GALILEI.
“Dans la Science nous sommes tous disciples de Galilée.”—TROUESSART.
“Bacon pointed out at a distance the road to true philosophy: Galileo
both pointed it out to others, and made himself considerable advances
in it.”—DAVID HUME.
113. To the generation which succeeded Tycho belonged two of the best
known of all astronomers, Galilei and Kepler. Although they were nearly
contemporaries, Galilei having been born seven years earlier than
Kepler, and surviving him by twelve years, their methods of work and
their contributions to astronomy were so different in character, and
their influence on one another so slight, that it is convenient to make
some departure from strict chronological order, and to devote this
chapter exclusively to Galilei, leaving Kepler to the next.
_Galileo Galilei_ was born in 1564, at Pisa, at that time in the Grand
Duchy of Tuscany, on the day of Michel Angelo’s death and in the year
of Shakespeare’s birth. His father, Vincenzo, was an impoverished
member of a good Florentine family, and was distinguished by his skill
in music and mathematics. Galileo’s talents shewed themselves early,
and although it was originally intended that he should earn his living
by trade, Vincenzo was wise enough to see that his son’s ability and
tastes rendered him much more fit for a professional career, and
accordingly he sent him in 1581 to study medicine at the University
of Pisa. Here his unusual gifts soon made him conspicuous, and he
became noted in particular for his unwillingness to accept without
question the dogmatic statements of his teachers, which were based not
on direct evidence, but on the authority of the great writers of the
past. This valuable characteristic, which marked him throughout his
life, coupled with his skill in argument, earned for him the dislike of
some of his professors, and from his fellow-students the nickname of
The Wrangler.
114. In 1582 his keen observation led to his first scientific
discovery. Happening one day in the Cathedral of Pisa to be looking at
the swinging of a lamp which was hanging from the roof, he noticed that
as the motion gradually died away and the extent of each oscillation
became less, the time occupied by each oscillation remained sensibly
the same, a result which he verified more precisely by comparison with
the beating of his pulse. Further thought and trial shewed him that
this property was not peculiar to cathedral lamps, but that any weight
hung by a string (or any other form of pendulum) swung to and fro
in a time which depended only on the length of the string and other
characteristics of the pendulum itself, and not to any appreciable
extent on the way in which it was set in motion or on the extent of
each oscillation. He devised accordingly an instrument the oscillations
of which could be used while they lasted as a measure of time, and
which was in practice found very useful by doctors for measuring the
rate of a patient’s pulse.
115. Before very long it became evident that Galilei had no special
taste for medicine, a study selected for him chiefly as leading to a
reasonably lucrative professional career, and that his real bent was
for mathematics and its applications to experimental science. He had
received little or no formal teaching in mathematics before his second
year at the University, in the course of which he happened to overhear
a lesson on Euclid’s geometry, given at the Grand Duke’s court, and
was so fascinated that he continued to attend the course, at first
surreptitiously, afterwards openly; his interest in the subject was
thereby so much stimulated, and his aptitude for it was so marked,
that he obtained his father’s consent to abandon medicine in favour of
mathematics.
In 1585, however, poverty compelled him to quit the University without
completing the regular course and obtaining a degree, and the next four
years were spent chiefly at home, where he continued to read and to
think on scientific subjects. In the year 1586 he wrote his first known
scientific essay,[66] which was circulated in manuscript, and only
printed during the present century.
116. In 1589 he was appointed for three years to a professorship
of mathematics (including astronomy) at Pisa. A miserable stipend,
equivalent to about five shillings a week, was attached to the post,
but this he was to some extent able to supplement by taking private
pupils.
In his new position Galilei had scope for his remarkable power
of exposition, but far from being content with giving lectures
on traditional lines he also carried out a series of scientific
investigations, important both in themselves and on account of the
novelty in the method of investigation employed.
It will be convenient to discuss more fully at the end of this chapter
Galilei’s contributions to mechanics and to scientific method, and
merely to refer here briefly to his first experiments on falling
bodies, which were made at this time. Some were performed by dropping
various bodies from the top of the leaning tower of Pisa, and others
by rolling balls down grooves arranged at different inclinations.
It is difficult to us nowadays, when scientific experiments are so
common, to realise the novelty and importance at the end of the 16th
century of such simple experiments. The mediaeval tradition of carrying
out scientific investigation largely by the interpretation of texts
in Aristotle, Galen, or other great writers of the past, and by the
deduction of results from general principles which were to be found in
these writers without any fresh appeal to observation, still prevailed
almost undisturbed at Pisa, as elsewhere. It was in particular commonly
asserted, on the authority of Aristotle, that, the cause of the fall of
a heavy body being its weight, a heavier body must fall faster than a
lighter one and in proportion to its greater weight. It may perhaps be
doubted whether any one before Galilei’s time had clear enough ideas
on the subject to be able to give a definite answer to such a question
as how much farther a ten-pound weight would fall in a second than a
one-pound weight; but if so he would probably have said that it would
fall ten times as far, or else that it would require ten times as long
to fall the same distance. To actually try the experiment, to vary
its conditions, so as to remove as many accidental causes of error as
possible, to increase in some way the time of the fall so as to enable
it to be measured with more accuracy, these ideas, put into practice by
Galilei, were entirely foreign to the prevailing habits of scientific
thought, and were indeed regarded by most of his colleagues as
undesirable if not dangerous innovations. A few simple experiments were
enough to prove the complete falsity of the current beliefs in this
matter, and to establish that in general bodies of different weights
fell nearly the same distance in the same time, the difference being
not more than could reasonably be ascribed to the resistance offered by
the air.
These and other results were embodied in a tract, which, like most of
Galilei’s earlier writings, was only circulated in manuscript, the
substance of it being first printed in the great treatise on mechanics
which he published towards the end of his life (§ 133).
These innovations, coupled with the slight respect that he was in the
habit of paying to those who differed from him, evidently made Galilei
far from popular with his colleagues at Pisa, and either on this
account, or on account of domestic troubles consequent on the death of
his father (1591), he resigned his professorship shortly before the
expiration of his term of office, and returned to his mother’s home at
Florence.
117. After a few months spent at Florence he was appointed, by the
influence of a Venetian friend, to a professorship of mathematics at
Padua, which was then in the territory of the Venetian republic (1592).
The appointment was in the first instance for a period of six years,
and the salary much larger than at Pisa. During the first few years
of Galilei’s career at Padua his activity seems to have been very
great and very varied; in addition to giving his regular lectures,
to audiences which rapidly increased, he wrote tracts, for the most
part not printed at the time, on astronomy, on mechanics, and on
fortification, and invented a variety of scientific instruments.
No record exists of the exact time at which he first adopted the
astronomical views of Coppernicus, but he himself stated that in 1597
he had adopted them some years before, and had collected arguments in
their support.
In the following year his professorship was renewed for six years with
an increased stipend, a renewal which was subsequently made for six
years more, and finally for life, the stipend being increased on each
occasion.
