_Galileo re-elected Professor at Padua—New star—Compass of
proportion—Capra—Gilbert—Proposals to return to Pisa—Lost
writings—Cavalieri._
GALILEO'S reputation was now rapidly increasing: his lectures were
attended by many persons of the highest rank; among whom were the
Archduke Ferdinand, afterwards Emperor of Germany, the Landgrave of
Hesse, and the Princes of Alsace and Mantua. On the expiration of the
first period for which he had been elected professor, he was rechosen
for a similar period, with a salary increased to 320 florins. The
immediate occasion of this augmentation is said by Fabroni[26], to have
arisen out of the malice of an ill wisher of Galileo, who, hoping to do
him disservice, apprized the senate that he was not married to Marina
Gamba, then living with him, and the mother of his son Vincenzo. Whether
or not the senate might consider themselves entitled to inquire into the
morality of his private life, it was probably from a wish to mark their
sense of the informer's impertinence, that they returned the brief
answer, that "if he had a family to provide for, he stood the more in
need of an increased stipend."
During Galileo's residence at Padua, and, according to Viviani's
intimation, towards the thirtieth year of his age, that is to say in
1594, he experienced the first attack of a disease which pressed
heavily on him for the rest of his life. He enjoyed, when a young man, a
healthy and vigorous constitution, but chancing to sleep one afternoon
near an open window, through which was blowing a current of air cooled
artificially by the fall of water, the consequences were most disastrous
to him. He contracted a sort of chronic complaint, which showed itself
in acute pains in his limbs, chest, and back, accompanied with frequent
hæmorrhages and loss of sleep and appetite; and this painful disorder
thenceforward never left him entirely, but recurred intermittingly, with
greater or less violence, as long as he lived. Others of the party did
not even escape so well, but died shortly after committing this
imprudence.
In 1604, the attention of astronomers was called to the contemplation of
a new star, which appeared suddenly with great splendour in the
constellation Serpentarius, or Ophiuchus, as it is now more commonly
called. Maestlin, who was one of the earliest to notice it, relates his
observations in the following words: "How wonderful is this new star! I
am certain that I did not see it before the 29th of September, nor
indeed, on account of several cloudy nights, had I a good view till the
6th of October. Now that it is on the other side of the sun, instead of
surpassing Jupiter as it did, and almost rivalling Venus, it scarcely
matches the Cor Leonis, and hardly surpasses Saturn. It continues
however to shine with the same bright and strongly sparkling light, and
changes its colours almost with every moment; first tawny, then yellow,
presently purple and red, and, when it has risen above the vapours, most
frequently white." This was by no means an unprecedented phenomenon; and
the curious reader may find in Riccioli[27] a catalogue of the principal
new stars which have at different times appeared. There is a tradition
of a similar occurrence as early as the times of the Greek astronomer
Hipparchus, who is said to have been stimulated by it to the formation
of his catalogue of the stars; and only thirty-two years before, in
1572, the same remarkable phenomenon in the constellation Cassiopeia was
mainly instrumental in detaching the celebrated Tycho Brahe from the
chemical studies, which till then divided his attention with astronomy.
Tycho's star disappeared at the end of two years; and at that time
Galileo was a child. On the present occasion, he set himself earnestly
to consider the new phenomenon, and embodied the results of his
observations in three lectures, which have been unfortunately lost. Only
the exordium of the first has been preserved: in this he reproaches his
auditors with their general insensibility to the magnificent wonders of
creation daily exposed to their view, in no respect less admirable than
the new prodigy, to hear an explanation of which they had hurried in
crowds to his lecture room. He showed, from the absence of parallax,
that the new star could not be, as the vulgar hypothesis represented, a
mere meteor engendered in our atmosphere and nearer the earth than the
moon, but must be situated among the most remote heavenly bodies. This
was inconceivable to the Aristotelians, whose notions of a perfect,
simple, and unchangeable sky were quite at variance with the
introduction of any such new body; and we may perhaps consider these
lectures as the first public declaration of Galileo's hostility to the
old Ptolemaic and Aristotelian astronomy.
