The life of Galileo Galilei, with illustrations of the advancement of experimental philosophy ; Life of Kepler

THE LIBRARY

OF

THE UNIVERSITY
OF CALIFORNIA

PRESENTED BY

PROF. CHARLES A. KOFOID AND
MRS. PRUDENCE W. KOFOID

THE

LIFE

OF

GALILEO GALILEI,

WITH

ILLUSTRATIONS OF THE ADVANCEMENT

OF

EXPERIMENTAL PHILOSOPHY.

MDCCCXXX.

LONDON.

GIFT

LIFE OF GALILEO

WITH ILLUSTRATIONS OF THE ADVANCEMENT
OF EXPERIMENTAL PHILOSOPHY.

CHAPTER I.
Introduction.

THE knowledge which we at present
possess of the phenomena of nature and
of their connection has not by any
means been regularly progressive, as we.
might have expected, from the time
when they first drew the attention of
mankind. Without entering into the
question touching the scientific acquire-
ments of eastern nations at a remote
period, it is certain that some among
the early Greeks were in possession of
several truths, however acquired, con-
nected with the economy of the universe,
which were afterwards suffered to fall
into neglect and oblivion. But the phi-
losophers of the old school appear in
general to have confined themselves at
the best to observations ; very few traces
remain of their having instituted experi-
ments, properly so called. This putting
of nature to the tor.ture, as Bacon calls
it, has occasioned the principal part of
modern philosophical discoveries. The
experimentalist may so order his exami-
nation of nature as to vary at pleasure
the circumstances in which it is made,
often to discard accidents which com-
plicate the general appearances, and
at once to bring any theory which he
may form to a decisive test. The pro-
vince of the mere observer is necessarily
limited : the power of selection among
the phenomena to be presented is in
great measure denied to him, arid he
may consider himself fortunate if they
are such as to lead him readily to a
knowledge of the laws which they fol-
low.

Perhaps to this imperfection of me-
thod it may be attributed that natural
philosophy continued to be stationary,
or even to decline, during a long series
of ages, until little more than two cen-
turies ago. Within this comparatively
short period it has rapidly reached a
degree of perfection so different from its
former degraded state, that we can
hardly institute any comparison between
the two. Before that epoch, a- few insu-
lated facts, such as might first happen

to be noticed, often inaccurately ob-
served and always too hastily general-
ized, were found sufficient to excite the
naturalist's lively imagination ; and hav-
ing once pleased his fancy with the sup-
posed fitness of his artificial scheme,
his perverted ingenuity was thencefor-
ward employed in forcing the observed
phenomena into an imaginary agreement
with the result of his theory ; instead of
taking the more rational, and it should
seem, the more obvious, method of cor-
recting the theory by the result of his
observations, and considering the one
merely as the general and abbreviated
expression of the other. But natural
phenomena were not then valued on
their own account, and for the proofs
which they afford of a vast and benefi-
cent design in the structure of the uni-
verse, so much as for the fertile topics
which the favourite mode of viewing the
subject supplied to the spirit of scholas-
tic disputation : and it is a humiliating
reflection that mankind never reasoned
so ill as when they most professed to
cultivate the art of reasoning. How-
ever specious the objects, and alluring
the announcements of this art, the then
prevailing manner ot studying it curbed
and corrupted all that is free and noble
in the human mind. Innumerable falla-
cies lurked every where among the
most generally received opinions, and
crowds of dogmatic and self-sufficient
pedants fully justified the lively defini-
tion, that " logic is the art of talking un-
intelligibly on things of which we are
ignorant."*

The error which lay at the root of the
philosophy of the middle ages was this :
— from the belief that general laws and
universal principles might be discovered,
of which the natural phenomena were
effects, it was thought that the proper
order of study was, first to detect the
general cause, and then to pursue it into
its consequences ; it was considered ab-
surd to begin with the effect instead of
the cause ; whereas the real choice lay
between proceeding from particular facts

* Menage.

M8797'77

GALILEO.

to general facts, or from general facts
to particular facts ; and it was under
this misrepresentation of the real ques-
tion that all the sophistry lurked. As
soon as it is well understood that the
general cause is no other than a single
fact, common to a great number of phe-
nomena, it is necessarily perceived that
an accurate scrutiny of these latter must
precede any safe reasoning with respect
to the former. But at the time of which
we are speaking, those who adopted this
order of reasoning, and who began their
inquiries by a minute and sedulous in-
vestigation of facts, were treated with
disdain, as men who degraded the
lofty name of philosophy by bestowing
it upon mere mechanical operations.
Among the, earliest and noblest of these
was Galileo.

It is common, especially in this coun-
try, to name Bacon as the founder of
the present school of experimental phi-
losophy ; we speak of the Baconian or
inductive method of reasoning as syno-
nimous and convertible terms, and we
are apt to overlook what Galileo had
already done before Bacon's writings
appeared. Certainly the Italian did not
range over the circle of the sciences with
the supreme and searching glance of
the English philosopher, but we find in
every part of his writings philosophical
maxims which do not lose by com-
parison with those of Bacon ; and
Galileo deserves the additional praise,
that he himself gave to the world a
splendid practical illustration of the
value of the principles which he con-
stantly recommended. In support of
this view of the comparative deserts of
these two celebrated men, we are able
to adduce the authority of Hume, who
will be readily admitted as a competent
judge of philosophical merit, where his
prejudices cannot bias his decision. Dis-
cussing the character of Bacon, he says,
" If we consider the variety of talents
displayed by this man, as a public
speaker, a man of business, a wit, a
courtier, a companion, an author, a
philosopher, he is justly the object of
great admiration. If we consider him
merely as an author and philosopher,
the light in which we view him at pre-
sent, though very estimable, he was yet
inferior to his contemporary Galileo,
perhaps even to Kepler. Bacon pointed
out at a distance the road to true phi-
losophy : Galileo both pointed it out to
others, and made himself considerable
advances in it. The Englishman was

ignorant of geometry : the Florentine
revived that science, excelled in it, and
was the first that applied it, together
with experiment, to natural philosophy.
The former rejected with the most posi-
tive disdain the system of Copernicus:
the latter fortified it with new proofs
derived both from reason and the
senses."*

If we compare them from another
point of view, not so much in respect of
their intrinsic merit, as of the influence
which each exercised on the philosophy
of his age, Galileo's superior talent or
better fortune, in arresting the attention
of his contemporaries, seems indis-
putable. The fate of the two writers is
directly opposed the one to the other ;
Bacon's works seem te be most studied
and appreciated when his readers have
come to their perusal, imbued with
knowledge and a philosophical spirit,
which, however, they have attained inde-
pendently of his assistance. The proud
appeal to posterity which he uttered in
his will, " For my name and memory, I
leave it to men's charitable speeches,
and to foreign nations, and the next
ages," of itself indicates a consciousness
of the fact that his contemporary coun-
trymen were but slightly affected by his
philosophical precepts. But Galileo's
personal exertions changed the general
character of philosophy in Italy : at the
time of his death, his immediate pupils
had obtained possession of the most ce-
lebrated universities, and were busily en-
gaged in practising and enforcing the
lessons which he had taught them ; nor
was it then easy to find there a single
student of natural philosophy who did
not readily ascribe the formation of his
principles to the direct or remote influ-
ence of Galileo's example. Unlike Ba-
con's, his reputation, and the value of
his writings, were higher among his
contemporaries than they have since be-
come. This judgment perhaps awards
the highest intellectual prize to him
whose disregarded services rise in esti-
mation with the advance of knowledge ;
but the praise due to superior usefulness
belongs to him who succeeded in train-
ing round him a school of imitators,
and thereby enabled his imitators to
surpass himself.

The biography of men who have de-
voted themselves to philosophical pur-
suits seldom affords so various and stri-
king a succession of incidents as that

* Hume's England, James I.

GALILEO.

of a soldier or statesman. The life of
a man who is shut up during the greater
part of his time in his study or labora-
tory supplies but scanty materials for
personal details ; and the lapse of time
rapidly removes from us the opportuni-
ties of preserving such peculiarities as
might have been worth recording. An
account of it will therefore consist chiefly
in a review of his works and opinions,
and of the influence which he and they
have exercised over his own and suc-
ceeding ages. Viewed in this light, few
lives can be considered more interesting
than that of Galileo ; and if we compare
the state in which he found, with that in
which he left, the study of nature, we
shall feel how justly an enthusiastic
panegyric pronounced upon the age
immediately following him may be trans-
ferred to this earlier period. " This is the
age wherein all men's minds are in a
kind of fermentation, and the spirit of
wisdom and learning begins to mount
and free itself from those drossie and
terrene impediments wherewith it has
been so long clogged, and from the in-
sipid phlegm and caput mortuum of
useless notions in which it hath endured
so violent and long a fixation. This is
the age wherein, methinks, philosophy
comes in with a spring tide, and the pe-
ripatetics may as well hope to stop the
current of the tide, or, with Xerxes, to
fetter the ocean, as hinder the overflowing
of free philosophy. Methinks I see how
all the old rubbish must be throwaaway,
and the rotten buildings be overthrown
and carried away, with so powerful an
inundation. These are the days that must
lay a new foundation of a more magnifi-
cent philosophy, never to be overthrown,
that will empirically and sensibly can-
vass the phenomena of nature, deducing
the causes of things from such originals
in nature as we observe are producible
by art, and the infallible demonstration
of mechanics : and certainly this is the
way, and no other, to build a true and
permanent philosophy."*

CHAPTER II.

Galileo 's Birth — Family — Education —
Observation of the Pendulum — Pul-
silogies — Hydrostatical Balance —
Lecturer at Pisa.

GALILEO GALILEI was born at Pisa, on
the 15th day ot February, 1564, of a noble

* Power's Experimental Philosophy, 1663,

and ancient Florentine family, which,
in the middle of the fourteenth century,
adopted this surname instead of Bona-
juti, under which several of their an-
cestors filled distinguished offices in the
Florentine state. Some misapprehen-
sion has occasionally existed, in conse-
quence of the identity of his proper
name with that of his family ; his most
correct appellation would perhaps be
Galileo de' Galilei, but the surname
usually occurs as we have written it.
He is most commonly spoken of by
his Christian name, agreeably to the Ita-
lian custom ; just as Sanzio, Buonarotti,
Sarpi, Reni, Vecelli, are universally
known by their Christian names of Ra-
phael, Michel Angelo, Fra Paolo, Gui-
do, and Titian.

Several authors have followed Rossi
in styling Galileo illegitimate, but without
having any probable grounds even when
they wrote, and the assertion has since
been completely disproved by an inspec-
tion of the registers at Pisa and Florence,
in which are preserved the dates of his
birth, and of his mother's marriage,
eighteen months previous to it.*

His father, Vmcenzo Galilei, was a
man of considerable talent and learning,
with a competent knowledge of mathe-
matics, and particularly devoted to the
theory and practice of music, on which
he published several esteemed treatises.
The only one which it is at present easy
to procure — his Dialogue on ancient and
modern music — exhibits proofs, not only
of a thorough acquaintance with his
subject, but of a sound and vigorous
understanding applied to other topics
incidentally discussed. There is a pas-
sage in the introductory part, which
becomes interesting when considered as
affording some traces of the precepts
by which Galileo was in all probability
trained to reach his preeminent station
in the intellectual world. " It appears
to me," says one of the speakers in the
dialogue, " that they who in proof of
any assertion rely simply on the weight
of authority, without, adducing any ar-
gument in support of it, act very
absurdly : I, on the contrary, wish to be
allowed freely to question and freely to
answer you without any sort of adula-
tion, as well becomes those who are
truly in search of truth." Sentiments
like these were of rare occurrence at
the close of the sixteenth century, and it is

* Erythraeus, Pinacotheca, vol. i. ; Salusbury's
Life of Galileo. Nelli, Vita di Gal. Galilei.
13 2

GALILEO.

to be regretted that Vincenzo hardly
lived long enough to witness his idea of
a true philosopher splendidly realized in
the person of his son. Vincenzo died
at an advanced age, in 1591. His
family consisted of three sons, Galileo,
Michel Angelo, and Benedetto, and the
same number of daughters, Giulia, Vir-
ginia, and Livia. After Vincenzo's death
the chief support of the family devolved
upon Galileo, who seems to have as-
sisted them to his utmost power. In a
letter to his mother, dated 1600, relative
to the intended marriage of his sister
Livia with a certain Pompeo Baldi, he
agrees to the match, but recommends
its temporary postponement, as he was
at that time exerting himself to furnish
money to his brother Michel Angelo,
who had received the offer of an ad-
vantageous settlement in Poland. As
the sum advanced to his brother, which
prevented him from promoting his
sister's marriage, did not exceed 200
crowns, it may be inferred that the
family were in a somewhat straitened
condition. However he promises, as
soon as his brother should repay him,
" to take measures for the young lady,
since she too is bent upon coming out
to prove the miseries of this world."
— As Livia was at the date of Ihis
letter in a convent, the last expression
seems to denote that she had been
destined to take the veil. This pro-
posed marriage never took place, but
Livia was afterwards married to Taddeo
Galletti : her sister Virginia married
Benedetto Landucci. Galileo mentions
one of his sisters, (without naming her)
as living with him in 1619 at Bellos-
guardo. Michel Angelo is probably the
same brother of Galileo who is men-
tioned by Liceti as having communi-
cated from Germany some observations
on natural history.* He finally settled
in the service of the Elector of Bavaria ;
in what situation is not known, but
upon his death the Elector granted a
pension to his family, who then took up
their abode at Munich. On the taking
of*that city in 1636, in the course of
the bloody thirty years' war, which was
then raging between the Austrians and
Swedes, his widow and four of his
children were killed, and every thing
which they possessed was either burnt
or carried away. Galileo sent for his
two nephews, Alberto and a younger
brother, to Arcetri near Florence, where

* De his quae diu vivunt, Patavii, 1612.

he was then living. These two were
then the only survivors of Michel An-
gelo's family ; and many of Galileo's
letters about that date contain allusions
to the assistance he had been affording
them. The last trace of Alberto is on
his return into Germany to the Elector,
in whose service his father had died.
These details include almost every thing
which is known of the rest of Vincenzo's
family.

Galileo exhibited early symptoms of
an active and intelligent mind, and
distinguished himself in his childhood
by his skill in the construction of in-
genious toys and models of machinery,
supplying the deficiencies of his infor-
mation from the resources of his own
invention ; and he conciliated the uni-
versal good-will of his companions by
the ready good nature with which he
employed himself in their service and
for their amusement. It is worthy of
observation, that the boyhood of his
great follower Newton, whose genius in
many respects so closely resembled his
own, was marked by a similar talent.
Galileo's father was not opulent, as
has been already stated : he was bur-
dened with a large family, and was
unable to provide expensive instructors
for his son ; but. Galileo's own ener-
getic industry rapidly supplied the want
of better opportunities ; and he acquired,
under considerable disadvantages, the
ordinary rudiments of a classical educa-
tion, and a competent knowledge of the
other branches of literature which were
then usually studied. His leisure hours
were applied to music and drawing ; for
the former accomplishment he inherited
his father's talent, being an excellent
performer on several instruments, espe-
cially on the lute ; this continued to be
a favourite recreation during the whole
of his life. He was also passionately
fond of painting, and at one time he
wished to make it his profession : and
his skill and judgment of pictures were
highly esteemed by the most eminent
contemporary artists, who did not scru-
ple to own publicly their deference to
young Galileo's criticism.

When he had reached his nineteenth
year, his father, becomingdailymore sen-
sible of his superior genius, determined,
although at a great personal sacrifice, to
give him the advantages of an university
education. Accordingly, in 1581, he
commenced his academical studies in
the university of his native town, Pisa,
his father at this time intending that

GALILEO.

he should adopt the profession of me-
dicine. In the matriculation lists at Pisa,
he is styled Galileo, the son of Vincenzo
Galilei, a Florentine, Scholar in Arts.
It is dated 5th November, 1581. Vi-
viani, his pupil, friend, and panegy-
rist, declares that, almost from the
first day of his being enrolled on the
lists of the academy, he was noticed
for the reluctance with which he lis-
tened to the dogmas of the Aristote-
lian philosophy, then universally taught;
and he soon became obnoxious to
the professors from the boldness with
which he promulgated what they styled
his philosophical paradoxes. His early
habits of free inquiry were irrecon-
cileable with the mental quietude of
his instructors, whose philosophic
doubts, when they ventured to entertain
any, were speedily lulled by a quota-
tion from Aristotle. Galileo thought
himself capable of giving the world
an example of a sounder and more
original mode of thinking; he felt him-
self destined to be the founder of a new
school of rational and experimental
philosophy. Of this we are now se-
curely enjoying the benefits ; and it
is difficult at this time fully to appre-
ciate the obstacles which then pre-
sented themselves to free inquiry : but
we shall see, in the course of this nar-
rative, how arduous their struggle was
who happily effected this important re-
volution. The vindictive rancour with
which the partisans of the old phi-
losophy never ceased to assail Galileo
is of itself a sufficient proof of the
prominent station which he occupied
in the contest.

Galileo's earliest mechanical disco-
very, to the superficial observer appa-
rently an unimportant one, occurred
during the period of his studies at Pisa.
His attention was one day arrested by
the vibrations of a lamp swinging from
the roof of the cathedral, which, whether
great or small, seemed to recur at equal
intervals. The instruments then em-
ployed for measuring time were very
imperfect : Galileo attempted to bring
his observation to the test before quit-
ting the church, by comparing the vi-
brations with the beatings of his own
pulse, and his mind being then princi-
pally employed upon his intended pro-
fession, it occurred to him, when he had
further satisfied himself of their regula-
rity by repeated and varied experiments,
that the process he at first adopted
might be reversed, and that an instru-
ment on this principle might be usefully

employed in ascertaining the rate of the
pulse, and its variation from day to
day. He immediately carried the idea
into execution, and it was for this sole
and limited purpose that the first pen-
dulum was constructed. Viviani tells
us, that the value of the invention was
rapidly appreciated by the physicians of
the day, and was in common use in
1654, when he wrote.

Santorio, who was professor of medi-
cine at Padua, has given representa-
tions of four different forms of these

.TV? 2. i

7

=^z:z^f-

-\ro o ^-rrrrrr^

instruments, which he calls pulsilogies,
(pulsilogias,) and strongly recommends
to medical practitioners.* These instru-
ments seem to have been used in the
following manner: No. 1. consists merely
of a weight fastened to a string and a
graduated scale. The string being gather
ed up into the hand till the vibrations of
the weight coincided with the beatings of
the patient's pulse, the length was ascer-
tained from the scale, which, of course,
if great, indicated a languid, if shorter,
a more lively action. In No. 2 the im-
provement is introduced of connecting
the scale and string, the length of the
latter is regulated by the turns of a peg
at a, and a bead upon the string at b
showed the measure. No. 3 is still
more compact, the string being short-
ened by winding upon an axle at the
back of the dial-plate. The construc-
tion of No. 4, which Santorio claims as
his own improvement, is not given, but
it is probable that the principal index,
by its motion, shitted a weight to differ-
ent distances from the point of suspen-
sion, and that the period of vibration

* Comment, in Avicennam. Venetiis, 1625.

GALILEO.

was still more accurately adjusted by a
smaller weight connected with the se-
cond index. Venturi seems to have
mistaken the third figure for that of a
pendulum clock, as he mentions this as
one of the earliest adaptations of Gali-
leo's principle to that purpose* ; but it
is obvious, from Santorio's description,
that it is nothing more than a circular
scale, the index showing, by the figure
to which it points, the length of string
remaining unwound upon the axis. We
shall, for the present, postpone the con-
sideration of the invention of pendulum
clocks, and the examination of the dif-
ferent claims to the honour of their first
construction.

At the time of which we are speaking,
Galileo was entirely ignorant of mathe-
matics, the study of which was then at a
low ebb, not only in Italy, but in every
part of Europe. Commandine had re-
cently revived a taste for the writings of
Euclid and Archimedes, and Vieta Tar-
talea and others had made considerable
progress in algebra, Guido Ubaldi and
Benedetti had done something towards
establishing the principles of statics,
which was the only part of mechanics
as yet cultivated ; but with these incon-
siderable exceptions the application of
mathematics to the phenomena of na-
ture was scarcely thought of. Galileo's
first inducement to acquire a knowledge
of geometry arose from his partiality for
drawing and music, and from the wish
to understand their principles and the-
ory. His father, fearful lest he should
relax his medical studies, refused
openly to encourage him in this new
pursuit ; but he connived at the instruc-
tion which his son now began to receive
in the writings of Euclid, from the
tuition of an intimate friend, named
Ostilio Ricci, who was one of the pro-
fessors in the university. Galileo's
whole attention was soon directed to the
enjoyment of the new sensations thus
communicated to him, insomuch that
Vincenzo, finding his prognostics veri-
fied, began to repent his indirect sanc-
tion, and privately requested Ricci to in-
vent some excuse for discontinuing his
lessons. But it was fortunately too late ;
the impression was made and could not
be effaced ; from that time Hippocrates
and Galen lay unheeded before the
young physician, and served only to
conceal from his father's sight the mathe-
matical volumes on which the whole of
his time was really employed. His pro-

* Essai sur les Ouvrages de Leonard da Vinci.
Paris, 1797.

gress soon revealed the tine nature of
his pursuits : Vincenzo yielded to the
irresistible predilection of his son's mind,
and no longer attempted to turn him
from the speculations to which his whole
existence was thenceforward abandoned.
After mastering the elementary wri-
ters, Galileo proceeded to the study of
Archimedes, and, whilst perusing the
Hydrostatics of that author, composed
his earliest work, — an Essay on the Hy-
drostatical Balance. In this he explains
the method probably adopted by Archi-
medes for the solution of Hiero's cele-
brated question*, and shows himself
already well acquainted with the true
principles of specific gravities. This
essay had an immediate and important
influence on young Galileo's fortunes,
for it introduced him to the approving
notice of Guido Ubaldi, then one of
the most distinguished mathematicians
of Italy. At his suggestion Galileo ap-
plied himself to consider the position of
the centre of gravity in solid bodies, a
choice of subject that sufficiently showed
the estimate Ubaldi had formed of his
talents ; for it was a question on which
Commandine had recently written, and
which engaged at that time the attention
of geometricians of the highest order.
Galileo tells us himself that he disconti-
nued these researches on meeting with
Lucas Valerie's treatise on the same
subject. Ubaldi was so much struck with
the genius displayed in the essay, with
which Galileo furnished him, that he in-
troduced him to his brother, the Cardi-
nal Del Monte : by this latter he was
mentioned to Ferdinand de' Medici, the
reigning Duke of Tuscany, as a young
man of whom the highest expectations
might be entertained. By the Duke's
patronage he was nominated, in 1589,
to the lectureship of mathematics at
Pisa, being then in his twenty-sixth year.
His public salary was fixed at the insigni-
ficant sum of sixty crowns annually, but
he had an opportunity of greatly adding
to his income by private tuition.