Galilei’s first contribution to astronomical discovery was made in
1604, when a star appeared suddenly in the constellation Serpentarius,
and was shewn by him to be at any rate more distant than the planets, a
result confirming Tycho’s conclusions (chapter V., § 100) that changes
take place in the celestial regions even beyond the planets, and are
by no means confined—as was commonly believed—to the earth and its
immediate surroundings.
118. By this time Galilei had become famous throughout Italy, not only
as a brilliant lecturer, but also as a learned and original man of
science. The discoveries which first gave him a European reputation
were, however, the series of telescopic observations made in 1609 and
the following years.
Roger Bacon (chapter III., § 67) had claimed to have devised a
combination of lenses enabling distant objects to be seen as if they
were near; a similar invention was probably made by our countryman
_Leonard Digges_ (who died about 1571), and was described also by the
Italian _Porta_ in 1558. If such an instrument was actually made by
any one of the three, which is not certain, the discovery at any rate
attracted no attention and was again lost. The effective discovery
of the telescope was made in Holland in 1608 by _Hans Lippersheim_
(?-1619), a spectacle-maker of Middleburg, and almost simultaneously by
two other Dutchmen, but whether independently or not it is impossible
to say. Early in the following year the report of the invention
reached Galilei, who, though without any detailed information as to
the structure of the instrument, succeeded after a few trials in
arranging two lenses—one convex and one concave—in a tube in such a
way as to enlarge the apparent size of an object looked at; his first
instrument made objects appear three times nearer, consequently three
times greater (in breadth and height), and he was soon able to make
telescopes which in the same way magnified thirty-fold.
That the new instrument might be applied to celestial as well as
to terrestrial objects was a fairly obvious idea, which was acted
on almost at once by the English mathematician _Thomas Harriot_
(1560-1621), by _Simon Marius_ (1570-1624) in Germany, and by Galilei.
That the credit of first using the telescope for astronomical
purposes is almost invariably attributed to Galilei, though his first
observations were in all probability slightly later in date than those
of Harriot and Marius, is to a great extent justified by the persistent
way in which he examined object after object, whenever there seemed any
reasonable prospect of results following, by the energy and acuteness
with which he followed up each clue, by the independence of mind with
which he interpreted his observations, and above all by the insight
with which he realised their astronomical importance.
119. His first series of telescopic discoveries were published early
in 1610 in a little book called _Sidereus Nuncius_, or _The Sidereal
Messenger_. His first observations at once threw a flood of light
on the nature of our nearest celestial neighbour, the moon. It was
commonly believed that the moon, like the other celestial bodies, was
perfectly smooth and spherical, and the cause of the familiar dark
markings on the surface was quite unknown.[67]
[Illustration: FIG. 53.—One of Galilei’s drawings of the moon. From the
_Sidereus Nuncius_.]
Galilei discovered at once a number of smaller markings, both bright
and dark (fig. 53), and recognised many of the latter as shadows of
lunar mountains cast by the sun; and further identified bright spots
seen near the boundary of the illuminated and dark portions of the moon
as mountain-tops just catching the light of the rising or setting sun,
while the surrounding lunar area was still in darkness. Moreover, with
characteristic ingenuity and love of precision, he calculated from
observations of this nature the height of some of the more conspicuous
lunar mountains, the largest being estimated by him to be about
four miles high, a result agreeing closely with modern estimates of
the greatest height on the moon. The large dark spots he explained
(erroneously) as possibly caused by water, though he evidently had
less confidence in the correctness of the explanation than some of his
immediate scientific successors, by whom the name of =seas= was given
to these spots (chapter VIII., § 153). He noticed also the absence of
clouds. Apart however from details, the really significant results of
his observations were that the moon was in many important respects
similar to the earth, that the traditional belief in its perfectly
spherical form had to be abandoned, and that so far the received
doctrine of the sharp distinction to be drawn between things celestial
and things terrestrial was shewn to be without justification; the
importance of this in connection with the Coppernican view that the
earth, instead of being unique, was one of six planets revolving round
the sun, needs no comment.
One of Galilei’s numerous scientific opponents[68] attempted to explain
away the apparent contradiction between the old theory and the new
observations by the ingenious suggestion that the apparent valleys
in the moon were in reality filled with some _invisible_ crystalline
material, so that the moon was in fact perfectly spherical. To this
Galilei replied that the idea was so excellent that he wished to extend
its application, and accordingly maintained that the moon had on it
mountains of this same invisible substance, at least ten times as high
as any which he had observed.
120. The telescope revealed also the existence of an immense number
of stars too faint to be seen by the unaided eye; Galilei saw, for
example, 36 stars in the Pleiades, which to an ordinary eye consist
of six only. Portions of the Milky Way and various nebulous patches
of light were also discovered to consist of multitudes of faint stars
clustered together; in the cluster Præsepe (in the Crab), for example,
he counted 40 stars.
121. By far the most striking discovery announced in the _Sidereal
Messenger_ was that of the bodies now known as the moons or satellites
of Jupiter. On January 7th, 1610, Galilei turned his telescope on to
Jupiter, and noticed three faint stars which caught his attention on
account of their closeness to the planet and their arrangement nearly
in a straight line with it. He looked again next night, and noticed
that they had changed their positions relatively to Jupiter, but that
the change did not seem to be such as could result from Jupiter’s own
motion, if the new bodies were fixed stars. Two nights later he was
able to confirm this conclusion, and to infer that the new bodies
were not fixed stars, but moving bodies which accompanied Jupiter in
his movements. A fourth body was noticed on January 13th, and the
motions of all four were soon recognised by Galilei as being motions of
revolution round Jupiter as a centre. With characteristic thoroughness
he watched the motions of the new bodies night after night, and by the
date of the publication of his book had already estimated with very
fair accuracy their periods of revolution round Jupiter, which ranged
between about 42 hours and 17 days; and he continued to watch their
motions for years.
[Illustration: FIG. 54.—Jupiter and its satellites as seen on Jan. 7,
1610. From the _Sidereus Nuncius_.]
The new bodies were at first called by their discoverer Medicean
planets, in honour of his patron Cosmo de Medici, the Grand Duke of
Tuscany; but it was evident that bodies revolving round a planet, as
the planets themselves revolved round the sun, formed a new class of
bodies distinct from the known planets, and the name of =satellite=,
suggested by Kepler as applicable to the new bodies as well as to the
moon, has been generally accepted.
The discovery of Jupiter’s satellites shewed the falsity of the old
doctrine that the earth was the only centre of motion; it tended,
moreover, seriously to discredit the infallibility of Aristotle and
Ptolemy, who had clearly no knowledge of the existence of such bodies;
and again those who had difficulty in believing that Venus and Mercury
could revolve round an apparently moving body, the sun, could not
but have their doubts shaken when shewn the new satellites evidently
performing a motion of just this character; and—most important
consequence of all—the very real mechanical difficulty involved in the
Coppernican conception of the moon revolving round the moving earth and
not dropping behind was at any rate shewn not to be insuperable, as
Jupiter’s satellites succeeded in performing a precisely similar feat.