In 1606 he was reappointed to the lectureship, and his salary a second
time increased, being raised to 520 florins. His public lectures were at
this period so much thronged that the ordinary place of meeting was
found insufficient to contain his auditors, and he was on several
occasions obliged to adjourn to the open air,—even from the school of
medicine, which was calculated to contain one thousand persons.
About this time he was considerably annoyed by a young Milanese, of the
name of Balthasar Capra, who pirated an instrument which Galileo had
invented some years before, and had called the geometrical and military
compass. The original offender was a German named Simon Mayer, whom we
shall meet with afterwards arrogating to himself the merit of one of
Galileo's astronomical discoveries; but on this occasion, as soon as he
found Galileo disposed to resent the injury done to him, he hastily
quitted Italy, leaving his friend Capra to bear alone the shame of the
exposure which followed. The instrument is of simple construction,
consisting merely of two straight rulers, connected by a joint; so that
they can be set to any required angle. This simple and useful
instrument, now called the Sector, is to be found in almost every case
of mathematical instruments. Instead of the trigonometrical and
logarithmic lines which are now generally engraved upon it, Galileo's
compass merely contained, on one side, three pairs of lines, divided in
simple, duplicate, and triplicate proportion, with a fourth pair on
which were registered the specific gravities of several of the most
common metals. These were used for multiplications, divisions, and the
extraction of roots; for finding the dimensions of equally heavy balls
of different materials, &c. On the other side were lines contrived for
assisting to describe any required polygon on a given line; for finding
polygons of one kind equal in area to those of another; and a multitude
of other similar operations useful to the practical engineer.
Unless the instrument, which is now called Gunter's scale, be much
altered from what it originally was, it is difficult to understand on
what grounds Salusbury charges Gunter with plagiarism from Galileo's
Compass. He declares that he has closely compared the two, and can find
no difference between them.[28] There has also been some confusion, by
several writers, between this instrument and what is now commonly called
the Proportional Compass. The latter consists of two slips of metal
pointed at each end, and connected by a pin which, sliding in a groove
through both, can be shifted to different positions. Its use is to find
proportional lines; for it is obvious that the openings measured by each
pair of legs will be in the same proportion in which the slips are
divided by the centre. The divisions usually marked on it are calculated
for finding the submultiples of straight lines, and the chords of
submultiple arcs. Montucla has mentioned this mistake of one instrument
for the other, and charges Voltaire with the more inexcusable error of
confounding Galileo's with the Mariner's Compass. He refers to a
treatise by Hulsius for his authority in attributing the Proportional
Compass to Burgi, a Swiss astronomer of some celebrity. Horcher also has
been styled the inventor; but he did no more than describe its form and
application. In the frontispiece of his book is an engraving of this
compass exactly similar to those which are now used.[29] To the
description which Galileo published of his compass, he added a short
treatise on the method of measuring heights and distances with the
quadrant and plumb line. The treatise, which is printed by itself at the
end of the first volume of the Padua edition of Galileo's works,
contains nothing more than the demonstrations belonging to the same
operations. They are quite elementary, and contain little or nothing
that was new even at that time.
Such an instrument as Galileo's Compass was of much more importance
before the grand discovery of logarithms than it can now be considered:
however it acquires an additional interest from the value which he
himself set on it. In 1607, Capra, at the instigation of Mayer,
published as his own invention what he calls the proportional hoop,
which is a mere copy of Galileo's instrument. This produced from Galileo
a long essay, entitled "A Defence of Galileo against the Calumnies and
Impostures of Balthasar Capra." His principal complaint seems to have
been of the misrepresentations which Capra had published of his lectures
on the new star already mentioned, but he takes occasion, after pointing
out the blunders and falsehoods which Capra had committed on that
occasion, to add a complete proof of his piracy of the geometrical
compass. He showed, from the authenticated depositions of workmen, and
of those for whom the instruments had been fabricated, that he had
devised them as early as the year 1597, and had explained their
construction and use both to Balthasar himself and to his father Aurelio
Capra, who was then residing in Padua. He gives, in the same essay, the
minutes of a public meeting between himself and Capra, in which he
proved, to the satisfaction of the university, that wherever Capra had
endeavoured to introduce into his book propositions which were not to be
met with in Galileo's, he had fallen into the greatest absurdities, and
betrayed the most complete ignorance of his subject. The consequence of
this public exposure, and of the report of the famous Fra Paolo Sarpi,
to whom the matter had been referred, was a formal prohibition by the
university of Capra's publication, and all copies of the book then on
hand were seized, and probably destroyed, though Galileo has preserved
it from oblivion by incorporating it in his own publication.