CHAPTER III.

Galileo at Pisa — Aristotle — Leonardo
da Vinci — Galileo becomes a Coper -
nican — Urstisius — Bruno — Experi-
ments on falling bodies — Galileo at
Padua — Thermometer.

No sooner was Galileo settled in his
new office than he renewed his inquiries
into the phenomena of nature with in-
creased diligence. He instituted a course

* See Treatise on HYDROSTATICS.

GALILEO.

of experiments for the purpose of put-
ting to the test the mechanical doctrines
of Aristotle, most of which he found un-
supported even by the pretence of ex-
perience. It is to be regretted that we
do not more frequently find detailed his
method of experimenting, than occasion-
ally in the course of his dialogues, and
it is chiefly upon the references which
he makes to the results with which the
experiments furnished him, and upon
the avowed and notorious character of
his philosophy, that the truth of these
accounts must be made to depend. Ven-
turi has found several unpublished pa-
pers by Galileo on the subject of motion,
in the Grand Duke's private library at
Florence, bearing the date of 1590, in
.which are many of the theorems which
he afterwards developed in his Dialogues
on Motion. These were not published
till fifty years afterwards, and we shall
reserve an account of their contents till
we reach that period of his life.

Galileo was by no means the first who
had ventured to call in question the au-
thority of Aristotle in matters of science,
although he was undoubtedly the first
whose opinions and writings produced a
very marked and general effect. Nizzoli,
a celebrated scholar who lived in the early
part of the ] 6th century, had condemned
Aristotle's philosophy, especially his Phy-
sics, in very unequivocal and forcible
terms, declaring that, although there
were many excellent truths in his wri-
tings, the number was scarcely less of
false, useless, and ridiculous proposi-
tions*. About the time of Galileo's
birth, Benedetti had written expressly
in confutation of several propositions
contained in Aristotle's mechanics, and
had expounded in a clear manner some
of the doctrines of statical equilibrium. f
Within the last forty years it has been
established that the celebrated painter
Leonardo da Vinci, who died in 1519,
amused his leisure hours in scientific
pursuits ; and many ideas appear to
have occurred to him which are to be
found in the writings of Galileo at a later
date. It is not impossible (though there
are probably no means of directly ascer-
taining the fact) that Galileo may have
been acquainted with Leonardo's inves-
tigations, although they remained, till
very lately, almost unknown to the ma-
thematical world. This supposition is
rendered more probable from the fact,
that Mazenta, the preserver of Leonardo's
manuscripts, was, at the very time of

* Antibarbarus Philosophicus. Francofurti, 1674.
t Speculationum liber. Venetiis, 1585.

their discovery, a contemporary student
with Galileo at Pisa. Kopernik, or, as
he is usually called, Copernicus, a na-
tive of Thorn in Prussia, had published
his great work, De Revolutionibus, in
1543, restoring the knowledge of the
true theory of the solar system, and his
opinions were gradually and silently
gaining ground.

It is not satisfactorily ascertained at
what period Galileo embraced the new
astronomical theory. Gerard Voss attri-
butes his conversion to a public lecture
of Maestlin, the instructor of Kepler; and
later writers (among whom is Laplace)
repeat the same story, but without re-
ferring to any additional sources of in-
formation, and in most instances merely
transcribing Voss's words, so as to shew
indisputably whence they derived their
account. Voss himself gives no author-
ity, and his general inaccuracy makes
his mere word not of much weight.
The assertion appears, on many accounts,
destitute of much probability. If the
story were correct, it seems likely that
some degree of acquaintance, if not of
friendly intercourse, would have sub-
sisted between Maestlin, and his sup-
posed pupil, such as in fact we find
subsisting between Maestlin and his ac-
knowledged pupil Kepler, the devoted
friend of Galileo ; but, on the contrary,
we find Maestlin writing to Kepler him-
self of Galileo as an entire stranger,
and in the most disparaging terms. If
Maestlin could lay claim to the honour of
so celebrated a disciple, it is not likely
that he could fail so entirely to compre-
hend the distinction it must confer upon
himself as to attempt diminishing it
by underrating his pupil's reputation.
There is a passage in Galileo's works
which more directly controverts the claim
advanced for Maestlin, although Salus-
bury, in his life of Galileo, haying appa-
rently an imperfect recollection of its
tenor, refers to this very passage in con-
firmation of Voss's statement. In the
second part of the dialogue on the Co-
pernican system, Galileo makes Sagredo,
one of the speakers in it, give the fol-
lowing account: — " Being very young,
and having scarcely finished my course
of philosophy, which I left off as
being set upon other employments, there
chanced to come into these parts a cer-
tain foreigner of Rostoch, whose name,
as I remember, was Christianus Ursli-
sius, a follower of Copernicus, who, in
an academy, gave two or three lectures
upon this point, to whom many flocked
as auditors ; but I, thinking they went

GALILEO.

more for the novelty of the subject than
otherwise, did not go to hear him ; for
I had concluded with myself that that
opinion could be no other than a solemn
madness ; and questioning some of those
•who had been there, I perceived they all
made a jest thereof, except one, who
told me that the business was not alto-
gether to be laughed at : and because
the man was reputed by me to be very
intelligent and wary, I repented that I
was not there, and began from that
time forward, as oft as I met with any
one of the Copernican persuasion, to
demand of them if they had been always
of the same judgment. Of as many as
I examined I found not so much as one
who told me not that he had been a long
time of the contrary opinion, but to have
changed it for this, as convinced by the
strength of the reasons proving the same ;
and afterwards questioning them one by
one, to see wrhether they were well pos-
sessed of the reasons of the other side,
I found them all to be very ready and
perfect in them, so that I could not truly
say that they took this opinion out of
ignorance, vanity, or to show the acute-
ness of their wits. On the contrary, of
as many of the Peripatetics and Ptole-
means as I have asked, (and out of cu-
riosity I have talked with many,) what
pains they had taken in the book of
Copernicus, I found very few that had
so much as superficially perused it, but
of those who I thought had under-
stood the .same, not one : and, moreover,
I have inquired amongst the followers of
the Peripatetic doctrine, if ever any of
them had held the contrary opinion, and
likewise found none that had. Where-
upon, considering that there was no
man who followed the opinion of Coper-
nicus that had not been first on the
contrary side, and that was not very
well acquainted with the reasons of
Aristotle and Ptolemy, and, on the con-
trary, that there was not one of the follow-
ers of Ptolemy that had ever been of the
judgment of Copernicus, and had left
that to embrace this of Aristotle ; — con-
sidering, I say, these things, I began to
think that one who leaveth an opinion
imbued with his milk and followed by
very many, to take up another, owned
by very few, and denied by all the
schools, and that really seems a great
paradox, must needs have been moved,
not to say forced, by more powerful
reasons. For this cause I am become
very curious to dive, as they say, into
the bottom of this business." It seems
improbable that Galileo should think

it worth while to give so detailed an
account of the birth and growth of opi-
nion in any one besides himself; and
although Sagredo is not the personage
who generally in the dialogue represents
Galileo, yet as the real Sagredo was a
young nobleman, a pupil of Galileo him-
self, the account cannot refer to him.
The circumstance mentioned of the in-
termission of his philosophical studies,
though in itself trivial, agrees very well
with Galileo's original medical destina-
tion. Urstisius is not a fictitious name,
as possibly Salusbury may have thought,
when alluding to this passage ; he was
mathematical professor at Bale, about
1567, and several treatises by him are
still extant. In 1568 Voss informs us
that he published some new questions on
Purbach's Theory of the Planets. He
died at Bale in 1588, when Galileo was
about twenty-two years old.

It is not unlikely that Galileo also, in
part, owed his emancipation from popu-
lar prejudices to the writings of Gior-
dano Bruno, an unfortunate man, whose
unsparing boldness in exposing fallacies
and absurdities was rewarded by a judi-
cial murder, and by the character of
heretic and infidel, with which his exe-
cutioners endeavoured to stigmatize him
for the purpose of covering over their
own atrocious crime. Bruno was burnt
at Home in 1600, but not, as Montucla
supposes, on account, of his '* Spaccio
della Bestia trionfante." The title of
this book has led him to suppose that it
was directed against the church of
Rome, to which it does not in the slight-
est degree relate. Bruno attacked the
fashionable philosophy alternately with
reason and ridicule, and numerous pas-
sages in his writings, tedious and obscure
as they generally are, show that he had
completely outstripped the age in which
he lived. Among his astronomical opi-
nions, he believed that the universe con-
sisted of innumerable systems of suns
with assemblages of planets revolving
round each of them, like our own earth,
the smallness of which, alone, prevented
their being observed by us. He re-
marked further, " that it is by no means
improbable that there are yet other
planets revolving round our own sun,
which we have not yet noticed, either on
account of their minute size or too re-
mote distance from us." He declined
asserting that all the apparently fixed
stars are really so, considering this as
riot sufficiently proved, " because at such
enormous distances the motions become
difficult to estimate, and it is only by

GALILEO.

9

long observation that we can determine
if any of these move round each other,
or what other motions they may have/'
He ridiculed the Aristotelians in no very
measured terms—" They harden them-
selves, and heat themselves, and embroil
themselves for Aristotle ; they call them-
selves his champions, they hate all but
Aristotle's friends, they are ready to live
and die for Aristotle, and yet they do
not understand so much as the titles of
Aristotle's chapters." And in another
place he introduces an Aristotelian
inquiring, " Do you take Plato for an
ignoramus — Aristotle for an ass?" to
whom he answers, " My son, I neither
call them asses, nor you mules, — them
baboons, nor you apes, — as you would
have me : I told you that I esteem them
the heroes of the world, but I will not
credit them without sufficient reason ;
and if you were not both blind and deaf,
you would understand that I must dis-
believe their absurd and contradictory
assertions.11* Bruno's works, though in
general considered those of a visionary
and madman, were in very extensive
circulation, probably not the less eagerly
sought after from being included among
the books prohibited by the Romish
church; and although it has been re-
served for later observations to furnish
complete verification of his most daring
speculations, yet there was enough, ab-
stractedly taken, in the wild freedom of
his remarks, to attract a mind like Gali-
leo's ; and it is with more satisfaction
that we refer the formation of his opinions
to a man of undoubted though eccentric
genius, like Bruno, than to such as
Maestlin, who, though a diligent and
careful Observer, seems seldom to have
taken any very enlarged views of the
science on which he was engaged.

With a few exceptions similar to
those above mentioned, the rest of Gali-
leo's contemporaries well deserved the
contemptuous epithet which he fixed on
them of Paper Philosophers, for, to use
his own words, in a letter to Kepler on
this subject, " this sort of men fancied
philosophy was to • be studied like the
JEneid or Odyssey, and that the true
reading of nature was to be detected by
the collation of texts." Galileo's own
method of philosophizing was widely
different ; seldom omitting to bring with
every new assertion the test of experi-
ment, either directly in confirmation of
it, or tending to show its probability and
consistency. We have already seen that

* De 1'Infinito Universe. Dial. 3. La Cena de le
Cenere, 1584.

he engaged in a series of experiments
to investigate the truth of some of Aris-
totle's positions. As fast as he suc-
ceeded in demonstrating the falsehood
of any of them, he denounced them from
his professorial chair with an energy and
success which irritated more and more
against him the other members of the
academic body.

There seems something in the stub-
born opposition which he encountered
in establishing the truth of his mecha-
nical theorems, still more stupidly ab-
surd than in the ill will to which, at
a later period of his life, his astrono-
mical opinions exposed him: it is in-
telligible that the vulgar should withhold
their assent from one who pretended
to discoveries in the remote heavens,
which few possessed instruments to
verify, or talents to appreciate ; but it
is difficult to find terms for stigmatizing
the obdurate folly of those who preferred
the evidence of their books to that of
their senses, in judging of phenomena so
obvious as those, for instance, presented
by the fall of bodies to the ground.
Aristotle had asserted, that if two dif-
ferent weights of the same material were
let fall from the same height, the heavier
one would reach the ground sooner than
the other, in the proportion of their
weights. The experiment is certainly not
a very difficult one, but nobody thought
of that method of argument, and con-
sequently this assertion had been long
received, upon his word, among the
axioms of the science of motion. Gali-
leo ventured to appeal from the au-
thority of Aristotle to that of his own
senses, and maintained that, with the
exception of an inconsiderable differ-
ence, which he attributed to the dis-
proportionate resistance of the air, they
would fall in the same time. The Aris-
totelians ridiculed and refused to listen
to such an idea. Galileo repeated his
experiments in their presence from the
famous leaning tower at Pisa : and with
the sound of the simultaneously falling
weights still ringing in their ears, they
could persist in gravely maintaining that
a weight of ten pounds would reach the
ground in a tenth part of the time taken
by one of a single pound, because they
were able to quote chapter and verse in
which Aristotle assures them that such
is the fact. A temper of mind like this
could not fail to produce ill will towards
him who felt no scruples in exposing
their wilful folly ; and the watchful ma-
lice of these men soon found the means
of making Galileo desirous of quitting

10

GALILEO.

his situation at Pisa. Don Giovanni
de' Medici, a natural son of Cosmo,
who possessed a slight knowledge of
mechanics on which he prided himself,
had proposed a contrivance for cleans-
ing the port of Leghorn, on the effi-
ciency of which Galileo was consulted.
His opinion was unfavourable, and the
violence of the inventor's disappoint-
ment, (for Galileo's judgment was veri-
fied by the result,) took the somewhat
unreasonable direction of hatred to-
wards the man whose penetration had
foreseen the failure. Galileo's situation
was rendered so unpleasant by the ma-
chinations of this person, that he de-
cided on accepting overtures elsewhere,
which had already been made to him ;
accordingly, under the negotiation of his
staunch iriend Guido Ubaldi, and with
the consent of Ferdinand, he procured
from the republic of Venice a nomina-
tion for six years to the professorship of
mathematics in the university of Padua,
whither he removed in September 1592.
Galileo's predecessor in the mathe-
matical chair at Padua was Moleti, who
died in 1588, and the situation had re-
mained unfilled during the intervening
four years. This seems to show that
the directors attributed but little im-
portance to the knowledge which it was
the professor's duty to impart. This in-
ference is strengthened by the fact, that
the amount of the annual salary at-
tached to it did not exceed 1 80 florins,
whilst the professors of philosophy and
civil law, in the same university, were
rated at. the annual stipends of 1400
and 1680 florins.* Galileo joined the
university about a year after its triumph
over the Jesuits, who had established a
school in Padua about the year 1542,
and, increasing yearly in influence, had
shown symptoms of a design to get the
whole management of the public edu-
cation into the hands of their own
body.t After several violent disputes it
was at length decreed by the Venetian
senate, in 1591, that no Jesuit should
be allowed to give instruction at Padua
in any of the sciences professed in the
university. It does not appear that after
this decree they were again troublesome
to the university, but this first decree
against them was followed, in 1C 06,
by a second more peremptory, which
banished them entirely from the Vene-
tian territory. Galileo would of course
find his fellow-professors much embit-

Riccuboni, Comment arii de Gymnasio Patavino,

Nelii.

tered against ttyat society, and would
naturally feel inclined to make common
cause with them, so that it is not un-
likely that the hatred which the Jesuits
afterwards bore to Galileo on personal
considerations, might be enforced by
their recollection of the university to
which he had belonged.

Galileo's writings now began to follow
each other with great rapidity, but he
was at this time apparently- so careless
of his reputation, that many of his
works and inventions, after a long cir-
culation in manuscript among his pupils
and friends, found their way into the
hands of those who were not ashamed
to publish them as their own, and to
denounce Galileo's claim to the author-
ship as the pretence of an impudent
plagiarist. He was, however, so much
beloved and esteemed by his friends,
that they vied with each other in resent-
ing affronts of this nature ottered to him,
and in more than one instance he was
relieved, by their full and triumphant
answers, from the trouble of vindicating
his own character.

To this epoch of Galileo's life may
be referred his re-invention of the ther-
mometer. The original idea of this
useful instrument belongs to the Greek
mathematician Hero; and Santorio him-
self, who has been named as the in-
ventor by Italian writers, and at one
time claimed it himself, refers it to
him. In 1633, Castelli wrote to Ce-
sarini that " he remembered an experi-
ment shown to him more than thirty-
five years back by Galileo, who took a
small glass bottle, about the size of a
hen's egg, the neck of which was twenty-
two inches long, and as narrow as a
straw. Having well heated the bulb in
his hands, and then introducing its
mouth into a vessel in which was a
little water, and withdrawing the heat
of his hand from the bulb, the water
rose in the neck of the bottle more than
eleven inches above the level in the ves-
sel, and Galileo employed this principle
in the construction of an instrument for
measuring heat and cold."* In 1613,
a Venetian nobleman named Sagredo,
who has been already mentioned as
Galileo's friend and pupil, writes to
him in the following words : " 1 have
brought the instrument which you in-
vented for measuring heat into several
convenient and perfect forms, so that
the difference of temperature between
two rooms is seen as far as 100 de-

• Nelli.

GALILEO.

11

grees."* This date is anterior to the
claims both of Santorio and Drebbel, a
Dutch physician, who was the first to
introduce it into Holland.

Galileo's thermometer, as we have just
seen, consisted merely of a glass tube
ending in a bulb, the air in which, being
partly expelled by heat, was replaced
by water from a glass into which the
open end of the tube was plunged, and
the different degrees of temperature
were indicated by the expansion of the
air which yet remained in the bulb, so
that the scale would be the reverse of
that of the thermometer now in use, for
the water would stand at the highest level
in the coldest weather. It was, in truth,
a barometer also, in consequence of the
communication between the tube and
external ^lir, although Galileo did not
intend it for this purpose, and when
he attempted to determine the relative
weight of the air, employed a contri-
vance still more imperfect than this rude
barometer would have been. A passage
among his posthumous fragments inti-
mates that he subsequently used spirit
of wine instead of water.

Viviani attributes an improvement of
this imperfect instrument, but without
specifying its nature, to Ferdinand II. ,
a pupil and subsequent patron of Gali-
leo, and, after the death of his father
Cosmo, reigning duke of Florence. It
was still further improved by Ferdi-
nand's younger brother, Leopold de'
Medici, who invented the modern process
of expelling all the air from the tube
by boiling the spirit of wine in it, and
of hermetically sealing the end of the
tube, whilst the contained liquid is in
this expanded state, which deprived it
of its barometrical character, and first
made it an accurate thermometer. The
final improvement was the employment
of mercury instead of spirit of wine,
which is recommended by Lana so
earty as 1670, on account of its equable
expansion.-!* For further details on the
history and use of this instrument, the
reader may consult the Treatises on the
THERMOMETER and PYROMETER.

CHAPTER IV.

Astronomy before Copernicus — Fracas-
tor o — Bacon — Kepler — Galileo 's
Treatise on the Sphere.
THIS period of Galileo's lectureship at
Padua derives interest from its inclu-

* Venturi. Memurie e Lettere di Gal. Galilei.
Modena, 1821.
f Prodromo all' Arte Maestra. Brescia, 16?0.

ding the first notice which we find of
his having embraced the doctrines of
the Copernican astronomy. Most of
our readers are aware of the principles
of the theory of the celestial motions
which Copernicus restored ; but the num-
ber of those who possess much know-
ledge of the cumbrous and unwieldy
system which it superseded is perhaps
more limited. The present is not a tit
.opportunity to enter into many details
respecting it ; these will find their proper
place in the History of Astronomy: but
a brief sketch of its leading principles
is necessary to render what follows in-
telligible.

The earth was supposed to be im-
moveably fixed in the centre of the uni-
verse, and immediately surrounding it
the atmospheres of air and fire, beyond
which the sun, moon, and planets, were
thought to be carried round the earth,
fixed each to a separate orb or heaven
of solid but transparent matter. The
order of distance in which they were
supposed to be placed with regard to
the central earth was as follows : The
Moon, Mercury, Venus, The Sun, Mars,
Jupiter, and Saturn. It became a
question in the ages immediately pre-
ceding Copernicus, whether the Sun
was not nearer the Earth than Mer-
cury, or at least than Venus ; and this
'question was one on which the astro-
nomical theorists were then chiefly
divided.

We possess at this time a curious
record of a former belief in this arrange-
ment of the Sun and planets, in the
order in which the days of the week have
been named from them. According to
the dreams of Astrology, each planet
was siipposed to exert its influence in
succession, reckoning from the most
distant down to the nearest, over each
hour of the twrenty-four. The planet
which was supposed to predominate
over the first hour, gave its name to
that day.* The general reader will
trace this curious fact more easily with
the French or Latin names than with
the English, which have been translated
into the titles of the corresponding
Saxon deities. Placing the Sun and
planets in the following order, and be-
ginning, for instance, with Monday,
or the Moon's day ; Saturn ruled the
second hour of that day, Jupiter the
third, and so round till we come again
and again to the Moon on the 8th, 15th,
and 22d hours ; Saturn ruled the 23d,

* Dion Cassius, lib. 3?.