The same reasons which rendered Galilei’s telescopic discoveries of
scientific importance made them also objectionable to the supporters
of the old views, and they were accordingly attacked in a number of
pamphlets, some of which are still extant and possess a certain amount
of interest. One _Martin Horky_, for example, a young German who had
studied under Kepler, published a pamphlet in which, _after_ proving to
his own satisfaction that the satellites of Jupiter did not exist, he
discussed at some length what they were, what they were like, and why
they existed. Another writer gravely argued that because the human body
had seven openings in it—the eyes, ears, nostrils, and mouth—therefore
by analogy there must be seven planets (the sun and moon being
included) and no more. However, confirmation by other observers was
soon obtained and the pendulum even began to swing in the opposite
direction, a number of new satellites of Jupiter being announced by
various observers. None of these, however, turned out to be genuine,
and Galilei’s four remained the only known satellites of Jupiter till a
few years ago (chapter XIII., § 295).
122. The reputation acquired by Galilei by the publication of the
_Messenger_ enabled him to bring to a satisfactory issue negotiations
which he had for some time been carrying on with the Tuscan court.
Though he had been well treated by the Venetians, he had begun to feel
the burden of regular teaching somewhat irksome, and was anxious to
devote more time to research and to writing. A republic could hardly
be expected to provide him with such a sinecure as he wanted, and he
accordingly accepted in the summer of 1610 an appointment as professor
at Pisa, and also as “First Philosopher and Mathematician” to the
Grand Duke of Tuscany, with a handsome salary and no definite duties
attached to either office.
123. Shortly before leaving Padua he turned his telescope on to Saturn,
and observed that the planet appeared to consist of three parts, as
shewn in the first drawing of fig. 67 (chapter VIII., § 154). On
subsequent occasions, however, he failed to see more than the central
body, and the appearances of Saturn continued to present perplexing
variations, till the mystery was solved by Huygens in 1655 (chapter
VIII., § 154).
The first discovery made at Florence (October 1610) was that Venus,
which to the naked eye appears to vary very much in brilliancy but not
in shape, was in reality at times crescent-shaped like the new moon
and passed through phases similar to some of those of the moon. This
shewed that Venus was, like the moon, a dark body in itself, deriving
its light from the sun; so that its similarity to the earth was thereby
made more evident.
[Illustration: FIG. 55.—Sun-spots. From Galilei’s _Macchie Solari_.]
124. The discovery of dark spots on the sun completed this series of
telescopic discoveries. According to his own statement Galilei first
saw them towards the end of 1610,[69] but apparently paid no particular
attention to them at the time; and, although he shewed them as a matter
of curiosity to various friends, he made no formal announcement of the
discovery till May 1612, by which time the same discovery had been
made independently by Harriot (§ 118) in England, by _John Fabricius_
(1587-? 1615) in Holland, and by the Jesuit _Christopher Scheiner_
(1575-1650) in Germany, and had been published by Fabricius (June
1611). As a matter of fact dark spots had been seen with the naked
eye long before, but had been generally supposed to be caused by the
passage of Mercury in front of the sun. The presence on the sun of such
blemishes as black spots, the “mutability” involved in their changes in
form and position, and their formation and subsequent disappearance,
were all distasteful to the supporters of the old views, according
to which celestial bodies were perfect and unchangeable. The fact,
noticed by all the early observers, that the spots appeared to move
across the face of the sun from the eastern to the western side (_i.e._
roughly from left to right, as seen at midday by an observer in our
latitudes), gave at first sight countenance to the view, championed by
Scheiner among others, that the spots might really be small planets
revolving round the sun, and appearing as dark objects whenever they
passed between the sun and the observer. In three letters to his friend
Welser, a merchant prince of Augsburg, written in 1612 and published
in the following year,[70] Galilei, while giving a full account of his
observations, gave a crushing refutation of this view; proved that
the spots must be on or close to the surface of the sun, and that the
motions observed were exactly such as would result if the spots were
attached to the sun, and it revolved on an axis in a period of about a
month; and further, while disclaiming any wish to speak confidently,
called attention to several of their points of resemblance to clouds.
One of his arguments against Scheiner’s views is so simple and at the
same time so convincing, that it may be worth while to reproduce it as
an illustration of Galilei’s method, though the controversy itself is
quite dead.
Galilei noticed, namely, that while a spot took about fourteen days
to cross from one side of the sun to the other, and this time was the
same whether the spot passed through the centre of the sun’s disc, or
along a shorter path at some distance from it, its rate of motion was
by no means uniform, but that the spot’s motion always appeared much
slower when near the edge of the sun than when near the centre. This he
recognised as an effect of foreshortening, which would result if, and
only if, the spot were near the sun.
If, for example, in the figure, the circle represent a section of
the sun by a plane through the observer at O, and A, B, C, D, E be
points taken at equal distances along the surface of the sun, so as
to represent the positions of an object on the sun at equal intervals
of time, on the assumption that the sun revolves uniformly, then the
apparent motion from A to B, as seen by the observer at O, is measured
by the angle A O B, and is obviously much less than that from D to E,
measured by the angle D O E, and consequently an object attached to
the sun must appear to move more slowly from A to B, _i.e._ near the
sun’s edge, than from D to E, near the centre. On the other hand, if
the spot be a body revolving round the sun at some distance from it,
_e.g._ along the dotted circle _c d e_, then if _c_, _d_, _e_ be taken
at equal distances from one another, the apparent motion from _c_ to
_d_, measured again by the angle _c_ O _d_, is only very slightly less
than that from _d_ to _e_, measured by the angle _d_ O _e_. Moreover,
it required only a simple calculation, performed by Galilei in several
cases, to express these results in a numerical shape, and so to infer
from the actual observations that the spots could not be more than
a very moderate distance from the sun. The only escape from this
conclusion was by the assumption that the spots, if they were bodies
revolving round the sun, moved irregularly, in such a way as always to
be moving fastest when they happened to be between the centre of the
sun and the earth, whatever the earth’s position might be at the time,
a procedure for which, on the one hand, no sort of reason could be
given, and which, on the other, was entirely out of harmony with the
uniformity to which mediæval astronomy clung so firmly.
[Illustration: FIG. 56.—Galilei’s proof that sun-spots are not planets.]
The rotation of the sun about an axis, thus established, might
evidently have been used as an argument in support of the view that
the earth also had such a motion, but, as far as I am aware, neither
Galilei nor any contemporary noticed the analogy. Among other facts
relating to the spots observed by Galilei were the greater darkness
of the central parts, some of his drawings (see fig. 55) shewing, like
most modern drawings, a fairly well-marked line of division between
the central part (or =umbra=) and the less dark fringe (or =penumbra=)
surrounding it; he noticed also that spots frequently appeared in
groups, that the members of a group changed their positions relatively
to one another, that individual spots changed their size and shape
considerably during their lifetime, and that spots were usually
most plentiful in two regions on each side of the sun’s equator,
corresponding roughly to the tropics on our own globe, and were never
seen far beyond these limits.