Nearly at the same time, 1607, or immediately after, he first turned his
attention towards the loadstone, on which our countryman Gilbert had
already published his researches, conducted in the true spirit of the
inductive method. Very little that is original is to be found in
Galileo's works on this subject, except some allusions to his method of
arming magnets, in which, as in most of his practical and mechanical
operations, he appears to have been singularly successful. Sir Kenelm
Digby[30] asserts, that the magnets armed by Galileo would support twice
as great a weight as one of Gilbert's of the same size. Galileo was well
acquainted, as appears from his frequent allusions in different parts of
his works, with what Gilbert had done, of whom he says, "I extremely
praise, admire, and envy this author;—I think him, moreover, worthy of
the greatest praise for the many new and true observations that he has
made to the disgrace of so many vain and fabling authors, who write, not
from their own knowledge only, but repeat every thing they hear from the
foolish vulgar, without attempting to satisfy themselves of the same by
experience, perhaps that they may not diminish the size of their books."
Galileo's reputation being now greatly increased, proposals were made to
him, in 1609, to return to his original situation at Pisa. He had been
in the habit of passing over to Florence during the academic vacation,
for the purpose of giving mathematical instruction to the younger
members of Ferdinand's family; and Cosmo, who had now succeeded his
father as duke of Tuscany, regretted that so masterly a genius had been
allowed to leave the university which he naturally should have graced. A
few extracts from Galileo's answers to these overtures will serve to
show the nature of his situation at Padua, and the manner in which his
time was there occupied. "I will not hesitate to say, having now
laboured during twenty years, and those the best of my life, in dealing
out, as one may say, in detail, at the request of any body, the little
talent which God has granted to my assiduity in my profession, that my
wish certainly would be to have sufficient rest and leisure to enable
me, before my life comes to its close, to conclude three great works
which I have in hand, and to publish them; which might perhaps bring
some credit to me, and to those who had favoured me in this undertaking,
and possibly may be of greater and more frequent service to students
than in the rest of my life I could personally afford them. Greater
leisure than I have here I doubt if I could meet with elsewhere, so long
as I am compelled to support my family from my public and private
lectures, (nor would I willingly lecture in any other city than this,
for several reasons which would be long to mention) nevertheless not
even the liberty I have here is sufficient, where I am obliged to spend
many, and often the best hours of the day at the request of this and
that man.—My public salary here is 520 florins, which I am almost
certain will be advanced to as many crowns upon my re-election, and
these I can greatly increase by receiving pupils, and from private
lectures, to any extent that I please. My public duty does not confine
me during more than 60 half hours in the year, and even that not so
strictly but that I may, on occasion of any business, contrive to get
some vacant days; the rest of my time is absolutely at my own disposal;
but because my private lectures and domestic pupils are a great
hindrance and interruption of my studies, I wish to live entirely exempt
from the former, and in great measure from the latter: for if I am to
return to my native country, I should wish the first object of his
Serene Highness to be, that leisure and opportunity should be given me
to complete my works without employing myself in lecturing.—And, in
short, I should wish to gain my bread from my writings, which I would
always dedicate to my Serene Master.—The works which I have to finish
are principally—two books on the system or structure of the Universe,
an immense work, full of philosophy, astronomy, and geometry; three
books on Local Motion, a science entirely new, no one, either ancient or
modern, having discovered any of the very many admirable accidents which
I demonstrate in natural and violent motions, so that I may with very
great reason call it a new science, and invented by me from its very
first principles; three books of Mechanics, two on the demonstration of
principles and one of problems; and although others have treated this
same matter, yet all that has been hitherto written, neither in
quantity, nor otherwise, is the quarter of what I am writing on it. I
have also different treatises on natural subjects; On sound and speech;
On light and colours; On the tide; On the composition of continuous
quantity; On the motions of animals;—And others besides. I have also
an idea of writing some books relating to the military art, giving not
only a model of a soldier, but teaching with very exact rules every
thing which it is his duty to know that depends upon mathematics; as the
knowledge of castrametation, drawing up battalions, fortifications,
assaults, planning, surveying, the knowledge of artillery, the use of
instruments, &c. I also wish to reprint the 'Use of my Geometrical
Compass,' which is dedicated to his highness, and which is no longer to
be met with; for this instrument has experienced such favour from the
public, that in fact no other instruments of this kind are now made, and
I know that up to this time several thousands of mine have been made.—I
say nothing as to the amount of my salary, feeling convinced that as I
am to live upon it, the graciousness of his highness would not deprive
me of any of those comforts, which, however, I feel the want of less
than many others; and therefore I say nothing more on the subject.