12

GALILEO.

Jupiter the 24th, so that the next day
would be the day of Mars, or, as the
Saxons translated it, Tuisco's day, or
Tuesday. In the same manner the fol-
lowing days would belong respectively
to Mercury or Woden, Jupiter or Thor,
Venus or Frea, Saturn or Seater, the
Sun, and again the Moon. In this man-
ner the whole week will be found to
complete the cycle of the seven planets.

The other stars were supposed to be
fixed in an outer orb, beyond which were
two crystalline spheres, (as they were
called,) and on the outside of all, the
primum mobile or first moveable, which
sphere was supposed to revolve round
the earth in twenty-four hours, and by
its friction, or rather, as most of the phir
losophers of that day chose to term it, by
the sort of heavenly influence which it
exercised on the interior orbs, to carry
them round with a similar motion.
Hence the diversity of day and night.
But beside this principal and general
motion, each orb was supposed to have
one of its own, which was intended to
account for the apparent changes of
position of the planets with respect to
the fixed stars and to each other. This
supposition, however, proving insuf-
ficient to account for all the irregu-
larities of motion observed, two hy-
potheses were introduced. — First, that
to each planet belonged several con-
centric spheres or heavens, casing each
other like the coats of an onion, and,
secondly, that the centres of these solid
spheres, with which the planet revolved,
were placed in the circumference of a
secondary revolving sphere, the centre
of which secondary sphere was situated
at the earth. They thus acquired the
names of Eccentrics or Epicycles, the
latter word signifying a circle upon a
circle. The whole art of astronomers
was then directed towards inventing and

combining different eccentric and epicy-
clical motions, so as to represent with
tolerable fidelity the ever varying phe-
nomena of the heavens. Aristotle had
lent his powerful assistance in this, as
in other branches of natural philosophy,
in enabling the false system to prevail
against and obliterate the knowledge of
the true, which, as we gather from his
own writings, was maintained by some
philosophers before his time. Of these
ancient opinions, only a few traces now
remain, principally preserved in the
works of those who were adverse to
them. Archimedes says expressly that
Aristarchus of Samos, who lived about
300 B. C., taught the immobility of the
sun and stars, and that the earth is
carried round the central sun.* Aris-
totle's words are : " Most of those who
assert that the whole concave is finite,
say that the earth is situated in the
middle point of the universe: those
who are called Pythagoreans, who live
in Italy, are of a contrary opinion.
For they say that fire is in the centre,
and that the earth, which, according to
them, is one of the stars, occasions the
change of day and night by its own mo-
tion, with which it is carried about the
centre." It might be doubtful, upon
this passage alone, whether the Pytha-
gorean theory embraced more than the
diurnal motion of the earth, but a lit-
tle farther, we find the following passage :
" Some, as we have said, make the earth
to be one of the stars : others say that
it is placed in the centre of the Universe,
and revolves on a central axis."t From

» The pretended translation by Roberval of an
Arabic version of Aristarchus, " De Systemate Mun-
di," in which the Copernican system is fully deve-
loped, is spurious. Menage asserts this in his observa-
tions on Diogen. Laert. lib. 8, sec. 85, torn, ii., p. 389.
(Kd. Atnst. 169 J.) The commentary contains many
authorities well worth consulting. Delambre, His-
toire de 1'Astronomie, infers it from its nor containing
some opinions which Archimedes tells us were held by
Aristarchus. A more direct proof may be gathered
from the following blunder of the supposed translator.
Astronomers had been long aware that the earth
in different parts of her orbit is at different distances
from the sun. Roberval wished to claim for Aris-
tarchus the credit of havint? known this, and intro-
duced into his book, not only the mention of the fact,
but an explanation of its cause. Accordingly he
makes Aristarchus give a reason *• why the sun's apo-
gee (or place of greatest distaneefrom the earth) must
always be at the north summer solstice." In fact, it
was there, or nearly so, in Roberval's time, and he
knew not but that it had always been there. It is
however moveable, and, when Aristarchus lived,
was nearly half way between the solstices and equi-
noxes. He therefore would hardly have given a
reason for the necessity of a phenomenon of which, if
he observed anything on the subject, he must have
observed the contrary. The change in the obliquity
of the earth's axis to the ecliptic was known in the
time of Rol*rval, and he accordingly has introduced
the proper value which it had in Aristarchus's time.

t De Crelo. lib. 2.

GALILEO.

\vhich, in conjunction with the former
extract, it very plainly appears that the
Pythagoreans maintained both the diur-
nal and annual motions of the earth.

Some idea of the supererogatory la-
bour entailed upon astronomers by the
adoption of the system which places the
earth in the centre, may be formed in a
popular manner by observing, in pass-
ing through a thickly planted wood,
in how complicated a manner the re-
lative positions of the trees appear at
each step to be continually changing,
and by considering the difficulty with
which the laws of their apparent mo-
tions could be traced, if we were to
attempt to refer these changes to a real
motion of the trees instead of the tra-
veller. The apparent complexity in
the heavens is still greater than in the
case suggested ; because, in addition to
the earth's motions, with which all the
stars appear to be impressed, each of
the planets has also a real motion of
its own, which of course greatly con-
tributes to perplex and complicate the
general appearances. Accordingly the
heavens rapidly became, under this sys-
tem,

" With centric and eccentric scribbled o'er,
Cycle and epicycle, orb in orb ;"*

crossing and penetrating each other
in every direction. Maestlin has given
a concise enumeration of the prin-
cipal orbs which belonged to this
theory. After warning the readers that
" they are not mere iictions which
have nothing to correspond with them
out of the imagination, but that they
exist really, and bodily in the hea-
vens,"i he describes seven principal
spheres belonging to each planet, which
he classes as Eccentrics, Epicycles, and
Concentrepicycles, and explains their
use in accounting for the planet's re-
volutions, motions of the apogee, and
nodes, &c. &c. In what manner this
multitude of solid and crystalline orbs
were secured from injuring or interfe-
ring with each other was not very closely
inquired into.

The reader will cease 1o expect any
very intelligible explanation of this
and numberless other difficulties which
belong to this unwieldy machinery
when he is introduced to the reasoning
by which it was upheld. Gerolamo Fra-

* Paradise Lost, b. viii. v. 83.

f Itaque tarn circulosprimi motus quam orbes s-e-
cundoruin mobilinm revera in coelesti corpore essecon-
cludimus, &c. Non ergo sunt meratigmenta, quibus
extra mentem nibil correspondeat. M. Maestlini,
De Astronomies Hypothesibu-, disputatio, Heidelbergse,

castoro, who lived in the sixteenth cen-
tury, writes in the following terms, in his
work entitled Homocentrica, (certainly
one of the best productions of the day, )
in which he endeavours to simplify the
necessary apparatus, and to explain all
the phenomena (as the title of his book
implies) by concentric spheres round
the earth. " There are some, not only
of the ancients but also among the
moderns, who believe that the stars
move freely without any such agency ;
but it is difficult to conceive in what
manner they have imbued themselves
with this notion, since not only reason,
but the very senses, inform us that all
the stars are carried round fastened to
solid spheres." What ideas Fracastoro
entertained of the evidence of the " senses"
it is not now easy to guess, but he
goes on to give a specimen of the " rea-
soning" which appeared to him so in-
controvertible. " The planets are ob-
served to move one while forwards, then
backwards, now to the right, now to
the left, quicker and slower by turns ;
which variety is consistent with a com-
pound structure like that of an animal,
which possesses in itself various springs
and principles of action, but is totally
at variance with our notion of a simple
and undecaying substance like the hea-
vens and heavenly bodies. For that
which is simple, is altogether single,
and singleness is of one only nature,
and one nature can be the cause of
only one effect ; and therefore it is alto-
gether impossible that the stars of them-
selves should move with such variety
of motion. And besides, if the stars
move by themselves, they either move in
an empty space, or in a fluid medium
like the air. But there cannot be such
a thing as empty space, and if there
were such a medium, the motion of the
star would occasion condensation and
rarefaction in different parts of it, which
is the property of corruptible bodies
and where they exist some violent mo-
tion is going on ; but the heavens are
incorruptible and are not susceptible
of violent motion, and hence, and from
many other similar reasons, any one
who is not obstinate may satisfy him-
self that the stars cannot have any
independent motion."

Some persons may perhaps think that
arguments of this force are unnecessarily
dragged from the obscurity to which
they are now for the most part happily
consigned ; but it is essential, in order
to set Galileo's character and merits in
their true light, to show how low at this

14

GALILEO.

time philosophy had fallen. For we
shall form a very inadequate notion of
his powers and deserts if we do not
contemplate him in the midst of men
who, though of undoubted talent and
ingenuity, could so far bewjlder them-
selves as to mistake such a string of
unmeaning phrases for argument : we
must reflect on the difficulty every one
experiences in delivering himself from
the erroneous impressions of infancy,
which will remain stamped upon the
imagination in spite of all the eiforts of
matured reason to erase them, and con-
sider every step of Galileo's course as a
triumph over difficulties of a like nature.
We ought to be fully penetrated with this
feeling before we sit down to the pe-
rusal of his works, every line of which
will then increase our admiration of
the penetrating acuteness of his inven-
tion and unswerving accuracy of his
judgment. In almost every page we
discover an allusion to some new ex-
periment, or the germ of some new
theory; and amid all this wonderful
fertility it is rarely indeed that we find
the exuberance of his imagination
seducing him from the rigid path of
philosophical induction. This is the
more remarkable as he was surrounded
by friends and contemporaries of a
different temperament and much less
cautious disposition. A disadvantageous
contrast is occasionally furnished even
by the sagacious Bacon, who could so far
deviate from the soundprinciples of induc-
tive philosophy, as to write, for instance,
in the following strain, bordering upon
the worst manner of the Aristotelians : —
** Motion in a circle has no limit, and
seems to emanate from the appetite of
the body, which moves only for the sake
of moving, and that it may follow itself
and seek its own embraces, and put in
action and enjoy its own .nature, and
exercise its peculiar operation : on the
contrary, motion in a straight line see.i:s
transitory, and to move towards a limit
of cessation or rest, and that it may
reach some point, and then put off' its
motion."* Bacon rejected ail the ma-
chinery of the primum mobile and the
solid spheres, the eccentrics and the
epicycles, and carried his dislike of
these doctrines so far as to assert
that nothing short of their gross ab-
surdity could have driven theorists to
the extravagant supposition of the mo-
tion ot the earth, which, said he, " we

• Opusoula Philosophic*, Thema Coeli,

know to be most false."* Instances of
extravagant suppositions and premature
generalizations are to be found in al-
most every page of his other great con-
temporary, Kepler.

It is with pain that we observe De-
lambre taking every opportunity, in his
admirable History of Astronomy, to un-
dervalue and sneer at Galileo, seem-
ingly for the sake of elevating the
character of Kepler, who appears his
principal favourite, but whose merit as a
philosopher cannot safely be brought
into competition with that of his illus-
trious contemporary. Delambre is es-
pecially dissatisfied with Galileo, for
taking no notice, in his *' System of
the World," of the celebrated laws
of the planetary motions which Kep-
ler discovered, and which are now
inseparably connected with his name.
The analysis of Newton and his suc-
cessors has now identified those ap-
parently mysterious laws with the ge-
neral phenomena of motion, and has
thus entitled them to an attention of
which,beforethat time, they were scarcely
worthy ; at any rate not more than is at
present the empirical law which includes
the distances of all the planets from the
sun (roughly taken) in one algebraical
formula. The observations of Kepler's
day were scarcely accurate enough to
prove that the relations which he disco-
vered between the distances of the planets
from the sun and the periods of their
revolutions around him were neces-
sarily to be received as demonstrated
truths; and Galileo surely acted most
prudently and philosophically in hold-
ing himself altogether aloof from Kep-
ler's fanciful devices and numeral con-
cinnities, although, with all the extra-
vagance, they possessed much of the
genius of the Platonic reveries, and al-
though it did happen that Galileo, by
systematically avoiding them, failed to
recognise some important truths. Ga-
lileo probably was thinking of those
very laws, when he said of Kepler,
" He possesses a bold and free genius,
perhaps too much so; but his mode
of philosophizing is widely different from
mine." We shall have turther occasion
in the sequel to recognise the justice of
this remark.

In the treatise on the Sphere which
bears Galileo's name, and which, if he
be indeed the author of it, was composed
during the early part of his residence at

* "Nobis constat falsissiuiu'm esse." De AUK. Sci«
eat.Ub, m, c.3, 1623.

GALILEO.

15

Padua, he also adopts the Ptolemaic
system, placing the earth immoveable
in the centre, and adducing against its
motion the usual arguments, which in
his subsequent writings he ridicules
and refutes. Some doubts have been
expressed of its authenticity ; but, how-
ever this may be, we have it under
Galileo's own hand that he taught the
Ptolemaic system, in compliance with
popular prejudices, for some time after
he had privately become a convert
to the contrary opinions. In a letter,
apparently the first which he wrote to
Kepler, dated from Padua, 1597, he
says, acknowledging the receipt of Kep-
ler's Mysterium Cosmographicum, " I
have as yet read nothing beyond the
preface of your book, from which how-
ever I catch a glimpse of your meaning,
and feel great joy on meeting with so
powerful an associate in the pursuit of
truth, and consequently such a friend to
truth itself, for it is deplorable that there
should be so few who care about truth,
and who do not persist in their perverse
mode of philosophizing ; but as this is
not the fit time for lamenting the me-
lancholy condition of our times, but
for congratulating you on your elegant
discoveries in confirmation of the truth,
I shall only add a promise to peruse
your book dispassionately, and with a
conviction that I shall find in it much
to admire. This I shall do the more
willingly because many years ago I
became a convert to the opinions of
Copernicus* and by that theory have
succeeded in fully explaining many phe-
nomena, which on the contrary hypo-
thesis are altogether inexplicable. I
have arranged many arguments and
confutations of the opposite opinions,
which however I have not yet dared to
publish, fearing the fate of our master
Copernicus, who, although he has
earned immortal fame among a few,
yet by an infinite number (for so only
can the number of fools be measured)
is exploded and derided. If there
were many such as you, I would ven-
ture to publish my speculations; but,
since that is not so, I shall lake time to
consider of it." This interesting letter
was the beginning of the friendship of
these two great men, which lasted un-
interruptedly till 1632, the date of
Kepler's death. That extraordinary ge-
nius never omitted an opportunity of
testifying his admiration of Galileo,

* Id autum eo libentius faciam, quod in Copernici
sententiam muHis abhinc annis yen erim. — Kepi.
Epistolae.

although there were not wanting per-
sons envious of their good understand-
ing, who exerted themselves to provoke
coolness and quarrel between them.
Thus Brutlus writes to Kepler in 1602*:
" Galileo tells me he has written to you,
and has got your book, which however
he denied to Magini, and I abused him
for praising you with too many qualifi-
cations. I know it to be a fact that,
both in his lectures, and elsewhere, he
is publishing your inventions as his
own ; but I have taken care, and shall
continue to do so, that all this shall
redound not to his credit but to yours."
The only notice which Kepler took of
these repeated insinuations, which ap-
pear to have been utterly groundless,
was, by renewed expressions of respect
and admiration, to testify the value he
set upon his friend and fellow-labourer
in philosophy.

CHAPTER V.

Galileo re-elected Professor at Padua
— New star — Compass of propor-
tion— Capra — Gilbert — Proposals to
return to Pisa — Lost writings — Ca-
valieri.

GALILEO'S reputation was now rapidly
increasing: his lectures were attended
by many persons of the highest rank ;
among whom wreie the Archduke Fer-
dinand, afterwards Emperor of Ger-
many, the Landgrave of Hesse, and
the Princes of Alsace and Mantua. On
the exphrtion 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 aug-
mentation is said by Fabronit, to have
arisen out of the malice of an ill wisher
of Galileo, who, hoping to do him dis-
service, 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 in-
quire into the morality of his private
life, it was probably from a wish to
mark their sense of the informer's im-
pertinence, 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 Viviam's intimation,
towards the thirtieth year of his age,
that is to say in 1594, he experienced

* Kepleri Epistolae.

•j- Vitae Italorum IJlustrium.

GALILEO.

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 blow-
ing 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
haemorrhages and loss of sleep and ap-
petite ; and this painful disorder thence-
forward never left him entirely, but re-
curred 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 how-
ever 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 inRiccioli* a catalogue of the
principal new stars which have at dif-
ferent times appeared. There is a tra-
dition 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 ca-
talogue of the stars ; and only thirty-two
years before, in 1572, the same remark-
able 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 astro-
nomy. Tycho's star disappeared at the

* Alnrtgestuui Nyvuui, vol. i.

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 em-
bodied the results of his observations
in three lectures, which have been un-
fortunately lost. Only the exordium of
the first has been preserved : in this he
reproaches his auditors with their ge-
neral insensibility to the magnificent
wonders of creation daily exposed to
their view, in no respect less admirable
than the new prodigy, to hear an ex-
planation 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 re-
mote heavenly bodies. This was in-
conceivable to the Aristotelians, whose
notions of a perfect, simple, and un-
changeable sky were quite at variance
with the introduction of any such new
body; and we may perhaps consider
these lectures as the first public decla-
ration 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 in-
vented 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 as-
tronomical discoveries ; but on this oc-
casion, 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 in-
strument is of simple construction, con-
sisting 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

GALILEO.

17

case of mathematical instruments. In-
stead of the tri«:ono metrical and logarith-
mic lines which are now generally en-
graved 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 multipli-
cations, divisions, and the extraction of
roots ; for finding the dimensions of
equally heavy balls of different ma-
terials, &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 mul-
titude 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 diffi-
cult to understand on what grounds
Salusbury charges Gunter with plagi-
arism from Galileo's Compass. He de-
clares that he has closely compared the
two, and can find no difference between
them.* There has also been some con-
fusion, 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 po-
sitions. 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 inex-
cusable error of confounding Galileo's
with the Mariner's Compass. He re-
fers to a treatise by Hulsius for his
authority in attributing the Proportional
Compass to Burg, a German astrono-
mer 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.f To the description which Ga-
lileo published of his compass, he added

* M.-ith. Coll. vol. ii.

f Constructio Circini Proportionum. Moguntiae,
1605.

a short treatise on the method of mea-
suring 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 Com-
pass was of much more importance
before the grand discovery of loga-
rithms than it can now be considered :
however it acquires an additional in-
terest from the value which he himself
set on it. In 1607, Capra, at the insti-
gation 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 Im-
postures of Balthasar Capra." His prin-
cipal 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 com-
mitted on that occasion, to add a com-
plete proof of his piracy of the geo-
metrical 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 expo-
sure, and of the report of the famous
Fra Paolo Sarpi, to whom the matter
had been referred, was a formal prohi-
bition by the university of Capra' s pub-
lication, and all copies of the book then
on hand were seized, and probably de-
stroyed, though Galileo has preserved
it from oblivion by incorporating it in
his own publication.

Nearly at the same time, 1607, or im-
mediately after, he first turned his atten-
tion towards the loadstone, on which our
c

18

GALILEO.

countryman Gilbert had already pub-
lished 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 success-
ful. Sir Kenelm Digby* 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

? raise, admire, and envy this author ; —
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, with-
out attempting to satisfy themselves of
the same by experience, perhaps that
they may not dimmish the size of their
books."

Galileo's reputation being now greatly
increased, proposals were made to him,
in 1609, to return to his original situ-
ation at Pisa. He had been in the
habit of passing over to Florence du-
ring the academic vacation, for the pur-
pose of giving mathematical instruc-
tion to the younger members of Ferdi-
nand'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 Ga-
lileo'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 anybody, the
little talent which God has granted to
my assiduity in my profession, that my
wish certainly would be to have suffi-
cient rest and leisure to enable me, be-
fore my life comes to its close, to conclude
three great works which I have in hand,
and to publish them ; which might per-
haps bring some credit to me, and to
those who had favoured me in this
undertaking, and possibly may be of

• Treatise of the Nature of Bodies, London, 1665.

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) never-
theless 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 1 am almost certain will be ad-
vanced to as many crowns upon my re-
election, and these I can greatly increase
by receiving pupils, and from private lec-
tures, 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 do-
mestic 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 coun-
try, I should wish the first object of his
Serene Highness to be, that leisure and
opportunity should be given me to com-
plete my works without employing my-
self in lecturing. — And, in short, I
should wish to gain my bread from my
writings, which I would always dedi-
cate to my Serene Master. — The works
which I have to finish are principally
— two books on the system or struc-
ture of the Universe, an immense work,
full of philosophy, astronomy, and geo-
metry ; three books on Local Motion,
a science entirely new, no one, either
ancient or modern, having discovered
any of the very many admirable acci-
dents 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 com-
position of continuous quantity ; On the

GALILEO.

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 teach-
ing with very exact rules every thing
which it is his duty to know that de-
pends upon mathematics ; as the know-
ledge of castrametation, drawing up
battalions, fortifications, assaults, plan-
ning, surveying, the knowledge of artil-
lery, the use of instruments, &c. I
also wish to reprint the ' Use of my Geo-
metrical 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 con-
vinced that as I am to live upon it,
the graciousness of his highness would
not deprive me of any of those com-
forts, which, however, I feel the want
of less than many others ; and there-
fore 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 num-
ber 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 high-
nesses see as often as it shall please
them to give me an opportunity of dis-
cussing 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 under-
value 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 per-
haps almost impossible for him to have
remained entirely blind to his vast supe-
riority 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 sub-
mitted to this expurgation. It is also

supposed that many were burnt by his
infatuated grandson Cosimo, who con-
ceived he was thus offering a proper
and pious sacrifice before devoting him-
self to the life of a missionary. A Trea-
tise 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 read-
ers a compendium of the most approved
Erinciples then already known. It has
een 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 de-
serves notice only from its having been
made the subject of controversy.