Similar observations were made by other telescopists, and to Scheiner
belongs the credit of fixing, with considerably more accuracy than
Galilei, the position of the sun’s axis and equator and the time of its
rotation.
125. The controversy with Scheiner as to the nature of spots
unfortunately developed into a personal quarrel as to their respective
claims to the discovery of spots, a controversy which made Scheiner his
bitter enemy, and probably contributed not a little to the hostility
with which Galilei was henceforward regarded by the Jesuits. Galilei’s
uncompromising championship of the new scientific ideas, the slight
respect which he shewed for established and traditional authority, and
the biting sarcasms with which he was in the habit of greeting his
opponents, had won for him a large number of enemies in scientific
and philosophic circles, particularly among the large party who spoke
in the name of Aristotle, although, as Galilei was never tired of
reminding them, their methods of thought and their conclusions would in
all probability have been rejected by the great Greek philosopher if he
had been alive.
It was probably in part owing to his consciousness of a growing
hostility to his views, both in scientific and in ecclesiastical
circles, that Galilei paid a short visit to Rome in 1611, when he
met with a most honourable reception and was treated with great
friendliness by several cardinals and other persons in high places.
Unfortunately he soon began to be drawn into a controversy as to the
relative validity in scientific matters of observation and reasoning
on the one hand, and of the authority of the Church and the Bible on
the other, a controversy which began to take shape about this time and
which, though its battle-field has shifted from science to science, has
lasted almost without interruption till modern times.
In 1611 was published a tract maintaining Jupiter’s satellites to
be unscriptural. In 1612 Galilei consulted Cardinal Conti as to the
astronomical teaching of the Bible, and obtained from him the opinion
that the Bible appeared to discountenance both the Aristotelian
doctrine of the immutability of the heavens and the Coppernican
doctrine of the motion of the earth. A tract of Galilei’s on floating
bodies, published in 1612, roused fresh opposition, but on the other
hand Cardinal Barberini (who afterwards, as Urban VIII., took a leading
part in his persecution) specially thanked him for a presentation
copy of the book on sun-spots, in which Galilei, for the first time,
clearly proclaimed in public his adherence to the Coppernican system.
In the same year (1613) his friend and follower, Father Castelli, was
appointed professor of mathematics at Pisa, with special instructions
not to lecture on the motion of the earth. Within a few months Castelli
was drawn into a discussion on the relations of the Bible to astronomy,
at the house of the Grand Duchess, and quoted Galilei in support of his
views; this caused Galilei to express his opinions at some length in a
letter to Castelli, which was circulated in manuscript at the court.
To this a Dominican preacher, Caccini, replied a few months afterwards
by a violent sermon on the text, “Ye Galileans, why stand ye gazing
up into heaven?”[71] and in 1615 Galilei was secretly denounced to
the Inquisition on the strength of the letter to Castelli and other
evidence. In the same year he expanded the letter to Castelli into a
more elaborate treatise, in the form of a _Letter to the Grand Duchess
Christine_, which was circulated in manuscript, but not printed till
1636. The discussion of the bearing of particular passages of the
Bible (_e.g._ the account of the miracle of Joshua) on the Ptolemaic
and Coppernican systems has now lost most of its interest; it may,
however, be worth noticing that on the more general question Galilei
quotes with approval the saying of Cardinal Baronius, “That the
intention of the Holy Ghost is to teach us not how the heavens go, but
how to go to heaven,”[72] and the following passage gives a good idea
of the general tenor of his argument:—
“Methinks, that in the Discussion of Natural Problemes we ought not
to begin at the authority of places of Scripture; but at Sensible
Experiments and Necessary Demonstrations. For ... Nature being
inexorable and immutable, and never passing the bounds of the Laws
assigned her, as one that nothing careth, whether her abstruse reasons
and methods of operating be or be not exposed to the capacity of men;
I conceive that that concerning Natural Effects, which either sensible
experience sets before our eyes, or Necessary Demonstrations do prove
unto us, ought not, upon any account, to be called into question, much
less condemned upon the testimony of Texts of Scripture, which may
under their words, couch senses seemingly contrary thereto.”[73]
126. Meanwhile his enemies had become so active that Galilei thought
it well to go to Rome at the end of 1615 to defend his cause. Early
in the next year a body of theologians known as the Qualifiers of the
Holy Office (Inquisition), who had been instructed to examine certain
Coppernican doctrines, reported:—
“That the doctrine that the sun was the centre of the world and
immoveable was false and absurd, formally heretical and contrary
to Scripture, whereas the doctrine that the earth was not the
centre of the world but moved, and has further a daily motion, was
philosophically false and absurd and theologically at least erroneous.”
In consequence of this report it was decided to censure Galilei, and
the Pope accordingly instructed Cardinal Bellarmine “to summon Galilei
and admonish him to abandon the said opinion,” which the Cardinal
did.[74] Immediately afterwards a decree was issued condemning the
opinions in question and placing on the well-known _Index of Prohibited
Books_ three books containing Coppernican views, of which the _De
Revolutionibus_ of Coppernicus and another were only suspended “until
they should be corrected,” while the third was altogether prohibited.
The necessary corrections to the _De Revolutionibus_ were officially
published in 1620, and consisted only of a few alterations which
tended to make the essential principles; of the book appear as mere
mathematical hypotheses, convenient for calculation. Galilei seems to
have been on the whole well satisfied with the issue of the inquiry, as
far as he was personally concerned, and after obtaining from Cardinal
Bellarmine a certificate that he had neither abjured his opinions nor
done penance for them, stayed on in Rome for some months to shew that
he was in good repute there.
127. During the next few years Galilei, who was now more than fifty,
suffered a good deal from ill-health and was comparatively inactive.
He carried on, however, a correspondence with the Spanish court on
a method of ascertaining the longitude at sea by means of Jupiter’s
satellites. The essential problem in finding the longitude is to obtain
the time as given by the sun at the required place and also that at
some place the longitude of which is known. If, for example, midday at
Rome occurs an hour earlier than in London, the sun takes an hour to
travel from the meridian of Rome to that of London, and the longitude
of Rome is 15° east of that of London. At sea it is easy to ascertain
the local time, _e.g._ by observing when the sun is highest in the sky,
but the great difficulty, felt in Galilei’s time and long afterwards
(chapter X., §§ 197, 226), was that of ascertaining the time at some
standard place. Clocks were then, and long afterwards, not to be relied
upon to keep time accurately during a long ocean voyage, and some
astronomical means of determining the time was accordingly wanted.
Galilei’s idea was that if the movements of Jupiter’s satellites, and
in particular the eclipses which constantly occurred when a satellite
passed into Jupiter’s shadow, could be predicted, then a table could be
prepared giving the times, according to some standard place, say Rome,
at which the eclipses would occur, and a sailor by observing the local
time of an eclipse and comparing it with the time given in the table
could ascertain by how much his longitude differed from that of Rome.
It is, however, doubtful whether the movements of Jupiter’s satellites
could at that time be predicted accurately enough to make the method
practically useful, and in any case the negotiations came to nothing.