Finally, on the title and profession of my service, I should wish that
to the name of Mathematician, his highness would add that of
Philosopher, as I profess to have studied a greater number of years in
philosophy than months in pure mathematics; and how I have profited by
it, and if I can or ought to deserve this title, I may let their
highnesses see as often as it shall please them to give me an
opportunity of discussing such subjects in their presence with those who
are most esteemed in this knowledge." It may perhaps be seen in the
expressions of this letter, that Galileo was not inclined to undervalue
his own merits, but the peculiar nature of the correspondence should be
taken into account, which might justify his indulging a little more than
usual in self-praise, and it would have been perhaps almost impossible
for him to have remained entirely blind to his vast superiority over his
contemporaries.
Many of the treatises which Galileo here mentions, as well as another on
dialling, have been irrecoverably lost, through the superstitious
weakness of some of his relations, who after his death suffered the
family confessor to examine his papers, and to destroy whatever seemed
to him objectionable; a portion which, according to the notions then
prevalent, was like to comprise the most valuable part of the papers
submitted to this expurgation. It is also supposed that many were burnt
by his infatuated grandson Cosimo, who conceived he was thus offering a
proper and pious sacrifice before devoting himself to the life of a
missionary. A Treatise on Fortification, by Galileo, was found in 1793,
and is contained among the documents published by Venturi. Galileo does
not profess in it to give much original matter, but to lay before his
readers a compendium of the most approved principles then already known.
It has been supposed that Gustavus Adolphus of Sweden attended Galileo's
lectures on this subject, whilst in Italy; but the fact is not
satisfactorily ascertained. Galileo himself mentions a Prince Gustavus
of Sweden to whom he gave instruction in mathematics, but the dates
cannot well be made to agree. The question deserves notice only from its
having been made the subject of controversy.
The loss of Galileo's Essay on Continuous Quantity is particularly to be
regretted, as it would be highly interesting to see how far he succeeded
in methodizing his thoughts on this important topic. It is to his pupil
Cavalieri (who refused to publish his book so long as he hoped to see
Galileo's printed) that we owe "The Method of Indivisibles," which is
universally recognized as one of the first germs of the powerful methods
of modern analysis. Throughout Galileo's works we find many indications
of his having thought much on the subject, but his remarks are vague,
and bear little, if at all, on the application of the method. To this
the chief part of Cavalieri's book is devoted, though he was not so
entirely regardless of the principles on which his method of measuring
spaces is founded, as he is sometimes represented. This method consisted
in considering lines as made up of an infinite number of points,
surfaces in like manner as composed of lines, and solids of surfaces;
but there is an observation at the beginning of the 7th book, which
shews clearly that Cavalieri had taken a much more profound view of the
subject than is implied in this superficial exposition, and had
approached very closely to the apparently more exact theories of his
successors. Anticipating the objections to his hypothesis, he argues,
that "there is no necessity to suppose the continuous quantities made up
of these indivisible parts, _but only that they will observe the same
ratios as those parts do_." It ought not to be omitted, that Kepler also
had given an impulse to Cavalieri in his "New method of Gauging," which
is the earliest work with which we are acquainted, where principles of
this sort are employed.[31]
FOOTNOTES:
[26] Vitæ Italorum Illustrium.
[27] Almagestum Novum, vol. i.
[28] Math. Coll. vol. ii.
[29] Constructio Circini Proportionum. Moguntiæ, 1605.
[30] Treatise of the Nature of Bodies. London, 1665.
[31] Nova Stereometria Doliorum—Lincii, 1615.