The loss of Galileo's Essay on Conti-
nuous Quantity is particularly to be
regretted, as it. would be highly interest-
ing to see how far he succeeded in
methodizing his thoughts on this import-
ant 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 Indivisi-
bles," which is universally recognized as
one of the first germs of the powerful
methods of modern analysis. Through-
out Galileo's works we find many indi-
cations of his having thought much on
the subject, but his remarks are vague,
and bear little, if at all, on the appli-
cation 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, sur-
faces 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 pro-
found view of the subject than is implied
in this superficial exposition, and had
approached very closely to the appa-
rently mure exact theories of his suc-
cessors. Anticipating the objections to
his hypothesis, he argues, that " there
is no necessity to suppose the conti-
nuous quantities made up of these in-
divisible 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
c 2

20

GALILEO.

Cavalieri in his " New method of Gua-
ging," which is the earliest work with
which we are acquainted, where prin-
ciples of this sort are employed.*

CHAPTER VI.

Invention of the telesccpe—Fracastoro
— Porta — Reflecting telescope — Ro-
ger Bacon — Digges — De Dominis —
Jans en — Lipperhey — Galileo con-
structs telescopes — Microscopes — Re-
elected Professor at Padua for life.

THE year 1609 was signalized by
Galileo's discovery of the telescope,
•which, in the minds of many, is the prin-
cipal, if not the sole invention associated
with his name. It cannot be denied
that his fame, as the founder of the
school of experimental philosophy, has
been in an unmerited degree cast into
the shade by the splendour of his astro-
nomical discoveries; yet Lagrangef
surely errs in the opposite extreme, when
he almost denies that these form any
real or solid part of the glory of this
great man ; and MpntuclaJ omits an im- •
portant ingredient in his merit, when he
(in other respects very justly) remarks,
that it required far less genius to point
a telescope towards the heavens than to
trace the unheeded, because daily re-
curring, phenomena of motion up to its
simple and primary laws. We are to
remember that in the days of Galileo
a telescope could scarcely be pointed to
the heavens with impunity, and (that a
courageous mind was required to con-
tradict, and a strong one to bear down,
a party, who, when invited to look on
any object in the heavens which Aris-
totle had never suspected, immediately
refused all credit to those senses, to
which, on other occasions, they so confi-
dently appealed. It surely is a real
and solid part of Galileo's glory that he
consumed his life in laborious and inde-
fatigable observations, and that he per-
severed in announcing his discoveries
undisgusted by the invectives, and un-
dismayed by the persecutions, to which
they subjected him. Plagiarist ! liar !
impostor ! heretic ! were among the ex-
pressions of malignant hatred lavished
upon him, and although he also was
not without some violent and foul-
mouthed partisans, yet it must be told
to his credit that he himself seldom
condescended to notice these torrents
of abuse, otherwise than by good-

* Nova Stercometria Doliorum — Lincii, 1615.

+ Mecanique Analytiqne.

$ HUtoire des Matheuiatiques, torn. ii.

humoured retorts, and by prosecuting
his observations with renewed assiduity
and zeal.

The use of single lenses in aid of the
sight had been long known. Spectacles
were in common use at the beginning
of the fourteenth century, arid there are
several hints, more or less obscure, in
many early writers, of the effects which
might be expected from a combination
of glasses ; but it does not appear with
certainty that any of these authors had
attempted to reduce their ideas to prac-
tice. After the discovery of the tele-
scope, almost every country endeavoured
to find in the writings of its early
philosophers traces of the knowledge of
such an instrument, but in general with
success very inadequate to the zeal of
their national prepossessions- There
are two authors especially to whom the
attention of Kepler and others was
turned, immediately upon the promulga-
tion of the discovery, as containing the
germ of it in their works. These are
Baptista Porta, and Gerolamo Fracas -
toro. We have already had occasion
to quote the Homocentrica of Fracas-
toro, who died in 1553 ; the follow-
ing expressions, though they seem to
refer to actual experiment, yet fall short
of the meaning with which it has been
attempted to invest them. After ex-
plaining and commenting on some phe-
nomena of refraction through different
media, to which he was led by the
necessity of reconciling his theory with
the variable magnitudes of the planets,
he goes on to say — " For which rea-
son, those things which are seen at the
bottom of water, appear greater than
those which are at the top ; and if any
one look through two eyeglasses, one
placed upon the other, he" will see every
thing much larger and nearer." * It should
seem that this passage (asDelambrehas
already remarked) rather refers to the
close application of one glass upon an-
other, and it may fairly be doubted
whether any thing analogous to the
composition of the telescope was in the
writer's thoughts. Baptista Porta
writes on the same subject more fully ;
— " Concave lenses show distant objects
most clearly, convex those which are
nearer, whence they may be used to
assist the sight. With a concave glass
distant objects will be seen, small, but
distinct ; with a convex one those near
at hand, larger, but confused ; if you

* " Per dno specilla ocularia si quis perspiciat,
alteroalteri snperposito, majora multo et propinqniora
videtitomnia." — Fracast. Homocentrica, § *2, c. 8.

GALILEO.

21

know rightly how to combine one of
each sort, you will see both far and near
objects larger and clearer," * These
words show, if Porta really was then
unacquainted with the telescope, how
close it is possible to pass by an inven-
tion without lighting on it, for of pre-
cisely such a combination of a convex
and concave lens, fitted to the ends of
an organ pipe by way of tube, did the
whole of Galileo's telescope consist.
If Porta had stopped here he might
more securely have enjoyed the repu-
tation of the invention, but he then pro-
fesses to describe the construction of
his instrument, which has no relation
whatever to his previous remarks. " I
shall now endeavour to show in what
manner we may contrive to recognize
our friends at the distance of several
miles, and how those of weak sight may
read the most minute letters from a
distance. It is an invention of great
utility, and grounded on optical prin-
ciples, nor is it at all difficult of execu-
tion ; but it must be so divulged as not
to be understood by the vulgar, and yet
be clear to the sharpsighted." The
description which follows seems far
enough removed from the apprehended
danger of being too clear, and in-
deed every writer who has hitherto
quoted it has merely given the passage
in its original Latin, apparently despair.
ing of an intelligible translation. With
some alterations in the punctuation,
which; appear necessary to bring it into
any grammatical construction,-}- it may
be supposed to bear something like the
following meaning : — " Let a view be
contrived in the centre of a mirror,
where it is most effective. All the solar
rays are exceedingly dispersed, arid do
not in the least come together (in the
true centre) ; but there is a concourse of
all the rays in the central part of the
said mirror, half way towards the other
centre, where the cross diameters meet.
This view is contrived in the following
manner. A concave cylindrical mirror

* Si utrumqne recte componere noveris, et longin-
qua et proxima majora et clara videbis. — Mag. Nat.
lib. 17.

t The passage in the original, which is printed
alike in the editions of 1598, 1607, 16L9, and 1650, is
as follows : Visus constituatur centre valentissimus
speculi, ubi fief, et valentissime universales solares
radii disperguntur, et coeunt minime, sed centro prae-
dicti speculi in illius medio, ubi diametri transver-
sales, omnium ibi concursus. Constituitur hoc modo
speculum concavum columnare sequidistantibus late-
ribus, sed lateri uno obliquo sectionibus illis accomo-
detur, trianguli vero obtusiauguli, vel orthogonii
secentur, hijic inde duobus transversy-libus lineis, ex-
centro eductis. Et coijfectum erit speciUum, ad. id,

placed directly in front, but with its axis
inclined, must be adapted to that focus :
and let obtuse angled or right angled
triangles be cut out with two "cross lines
on each side drawn from the centre, and
aglass (specillum) will be completed.fit for
the purposes we mentioned.1' If it were not
for the word " specillum" which, in the
passage immediately preceding this,
Porta*1 contrasts with " speculum" and
which he afterwards explains to mean a
glass lens, it would be very clear that
the foregoing passage (supposing it to
have any meaning) must be referred to
a reflecting telescope, and it is a little
singular that while this obscure passage
has attracted universal attention, no
one, so far as we are aware, has taken
any notice of the following unequivocal
description of the principal part of
Newton's construction of the same in-
strument. It is in the 5th chapter
of the 17th book, where Porta explains
by what device exceedingly minute let-
ters may be read without difficulty.
" Place a concave mirror so that the
back of it may lie against your breast ;
opposite to it, and within the burning
point, place the writing; put a plane
mirror behind it, that may be under your
eyes. Then the images of the letters
which are in the concave mirror, and
which the concave has magnified, will
be reflected in the plane mirror, so that
you may read without difficulty."

We have not been able to meet with
the Italian translation of Porta' s Na-
tural Magic, which was published in
1611, under his own superintendence;
but the English translator of 1(558
would probably have known if any
intelligible interpretation were there
given of the mysterious passage above
quoted, and his 'translation is so devoid
of meaning as strongly to militate against
this idea. Porta, indeed, claimed the
invention as his own, and is believed to
have hastened his death, (which hap-
pened in 1615, he being then 80 years
old,) by the fatigue of composing a
Treatise on the Telescope, in which he
had promised to exhaust the subject. We
do not know whether this is the same
work which was published after his
death by Stelliola,t but which contains
no allusion to Porta's claim, and pos-
sibly Stelliola may have thought it most
for his friend's reputation to suppress
it. Schott^ says, a friend of his had

* Diximusde Ptolemaei speculo,sive specillo potius,
quo per saxcentena millia pervementes naves conspi:
oiebat. •)• II Telescopio, itiJj?.

GALILEO.

seen Porta's book in manuscript, and
that it did at that time contain the as-
sertion of Porta's title to the invention.
After all it is not improbable that he
may have derived his notions of mag-
nifying distant objects from our cele-
brated countryman Roger Bacon, who
died about the year 1300. He has been
supposed, not without good grounds,
to have been one of the first who re-
cognised the use of single lenses in
producing distinct vision, and he has
some expressions with respect to their
combination which promise effects ana-
logous to those held out by Porta. In
" The Admirable Force of Art and Na-
ture," he says, "Physical figurations
are far more strange, for in such manner
may we frame perspects and looking-
glasses that one thing shall appear
to be many, as one man shall seeme
a whole armie ; and divers sunnes and
moanes, yea, as many as we please,
shall appeare at one time, &c. And so
may the perspects be framed, that things
most farre off may seeme most nigh
unto us, and clean contrarie, soe that we
may reade very small letters an incredi-
ble distance from us, and behold things
how little soever they be, and make
stars to appeare wheresoever we will,
&c. And, besides all these, we may so
frame perspects that any man entering
into a house he shall indeed see gold,
and silver, and precious stones, and what
else he will, but when he maketh haste
to the place he shall find just nothing."
It seems plain, that the author is here
speaking solely of mirrors, and we must
not too hastily draw the conclusion, be-
cause in the first and last of these asser-
tions he is, to a certain extent, borne out
by facts, that he therefore was in posses-
sion of a method of accomplishing the
middle problem also. In the previous
chapter, he gives a long list of notable
things, (much in the style of the Mar-
quis of Worcester's Century of Inven-
tions) which if we can really persuade
ourselves that he was capable of accom-
plishing, we must allow the present age
to be still immeasurably interior to him
in science.

Thomas Digges, in the preface to
his Pantometria, (published in 159 1 ) de-
clares, " My father, by his continuall
painfull practises, assisted with de-
monstrations mathematical!, was able,
and sundry times hath by proportional!
glasses, duely situate in convenient
angles, not only discouered things farre
off, read letters, numbered peeces of
money, with the verye coyne and super-

scription thereof, cast by some of his
freends of purpose, upon downes in
open fields ; but also, seuen miles off,
declared what hath beene doone at that
instant in priuate places. He hath also
sundrie times, by the sunne beames, fired
powder and dischargde ordnance halfe
a mile and more distante ; which things
I am the boulder to report, for that
there are yet living diverse (of these his
dooings) occulati testes, (eye witnesses)
and many other matters farre more
strange and rare, which I omit as im-
pertinent to this place."

We find another pretender to the ho-
nour of the discovery, of the telescope in
the celebrated Antonio de Dominis,
Archbishop of Spalatro, famous in the
annals of optics for being one of the first
to explain the theory of the rainbow.
Montucla, following P. Boscovich, has
scarcely done justice to De Dominis,
whom he treats as a mere pretender
and ignorant person. The indisposition
of Boscovich towards him is suffi-
ciently accounted for by the circumstance
of his being a Catholic prelate who had
embraced the cause of Protestantism.
His nominal reconciliation with the
Church of Rome would probably not
have saved him from the stake, had not
a natural death released him when im-
prisoned on that account at Rome.
Judgment was pronounced upon him
notwithstanding, and his body and books
were publicly burnt in the Campo de'
Fiori, in 1624. His treatise, De Radiis,
(which is very rarely to be met with)
was published by Bartolo after the ac-
knowledged invention of the telescope
by Galileo ; but Bartolo tells us, in the
preface, that the manuscript was com-
municated to him from a collection of
papers written 20 years before, on his
inquiring the Archbishop's opinion with
respect to the newly discovered instru-
ment, and that he got leave to publish
it, " with the addition of one or two
chapters." The treatise contains a
complete description of a telescope,
which, however, is professed merely to
be an improvement on spectacles, and
if the author's intention had been to
interpolate an afterwritten account, in
order to secure to himself the undeserved
honour of the invention, it seems im-
probable that he would have suffered
an acknowledgment of additions, pre-
vious to publication, to be inserted in
the preface. Besides, the whole tone
of the work is that of a candid and
truth-seeking philosopher, very far
indeed removed from being, as Mon-

GALILEO.

tucla calls him, conspicuous for igno-
rance even among the ignorant men of
his age. He gives a drawing of a con-
vex and concave lens, and traces the
passage of the rays through them ; to
which he subjoins, that he has not
satisfied himself with any determination
of the precise distance to which the
glasses should be separated, according
to their convexity and concavity, but
recommends the proper distance to be
found by actual experiment, and tells
us, that the effect of the instrument will
be to prevent the confusion arising from
the interference of the direct and re-
fracted rays, and to magnify the object
by increasing the visible angle under
which it is viewed. These, among the
many claimants, are certainly the au-
thors who approached the most nearly
to the discovery: and the reader may
judire, from the passages ciled, whether
the knowledge of the telescope can with
probability be referred to a period ear-
lier than the commencement of the 17th
century. At all events, we can find no
earlier trace of its being applied to any
practical use ; the knowlege, if it existed,
remained speculative and barren.

In 1609, Galileo, then being on a visit
to a friend at Venice, heard a rumour
of the recent invention, by a Dutch
spectacle- maker, of an instrument which
was said to represent distant objects
nearer than they usually appeared.
According to his own account, this ge-
neral rumour, which was confirmed to
him by letters from Paris, was all that
he learned on the subject ; and returning
to Padua, he immediately applied him-
self to consider the means by which
such an effect could be produced.
Fuccarius, in an abusive letter which
he wrote on the subject, asserts that one
of the Dutch telescopes had been at
that time actually brought to Venice,
and that he (Fuccarius) had seen it;
which, even if true, is perfectly con-
sistent with Galileo's statement ; and
in fact the question, whether or not
Galileo saw the original instrument,
becomes important only from his ex-
pressly asserting the contrary, and pro-
fessing to give the train of reasoning by
which he discovered its principle ; so
that any insinuation that he had actually
seen the Dutch glass, becomes a direct
impeachment of his veracity. It is
certain, from the following extract of a
letter from Lorenzo Pignona to Paolo
Gualdo, that one at least of the Dutch
glasses had been sent to Italy. It is

dated Padua, 31st August, 1609.*
" We have no news, except the return
of His Serene Highness, and the re-
election of the lecturers, among whom
Sign. Galileo has contrived to get 1000
florins for life ; and it is said to be on
account of an eyeglass, like the one
which was sent from Flanders to Car-
dinal Borghese. We have seen some
here, and truly they succeed well."

It is allowed by every one that the
Dutchman, or rather Zealander, made his
discovery by mere accident, which
greatly derogates from any honour
attached to it ; but even this diminished
degree of credit has been fiercely dis-
puted. According to one account,
which appears consistent and probable,
it had been made for sometime before
its importance was in the slightest de-
gree understood or appreciated, but
was set up in the optician's shop as
a curious philosophical toy, show-
ing a large and inverted image of a
weathercock, towards which it was di-
rected. The Marquis Spinola, chancing
to see it, was struck with the phenome-
non, purchased the instrument, and
presented it either to the Archduke
Albert of Austria, or to Prince Maurice
of Nassau, whose name appears in
every version of the story, and who
first entertained the idea of employing
it in military reconnoissances.

Zacharias Jansen, and Henry Lipper-
hey, two spectacle-makers, living close
to each other, near the church of Mid-
dleburg, have both had strenuous sup-
porters of their title to the invention. A
third pretender appeared afterwards in
the person of James Metius of Alkmaer,
who is mentioned by Huyghens and
Des Cartes, but his claims rest upon
no authority whatever comparable to
that which supports the other two.
About half a century afterwards, Borelli
was at the pains to collect and publish
a number of letters and depositions
which he procured, as well on one side
as on the other .f It seems that the truth
lies between them, and that one, pro-
bably Jansen, was the inventor of the
microscope, which application of the
principle was unquestionably of an earr
lier date, perhaps as far back as 1590.
Jansen gave one of his microscopes to
the Archduke, who gave it to Cornelius
Drebbel, a salaried mathematician at
the court of our James the first, where
William Borelli (not the author above

* Lettere d'Uomini illustri. Venezia, 1?44.
t Borelli, De vero Telescopii inventore, 1655,

24

GALILEO.

mentioned) saw it many years after-
wards, when ambassador from the
United Provinces to England, and got
from Drebbel this account of the quar-
ter whence it came. Lipperhey after-
wards, in 1609, accidentally hit upon
the telescope, and on the fame of this
discovery it would not be difficult for
Jansen, already in possession of an
instrument so much resembling it, to
perceive the slight difference between
them, and to construct a telescope in-
dependently of Lipperhey, so that each,
with some show of reason, might claim
the priority of the invention. A notion
of this kind reconciles the testimony of
many conflicting witnesses on the sub-
ject, some of whom do not seem to
distinguish very accurately whether the
telescope or microscope is the instru-
ment to which their evidence refers.
Borelli arrives at the conclusion, that
Jansen was the inventor ; but not satis-
fied with this, he endeavours, with a
glaring partiality which makes his for-
mer determination suspicious, to secure
for him and his son the more solid re-
putation of having anticipated Galileo in
the useful employment of the invention.
He has however inserted in his collec-
tions a letter from John the son of Za-
charias, in which John, omitting all
mention of his father, speaks of his
own observation of the satellites of
Jupiter, evidently seeking to insinuate
that they were earlier than Galileo's ;
and in this sense the letter has since
been quoted,* although it appears from
John's own deposition, preserved in the
same collection, that at the time of their
discovery he could not have been more
than six years old. An oversight of
'this sort throws doubt on the whole of
the pretended observations, and indeed
the letter has much the air of being the
production of a person imperfectly in-
formed on the subject on which he
writes, and probably was compiled to
suit Borelli's purposes, which were to
make Galileo's share in the invention
appear as small as possible.

Galileo himself gives a very intelli-
gible account of the process of reason-
ing, by which he detected the secret. —
*'I argued in the following manner.
The contrivance consists either 'of one
glass or of more — one is not sufficient,
since.it must be either convex, concave,
or plane ; the last does not produce any
sensible alteration in objects, the con-
cave diminishes them : it is true that the

* gncyclopsodia BriUnuica, Art, TELESCOPE,

convex magnifies, but it renders them
confused and indistinct; consequently,
one glass is insufficient to produce the
desired effect. Proceeding to consider
two glasses, and bearing in mind that
the plane glass causes no change, I de-
termined that the instrument could not
consist of the combination of a plane
glass with either of the other two. I
therefore applied myself to make expe-
riments on combinations of the two
other kinds, and thus obtained that of
which I was in search." It has been
urged against Galileo that, if he really
invented the telescope on theoretical
principles, the same theory ought at
once to have conducted him to a more
perfect instrument than that which he
at first constructed ;* but it is plain, from
this statement, that he does not profess
to have theorized beyond the determi-
nation of the species of glass which he
should employ in his experiments, and
the rest of his operations he avows to
have been purely empirical. Besides, we.
must take into account the difficulty of
grinding the glasses, particularly when fit
tools were yet to be made, and some-
thing must be attributed to Galileo's
eagerness to bring his results to the test
of actual experiment, without waiting for
that improvement which a longer delay
might and did suggest. Galileo's lan-
guage bears a resemblance to the first
passage which we quoted from Bap-
tista Porta, sufficiently close to make it
not improbable that he might be as-
sisted in his inquiries by some recollec-
tion of it, and the same passage seems,
in like manner, to have recurred to the
mind of Kepler, as soon as he heard of
the invention. Galileo's telescope con-
sisted of a plano-convex and plano-con-
cave lens, the latter nearest the eye,
distant from each other by the differ-
ence of their focal lengths, being, in
principle, exactly the same with the mo-
dern opera-glass. He seems to have
thought that the Dutch glass was the
same, but this could not be the case,
if the above quoted particular of the in-
verted weathercock, which belongs to
most traditions of the story, be correct ;
because it is the peculiarity of this kind
of telescope not to invert objects, and
we should be thus furnished with a de-
monstrative proof of the falsehood of
Fuccarius's insinuation : in that case
the Dutch glass must have been similar
to what was afterwards called the astro-
nomical telescope, consisting of two

» Ibid,

GALILEO.