In 1618 three comets appeared, and Galilei was soon drawn into a
controversy on the subject with a Jesuit of the name of Grassi. The
controversy was marked by the personal bitterness which was customary,
and soon developed so as to include larger questions of philosophy and
astronomy. Galilei’s final contribution to it was published in 1623
under the title _Il Saggiatore_ (The Assayer), which dealt incidentally
with the Coppernican theory, though only in the indirect way which the
edict of 1616 rendered necessary. In a characteristic passage, for
example, Galilei says:—
“Since the motion attributed to the earth, which I, as a pious and
Catholic person, consider most false, and not to exist, accommodates
itself so well to explain so many and such different phenomena, I
shall not feel sure ... that, false as it is, it may not just as
deludingly correspond with the phenomena of comets”;
and again, in speaking of the rival systems of Coppernicus and Tycho,
he says:—
“Then as to the Copernican hypothesis, if by the good fortune of
us Catholics we had not been freed from error and our blindness
illuminated by the Highest Wisdom, I do not believe that such grace
and good fortune could have been obtained by means of the reasons and
observations given by Tycho.”
Although in scientific importance the _Saggiatore_ ranks far below
many others of Galilei’s writings, it had a great reputation as a
piece of brilliant controversial writing, and notwithstanding its
thinly veiled Coppernicanism, the new Pope, Urban VIII., to whom it
was dedicated, was so much pleased with it that he had it read aloud
to him at meals. The book must, however, have strengthened the hands
of Galilei’s enemies, and it was probably with a view to counteracting
their influence that he went to Rome next year, to pay his respects
to Urban and congratulate him on his recent elevation. The visit was
in almost every way a success; Urban granted to him several friendly
interviews, promised a pension for his son, gave him several presents,
and finally dismissed him with a letter of special recommendation to
the new Grand Duke of Tuscany, who had shewn some signs of being less
friendly to Galilei than his father. On the other hand, however, the
Pope refused to listen to Galilei’s request that the decree of 1616
should be withdrawn.
128. Galilei now set seriously to work on the great astronomical
treatise, the _Dialogue on the Two Chief Systems of the World, the
Ptolemaic and Coppernican_, which he had had in mind as long ago as
1610, and in which he proposed to embody most of his astronomical work
and to collect all the available evidence bearing on the Coppernican
controversy. The form of a dialogue was chosen, partly for literary
reasons, and still more because it enabled him to present the
Coppernican case as strongly as he wished through the mouths of some
of the speakers, without necessarily identifying his own opinions
with theirs. The manuscript was almost completed in 1629, and in the
following year Galilei went to Rome to obtain the necessary licence
for printing it. The censor had some alterations made and then gave
the desired permission for printing at Rome, on condition that the
book was submitted to him again before being finally printed off. Soon
after Galilei’s return to Florence the plague broke out, and quarantine
difficulties rendered it almost necessary that the book should be
printed at Florence instead of at Rome. This required a fresh licence,
and the difficulty experienced in obtaining it shewed that the Roman
censor was getting more and more doubtful about the book. Ultimately,
however, the introduction and conclusion having been sent to Rome for
approval and probably to some extent rewritten there, and the whole
work having been approved by the Florentine censor, the book was
printed and the first copies were ready early in 1632, bearing both the
Roman and the Florentine _imprimatur_.
129. The Dialogue extends over four successive days, and is carried on
by three speakers, of whom Salviati is a Coppernican and Simplicio an
Aristotelian philosopher, while Sagredo is avowedly neutral, but on
almost every occasion either agrees with Salviati at once or is easily
convinced by him, and frequently joins in casting ridicule upon the
arguments of the unfortunate Simplicio. Though many of the arguments
have now lost their immediate interest, and the book is unduly long,
it is still very readable, and the specimens of scholastic reasoning
put into the mouth of Simplicio and the refutation of them by the other
speakers strike the modern reader as excellent fooling.
Many of the arguments used had been published by Galilei in earlier
books, but gain impressiveness and cogency by being collected and
systematically arranged. The Aristotelian dogma of the immutability
of the celestial bodies is once more belaboured, and shewn to be not
only inconsistent with observations of the moon, the sun, comets, and
new stars, but to be in reality incapable of being stated in a form
free from obscurity and self-contradiction. The evidence in favour of
the earth’s motion derived from the existence of Jupiter’s satellites
and from the undoubted phases of Venus, from the suspected phases of
Mercury and from the variations in the apparent size of Mars, are once
more insisted on. The greater simplicity of the Coppernican explanation
of the daily motion of the celestial sphere and of the motion of the
planets is forcibly urged and illustrated in detail. It is pointed
out that on the Coppernican hypothesis all motions of revolution or
rotation take place in the same direction (from west to east), whereas
the Ptolemaic hypothesis requires some to be in one direction, some
in another. Moreover the apparent daily motion of the stars, which
appears simple enough if the stars are regarded as rigidly attached
to a material sphere, is shewn in a quite different aspect if, as
even Simplicio admits, no such sphere exists, and each star moves in
some sense independently. A star near the pole must then be supposed
to move far more slowly than one near the equator, since it describes
a much smaller circle in the same time; and further—an argument very
characteristic of Galilei’s ingenuity in drawing conclusions from
known facts—owing to the precession of the equinoxes (chapter II., §
42, and IV., § 84) and the consequent change of the position of the
pole among the stars, some of those stars which in Ptolemy’s time
were describing very small circles, and therefore moving slowly, must
now be describing large ones at a greater speed, and _vice versa_. An
extremely complicated adjustment of motions becomes therefore necessary
to account for observations which Coppernicus explained adequately by
the rotation of the earth and a simple displacement of its axis of
rotation.
Salviati deals also with the standing difficulty that the annual
motion of the earth ought to cause a corresponding apparent motion
of the stars, and that if the stars be assumed so far off that this
motion is imperceptible, then some of the stars themselves must be at
least as large as the earth’s orbit round the sun. Salviati points out
that the apparent or angular magnitudes of the fixed stars, avowedly
difficult to determine, are in reality almost entirely illusory, being
due in great part to an optical effect known as =irradiation=, in
virtue of which a bright object always tends to appear enlarged;[75]
and that there is in consequence no reason to suppose the stars nearly
as large as they might otherwise be thought to be. It is suggested
also that the most promising way of detecting the annual motion of
stars resulting from the motion of the earth would be by observing
the relative displacement of two stars close together in the sky (and
therefore nearly in the same direction), of which one might be presumed
from its greater brightness to be nearer than the other. It is, for
example, evident that if, in the figure, E, E′ represent two positions
of the earth in its path round the sun, and A, B two stars at different
distances, but nearly in the same direction, then to the observer at
E the star A appears to the left of B, whereas six months afterwards,
when the observer is at E′, A appears to the right of B. Such a motion
of one star with respect to another close to it would be much more
easily observed than an alteration of the same amount in the distance
of the star from some standard point such as the pole. Salviati points
out that accurate observations of this kind had not been made, and that
the telescope might be of assistance for the purpose. This method,
known as the =double-star= or =differential method of parallax=, was in
fact the first to lead—two centuries later—to a successful detection of
the motion in question (chapter XIII., § 278).
