-wheels to
looking after labourers, while he found that working at mathematics
behind a hedge was much more interesting than chaffering about the
price of bullocks in the market place. Fortunately for humanity his
mother, like a wise woman, determined to let her boy's genius have
the scope which it required. He was accordingly sent back to
Grantham school, with the object of being trained in the knowledge
which would fit him for entering the University of Cambridge.
[PLATE: TRINITY COLLEGE, CAMBRIDGE.
Showing Newton's rooms; on the leads of the gateway he placed
his telescope.]
It was the 5th of June, 1660, when Isaac Newton, a youth of eighteen,
was enrolled as an undergraduate of Trinity College, Cambridge.
Little did those who sent him there dream that this boy was destined
to be the most illustrious student who ever entered the portals of
that great seat of learning. Little could the youth himself have
foreseen that the rooms near the gateway which he occupied would
acquire a celebrity from the fact that he dwelt in them, or that the
ante-chapel of his college was in good time to be adorned by that
noble statue, which is regarded as one of the chief art treasures of
Cambridge University, both on account of its intrinsic beauty and the
fact that it commemorates the fame of her most distinguished alumnus,
Isaac Newton, the immortal astronomer. Indeed, his advent at the
University seemed to have been by no means auspicious or brilliant.
His birth was, as we have seen, comparatively obscure, and though he
had already given indication of his capacity for reflecting on
philosophical matters, yet he seems to have been but ill-equipped
with the routine knowledge which youths are generally expected to
take with them to the Universities.