25

convex glasses distant from each other
by the sum of their focal lengths. This
supposition is not controverted by the
fact, that this sort of telescope was never
employed by astronomers till long after-
wards ; for the fame of Galileo's obser-
vations, and the superior excellence of
the instruments constructed under his
superintendence, induced every one in
the first instance to imitate his con-
structions as closely as possible. The
astronomical telescope was however
eventually found to possess superior ad-
vantages over that which Galileo ima-
gined, and it is on this latter principle
that all modern refracting telescopes
are constructed; the inversion being
counteracted in those which are intended
for terrestrial observations, by the intro-
duction of a second pair of similar
glasses, which restore the inverted
image to its original position. For fur-
ther details on the improvements which
have been subsequently introduced, and
on the reflecting telescope, which was
not brought into use till the latter part
of the century, the reader is referred
to the Treatise on OPTICAL INSTRU-
MENTS.

Galileo, about the same time, con-
structed microscopes on the same prin-
ciple, for we find that, in 1612, he pre-
sented one to Sigisraund, King of Po-
land ; but his attention being principally
devoted to the employment and perfec-
tion of his telescope, the microscope
remained a long time imperfect in his
hands : twelve years later, in 1624,
he wrote to P. Federigo Cesi, that he
had delayed to send the microscope, the
use of which he there describes, because
he had only just brought it to perfec-
tion, having experienced some difficulty
in working the glasses. Schott tells an
amusing story, in his " Magic of Na-
ture," of a Bavarian philosopher, who,
travelling in the Tyrol with one of the
newly invented microscopes about him,
was taken ill on the road and died.
The authorities of the village took pos-
session of his baggage, and were pro-
ceeding to perform the last duties to his
body, when, on examining the little
glass instrument in his pocket, which
chanced to contain a flea, they were
struck with the greatest astonishment
and terror, and the poor Bavarian,
condemned by acclamation as a sor-
cerer who was in the habit of using
a portable familiar, was declared un-
worthy of Christian burial. Fortu-
nately for his character, some bold
sceptic ventured to open the instrument,

and discovered the true nature of the
imprisoned fiend.

As soon as Galileo's first telescope was
completed, he returned with it to Ve-
nice, and the extraordinary sensation
which it excited tends also strongly to
refute Fuccarius's assertion that the
Dutch glass was already known there.
During more than a month Galileo's
whole time was employed in exhibiting
his instrument to the principal inhabit-
ants of Venice, who thronged to his
house to satisfy themselves of the truth
of the wonderful stories in circulation ;
and at the end of that time the Doge,
Leonardo Donati, caused it to be in-
timated to him that such a present
would not be deemed unacceptable by
the senate. Galileo took the hint, and
his complaisance was rewarded by a
mandate confirming him for life in his
professorship at Padua, at the same
time doubling his yearly salary, which
was thus made to amount to 1000 flo-
rins.

It was long before the phrenzy of
public curiosity abated. Sirturi de-
scribes a ludicrous violence which was
done to himself, when, with the first
telescope which he had succeeded in.
making, he went up into the tower of
St. Mark, at Venice, in the vain hope of
being there entirely unmolested. Un-
luckily he was seen by some idlers in
the street : a crowd soon collected round
him, who insisted on taking possession
of his instrument, and, handing it one
to the other, detained him there for se-
veral hours till their curiosity was sa-
tiated, when he was allowed to return
home. Hearing them also inquire
eagerly at what inn he lodged, he thought
it better to quit Venice early the next
morning, and prosecute his observations
in a less inquisitive neighbourhood.* In-
struments of an inferior description were
soon manufactured, and vended every
where as philosophical playthings, much
in the way in which, in our own time, the
kaleidoscope spread over Europe as fast
as travellers could carry them. But the
fabrication of a better sort was long
confined, almost solely, to Galileo and
those whom he immediately instructed ;
and so late as the year 1637, we find
Gaertner, or as he chose to call him-
self, Hortensius, assuring Galileo that
none could be met with in Holland suf-
ficiently good to show Jupiter's disc
well defined ; and in 1634 Gassendi begs
for a telescope from Galileo, informing

iiiw, V<meti}», 1619, .

26

GALILEO.

him that he was unable to procure 'a
good one either in Venice, Paris, or
Amsterdam.

The instrument, on its first invention,
was generally known by the names of
Galileo's tube, the perspective, the dou-
ble eye-glass : the names of telescope
and microscope were suggested by
Demisiano, as we are told by Lagalla
in his treatise on the Moon.*

CHAPTER VII.

Discovery of Jupiter s satellites — Kepler
— Sizzi — Astrologers — Mcestlin —
Horky — Mayer.

As soon as Galileo had provided him-
self with a second instrument, he began
a careful examination of the heavenly
bodies, and a series of splendid discove-
ries soon rewarded his diligence. After
considering the beautiful appearances
which the varied surface of the moon
presented to this new instrument, he
turned his telescope towards Jupiter,
and his attention was soon arrested by
the singular position of three small stars,
near the body of that planet, which ap-
peared almost in a straight line with it,
and in the direction of the ecliptic. The
following evening he was surprised to
find that two of the three which had
been to the eastward of the planet, now
appeared on the contrary side, which he
could not reconcile with the apparent
motion of Jupiter among the fixed stars,
as given by the tables. Observing these
night after night, he could not fail to
remark that they changed their relative «
positions. A fourth also appeared, and
in a short time he could no longer re-
fuse to believe that these small stars
were four moons, revolving round Ju-
piter in the same manner in which our
earth is accompanied by its single at-
tendant. In honour of his patron Cos-
mo, he named them the Medicaean
stars. As they are now hardly known
by this appellation, his doubts, whether
he should call them Medicaean, after
Cosmo's family, or Cosmical, from his
individual name, are become of less
interest.

An extract from a letter which Gali-
leo received on this occasion from the
court of France, will serve to show
how highly the honour of giving a
name to these new planets was at that
time appreciated, and also how much
was expected from Galileo's first success
in examining the heavens. " The second

* De phsenomeais in orbe Lunse. Venetiis, 1612.

request, but the most pressing one which
I can make to you, is, that you should
determine, if you discover any other fine
star, to call it by the name of the great
star of France, as well as the most bril-
liant of all the earth ; and, if it seems
fit to you, call it rather by his proper
name of Henri, than by the family name
of Bourbon : thus you will have an op-
portunity of doing a thing just and due
and proper in itself, and at the same
time will render yourself and your family
rich and powerful for ever." The writer
then proceeds to enumerate the differ-
ent claims of Henri IV. to this honour,
not forgetting that he married into the
family of the Medici, &c.

The result of these observations was
given to the world, in an Essay which
Galileo entitled Nuncius Sidereus, or
the Intelligencer of the Stars ; and it is
difficult to describe the extraordinary
sensation which its publication pro-
duced. Many doubted, many positively
refused to believe, so novel an announce-
ment ; all were struck with the greatest
astonishment, according to their respec-
tive opinions, either at the new view of
the universe thus offered to them, or at
the daring audacity of Galileo in in-
venting such fables. We shall proceed
to extract a few passages from contem-
porary writers relative to this book, and
the discoveries announced in it.

Kepler deserves precedence, both
from his own celebrity, and from the
lively and characteristic account which
he gives of his first receiving the in-
telligence : — "I was sitting idle at
home, thinking of you, most excellent
Galileo, and your letters, when the
news was brought me of the dis-
covery of four planets by the help
of the double eye-glass. Wachenfels
stopped his carriage at my door to tell
me, when such a fit of wonder seized
me at a report which seemed so very
absurd, and I was thrown into such
agitation at seeing an old dispute be-
tween us decided in this way, that
between his joy, my colouring, and the
laughter of both, confounded as we
were by such a novelty, we were hardly
capable, he of speaking, or I of listening. «
My amazement was increased by the
assertion of Wachenfels, that those who
sent this news from Galileo were cele-
brated men, far removed by their learn-
ing, weight, and character, above vulgar
folly ; that the book was actually in the
press, and would be published immedi-
ately. On our separating, the authority
of Galileo had the greatest influence on

GALILEO.

27

me, earned by the accuracy of his judg-
ment, and excellence of his understand-
ing ; so I immediately fell to thinking
how there could he any addition to the
number of the planets without over-
turning my Mysterium Cosmographi-
cum, published thirteen years ago, ac-
cording to which Euclid's five regular
solids do not allow more than six pla-
nets round the sun."

This was one of the many wild notions
of Kepler's fanciful brain, among which
he was lucky enough at length to hit
upon the real and principal laws of the
planetary motions. His theory may be
briefly given in his own words : — " The
orbit "of the earth is the measure of the
rest. About it circumscribe a dodecahe-
dron. The sphere including this will be
that of Mars. About Mars' orbit de-
scribe a tetrahedron : the sphere contain-
ing this will be Jupiter's orbit. Round
Jupiter's describe a cube: the sphere in-
cluding this will be Saturn's. Within the
earth's orbit inscribe an icosahedron:
the sphere inscribed in it will beVenus's
orbit. In Venus inscribe an octahedron :
the sphere inscribed in it will be Mer-
cury's. You have now the reason of
the number of the planets :" for as there
are no more than the five regular solids
here enumerated, Kepler conceived this
to be a satisfactory reason why there
could be neither more nor less than six
planets. His letter continues : — " I am
so far from disbelieving the existence of
the four circumjovial planets, that I long
for a telescope to anticipate you, if pos-
sible, in discovering two round Mars, (as
the proportion seems to me to require,)
six or eight round Saturn, and perhaps
one each round Mercury and Venus."

The reader has here an opportunity
of verifying Galileo's observation, that
Kepler's method of philosophizing dif-
fered widely from his own. The proper
line is certainly difficult to hit between
the mere theorist and the mere observer.
It is not difficult at once to condemn the
former, and yet the latter will deprive
himself of an important, and often indis-
pensable assistance, if he neglect from
time to time to consolidate his observa-
tions, and thence to conjecture the course
of future observation most likely to re-
ward his assiduity. This cannot be
more forcibly expressed than in the
words of Leonardo da Vinci :* " Theory
is the general, experiments are the
soldiers. The interpreter of the works
of nature is experiment ; that is never

* Venturi, Essai sur les ouvrages de Leo, da
Vinci.

wrong; it is our judgment whteh is
sometimes deceived, because we are ex-
pecting results which experiment refuses
to give. We must consult experiment,
and vary the circumstances, till we have
deduced general rules, for it alone can
furnish us with them. But you will
ask, what is the use of these general
rules? I answer, that they direct us
in our inquiries into nature and the
operations of art. They keep us from
deceiving ourselves and others, by pro-
mising ourselves results which we can
never obtain."

In the instance before us, it is well
known that, adopting some of the opi-
nions of Bruno and Brutti, Galileo, even
before he had seen the satellites of Jupi-
ter, had allowed the possibility of the
discovery of new planets ; and we can
scarcely suppose that they had weakened
his belief in the probability of further
success, or discouraged him from exa-
mining the other heavenly bodies. Kep-
ler on the contrary had taken the op-
posite side of the argument ; but no
sooner was the fallacy of his first position
undeniably demonstrated, than, passing
at once from one extreme to the other,
he framed an unsupported theory to ac-
count for the number of satellites which
were round Jupiter, and for those which
he expected to meet with elsewhere.
Kepler has been styled the legislator of
the skies ; his laws were promulgated
rather too arbitrarily, and they often
failed, as all laws must do which are
not drawn from a careful observation
of the nature of those who are to
be governed by them. Astronomers
have reason to be grateful for the
theorems which he was the first to esta-
blish ; but so far as regards the progress
of the science of inductive reasoning, it
is perhaps to be regretted, that the se-
venteen years which he wasted in ran-
dom and unconnected guesses should
have been finally rewarded, by disco-
veries splendid enough to shed deceitful
lustre upon the method by which he ar-
rived at them.

Galileo himself clearly perceived the
fallacious nature of these speculations
on numbers and proportions, and has
expressed his sentiments concerning
them very unequivocally. " How great
and common an error appears to me the
mistake of those who persist in making
their knowledge and apprehension the
measure of the apprehension and know-
ledge of God ; as if that alone were per-
fect, which they understand to be so.
But J, on the contrary, observe that

28

GALILEO.

Nature has other scales of perfection,
which we cannot comprehend, and rather
seem disposed to class among imper-
fections. For instance, among the re-
lations of different numbers, those ap-
pear to us most perfect which exist be-
tween numbers nearly related to each
other , as the double, the triple, the pro-
portion of three to two, &c. ; those appear
less perfect which exist between num-
bers remote from, and prime to each
other; as 11 to 7, 17 to 13, 53 to 37,
&c. ; and most imperfect of all do those
appear which exist between incommen-
surable quantities, which by us are
nameless and inexplicable. Conse-
quently, if the task had been given to a
man, of establishing and ordering the
rapid motions of the heavenly bodies,
according to his notions of perfect pro-
portions, I doubt not that he would have
arranged them according to the former
rational proportions ; but, on the con-
trary, God, with no regard to our ima-
ginary symmetries, has ordered them in
proportions not only incommeasurable
and irrational, but altogether inappre-
ciable by our intellect. A man ignorant
of geometry may perhaps lament, that the
circumference of a circle does not happen
to be exactly three times the diameter,
or in some other assignable proportion
to it, rather than such that we have not
yet been able to explain what the ratio
between them is ; but one who has
more understanding will know that if
they were other than they are, thou-
sands of admirable conclusions would
have been lost, and that none of the
other properties of the circle would
have been true : the surface of the sphere
\vould not be quadruple of a great cir-
cle, nor the cylinder be to the sphere as
three to^two : in short, no part of geo-
metry would be true, and as it now is. If
one of our most celebrated architects had
had to distribute this vast multitude of
fixed stars through the great vault of
heaven, I believe he would have disposed
them with beautiful arrangements of
squares, hexagons, and octagons; he
would have dispersed the larger ones
among the middle sized and the less,
so as to correspond exactly with each
other ; and then he would think he had
contrived admirable proportions : but
God, on the contrary, has shaken them
out from His hand as if by chance, and
we, forsooth, must think that He has
scattered them up yonder without any
regularity, symmetry, and elegance."

It is worth remarking that the dan-
gerous ideas of aptitude and congruence

of numbers had taken such deep and
general root, that long afterwards, when
the reality of Jupiter's satellites was in-
contestably established, and Huyghens
had discovered a similar satellite near
Saturn, he was so rash as to declare his
belief, (unwarned by the vast pro-
gress which astronomy had made in his
own time,) that no more satellites would
be discovered, since the one which he
discovered near Saturn, with Jupiter's
four, and our moon, made up the num-
ber six, exactly equal to the number of
the principal planets. Every reader
knows that this notion, so unworthy
the genius of Huyghens, has been since
exploded by the discovery both of new
planets, and new satellites.

Francesco Sizzi, a Florentine astro-
nomer, took the matter up in a some-
what different strain from Kepler.*—
" There are seven windows given to
animals in the domicile of the head,
through which the air is admitted to
the rest of the tabernacle of the body,
to enlighten, to warm, and nourish it,
which are the principal parts of the
ftixzoxofffto; (or little world) ; two nostrils,
two eyes, two ears, and a mouth ; so
in the heavens, as in a petxcoxtrpos (or
great world), there are two favourable
stars, two unpropitious, two luminaries,
and Mercury alone undecided and in-
different. From which and many other
similar phenomena of nature, such as
the seven metak, Sec., which it were
tedious to enumerate, we gather that the
number of planets is necessarily seven.
Moreover, the satellites are invisible to
the naked eye, and therefore can exer-
cise no influence on the earth, and there-
fore would be useless, and therefore do
not exist. Besides, as well the Jews and
other ancient nations as modern Euro-
peans have [adopted the division of the
week into se'ven days, and have named
them from the 'seven planets : now if we
increase the number of the planets this
whole system falls to the ground." To
these remarks Galileo calmly replied,
that whatever their force might be, as a
reason for believing beforehand that no
more than seven planets would be dis-
covered, they hardly seemed of sufficient
weight to destroy the new ones when
actually seen.

Others, again, took a more dogged
line of opposition, without venturing
into the subtle analogies and arguments
of the philosopher just cited. They con-
tented themselves, and satisfied others,

* Pmnoia Astronomies, Yejjetijs, 16J.Q.

GALILEO.

29

with the simple assertion, that such
things were not, and could not be, and
the manner in which they maintained
themselves in their incredulity was suf-
ficiently ludicrous. " Oh, my dear
Kepler,"* says Galileo, "how I wish
that we could have one hearty laugh
together. Here, at Padua, is the prin-
cipal professor of philosophy, whom I
have repeatedly and urgently requested
to look at the moon and planets through
my srlass, which he pertinaciously refuses
to do. Why are you not here ? what
shouts of laughter we should have at
this glorious folly ! and to hear the pro-
fessor of philosophy at Pisa labouring
before the grand duke with logical ar-
guments, as if with magical incantations,
to charm the new planets out of the
sky."

Another opponent of Galileo deserves
to be named, were it only for the sin-
gular impudence of the charge he
ventures to bring against him. " We
are not to think," says Christmann,
in the Appendix to his Nodus Gor-
dius, " that Jupiter has four satellites
given him by nature, in order, by re-
volving round him, to immortalize the
name of the Medici, who first had notice
of the observation. These are the
dreams of idle men, who love ludicrous
ideas better than our laborious and in-
dustrious correction of the heavens. —
Nature abhors so horrible a chaos, and
to the truly wise such vanity is detest-
able.

Galileo was also urged by the astro-
logers to attribute some influence, ac-
cording to their fantastic notions, to the
satellites, and the account which he
gives his friend Dini of his answer to
one of this class is well worth extract-
ing, as a specimen of his method of
uniting sarcasm with serious expostula-
tion; " I must," says he, "tell you what
I said a few days back to one of those
nativity-casters, who believe that God,
when he created the heavens and the
stars, had no thoughts beyond what
they can themselves conceive, in order
to free myself from his tedious impor-
tunity ; for he protested, that unless
I would declare to him the effect of
the Medicaean planets, he would reject
and deny them as needless and super-
fluous. I believe this set of men to be
of Sizzi's opinion, that astronomers dis-
covered the other seven planets, not by
seeing them corporally in the skies, but
only from their effects on earth, — much

* Kepleri Epistolae.

in the manner in which some houses
are discovered to be haunted by evil
spirits, not by seeing them, but from the
extravagant pranks which are played
there. I replied, that he ought to recon-
sider the hundred or thousand opinions
which, in the course of his life, he might
have given, and particularly to examine
well the events which he had predicted
with the help of Jupiter, and if he
should find that all had succeeded con-
formably to his predictions, I bid him
prophecy merrily on, according to his
old and wonted rules; for I assured
him that the new planets would not in
any degree affect the things which are
already past, and that in future he
would not be a less fortunate conjuror
than he had been : but if, on the con-
trary, he should find the events depend-
ing on Jupiter,in some trifling particulars
not to have agreed with his dogmas and
prognosticating aphorisms, he ought to
set to work to find new tables for cal-
culating the constitution of the four
Jovial circulators at every bygone mo-
merit, and, perhaps, from the diversity of
their aspects, he would be able, with ac-
curate observations and multiplied con-
junctions, to discover the alterations and
variety of influences depending upon
them ; and I reminded him, that in ages
past they had not acquired knowledge
with little labour, at the expense of
others, from written books, but that the
first inventors acquired the most excel-
lent knowledge of things natural and
divine with study and contemplation of
the vast book which nature holds ever
open before those who have eyes in
their forehead and in their brain ; and
that it was a more honourable and
praiseworthy enterprize with their own
watching, toil, and study, to discover
something admirable and new among
the infinite number which yet remain
concealed in the darkest depths of phi-
losophy, than to pass a listless and lazy
existence, labouring only to darken the
toilsome inventions of their neighbours,
in order to excuse their own cowardice
and inaptitude for reasoning, while they
cry out that nothing can be added to
the discoveries already made."

The extract given above from Kepler,
is taken from an Essay, published with
the later editions of the Nuncius, the
object and spirit of which seem to
have been greatly misunderstood, even
by some of Kepler's intimate friends. —
They considered it as a covert attack
upon Galileo, and, accordingly, Maestlin
thus writes to him: — " In your Essay

30

GALILEO.

(which I have just received) you have
plucked Galileo's feathers well ; I
mean, that you have shown him not to
be the inventor of the telescope, not to
have been the first who observed the
irregularities of the moon's surface,
not to have been the first discoverer of
more worlds than the ancients were ac-
quainted with, &c. One source of
exultation was still left him, from the
apprehension of which Martin Horky
has now entirely delivered me." It is
difficult to discover in what part of
Kepler's book Maestlin found all this,
for it is one continued encomium
upon Galileo ; insomuch that Kepler
almost apologizes in the preface for
what may seem his intemperate admi-
ration of his friend. " Some might
wish I had spoken in more moderate
terms in praise of Galileo, in conside-
ration of the distinguished men who
are opposed to his opinions, but I have
written nothing fulsome or insincere.
I praise him, for myself ; I leave other
men's judgments free; and shall be
ready to join in condemnation when
some one wiser than myself shall, by
sound reasoning, point out his errors."
However, Maestlin was not the only
one who misunderstood Kepler's in-
tentions : the Martin Horky of whom
he speaks, a young German, also sig-
nalized himself by a vain attack upon
the book which he thought his patron
Kepler condemned. He was then travel-
ling in Italy, whence he wrote to Kepler
his first undetermined thoughts about the
new discoveries. " They are wonderful ;
they are stupendous ; whether they are
true or false I cannot tell." * He seems
soon to have decided that most repu-
tation was to be gained on the side of
Galileo's opponents, and his letters
accordingly became filled with the most
rancorous abuse of him. At the same
time, that the reader may appreciate
Horky's own character, we shall quote
a short sentence at the end of one of
his letters, where he writes of a paltry
piece of dishonesty with as great glee
as if he had solved an ingenious and
scientific problem. After mentioning
his meeting Galileo at Bologna, and
being indulged with a trial of his tele-
scope, which, he says, " does wonders
upon the earth, but represents celestial
objects falsely ;"t he concludes with

* Kepleri Epistolse.

fit may seem extraordinary that any one could
support an argument by this partial disbelief in thein-
btrumeiit, whicu wa» allowed on aii hands to if present
terresliai objects correctly. A similar instance of
obstinacy, in au almost identical case though in a

the following honourable sentence : — " I
must confide to you a theft which I
committed. I contrived to take a mould
of the glass in wax, without the know-
ledge of any one, and, when I get home,
I trust to make a telescope even better
than Galileo's own."