[Illustration: FIG. 57.—The differential method of parallax.]
130. Entirely new ground is broken in the _Dialogue_ when Galilei’s
discoveries of the laws of motion of bodies are applied to the problem
of the earth’s motion. His great discovery, which threw an entirely new
light on the mechanics of the solar system, was substantially the law
afterwards given by Newton as the first of his three laws of motion,
in the form: _Every body continues in its state of rest or of uniform
motion in a straight line, except in so far as it is compelled by force
applied to it to change that state._ Putting aside for the present
any discussion of _force_, a conception first made really definite by
Newton, and only imperfectly grasped by Galilei, we may interpret this
law as meaning that a body has no more inherent tendency to diminish
its motion or to stop than it has to increase its motion or to start,
and that any alteration in either the speed or the direction of a
body’s motion is to be explained by the action on it of some other
body, or at any rate by some other assignable cause. Thus a stone
thrown along a road comes to rest on account of the friction between
it and the ground, a ball thrown up into the air ascends more and more
slowly and then falls to the ground on account of that attraction
of the earth on it which we call its weight. As it is impossible to
entirely isolate a body from all others, we cannot experimentally
realise the state of things in which a body goes on moving indefinitely
in the same direction and at the same rate; it may, however, be shewn
that the more we remove a body from the influence of others, the less
alteration is there in its motion. The law is therefore, like most
scientific laws, an abstraction referring to a state of things to
which we may approximate in nature. Galilei introduces the idea in the
Dialogue by means of a ball on a smooth inclined plane. If the ball
is projected upwards, its motion is gradually retarded; if downwards,
it is continually accelerated. This is true if the plane is fairly
smooth—like a well-planed plank—and the inclination of the plane not
very small. If we imagine the experiment performed on an ideal plane,
which is supposed _perfectly_ smooth, we should expect the same results
to follow, however small the inclination of the plane. Consequently,
if the plane were quite level, so that there is no distinction between
up and down, we should expect the motion to be neither retarded nor
accelerated, but to continue without alteration. Other more familiar
examples are also given of the tendency of a body, when once in
motion, to continue in motion, as in the case of a rider whose horse
suddenly stops, or of bodies in the cabin of a moving ship which have
no tendency to lose the motion imparted to them by the ship, so that,
_e.g._, a body falls down to all appearances exactly as if the rest
of the cabin were at rest, and therefore, in reality, while falling
retains the forward motion which it shares with the ship and its
contents. Salviati states also that—contrary to general belief—a stone
dropped from the masthead of a ship in motion falls at the foot of the
mast, not behind it, but there is no reference to the experiment having
been actually performed.
This mechanical principle being once established, it becomes easy to
deal with several common objections to the supposed motion of the
earth. The case of a stone dropped from the top of a tower, which if
the earth be in reality moving rapidly from west to east might be
expected to fall to the west in its descent, is easily shewn to be
exactly parallel to the case of a stone dropped from the masthead of
a ship in motion. The motion towards the east, which the stone when
resting on the tower shares with the tower and the earth, is not
destroyed in its descent, and it is therefore entirely in accordance
with the Coppernican theory that the stone should fall as it does at
the foot of the tower.[76] Similarly, the fact that the clouds, the
atmosphere in general, birds flying in it, and loose objects on the
surface of the earth, shew no tendency to be left behind as the earth
moves rapidly eastward, but are apparently unaffected by the motion of
the earth, is shewn to be exactly parallel to the fact that the flies
in a ship’s cabin and the loose objects there are in no way affected
by the uniform onward motion of the ship (though the irregular motions
of pitching and rolling do affect them). The stock objection that
a cannon-ball shot westward should, on the Coppernican hypothesis,
carry farther than one shot eastward under like conditions, is met
in the same way; but it is further pointed out that, owing to the
imperfection of gunnery practice, the experiment could not really be
tried accurately enough to yield any decisive result.
The most unsatisfactory part of the _Dialogue_ is the fourth day’s
discussion, on the tides, of which Galilei suggests with great
confidence an explanation based merely on the motion of the earth,
while rejecting with scorn the suggestion of Kepler and others—correct
as far as it went—that they were caused by some influence emanating
from the moon. It is hardly to be wondered at that the rudimentary
mechanical and mathematical knowledge at Galilei’s command should not
have enabled him to deal correctly with a problem of which the vastly
more powerful resources of modern science can only give an imperfect
solution (cf. chapter XI., § 248, and chapter XIII., § 292).
131. The book as a whole was in effect, though not in form, a
powerful—indeed unanswerable—plea for Coppernicanism. Galilei tried to
safeguard his position, partly by the use of dialogue, and partly by
the very remarkable introduction, which was not only read and approved
by the licensing authorities, but was in all probability in part the
composition of the Roman censor and of the Pope. It reads to us like
a piece of elaborate and thinly veiled irony, and it throws a curious
light on the intelligence or on the seriousness of the Pope and the
censor, that they should have thus approved it:—
“Judicious reader, there was published some years since in _Rome_ a
salutiferous Edict, that, for the obviating of the dangerous Scandals
of the present Age, imposed a reasonable Silence upon the Pythagorean
Opinion of the Mobility of the Earth. There want not such as
unadvisedly affirm, that the Decree was not the production of a sober
Scrutiny, but of an informed passion; and one may hear some mutter
that Consultors altogether ignorant of Astronomical observations ought
not to clipp the wings of speculative wits with rash prohibitions. My
zeale cannot keep silence when I hear these inconsiderate complaints.
I thought fit, as being thoroughly acquainted with that prudent
Determination, to appear openly upon the Theatre of the World as a
Witness of the naked Truth. I was at that time in _Rome_, and had
not only the audiences, but applauds of the most Eminent Prelates of
that Court; nor was that Decree published without Previous Notice
given me thereof. Therefore it is my resolution in the present case
to give Foreign Nations to see, that this point is as well understood
in _Italy_, and particularly in _Rome_, as Transalpine Diligence can
imagine it to be: and collecting together all the proper speculations
that concerne the _Copernican Systeme_ to let them know, that the
notice of all preceded the Censure of the _Roman Court_; and that
there proceed from this Climate not only Doctrines for the health of
the Soul, but also ingenious Discoveries for the recreating of the
Mind.... I hope that by these considerations the world will know, that
if other Nations have Navigated more than we, we have not studied less
than they; and that our returning to assert the Earth’s stability, and
to take the contrary only for a Mathematical _Capriccio_, proceeds
not from inadvertency of what others have thought thereof, but (had
one no other inducements), from these reasons that Piety, Religion,
the Knowledge of the Divine Omnipotency, and a consciousness of the
incapacity of man’s understanding dictate unto us.”[77]
132. Naturally Galilei’s many enemies were not long in penetrating
these thin disguises, and the immense success of the book only
intensified the opposition which it excited; the Pope appears to have
been persuaded that Simplicio—the butt of the whole dialogue—was
intended for himself, a supposed insult which bitterly wounded his
vanity; and it was soon evident that the publication of the book
could not be allowed to pass without notice. In June 1632 a special
commission was appointed to inquire into the matter—an unusual
procedure, probably meant as a mark of consideration for Galilei—and
two months later the further issue of copies of the book was
prohibited, and in September a papal mandate was issued requiring
Galilei to appear personally before the Inquisition. He was evidently
frightened by the summons, and tried to avoid compliance through
the good offices of the Tuscan court and by pleading his age and
infirmities, but after considerable delay, at the end of which the
Pope issued instructions to bring him if necessary by force and in
chains, he had to submit, and set off for Rome early in 1633. Here
he was treated with unusual consideration, for whereas in general
even the most eminent offenders under trial by the Inquisition were
confined in its prisons, he was allowed to live with his friend
Niccolini, the Tuscan ambassador, throughout the trial, with the
exception of a period of about three weeks, which he spent within the
buildings of the Inquisition, in comfortable rooms belonging to one
of the officials, with permission to correspond with his friends,
to take exercise in the garden, and other privileges. At his first
hearing before the Inquisition, his reply to the charge of having
violated the decree of 1616 (§ 126) was that he had not understood
that the decree or the admonition given to him forbade the teaching
of the Coppernican theory as a mere “hypothesis,” and that his book
had not upheld the doctrine in any other way. Between his first and
second hearing the Commission, which had been examining his book,
reported that it did distinctly defend and maintain the obnoxious
doctrines, and Galilei, having been meanwhile privately advised by
the Commissary-General of the Inquisition to adopt a more submissive
attitude, admitted at the next hearing that on reading his book again
he recognised that parts of it gave the arguments for Coppernicanism
more strongly than he had at first thought. The pitiable state to which
he had been reduced was shewn by the offer which he now made to write
a continuation to the Dialogue which should as far as possible refute
his own Coppernican arguments. At the final hearing on June 21st he
was examined under threat of torture,[78] and on the next day he was
brought up for sentence. He was convicted “of believing and holding the
doctrines—false and contrary to the Holy and Divine Scriptures—that the
sun is the centre of the world, and that it does not move from east
to west, and that the earth does move and is not the centre of the
world; also that an opinion can be held and supported as probable after
it has been declared and decreed contrary to the Holy Scriptures.”
In punishment, he was required to “abjure, curse, and detest the
aforesaid errors,” the abjuration being at once read by him on his
knees; and was further condemned to the “formal prison of the Holy
Office” during the pleasure of his judges, and required to repeat the
seven penitential psalms once a week for three years. On the following
day the Pope changed the sentence of imprisonment into confinement at
a country-house near Rome belonging to the Grand Duke, and Galilei
moved there on June 24th.[79] On petitioning to be allowed to return
to Florence, he was at first allowed to go as far as Siena, and at the
end of the year was permitted to retire to his country-house at Arcetri
near Florence, on condition of not leaving it for the future without
permission, while his intercourse with scientific and other friends was
jealously watched.
[Illustration: GALILEI.]
The story of the trial reflects little credit either on Galilei or
on his persecutors. For the latter, it may be urged that they acted
with unusual leniency considering the customs of the time; and it
is probable that many of those who were concerned in the trial were
anxious to do as little injury to Galilei as possible, but were
practically forced by the party personally hostile to him to take some
notice of the obvious violation of the decree of 1616. It is easy to
condemn Galilei for cowardice, but it must be borne in mind, on the
one hand, that he was at the time nearly seventy, and much shaken
in health, and, on the other, that the Roman Inquisition, if not as
cruel as the Spanish, was a very real power in the early 17th century;
during Galilei’s lifetime (1600) Giordano Bruno had been burnt alive
at Rome for writings which, in addition to containing religious and
political heresies, supported the Coppernican astronomy and opposed
the traditional Aristotelian philosophy. Moreover, it would be unfair
to regard his submission as due merely to considerations of personal
safety, for—apart from the question whether his beloved science would
have gained anything by his death or permanent imprisonment—there
can be no doubt that Galilei was a perfectly sincere member of his
Church, and although he did his best to convince individual officers
of the Church of the correctness of his views, and to minimise the
condemnation of them passed in 1616, yet he was probably prepared,
when he found that the condemnation was seriously meant by the Pope,
the Holy Office, and others, to believe that in some senses at least
his views must be wrong, although, as a matter of observation and pure
reason, he was unable to see how or why. In fact, like many other
excellent people, he kept watertight compartments in his mind, respect
for the Church being in one and scientific investigation in another.
Copies of the sentence on Galilei and of his abjuration were at once
circulated in Italy and in Roman Catholic circles elsewhere, and a
decree of the Congregation of the Index was also issued adding the
_Dialogue_ to the three Coppernican books condemned in 1616, and to
Kepler’s _Epitome_ of the Coppernican Astronomy (chapter VII., §
145), which had been put on the _Index_ shortly afterwards. It may
be of interest to note that these five books still remained in the
edition of the _Index of Prohibited Books_ which was issued in 1819
(with appendices dated as late as 1821), but disappeared from the next
edition, that of 1835.
133. The rest of Galilei’s life may be described very briefly. With
the exception of a few months, during which he was allowed to be at
Florence for the sake of medical treatment, he remained continuously
at Arcetri, evidently pretty closely watched by the agents of the
Holy Office, much restricted in his intercourse with his friends, and
prevented from carrying on his studies in the directions which he liked
best. He was moreover very infirm, and he was afflicted by domestic
troubles, especially by the death in 1634 of his favourite child, a nun
in a neighbouring convent. But his spirit was not broken, and he went
on with several important pieces of work, which he had begun earlier
in his career. He carried a little further the study of his beloved
Medicean Planets and of the method of finding longitude based on
their movements (§ 127), and negotiated on the subject with the Dutch
government. He made also a further discovery relating to the moon, of
sufficient importance to deserve a few words of explanation.
[Illustration: FIG. 58.—The daily libration of the moon.]
It had long been well known that as the moon describes her monthly path
round the earth we see the same markings substantially in the same
positions on the disc, so that substantially the same face of the moon
is turned towards the earth. It occurred to Galilei to inquire whether
this was accurately the case, or whether, on the contrary, some change
in the moon’s disc could be observed. He saw that if, as seemed likely,
the line joining the centres of the earth and moon always passed
through the same point on the moon’s surface, nevertheless certain
alterations in an observer’s position on the earth would enable him to
see different portions of the moon’s surface from time to time. The
simplest of these alterations is due to the daily motion of the earth.
Let us suppose for simplicity that the observer is on the earth’s
equator, and that the moon is at the time in the celestial equator. Let
the larger circle in fig. 58 represent the earth’s equator, and the
smaller circle the section of the moon by the plane of the equator.