Horky having declared to Kepler,
" I will never concede his four new pla-
nets to that Italian from Padua though
I die for it," followed up this declara-
tion by publishing a book against Ga-
lileo, which is the one alluded to by
Maestlin, as having destroyed the little
credit which, according to his view,
Kepler's publication had left him.
This book professes to contain the ex-
amination of four principal questions
touching the alleged planets ; 1st, Whe-
ther they exist ? 2nd, What they are ?
3rd, What they are like? 4th, Why
they are ? The first question is soon
disposed of, by Horky's declaring
positively that he has examined the
heavens with Galileo's own glass, and
that no such thing as a satellite about
Jupiter exists. To the second, he
declares solemnly, that he does not more
surely know that he has a soul in his
body, than that reflected rays are the
sole cause of Galileo's erroneous ob-
servations. In regard to the third
question, he says, that these planets are
like the smallest fly compared to an
elephant ; and, finally, concludes on the
fourth, that the only use of them is to
gratify Galileo's " thirst of gold," and
to afford himself a subject of discussion.*

Galileo did not condescend to notice
this impertinent folly ; it was answered
by Roffini, a pupil of Magini, and by a
young Scotchman of the name of Wed-
derburn, then a student at Padua, and
afterwards a physician at the Court of
Vienna. In the latter reply we find it men-
tioned, that Galileo was also using his
telescope for the examination of insects,

more unpretending station, once came under the
writer's own observation. A farmer in Cambridge-
shire, who had acquired some confused notions of
the use of the quadrant, consulted him. ou a new
method of determining the distances and magnitudes
of the sun and moon, which he declared were far
different from the quantities usually assigned to them.
After a little conversation, the root of his error, cer-
tainly sufficiently gross, appeared to be that he had
confounded the angular measure of a degree, with
69£ miles, the linear measure of a degree on the
earth's surface. As a short way of showing his.mis-
take, he was desired to determine, in the same man-
ner, the height of his barn which stood about 30 yards
distant ; he lifted the quadrant to his eye, but per-
ceiving, probably, the monstrous size to which his
principles were forcing him, he said, " Oh, Sir, the
quadrant's only true lor the sky." He must have
been an objector of this kind, wiio said to Galileo.—
" Uh,',Sir, the telescope's only true for the earth."
* Venturi.

GALILEO.

31

&c.* Horky sent his performance tri-
umphantly to Kepler, and, as he returned
home before receiving an answer, he
presented himself before his patron in
1he same misapprehension under which
he had written, but the philosopher re-
ceived him with a burst of indignation
which rapidly undeceived him. The
conclusion of the story is characteristic
enough to be given in Kepler's own ac-
count, of the matter to Galileo, in which,
after venting his wrath against this
" scum of a fellow," whose " obscurity
had given him audacity," he says, that
Horky begged so hard to be forgiven,
that " I have taken him again into fa-
vour upon this preliminary condition,
to which he has agreed : — that I am to
shew him Jupiter's satellites, AND HE is
TO SEE THEM, and own that they are
there."

In the same letter Kepler writes, that
although he has himself perfect confi-
dence in the truth of Galileo's asser-
tions, yet he wishes he could furnish
him with some corroborative testimonies,
which Kepler could quote in arguing
the point with others. This request
produced the following reply, from which
the reader will also learn the new change
which had now taken place in Galileo's
fortunes, the result of the correspon-
dence with Florence, part of which we
have already extracted, t " In the first
place, I return you my thanks that you
first, and almost alone, before the ques-
tion had been sifted (such is your can-
dour and the loftiness of your mind),
put faith in my assertions. You tell
me you have some telescopes, but not
sufficiently good to magnify distant ob-
jects with clearness, and that you
anxiously expect a sight of mine, which
magnifies images more than a thousand
times. It is mine no longer, for the
Grand Duke of Tuscany has asked it of
me, and intends to lay it up in his mu-
seum, among his most rare and precious
curiosities, in eternal remembrance of
the invention : I have made no other of
equal excellence, for the mechanical la-
bour is very great : I have, however,
devised some instruments for figuring
and polishing them which I am un-
willing to construct here, as they could
not conveniently be carried to Florence,
where I shall in future reside. You
ask, my dear Kepler, for other testi-
monies : — I produce, for one, the
Grand Duke, who, after observing the
Medicsean planets several times with

* Quatuor probl. confut. per J. Wedderboraiuju,
Scotobritannum. Patayii, 1610.
t See page 18.

me at Pisa during 'the last months,
made me a present, at parting, worth
more than a thousand florins, and has
now invited me to attach myself to him
with the annual salary of one thousand
florins, and with the title of Philosopher
and Principal Mathematician to His
Highness ; without the duties of any
office to perform, but with the most
complete leisure ; so that I can com-
plete my Treatises on Mechanics, on
the Constitution of the Universe, and
on Natural and Violent Local Motion,
of which I have demonstrated geo-
metrically many new and admirable
phenomena. I produce, for another wit-
ness, myself, who, although already en-
dowed in this college with the noble
salary of one thousand florins, such as
no professor of mathematics ever before
received, and which I might securely
enjoy during my life, even if these pla-
nets had deceived me and should dis-
appear, yet quit this situation, and be-
take me where want and disgrace will
be my punishment should I prove to
have been mistaken."

It is difficult not to regret that Galileo
should be thus called on to resign his best
glasses, but it appears probable that
on becoming more familiar with the
Grand Duke, he ventured to suggest
that this telescope would be more advan-
tageously employed in his own hands,
than pompously laid up in a museum ;
for in 1637 we find him saying, in an-
swer to a request from his friend Mi-
canzio to send him a telescope — " I am
sorry that I cannot oblige you with the
glasses for your friend, but I am no
longer capable of making them, and I
have just parted with two tolerably good
ones which I had, reserving only my
old discoverer of celestial novelties whicl:
is already promised to the Grand Duke.
Cosmo was dead in 1637, and it is
his son Ferdinand who is here meant,
who appears to have inherited his fa-
ther's love of science. Galileo tells us,
in the same letter, that Ferdinand had
been amusing himself for some months
with making object-glasses, and al-
ways carried one with him to work at
wherever he went.

When forwarding this telescope to
Cosmo in the first instance, Galileo adds,
with a very natural feeling—" I send
it to his highness unadorned and un-
polished, as I made it for my own use,
and beg that it may always be left in
the same state ; for none of the old parts
ought to be displaced to make room
for new ones, which will have had
no share in the watchings and fatigues

GALILEO.

of these observations." A telescope
was in existence, though with the object
glass broken, at the end of the last cen-
tury, and probably still is in the Museum
at Florence, which was shewn as the
discoverer of Jupiter's satellites. Nelli,
on whose authority this is mentioned,
appears to question its genuineness. The
first reflecting telescope, made with New-
ton's own hands, and scarcely possess-
ing less interest than the first of Galileo's,
is preserved in the library of the Royal
Society.

By degrees the enemies of Galileo
and of the new stars found it impossible
to persevere in their disbelief, whether
real or pretended, and at length seemed
resolved to compensate for the sluggish-
ness of their perception, by its acute-
ness when brought into action. Simon .
Mayer published his ".Mundus Jovialis"
in 1614, in which he claims to have
been an original observer of the satel-
lites, but, with an affectation of candour,
allows that Galileo observed them pro-
bably about the same time. The earliest
observation which he has recorded is
dated 29th December, 1609, but, not
to mention the total want of probability
that Mayer would not have immediately
published so interesting a discovery, it
is to be observed, that, as he used
the old style, this date of 29th December
agrees with the 8th January, .1 6 1 0, of
the new style, which was the date of
Galileo's second observation, and Gali-
leo ventured to declare his opinion, that
this pretended observation was in fact
a plagiarism.

Scheiner counted five, Rheita nine,
and other observers, with increasing
contempt for Galileo's imperfect an-
nouncements, carried the number as
high as twelve.* In imitation of Gali-
leo's nomenclature, and to honour the
sovereigns of the respective observers,
these supposed additional satellites were
dignified with the names of Vladisla-
vian, Agrippine, Urbanoctavian, and
Ferdinandotertian planets ; but a very
short time served to show it was as
unsafe to exceed as to fall short of
the number which Galileo had fixed
upon, for Jupiter rapidly removed him-
self from the neighbourhood of the
fixed stars, which gave rise to these
pretended discoveries, carryingwith him
only his four original attendants, which
continued in every part of his orbit to
revolve regularly about him.

Perhaps we cannot better wind up
this account of the discovery of Jupi-
ter's satellites, and of the intense interest

* Sherbunie's sphere of Mauilius. London, 1675. ,

they have at all times inspired, than in
the'words of one who inherits a name
worthy to be ranked with that, of Galileo
in the list of astronomical discoverers,
and who takes his own place among
the most accomplished mathematicians
of the present times. " The discovery
of these bodies was one of the first bril-
liant results of the invention of the tele-
scope ; one of the first great facts which
opened the eyes of mankind to the
system of the universe, which taught
them the comparative insignificance of
their own planet, and the superior vast-
ness and nicer mechanism of those
other bodies, which had before been dis-
tinguished from the stars only by their
motion, and wherein none but the bold-
est thinkers had ventured to suspect a
community of nature with our own
globe. This discovery gave the holding
turn to the opinions of mankind respect-
ing the Copernican system ; the analogy
presented by these little bodies (little
however only in comparison with the
great central body about which they
revolve) performing their beautiful revo-
lutions in perfect harmony and order
about it, being too strong to be resisted.
This elegant system was watched with
all the curiosity and interest the sub-
ject naturally inspired. The eclipses of
the satellites speedily attracled attention,
and the more when it was discerned,
as it speedily was, by Galileo himself,
that they afforded a ready method of
determining the difference of longitudes
of distant places on the earth's surface,
by observations of the instants of their
disappearances and reappearances, si-
multaneously made. Thus the first
astronomical solution of the great pro-
blem of the longitude, the first mighty
step which pointed out a connection
between speculative astronomy and
practical utility, and which, replacing
the fast dissipating dreams of astrology
by nobler visions, showed how the stars
might really, and without fiction, be
called arbiters of the destinies of em-
pires, we owe to the satellites of
Jupiter, those atoms imperceptible to
the naked eye, and floating like motes
in the beam of their primary — itself an
atom to our sight, noticed only by the
careless vulgar as a large star, and by
the philosophers of former ages as some-
thing moving among the stars, they knew
not what, nor why : perhaps only to
perplex the wise with fruitless conjec-
tures, and harass the weak with fears
as idle as their theories."*

* Hersehel'a Address to the Astronomical So-
ciety, 1&27.

GALILEO.

33

CHAPTER VIII.

Observations on the Moon — Nebulce —
Saturn — Venus — Mars.

THERE were other discoveries an-
nounced in Galileo's book of great and
unprecedented importance, and which
scarcely excited less discussion than the
controverted Medicaean planets. His
observations on the moon threw addi-
tional light on the constitution of the
solar system, and cleared up the difficul-
ties which encumbered the explanation
of the varied appearance of her surface.
The different theories current at that
day, to account for these phenomena, are
collected and described by Benedetti,
and also with some liveliness, in a my-
thological poem, by Marini.* We are
told, that, in the opinion of some, the
dark shades on the moon's surface arise
from the interposition of opaque bodies
floating between her and the sun, which
prevents his light from reaching those
parts : others thought, that on account
of her vicinity to the earth, she was
partly tainted with the imperfection of
our terrestrial and elementary nature,
and was not of that entirely pure and
refined substance of which the more
remote heavens consist: a third party
looked on her as a vast mirror, and
maintained that the dark parts of her
surface were the reflected images of our
earthly forests and mountains.

Galileo's glass taught him to believe
that the surface of this planet, far from
being smooth and polished, as was gene-
rally taken for granted, really resembled
our earth in its structure ; he was able dis-
tinctly to trace on it the outlines of moun-
tains and other inequalities, the summits
of which reflected the rays of the sun
before these reached the lower parts,
and the sides of which, turned from his
beams, lay buried in deep shadow. He
recognised a distribution into something
similar to continents of land, and
oceans of water, which reflect the sun's
light to us with greater or less vivacity,
according to their constitution. These
conclusions were utterly odious to the
Aristotelians ; they had formed a pre-
conceived notion of what the moon
ought to be, and they loathed the doc-
trines of Galileo, who took delight, as
they said, in distorting and ruining the
fairest works of nature. It was in vain
he argued, as to the imaginary perfection

* Adone di Marini, Venetiis, 1G23, Cant. x.

of the spherical form, that although the
moon, or the earth, were it absolutely
smooth, would indeed be a more perfect
sphere than in its present rough state, yet
touching the perfection of the earth,
considered as a natural body calculated
for a particular purpose, every one must
see that absolute smoothness and sphe-
ricity would make it not only less per-
fect, but as far from being perfect as
possible. " What else," he demanded,
" would it be but a vast unblessed desert,
void of animals, of plants, of cities and
of men ; the abode of silence and inac-
tion; senseless, lifeless, soulless, and
stript of all those ornaments which make
it now so various and so beautiful ?"

He reasoned to no purpose with
the slaves of the ancient schools : no-
thing could console them for the de-
struction of their smooth unalterable
surface, and to such an absurd length
was this hallucination carried, that one
opponent of Galileo, Lodovico delle
Colombe, constrained to allow the evi-
dence of the sensible inequalities of the
moon's surface, attempted to reconcile
the old doctrine with the new observa-
tions, by asserting, that every part of the
moon, which to the terrestrial observer
appeared hollow and sunken, was in
fact entirely and exactly filled up with
a clear crystal substance, perfectly im-
perceptible by the senses, but which
restored to the moon her accurately
spherical and smooth surface. Galileo
met the argument in the manner most
fitting, according to one of Aristotle's
own maxims, that " it is foolish to re-
fute absurd opinions with too much
curiosity." " Truly," says he, " the
idea is admirable, its only fault is that
it is neither demonstrated nor demonstra-
ble : but I am perfectly ready to believe
it, provided that, with equal courtesy,
I may be allowed to raise upon your
smooth surface, crystal mountains(which
nobody can perceive) ten times higher
than those which I have actually seen
and measured." By threatening to pro-
ceed to such extremities, he seems to
have scared the opposite party into mo-
deration, for we do not find that the
crystalline theory was persevered in.

In the same essay, Galileo also ex-
plained at some length the cause of that
part of the moon being visible, which is
unenlightened directly by the sun in her
first and last quarter. Maestlin, and be-
fore him Leonardo da Vinci, had already
declared this ;to arise from what may
be called earthshine, or the reflec-

34

GALILEO.

tion of the sun's light from the terres-
trial globe, exactly similar to that, which
the moon affords us when we are simi-
larly placed between her and the sun ; but
the notion had not been favourably re-
ceived, because one of the arguments
against the earth being a planet, revolv-
ing like the rest round the sun, was, that
it did not shine like them, and was
therefore of a different nature ; and this
argument, weak as it was in itself, the
theory of terrestrial reflection completely
overturned. The more popular opinions
ascribed this feeble light, some to the
fixed stars, some to Venus, some to the
rays of the sun, penetrating and shining
through the moon. Even the sagacious
Benedetti adopted the notion of this
light being caused by Venus, in the
same sentence in which he explains the
true reason of the faint light observed
during a total eclipse of the moon, point-
ing out that it is occasioned by those
rays of the sun, which reach the moon,
after being bent round the sides of
the earth by the action of our atmo-
sphere.*

Galileo also announced the detection
of innumerable stars, invisible to the
unassisted sight; and those remark-
able appearances in the heavens, ge-
nerally called nebulae, the most con-
siderable of which is familiar to all
under the name of the milky way, when
examined by his instrument, were found
to resolve themselves into a vast collec-
tion of minute stars, too closely congre-
gated to produce a separate impression
upon the unassisted eye.t Benedetti,
who divined that the dark shades on the
moon's surface arose from the constitu-
tion of those parts which suffered much
of the light to pass into them, and con-
sequently reflected a less portion of it,
had maintained that the milky way was
the result of the converse of the same
phenomenon, and declared, in the^lan-
guage of his astronomy, that it was a
part of the eighth orb, which did not,
like the rest, allow the sun's light to
traverse it freely, but reflected a small
part feebly to our sight*

The Anti-Copernicans would probably
have been well pleased, if by these eter-
nally renewed discussions and disputes,
they could have occupied Galileo's time

* Speculat. Lib Venetiis, 1585, Epistolae.
•j- This opinion, with respect to the milky way, had
been held by some of the ancient astronomers. See
Manillas. Lib. i. v. 753.

" Anne mngis densu stcllarum turba corona
~ Cuntexitjtaittmas, et cnmsu lumine candct,
JUtfulgore nitet collato clarior orbis."

sufficiently to detain his attention from
his telescope and astronomical observa-
tions ; but he knew too well where his
real strength lay, and they had scarcely
time to compound any thing like an ar-
gument against him and his theories,
before they found him in possession of
some new facts, which they were un-
prepared to meet, otherwise than by
the never*- failing resource of abuse and
affected contempt. The year had not
expired before Galileo had new intelli-
gence to communicate of the highest im-
portance. Perhaps he had been taught
caution irom the numerous piracies which
had been committed upon his discoveries,
and he first announced his new disco-
veries enigmatically, veiling their real
import by transpositions of the letters in
the words which described them, (a prac-
tice then common, and not disused even
at a much later date,) and inviting all
astronomers to declare, within a certain
time, if they had noted any thing new
in the heavens worthy of observation.
The transposed letters which he published
were —

" Smaismrmilme poeta leumi bvne nugttaviras."

Kepler, in the true spirit of his riddling
philosophy, endeavoured to decypher the
meaning, and fancied he had succeeded
when he formed a barbarous Latin
verse,

" Salve umbistineum geminatum Martia proles,"

conceiving that the discovery, whatever
it might be, related to the planet Mars,
to which Kepler's attention had before
been particularly directed. The reader,
however, need not weary himself in
seeking a translation of this solution,
for at the request of the Emperor Ro-
dolph, Galileo speedily sent to him the
real reading —

Altissimum planetam tcrgeminum observavi ;

that is, " I have observed that the most
distant planet is triple," or, as he further
explains the matter, " I have with great
admiration observed that Saturn is not
a single star, but three together, which
as it were touch each other ; they have no
relative motion, and are constituted in
this form oQo the middle being some-
what larger than the lateral ones. If
we examine them with an eye-glass which
magnifies the surface less than 1000
times, the three stars do not appear
very distinctly, but Saturn has an ob-
long appearance, like the appearance of
an olive, thus O. Now 1 have dis-
covered a court for Jupiter, and two
servants for this old man, who aid his

GALILEO.

35

steps and never quit his side." Galileo
was, however, no match in this style
of writing for Kepler, who disapproved
his friend's metaphor, and, in his usual
fanciful and amusing strain, — " I will
not," said he, " make an old man of
Saturn, nor slaves of his attendant
globes, but rather let this tricorporate
form be Geryon, so shall Galileo be
Hercules, and the telescope his club;
armed with which, he has conquered
that distant planet, and dragged him
from the remotest depths of nature, and
exposed him to the view of all." Gali-
leo's glass was not of sufficient power to
shew him the real constitution of this
extraordinary planet; it was reserved
for Huyghens, about the year 1656, to
declare to the world that these supposed
attendant stars are in fact part of a
ring which surrounds, and yet is com-
pletely distinct from the body of Saturn ;*
and the still more accurate observations
of Herschel have ascertained that it
consists of two concentric rings revolv-
ing round the planet, and separated
from each other by a space which our
most powerful telescopes scarcely enable
us to measure.

Galileo's second statement concluded
with the remark, that " in the other pla-
nets nothing new was to be observed ;"
but a month had scarcely elapsed, before
he communicated to the world another
enigma,

Hcec immatura d me jamfrustra leguntur oy,

which, as he said, contained the an-
nouncement of a new phenomenon, in
the highest degree important to the truth
of the Copernican system. The inter-
pretation of this is,

Cynthice Jiguras cemulatur muter amorum,

that is to say, — Venus rivals the ap-
pearances of the moon — for Venus
being now arrived at that part of her
orbit in which she is placed between the
earth and the sun, and consequently,
with only a part of her enlightened sur-
face turned towards the earth, the tele-
scope shewed her in a crescent form, like
the moon in a similar position, and tra-
cing her through the whole of her orbit
round the sun, or at least so long as she
was not invisible from his overpowering
light, Galileo had the satisfaction of

* Huyghens announced his discovery in this form :
aaaaaaac ccccdeee e eg hii i iiiil 1 1 1 mmnn
nnnnnnnoouoppqrrstttttuuuu K, which he
afterwards recomposed inlo the sentence. Annulu
cingitur, tcnui, piano, nusquam cohcerente, ad cclipti-
-cam inclinato. De Saturui Luna. Hagae, 1656.

seeing the enlightened portion in each
position assume the form appropriate to
that hypothesis. It was with reason,
therefore, that he laid stress on the im-
portance of this observation, which also
established another doctrine scarcely less
obnoxious to the Anti - Copernicans,
namely, that a new point of resemblance
was here found between the earth and
one of the principal planets ; and as the
reflection from the earth upon the moon
had shewn it to be luminous like the
planets when subjected to the rays of
the sun, so this change of apparent
figure demonstrated that one of the
planets not near the earth, and there-
fore probably all, were in their own
nature not luminous, and only reflected
the sun's light which fell upon them;
an inference, of which the probability
was still farther increased a few years
later by the observation of the transit of
Mercury over the sun's disc.