Then in about 12 hours the earth’s rotation carries the observer from
A, where he sees the moon rising, to B, where he sees it setting. When
he is at C, on the line joining the centres of the earth and moon, the
point O appears to be in the centre of the moon’s disc, and the portion
_c_ O _c′_ is visible, _c_ R _c′_ invisible. But when the observer is
at A, the point P, on the right of O, appears in the centre, and the
portion _a_ P _a′_ is visible, so that _c′ a′_ is now visible and _a
c_ invisible. In the same way, when the observer is at B, he can see
the portion _c b_, while _b′ c′_ is invisible and Q appears to be in
the centre of the disc. Thus in the course of the day the portion _a_ O
_b′_ (dotted in the figure) is constantly visible and _b_ R _a′_ (also
dotted) constantly invisible, while _a c b_ and _a′ c′ b′_ alternately
come into view and disappear. In other words, when the moon is rising
we see a little more of the side which is the then uppermost, and
when she is setting we see a little more of the other side which is
uppermost in this position. A similar explanation applies when the
observer is not on the earth’s equator, but the geometry is slightly
more complicated. In the same way, as the moon passes from south to
north of the equator and back as she revolves round the earth, we see
alternately more and less of the northern and southern half of the
moon. This set of changes—the simplest of several somewhat similar ones
which are now known as =librations= of the moon—being thus thought of
as likely to occur, Galilei set to work to test their existence by
observing certain markings of the moon usually visible near the edge,
and at once detected alterations in their distance from the edge, which
were in general accordance with his theoretical anticipations. A more
precise inquiry was however interrupted by failing sight, culminating
(at the end of 1636) in total blindness.
But the most important work of these years was the completion of the
great book, in which he summed up and completed his discoveries in
mechanics, _Mathematical Discourses and Demonstrations concerning
Two New Sciences, relating to Mechanics and to Local Motion_. It was
written in the form of a dialogue between the same three speakers who
figured in the Dialogue on the Systems, but is distinctly inferior in
literary merit to the earlier work. We have here no concern with a
large part of the book, which deals with the conditions under which
bodies are kept, at rest by forces applied to them (statics), and
certain problems relating to the resistance of bodies to fracture and
to bending, though in both of these subjects Galilei broke new ground.
More important astronomically—and probably intrinsically also—is what
he calls the science of local motion,[80] which deals with the motion
of bodies. He builds up on the basis of his early experiments (§
116) a theory of falling bodies, in which occurs for the first time
the important idea of =uniformly accelerated motion=, or =uniform
acceleration=, _i.e._ motion in which the moving body receives in every
equal interval of time an equal increase of velocity. He shews that
the motion of a falling body is—except in so far as it is disturbed
by the air—of this nature, and that, as already stated, the motion
is the same for all bodies, although his numerical estimate is not
at all accurate.[81] From this fundamental law he works out a number
of mathematical deductions, connecting the space fallen through, the
velocity, and the time elapsed, both for the case of a body falling
freely and for one falling down an inclined plane. He gives also a
correct elementary theory of projectiles, in the course of which he
enunciates more completely than before the law of inertia already
referred to (§ 130), although Galilei’s form is still much less general
than Newton’s:—
_Conceive a body projected or thrown along a horizontal plane, all
impediments being removed. Now it is clear by what we have said before
at length that its motion will be uniform and perpetual along the said
plane, if the plane extend indefinitely._
In connection with projectiles, Galilei also appears to realise that
a body may be conceived as having motions in two different directions
simultaneously, and that each may be treated as independent of the
other, so that, for example, if a bullet is shot horizontally out of
a gun, its downward motion, due to its weight, is unaffected by its
horizontal motion, and consequently it reaches the ground at the same
time as a bullet simply allowed to drop; but Galilei gives no general
statement of this principle, which was afterwards embodied by Newton in
his Second Law of Motion.
The treatise on the _Two New Sciences_ was finished in 1636, and, since
no book of Galilei’s could be printed in Italy, it was published after
some little delay at Leyden in 1638. In the same year his eyesight,
which he had to some extent recovered after his first attack of
blindness, failed completely, and four years later (January 8th, 1642)
the end came.
134. Galilei’s chief scientific discoveries have already been noticed.
The telescopic discoveries, on which much of his popular reputation
rests, have probably attracted more than their fair share of attention;
many of them were made almost simultaneously by others, and the rest,
being almost inevitable results of the invention of the telescope,
could not have been delayed long. But the skilful use which Galilei
made of them as arguments for the Coppernican system, the no less
important support which his dynamical discoveries gave to the same
cause, the lucidity and dialectic brilliance with which he marshalled
the arguments in favour of his views and demolished those of his
opponents, together with the sensational incidents of his persecution,
formed conjointly a contribution to the Coppernican controversy which
was in effect decisive. Astronomical textbooks still continued to give
side by side accounts of the Ptolemaic and of the Coppernican systems,
and the authors, at any rate if they were good Roman Catholics, usually
expressed, in some more or less perfunctory way, their adherence
to the former, but there was no real life left in the traditional
astronomy; new advances in astronomical theory were all on Coppernican
lines, and in the extensive scientific correspondence of Newton and
his contemporaries the truth of the Coppernican system scarcely ever
appears as a subject for discussion.
Galilei’s dynamical discoveries, which are only in part of astronomical
importance, are in many respects his most remarkable contribution to
science. For whereas in astronomy he was building on foundations laid
by previous generations, in dynamics it was no question of improving
or developing an existing science, but of creating a new one. From his
predecessors he inherited nothing but erroneous traditions and obscure
ideas; and when these had been discarded, he had to arrive at clear
fundamental notions, to devise experiments and make observations, to
interpret his experimental results, and to follow out the mathematical
consequences of the simple laws first arrived at. The positive results
obtained may not appear numerous, if viewed from the standpoint of our
modern knowledge, but they sufficed to constitute a secure basis for
the superstructure which later investigators added.
It is customary to associate with our countryman Francis Bacon
(1561-1627) the reform in methods of scientific discovery which
took place during the seventeenth century, and to which much of the
rapid progress in the natural sciences made since that time must be
attributed. The value of Bacon’s theory of scientific discovery is
very differently estimated by different critics, but there can be no
question of the singular ill-success which attended his attempts to
apply it in particular cases, and it may fairly be questioned whether
the scientific methods constantly referred to incidentally by Galilei,
and brilliantly exemplified by his practice, do not really contain a
large part of what is valuable in the Baconian philosophy of science,
while at the same time avoiding some of its errors. Reference has
already been made on several occasions to Galilei’s protests against
the current method of dealing with scientific questions by the
interpretation of passages in Aristotle, Ptolemy, or other writers;
and to his constant insistence on the necessity of appealing directly
to actual observation of facts. But while thus agreeing with Bacon in
these essential points, he differed from him in the recognition of
the importance, both of deducing new results from established ones by
mathematical or other processes of exact reasoning, and of using such
deductions, when compared with fresh experimental results, as a means
of verifying hypotheses provisionally adopted. This method of proof,
which lies at the base of nearly all important scientific discovery,
can hardly be described better than by Galilei’s own statement of it,
as applied to a particular case:—
“Let us therefore take this at present as a _Postulatum_, the truth
whereof we shall afterwards find established, when we shall see other
conclusions built upon this _Hypothesis_, to answer and most exactly
to agree with Experience.”[82]