It is curious that only twenty-five
years before this discovery of the phases
(or appearances) of Venus, a commen-
tator of Aristotle, under the name of
Lucillus Philalthaeas, had advanced the
doctrine that all the planets except the
moon are luminous of themselves, and
in proof of his assertion had urged,
" that if the other planets and fixed
stars received their light from the sun,
they would, as they approached and re-
ceded from him, or as he approached and
receded from them, assume the same
phases as the moon, which, he adds,
we have never yet observed."— He fur-
ther remarks, " that Mercury and Ve-
nus would, in the supposed case of their
being nearer the earth than the sun,
eclipse it occasionally, just as eclipses
are occasioned by the moon." Perhaps
it is still more remarkable, that these very
passages, in which the reasoning is so
correct, though the facts are too hastily
taken for granted, (the common error of
that school,) are quoted by Benedetti, ex-
pressly to shew the ignorance and pre-
sumption of the author. Copernicus,
whose want of instruments had pre-
vented him from observing the horned
appearance of Venus when between
the earth and sun, had perceived how
formidable an obstacle the non-appear-
ance of this phenomenon presented to
his system; he endeavoured, though
unsatisfactorily, to account for it by
supposing that the rays of the sun
passed freely through the body of the
planet, and Galileo takes occasion to
praise him for not being deterred from
D 2

36

GALILEO'.

adopting the system, which, on the whole,
appeared to agree best with the phe-
nomena, by meeting with some \vhich it
did not enable him to explain. Milton,
whose poem is filled with allusions to
Galileo and his astronomy, has not suf-
fered this beautiful phenomenon to pass
unnoticed. After describing the creation
of the Sun, he adds : —

Hither, as to their fountain, other stars

Repairing, in their golden urns draw light,

And hence the morning planet gilds her horns.* "•

Galileo also assured himself, at the
same time, that the fixed stars did not
receive their light from the sun. This he
ascertained by comparing the vividness
of their light, in all positions, with the
feebleness of that of the distant planets,
and by observing the different degrees
of brightness with which all the planets
shone at different distances from the
sun. The more remote planets did not,
of course, afford equal facilities with
Venus for so decisive an observation ;
but Galileo thought he observed, that
when Mars was in quadratures, (or in
the quarters, the middle points of his
path on either side,) his figure varied
slightly from a perfect circle. Galileo
concludes the letter, in which he an-
nounces these last observations to his
pupil Castelli, with the following ex-
pressions, shewing how justly he esti-
mated the opposition they encounter-
ed : — " You almost make me laugh by
saying that these clear observations are
sufficient to convince the most obstinate :
it seems you have yet to learn that long
ago the observations were enough to
convince those who are capable of rea-
soning, and those who wish to learn
the truth ; but that to convince the ob-
stinate, and those who care for nothing
beyond the vain applause of the stupid
and senseless vulgar, not even the testi-
mony of the stars would suffice, were
they to descend on earth to speak for
themselves. Let us then endeavour to
procure some knowledge for ourselves,
and rest contented with this sole satis-
faction ; but of advancing in popular
opinion, or gaining the assent of the
book-philosophers, let us abandon both
the hope and the desire."

CHAPTER IX.
Account of the Academia Lincea — Del

Cimento— Royal Society.
GALILEO'S resignation of the mathema-
tical professorship at Padua occasioned

"*~B vii. v. 364. Other passages maybe examined
in B. i. 286 ; in. 565—590, 722—733 ; iv, 589 ; v.
2b'l, 414; vii. 577; via. 1—178.

much dissatisfaction to all -those who
were connected with that university.
Perhaps not fully appreciating his de-
sire of returning to his native country,
and the importance to him and to the
scientific world in general, of the com-
plete leisure which Cosmo secured to
him at Florence, (for by the terms of his
diploma he was not even required to re-
side at Pisa, nor to give any lectures,
except on extraordinary occasions, to
sovereign princes and other strangers of
distinction,) the Venetians remembered
only that they had offered him an ho-
nourable asylum when almost driven
from Pisa ; that they had increased his
salary to four times the sum which any
previous professor had enjoyed ; and,
finally, by an almost unprecedented de-
cree, that they had but just secured him
in his post during the remainder of his
life. Many took such offence as to
refuse to have any further communica-
tion with him ; and Sagredo, a constant
friend of Galileo, wrote him word that
he had been threatened with a similar
desertion unless he should concur in
the same peremptoiy resolution, which
threats, however, Sagredo, at the same
time, intimates his intention of braving.
Early in the year 1611, Galileo made
his first appearance in Rome, where he
was received with marks of distinguished
consideration, and where all ranks were
•eager to share the pleasure of contem-
plating the new discoveries. " Whether
we consider cardinal, prince, or prelate,
he found an honourable reception from
them all, and had their palaces as open
and free to him as the houses of his pri-
vate friends."* Among other distinc-
tions he was solicited to become a mem-
ber of the newly-formed philosophical
society, the once celebrated Academia
Lincea, to which he readily assented.
The founder of this society was Federigo
Cesi.the Marchese di Monticelli, a young
Roman nobleman, the devotion of whose
time and fortune to the interests of sci-
ence has not been by any means re-
warded with a reputation commensurate
with his deserts. If the energy of his
mind had been less worthily employed
than in fostering the cause of science and
truth, and in extending the advantages
of his birth and fortune to as many as
were willing to co-operate with him, the
name of Federigo Cesi might have ap-
peared more prominently on the page of
history. Cesi had scarcely completed

• Salusbury, Math. Coll.

GALILEO.

37

his 18th year, when, in 1603, he formed
the plan of a philosophical society,
which in the first instance consisted
only of himself and three of his most
intimate friends, Hecke, a Flemish phy-
sician, Stelluti, and Anastasio de Filiis.
Cesi's father, the Duca d' Acquasparta,
who was of an arbitrary and extravagant
temper, considered such pursuits and
associates as derogatory to his son's
rank; he endeavoured to thwart the de-
sign by the most violent and unjusti-
fiable proceedings, in consequence of
which, Cesi in the beginning of 1605
privately quitted Rome, Hecke was
obliged to leave Italy altogether from
fear of the Inquisition, which was excited
against him, and the academy was for
a time virtually dissolved. The details
of these transactions are foreign to the
present narrative : it will be enough to
mention that, in 1609, Cesi, who had
never altogether abandoned his scheme,
found the opposition decaying which he
at first experienced, and with better suc-
cess he renewed the plan which he had
sketched six years before. A few extracts
from the Regulations will serve to shew
the spirit ill which this distinguished
society was conceived : —

" The Lyncean Society desires for its
academicians, philosophers eager for
real knowledge, who will give them-
selves to the study of nature, and espe-
cially to mathematics ; at the same time
it will not neglect the ornaments of ele-
gant literature and philology, which
like a graceful garment adorn the whole
body of science. — In the pious love of
wisdom, and to the praise of the most
good and most high God, let the Lyn-
ceans give their minds, first to obser-
vation and reflection, and afterwards
to writing and publishing. — It is not
within the Lyncean plan to find leisure
for recitations and declamatory assem-
blies ; the meetings will neither be fre-
quent nor full, and chiefly for transact-
ing the necessary business of the society:
but those who wish to enj oy such exercises
will in no respect be hindered, provided
they attend them as accessory studies,
decently and quietly, and without
making promises and professions of
how much they are about to do. For
there is ample philosophical employment
for everyone by himself, particularly
if pains are taken in travelling and in
the observation of natural phenomena,
and in the book of nature which every
one has at home, that is to say, the
heavens and the earth ; and enough may

be learned from the habits of constant
correspondence with each other, and
alternate offices of counsel and assist-
ance.— Let the first fruits of wisdom be
love ; and so let the Lynceans love each
other as if united by the strictest ties,
nor suffer any interruption of this sin-
cere bond of love and faith, emanating
from the source of virtue and philosophy.
— Let them add to their names the title
of Lyncean, which has been advisedly
chosen as a warning and constant sti-
mulus, especially when they write on
any literary subject, also in their private
letters to their associates, and in gene-
ral when any work comes from them
wisely and well performed. — The Lyn-
ceans will pass over in silence all poli
tical controversies and quarrels of every
kind, and wordy disputes, especially
gratuitous ones, which give occasion
to deceit, unfriendliness, and hatred;
like men who desire peace, and seek to
preserve their studies free from molesta-
tion, and to avoid every sort of disturb-
ance. And if any one by command of
his superiors, or from some other ne-
cessity, is reduced to handle such mat-
ters, since they are foreign to physical
and mathematical science, and conse-
quently alien to the object of the Aca-
demy, let them be printed without the
Lyncean name." *

The society which was eventually or-
ganized formed but a very trifling part
of the comprehensive scheme which
Cesi originally proposed to himself; it
had been his wish to establish a scien-
tific Order which should have corre-
sponding lodges in the principal towns of
Europe, and in other parts of the glcrbe,
each consisting of not more than five nor
less than three members, besides an un-
limited number of Academicians not
restricted to any particular residence or
regulations. The mortifications and
difficulties to which he was subjected
from his father's unprincipled behaviour,
render it most extraordinary and admi-
rable that he should have ventured to
undertake even so much as he actually
carried into execution. He promised to
furnish to the members of his society
such assistance as they might require in
the prosecution of their respective re-
searches, and also to defray the charges

* Perhaps it was to deprecate the hostility of the
Jesuits that, at the close of these Regulations, the
Lyuceans are directed to address their prayers,
among other Saints, especially to Ignatius Loyola,
as to one who greatly favoured the interests of learn-
ing. Odescalchi, Memorie dell' Acad. de' Lincei,
Roma. 1806.

38

GALILEO.

of publishing such of their" works as
should be thought worthy of appearing
with the common sanction. Such libe-
ral offers were not likely to meet with
an unfavourable reception : they were
thankfully accepted by many well quali
fied to carry his design into execution,
and Cesi was soon enabled formally to
open his academy, the distinctive title
of which he borrowed from the Lynx,
with reference to the piercing sight
which that animal has been supposed to
possess. This quality seemed to him an
appropriate emblem of those which he
desired to find in his academicians, for
the purpose of investigating the secrets
of nature ; and although, at the present
day, the name may appear to border on
the grotesque, it was conceived in the
spirit of the age, and the fantastic names
of the numberless societies which were
rapidly formed in various parts of Italy
far exceed whatever degree of quaint-
ness may be thought to belong to the
Lyncean name. The Inflamed — the
Transformed — the Uneasy — the Hu-
morists— the Fantastic — the Intricate —
the Indolent — the Senseless — the Un-
deceived— the Valiant — the ^Etherial
Societies are selected from a vast num-
ber of similar institutions, the names of
which, now almost their sole remains,
are collected by the industry of Morhof
and Tiraboschi*. The Humorists are
named by Morhof as the only Italian
philosophical society anterior to the
Lynceans; their founder was Paolo
Mancino, and the distinctive symbol
which they adopted was rain dropping
from a cloud, with the motto Redit ag-
mine duld ; — their title is derived from
the same metaphor. The object of their
union appears to have been similar to
that of the Lynceans, but they at no
time attained to the celebrity to which
Cesi's society rose from the moment of
its incorporation. Cesi took the presi-
dency for his life, and the celebrated
Baptista Porta was appointed vice pre-
sident at Naples. Stelluti acted as the
legal representative of the society, with
the title of procuratore. Of the other
two original members Anastasio de Filiis
was dead, and although Hecke returned
to Italy in 1614, and rejoined the Aca-
demy, yet he was soon afterwards struck
off the list in consequence of his lapsing
into insanity. Among the academicians
we find the names of Galileo, Fabio Co-

* PolyhistorLiterarius, &e.— Storia della Letterat.
Ital. The still existing: society of Chaff, more pene-
rally known by its Italian title, DeflaCrusca, belongs
to the same period.

lonna, Lucas Valeric, Guiducci, Welser,
Giovanni Fabro, Terrentio, Vira^nio Ce-
sarini, Ciampoli, Molitor, Cardinal Bar-
berino, (nephew of Pope Urban VIII.)
Stelliola, Salviati, &c.

The principal monument still remain-
ing of the zeal and industry to which
Cesi incited his academicians is the
Phytobasanos, a compendium of the
natural history of Mexico, which must
be considered a surprising performance
for the times in which it appeared. It
was written by a Spaniard named Her-
nandez ; and Reecho, who often has the
credit of the whole work, made great ad-
ditions to it. During fifty years the ma-
nuscript had been neglected, when Cesi
discovered it, and employed Terrentio,
Fabro, and Colonna, all Lynceans, to
publish it enriched with their notes and
emendations. Cesi himself published
several treatises,two of which are extant ;
his Tdbulce Phytosophicce, and a Disser-
tation on Bees entitled Apiarium, the
only known copy of which last is in the
library of the Vatican. His great work,
Theatrum Natures, was never printed ;
a circumstance which tends to shew that
he did not assemble the society round
him for the purpose of minist'ering to his
own vanity, but postponed the publica-
tion of his own productions to the la-
bours of his coadjutors. This, and many
other valuable works belonging to the
academy existed in manuscript till lately
in the Albani Library at Rome. Cesi
collected, not a large, but an useful li-
brary for the use of the academy, (which
was afterwards augmented on the pre-
mature death of Cesarini by the dona-
tion of his books) ; he filled a botanical
garden with the rarer specimens of
plants, and arranged a museum of natu-
ral curiosities ; his palace at Rome was
constantly open to the academicians ; his
purse and his influence were employed
with equal liberality in their service.

Cesi's death, in 1632, put a sudden
stop to the prosperity of the society, a
consequence which may be attributed
to the munificence with which he had
from the first sustained it: no one
could be found to fin his place in the
princely manner to which the academi-
cians were accustomed, and the society,
after lingering some years under the no-
minal patronage of Urban VIII., gra-
dually decayed, till, by the death of its
principal members, and dispersion of the
rest, it became entirely extinct*. Bianchi,

* F. Colonnae Phytobasanus Jano Planco Auctore.
Florent, 1?44.

GALILEO.

39

whose sketch of the academy was
almost the only one till the appearance
of Odescalchi's history, made an attempt
to revive it in the succeeding century,
but without any permanent effect. A
society under the same name has been
formed since 1784, and is still flourish-
ing in Rome. Before leaving the sub-
ject it may be mentioned, that one of the
earliest notices that Bacon's works were
known in Italy is to be found in a letter
to Cesi, dated 1625 ; in which Pozzo,
who had gone to Paris with Cardinal
Barberino, mentions having seen them
there with great admiration, and sug-
gests that Bacon would be a fit person
to be proposed as a member of their
society. After Galileo's death, three of
his principal followers, Viviani, Torri-
celli, and Aggiunti formed the plan of es-
tablishing a similar philosophical society,
and though Aggiunti and Torricelli died
before the scheme could be realized,
Viviani pressed it forward, and, under
the auspices of Ferdinand II., formed a
society, which, in 1657, merged in the
famous Academia del Cimento, or Ex-
perimental Academy. This latter held
its occasional meetings at the palace of
Ferdinand's brother, Leopold de' Medici :
it was composed chiefly, if not entirely,
of Galileo's pupils and friends. During
the few years that this society lasted, one
of the principal objects of which was
declared to be the repetition and deve-
lopement of Galileo's experiments, it
kept up a correspondence with the prin-
cipal philosophers in every part of Eu-
rope, but when Leopold was, in 1666,
created a cardinal, it appears to have
been dissolved, scarcely ten years after
its institutiont. This digression may be
excused in favour of so interesting an
establishment as the Academia Lincea,
which preceded by half a century the
formation of the Royal Society of Lon-
don, and Acade" mie Franchise of Paris.

These latter two are mentioned toge-
ther, probably for the first time, by Sa-
lusbury. The passage is curious in an his-
torical point of view, and worth extract-
ing:— "In imitation of these societies,
Paris and London have erected theirs of
Les Beaux Esprits, and of the Virtuosi :
the one by the countenance of the most
eminent Cardinal Richelieu, the other by
the royal encouragement of Ms sacred
Majesty that now is. The Beaux Esprits
have published sundry volumes of their
moral and physiological conferences,

* Nelli Saggio di Storia Literaria Fiorentina,
Lucca, 1759.

with the laws and history of their fellow-
ship; and I hope the like in due time
from our Royal Society; that so such as
envie their fame and felicity, and such
as suspect their ability and candor, may
be silenced and disappointed in their de-
tractions and expectations." *

CHAPTER X.

Spots on the Sun — Essay on Floating
Bodies — Scheiner — Change in Sa-
turn.

GALILEO did not indulge the curiosity
of his Roman friends by exhibiting only
the wonders already mentioned, which
now began to lose the gloss of novelty,
but disclosed a new discovery, which ap-
peared still more extraordinary, and, to
the opposite faction, more hateful than
anything of which he had yet spoken.
This was the discovery, which he first
made in the month of March, 1611, of
dark spots on the body of the sun. A
curious fact, and one which well serves to
illustrate Galileo's superiority in seeing
things simply as they are, is, that these
spots had been observed and recorded
centuries before he existed, but, for want
of careful observation, their true nature
had been constantly misapprehended.
One of the most celebrated occasions
was in the year 807 of our era, in which
a dark spot is mentioned as visible on
the face of the sun during seven or eight
days. It was then supposed to be Mer-
cury t. Kepler, whose astronomical
knowledge would not suffer him to over-
look that it was impossible that Mercury
could remain so long in conjunction with
the sun, preferred to solve the difficulty
by supposing that, in Aimoin's original
account, the expression was not octo
dies (eight days), but octoties — a barba-
rous word, which he supposed to have
been written for octies (eight times) ; and
that the other accounts (in which the
number of days mentioned is different)
copying loosely from the first, had both
mistaken the word, and misquoted the
time which they thought they found men-
tioned there. It is impossible to look
on this explanation as satisfactory, but
Kepler, who at that time did not dream
of spots on the sun, was perfectly con-
tented with it. In 1609, he himself ob-
served upon the sun a black spot, which
he in like manner mistook for Mercury,
and unluckily the day, being cloudy, did

* Salisbury's Math. Coll. vol. ii. London, 1664.
•j Aimoini Hist. Francorum. Parisiis. 1567.

40

GALILEO.

not allow him to contemplate it suffici-
ently long to discover his error, which
the slowness of its apparent motion would
soon have pointed out.* He hastened to
publish his supposed observation, but no
sooner was Galileo's discovery of the solar
spots announced, than he, with that
candour which as much as his flighty
disposition certainly characterized him
at all times, retracted his former opinion,
and owned his belief that he had been
mistaken. In fact it is known from the
more accurate theory which we now pos-
sess of Mercury's motions, that it did not
pass over the sun's face at the time when
Kepler thought he perceived it there.

Galileo's "observations were in their
consequences to him particularly unfor-
tunate, as in the course of the contro-
versy in which they engaged him, he first
became personally embroiled with the
powerful party, whose prevailing influ-
ence was one of the chief causes of his
subsequent misfortunes. Before we enter
upon that discussion, it will be proper to
mention another famous treatise which
Galileo produced soon after his return
from Rome to Florence, in 1612. This
is, his Discourse on Floating Bodies,
which restored Archimedes' theory of
hydrostatics, and has, of course, met with
the opposition which few of Galileo's
works failed to encounter. In the com-
mencement, he thought it necessary to
apologize for writing on a subject so dif-
ferent from that which chiefly occupied
the public attention, and declared that he
had been too closely occupied in calcu-
lating the periods of the revolutions of
Jupiter's satellites to permit him to pub-
lish anything earlier. These periods he
had succeeded in determining during the
preceding year, whilst at Rome, and he
now announced them to complete their
circuits, the first in about 1 day, 18£
hours ; the second in 3 days, 13 hours,
20 minutes ; the third in 7 days, 4 hours ;
and the outermost in 16 days, 18 hours.
All these numbers he gave merely as
approximately true, and promised to con-
tinue his observations, for the purpose of
correcting the results. He then adds an
announcement of his recent discovery of
the solar spots, " which, as they change
their situation, offer a strong argument,
either that the sun revolves on itself, or
that, perhaps, other stars, like Venus and
Mercury, revolve about it, invisible at all
other times, on account of the small dis-
tance to which they are removed from

* Mercurius in sole visits. 1609.

him." To this he afterwards subjoined,
that, by continued observation, he had
satisfied himself that these solar spots
were in actual contact with the surface
of the sun, where they are continually
appearing and disappearing ; that their
figures were very irregular, some being
very dark, and others not so black ; that
one would often divide into three or four,
and, at other times, two, three, or more
would unite into one ; besides which,
that they had all a common and regular
motion, with which they revolved ground
with the sun, which turned upon its axis
in about the time of a lunar month.

Having by these prefatory observa-
tions assuaged the public thirst for as-
tronomical novelties, he ventures to in-
troduce the principal subject of the trea-
tise above mentioned. The question of
floating bridges had been discussed at
one of the scientific parties, assembled
at the house of Galileo's friend Salviati,
and the general opinion of the com-
pany appearing to be that the floating
or sinking of a body depended princi-
pally upon its shape, Galileo undertook
to convince them of their error. If he
had not preferred more direct arguments,
he might merely have told them that in
this instance they were opposed to their
favourite Aristotle, whose words are very
unequivocal on the point in dispute.
" Form is not the cause why a body
moves downwards rather than upwards,
but it does affect the swiftness with
which it moves ; " * which is exactly the
distinction which those who called them-
selves Aristotelians were unable to per-
ceive, and to which the opinions of Aris-
totle himself were not always true. Ga-
lileo states the discussion to have imme-
diately arisen from the assertion of some
one in the company, that condensation is
the effect of cold, and ice was mentioned
as an instance. On this, Galileo observed,
that ice is rather water rarefied than con-
densed, the proof of which is, that ice
always floats upon water/}- It was re-
plied, that the reason of this phenomenon
was, not the superior lightness of the
ice, but its incapacity, owing to its flat
shape, to penetrate and overcome the
resistance of the water. Galileo denied
this, and asserted that ice of any shape
would float upon water, and that, if a

i * De Coelo. lib. 4.

t For a discussion of this singular phenomenon,
see Treatise on Heat, p. 12 ; and it is worth while to
remark in passing, what an admirable instance it
affords of Galileo's instantaneous abandonment of a
theory so soon as it became inconsistent with ex-
periment.

GALILEO.

41

flat piece of ice were forcibly taken to
the bottom, it would of itself rise again
to the surface. Upon this assertion it
appears that the conversation became so
clamorous, that Galileo thought it perti-
nent to commence his Essay with the
following observation on the advantage
of delivering scientific opinions in writ-
ing, " because in conversational argu-
ments, either one or other party, or per-
haps both, are apt to get overwarm, and
to speak overloud, and either do not
suffer each other to be heard, or else,
transported with the obstinacy of not
yielding, wander far away from the ori-
ginal proposition, and confound both
themselves and their auditors with the
novelty and variety of their assertions."
After this gentle rebuke he proceeds with
his argument, in which he takes occa-
sion to state the famous hydrostatical
paradox, of which the earliest notice is
to be found in Stevin's works, a contem-
porary Flemish engineer, and refers it to
a principle on which we shall enlarge in
another chapter. He then explains the
true theory of buoyancy, and refutes the
false reasoning on which the contrary
opinions were founded, with a variety of
experiments.

The whole value and interest of expe-
rimental processes generally depends on
a variety of minute circumstances, the
detail of which would be particularly
unsuited to a sketch like the present
one, For those who are desirous of be-
coming more familiar with Galileo's
mode of conducting an argument, it is
fortunate that such a series of experi-
ments exists as that contained in this
essay ; experiments which, from their
simplicity, admit of being for the most
part concisely enumerated, and at the
same time possess so much intrinsic
beauty and characteristic power of forc-
ing conviction. They also present an ad-
mirable specimen of the talent for which
Galileo was so deservedly famous, of in-
venting ingenious arguments in favour
of his adversaries' absurd opinions before
he condescended to crush them, shew-
ing that nothing but his love of truth
stood in the way of his being a more
subtle sophist than any amongst them.
In addition to these reasons for giving
these experiments somewhat in detail,
is the fact that all explanation of one of
the principal phenomena to which they
allude is omitted in many more modern
treatises on Hydrostatics ; and in some
it is referred precisely to the false doc-
trines here confuted.

The marrow of the dispute is included
in Galileo's assertion, that "The diversity
of figure given to any solid cannot be in
any way the cause of its absolutely sink-
ing or floating ; so that if a solid, when
formed for example into a spherical
figure, sinks or floats in the water, the
same body will sink or float in the same
water, when put into any other form.
The breadth of the figure may indeed
retard its velocity, as well of ascent as
descent, and more and more according
as the said figure is reduced to a greater
breadth and thinness ; but that it may
be reduced to such a form as absolutely
to put an end to its motion in the same
fluid, I hold to be impossible. In this
I have met with great contradictors
who, producing some experiments, and
in particular a thin board of ebony,
and a ball of the same wood, and shew-
ing that the ball in water sinks to the
bottom*, and that the board if put lightly
on the surface floats, have held and con-
firmed themselves in their opinion with
the authority of Aristotle, that the cause
of that rest is the breadth of the figure,
unable by its small weight to pierce and
penetrate the resistance of the water's
thickness, which is readily overcome by
the other spherical figure." — For the pur-
pose of these experiments, Galileo re-
commends a substance such as wax,
which may be easily moulded into any
shape, and with which, by the addition
of a few filings of lead, a substance may
be readily made of any required specific
gravity. He then declares that if a ball
of wax of the size of an orange, or bigger,
be made in this manner heavy enough
to sink to the bottom, but so lightly that
if we take from it only one grain of lead
it returns to the top ; and if the same
wax be afterwards moulded into a broad
and thin cake, or into any other figure,
regular or irregular, the addition of the
same grain of lead will always make it
sink, and it will again rise when we re-
move the lead from it. — " But methinks
I hear some of the adversaries raise a
doubt upon my produced experiment:
and, first, they offer to my consideration
that the figure, as a figure simply, and
disjunct from the matter, works no effect,
but requires to be conjoined with the
matter ; and, moreover, not with every
matter, but with those only wherewith
it may be able to execute the desired
operation. Just as we see by experience

* Ebony is one of the few -\voods heavier than
water. See Treatise on Hydrostatics.

GALILEO.

that an acute and sharp angle is more
apt to cut than an obtuse ; yet always
provided that both one and the other are
joined with a matter fit to cut, as for in-
stance, steel. Therefore a knife with a
fine and sharp edge cuts bread or wood
with much ease, which it will not do if
the edge be blunt and thick ; but if, in-
stead of steel, any one will take wax and
mould it into a knife, undoubtedly he will
never learn the effects of sharp and
blunt edges, because neither of them
will cut ; the wax being unable, by reason
of its flexibility, to overcome the hard-
ness of the wood and bread. And there-
fore, applying the like discourse to our
argument, they say that the difference of
figure will shew different effects with
regard to floating and sinking, but not
conjoined with any kind of matter, but
only with those matters which by their
weight are able to overcome the visco-
sity of the water (like the ebony which
they have selected) ; and he that will
select cork or other light wood to form
solids of different figures, would in vain
seek to find out what operation figure
has in sinking or floating, because all
would swim, and that not through any
property of this or that figure, but
through the debility of the matter."

" When I begin to examine one by one
all the particulars here produced, I allow
not only that figures, simply as such, do
not operate in natural things, but also that
they are never separated from fehe corpo-
real substance, nor have I ever alleged
them to be stript of sensible matter:
and also 1 freely admit, that in our en-
deavours to examine the diversity of
accidents which depend upon the variety
of figures, it is necessary to apply them
to matters which obstruct not the various
operations of those various figures. I
admit and grant that I should do very ill
if 1 were to try the influence of a sharp
edge with a knife of wax, applying it to
cut an oak, because no sharpness in wax
is able to cut that very hard wood. But
yet, such an experiment of this knife
would not be beside the purpose to cut
curded milk, or other very yielding mat-
ter; nay, in such matters, the wax is
more convenient than steel for finding
the difference depending on the acute-
ness of the angles, because milk is cut
indifferently with a razor, or a blunt
knife. We must therefore have regard
not only to the hardness, solidity, or
weight of the bodies which, under dif-
ferent figures, are to divide some mat-
ters asunder; but also, oji the other

hand, to the resistance of the matter to
be penetrated. And, since I have chosen
a matter which does penetrate the resist-
ance of the water, and in all figures de-
scends to the bottom, my antagonists
can charge me with no defect ; nor (to
revert to their illustration) have I at-
tempted to test the efficacy of acuteness
by cutting with matters unable to cut.
I subjoin withal, that all caution, dis-
tinction, and election of matter would
be superfluous and unnecessary, if the
body to be cut should not at all resist
the cutting : if the knife were to be used
in cutting a mist, or smoke, one of paper
would serve the purpose as well as one of
Damascus steel ; and I assert that this is
the case with water, and that there is not
any solid of such lightness or of such a
figure, that being put on the water it
will not divide and penetrate its thick-
ness ; and if you will examine more
carefully your thin boards of wood, you
will see that they have part of their
thickness under water ; and, moreover,
you will see that the shavings of ebony,
stone, or metal, when they float, have
not only thus broken the continuity of
the water, but are with all their thick-
ness under the surface of it ; and that
more and more, according as the float-
ing substance is heavier, so that a thin
floating plate of lead will be lower than
the surface of the surrounding water by
at least twelve times the thickness of the
plate, and gold will dive below the level
of the water almost twenty times the
thickness of the plate, as I shall shew
presently."

In order to illustrate more clearly
the non-resistance of water to pene-
tration, Galileo then directs a cone
to be made of wood or wax, and as-
serts that when it floats, either with its
base or point in the water, the solid
content of the part immersed will be the
same, although the point is, by its shape,
better adapted to overcome the resist-
ance of the water to division, if that
were the cause of the buoyancy. Or the
experiment may be varied by tempering
the wax with filings of lead, till it sinks
in the water, when it will be found that
in any figure the same cork must be
added to it to raise it to the surface. —
" This silences not my antagonists ; but
they say that all the discourse hitherto
made by me imports little to them, and
that it serves their turn, that they have
demonstrated in one instance, and in such
manner and figure as pleases them best,
namely, in a board and a ball of ebony,

GALILEO.

43

that one, when put into the water, sinks
to the bottom, and that the other stays
to swim at the top; and the matter
being the same, and the two bodies dif-
fering in nothing but in figure, they
affirm that with all perspicuity they
have demonstrated and sensibly mani-
fested what they undertook. Neverthe-
less I believe, and think I can prove
that this very experiment proves nothing
against my theory. And first it is
false that the ball sinks, and the board
not ; for the board will sink too, if you
do to both the figures as the words of
our question require ; that is, if you put
them both in the water ; for to be in
the water implies to be placed in the
water, and by Aristotle's own definition
of place, to be placed imports to be en-
vironed by the surface of the am,bient
body ; but when my antagonists shew
the floating board of ebony, they put it
not into the water, but upon the water ;
where, being detained by a certain im-
pediment (of which more anon) it is sur-
rounded, partly with water, partly with
air, which is contrary to our agreement,
for that was that the bodies should be
in the water, and not part in the water,
part in the air. I will not omit another
reason, founded also upon experience,
and, if I deceive not myself, conclu-
sive against the notion that figure, and
the resistance of the water to" penetra-
tion have anything to do with the buoy-
ancy of bodies. Choose a piece of wood
or other matter, as for instance walnut-
wood, of which a ball rises from the
bottom of the water to the surface more
slowly than a ball of ebony of the same
size sinks, so that clearly the ball of
ebony divides the water more readily in
sinking than does the walnut in rising.
Then take a board of walnut-tree equal
to and like the floating ebony one of
my antagonists ; and if it be true that
this latter floats by reason of the figure
being unable to penetrate the water, the
other of walnut-tree, without all ques-
tion, if thrust to the bottom ought to
stay there, as having the same impeding
figure, and being less apt to overcome
the said resistance of the water. But if
we find by experience that not only the
thin board, but every other figure of the
same walnut-tree will return to float, as
unquestionably we shall, then I must
desire my opponents to forbear to attri-
bute the floating of the ebony to the
figure of the board, since the resistance
of the water is the same in rising as in
sinking, and the force of ascension of

the walnut-tree is less than the ebony's
force for going to the bottom."

"Now, let us return to the thin plate of
gold or silver, or the thin board of ebony,
and let us lay it lightly upon the water, so
that it may stay there without sinking,
and carefully observe the effect. It will
appear clearly that the plates are a consi-
derable matter lower than the surface of
the water which rises up, and makes a
kind of rampart round them on every
side, in the manner shewn in the an-
nexed figure, in which B D L F repre-

sents the surface of the water, and
A E I O the surface of the plate. But if
it have already penetrated and overcome
the continuity of the water, and is of its
own nature heavier than the water, why
does it not continue to sink, but stop
and suspend itself in that little dimple
that its weight has made in the water ?
My answer is, because in sinking till its
surface is below the water which rises
up in a bank round it, it draws after and
carries along with it the air above it, so
that that which in this case descends and
is placed in the water, is not only the
board of ebony or plate of iron, but a
compound of ebony and air, from which
composition results a solid no longer
specifically heavier than the water, as was
the ebony or gold alone. But, Gentlemen,
we want the same matter; you are to
alter nothing but the shape, "and there-
fore have the goodness to remove this
air, which may be done simply by wash-
ing the upper surface of the board, for
the water having once got between the
board and air will run together, and the
ebony will go to the bottom ; and if it
does not, you have won the day. But
methinks I hear some of my antagonists
cunningly opposing this, and telling me
that they wul not on any account allow
their board to be wetted, because the
weight of the water so added, by making
it heavier than it was before, draws it to
the bottom, and that the addition of new
weight is contrary to our agreement,
which was that the matter should be the
same."

" To this I answer first, that nobody
can suppose bodies to be put into the
water without their being wet, nor do I

44

GALILEO.

wish to do more to the board than you
may do to the ball. Moreover, it is not
true that the board sinks on account of
the weight of the water added in the
washing ; for I will put ten or twenty
drops on the floating board, and so long
as they stand separate it shall not sink ;
but if the board be taken out, and all
that water wiped off, and the whole sur-
face bathed with one single drop, and
put it again upon the water, there is no
question but it will sink, the other water
running to cover it, being no longer
hindered by the air. In the next place
it is altogether false that water can in
any way increase the weight of bodies
immersed in it, for water has no weight
in water, since it does not sink. Now,
just as he who should say that brass
by its own nature sinks, but that when
formed into the shape of a kettle, it ac-
quires from that figure a virtue of lying
in the water without sinking, would say
what is false, because that is not purely
brass which then is put into the water,
but a compound of brass and air ; so is
it neither more nor less false, that a thin
plate of brass or ebony swims by virtue
of its dilated and broad figure. Also I
cannot omit to tell my opponents, that
this conceit of refusing to bathe the sur-
face of the board, might beget an opinion
in a third person of a poverty of argu-
ments on their side, especially as the
conversation began about flakes of ice,
in which it would be simple to require
that the surfaces should be kept dry;
not to mention that such pieces of ice,
whether wet or dry, always float, and
as my antagonists say, because of their
shape.1'

" Some may wonder that I affirm this
power to be in the air of keeping the
plate of brass or silver above water, as
if in a certain sense I would attribute to
the air a kind of magnetic virtue for sus-
taining heavy bodies with which it is
in contact. To satisfy all these doubts,
I have contrived the following experi-
ment to demonstrate how truly the air
does support these solids ; for I have
found, when one of these bodies which
floats when placed lightly on the water,
is thoroughly bathed and sunk to the
bottom, that by carrying down to it a
little air without otherwise touching it
in the least, I am able to raise and carry
it back to the top, where it floats as
before. To this effect I take a ball of
wax, and with a little lead make it just
heavy enough to sink very slowly to the
bottom, taking care that its surface be

quite smooth 'and even. This, if put
gently into the water, submerges almost
entirely, there remaining visible only a
little of the very top, which, so long as
it is joined to the air, keeps the ball
afloat ; but if we take away the contact
of the air by wetting this 'top, the ball
sinks to the bottom, and remains there.
Now to make it return to the surface
by virtue of the air which before sus-
tained it, thrust into the water a glass,
with the mouth downwards, which will
carry with it the air it contains ; and
move this down towards the ball, until
you see by the transparency of the glass
that the air has reached the top of it ;
then gently draw the glass upwards, and
you will see the ball rise, and afterwards
stay on the top of the water, if you care-
fully part the glass and water without
too much disturbing it*. There is
therefore a certain affinity between the
air and other bodies, which holds them
united, so that they separate not without
a kind of violence, just as between water
and other bodies ; for in drawing them
wholly out of the water, we see the water
follow them, and rise sensibly above the
level before it quits them." Having
established this principle by this exceed-
ingly ingenious and convincing experi-
ment, Galileo proceeds to shew from it
what must be the dimensions of a plate
of any substance which will float as the
wax does, assuming in each case that
we know the greatest height at which
the rampart of water will stand round
it. In like manner he shows that a py-
ramidal or conical figure may be made
of any substance, such that by help of
the air, it shall rest upon the water with-
out wetting more than its base ; and
that we may so form a cone of any sub-
stance that it shall float if placed gently
on the surface, with its point downwards,
whereas no care or pains will enable it
to float, with its base downwards, owing
to the different proportions of air which
in the two positions remain connected
with it. With this parting blow at his
antagonist's theory we close our ex-
tracts from this admirable essay.

The first elements of the theory of
running waters were reserved for Castelli,
an intimate friend and pupil of Galileo.
On the present occasion, Castelli ap-
peared as the ostensible author of a de-

* In making this very beautiful experiment, it is
best to keep the glass a few seconds in the water, to
give time for the surface of the ball to dry. It will
also succeed with a light needle, if carefully con-
ducted.

GALILEO.

fence against the attacks made by Vin-
cenzio di Grasia and by Lodovico delle
Columbe (the author of the crystalline
composition of the moon) on the ob-
noxious theory. After destroying all the
objections which they produced, the ,
writer tauntingly bids them remember,
that he was merely Galileo's pupil, and
consider how much more effectually
Galileo himself would have confuted
them, had he thought it worth while. It
was not known till several years after
his death, that this Essay was in fact
written by Galileo himself.*

These compositions merely occupied
the leisure time which he could withhold
from the controversy on the solar spots
to which we have already alluded. A
German Jesuit named Christopher
Scheiner, who was professor of mathe-
matics at Ingolstadt, in imitation of Ga-
lileo had commenced a series of obser-
vations on them, but adopted the theory
which, as we have seen, Galileo had exa-
mined and rejected, that these spots are
planets circulating at some distance from
the body of the sun. The same opinion
had been taken up by a French astrono-
mei, who in honour of the reigning fa-
mily called them Borbonian stars.
Scheiner promulgated his notions in
three letters, addressed to their common
friend Welser, under the quaint signature
of " Apelles latenspost tabulam." Galileo
replied to Schemer's letters by three
others, also addressed to Welser, and
although the dispute was carried on amid
mutual professions of respect and es-
teem, it laid the foundation of the total
estrangement which afterwards took
place between the two authors. Galileo's
part of this controversy was published
at Rome by the Lyncean Academy in
1613. To the last of his letters, writ-
ten in December, 1612, is annexed a
table of the expected positions of Ju-
piter's satellites during the months of
March and April of the following year,
which, imperfect as it necessarily was,
cannot be looked upon without the
greatest interest.

In the same letter it is mentioned that
Saturn presented a novel appearance,
which, for an instant, almost induced
Galileo to mistrust the accuracy of his
earlier observations. The lateral ap-
pendages of this planet had disappeared,
and the accompanying extract will show
the uneasiness which Galileo could not
conceal at the sight of this phenome-

.* Nelli. Saggio di Stor. Liter, Fiorent.

non, although it is admirable to see
the contempt with which, even in that
trying moment, he expresses his con-
sciousness that his adversaries were
unworthy of the triumph they appeared
on the point of celebrating. — " Looking
on Saturn within these few days, 1 found
it solitary, without the assistance of its
accustomed stars, and in short, per-
fectly round and defined like Jupiter, and
such it still remains. Now what can
be said of so strange a metamorphosis ?
are perhaps the two smaller stars con-
sumed, like the spots on the sun ? have
they suddenly vanished and fled ? or has
Saturn devoured his own children? or
was the appearance indeed fraud and
illusion, with which the glasses have for
so long,a time mocked me, and so many
others who have often observed with me. J
Now perhaps the time is come to revive '
the withering hopes of those, who, guided
by more profound contemplations, have
fathomed all the fallacies of the new ob-
servations and recognised their impossi-
bility ! 1 cannot resolve what to say in
a chance so strange, so new, and so un-
expected ; the shortness of the time, the
unexampled occurrence, the weakness of
my intellect, and the terror of being mis-
taken, have greatly confounded me."
These first expressions of alarm are not
to be wondered at; however, he soon
recovered courage, and ventured to fore-
tel the periods at which the lateral stars
would again show themselves, protest-
ing at the same time, that he was in no
respect to be understood as classing this
prediction among the results which de-
pend on certain principles and sound
conclusions, but merely on some conjec-
tures which appeared to him probable.
From one of the Dialogues on the Sys-
tem, we learn that this conjecture was,
that Saturn might revolve upon his axis,
but the period which he assumed is very
different from the true one, as might be
expected from its being intended to ac-
count for a phenomenon of which Galileo
had not rightly apprehended the cha-
racter.

He closed this letter with renewed
professions of courtesy and friendship
towards Apelles, enjoining Welser not
to communicate it without adding his
excuses, if he should be thought to dis-
sent too violently from his antagonist's
ideas, declaring that his only object was
the discovery of truth, and that he had
freely exposed his own opinion, which he
was still ready to change, so soon as his
errors should be made manifest to him ;

46

GALILEO.

and that he would consider himself under
special obligation to any one who would
be kind enough to discover and correct
them. These letters were written from
the villa of his friend Salviati at Selve
near Florence, where he passed great
part of his time, particularly during his
frequent indispositions, conceiving that
the air of Florence was prejudicial to him.
Cesi was very anxious for their appear-
ance, since they were (in his own words)
so hard a morsel for the teeth of the
Peripatetics, and he exhorted Galileo, in
the name of the society, " to continue
to give them, and the nameless Jesuit,
something to gnaw."

CHAPTER XI.

Letter to Christina, Arch-Duchess of
Tuscany — Caccini — Galileo revisits
Rome — Inchoffer — Problem of Lon-
gitudes.

THE uncompromising boldness with
which Galileo published and supported
his opinions, with little regard to the
power and authority of those who ad-
vocated the contrary doctrines, had
raised against Mm a host of enemies,
who each had objections to him peculiar
to themselves, but who now began to
perceive the policy of uniting their
strength in the common cause, to crush
if possible so dangerous an innovator.
All the professors of the old opinions,
who suddenly found the knowledge on
which their reputation was founded
struck from under them, and who could
not reconcile themselves to their new
situation of learners, were united against
him ; and to this powerful cabal was
now added the still greater influence of
the Jesuits and pseudo-theological party,
who fancied they saw in the spirit of
Galileo's writings the same inquisitive
temper which they had already found
so inconvenient in Luther and his ad-
herents. The alarm became greater
every day, inasmuch as Galileo had
succeeded in training round him a nu-
merous band of followers who all ap-
peared imbued with the same dangerous
spirit of innovation, and his favourite
scholars were successful candidates for
professorships in many of the most cele-
brated universities of Italy.

At the close of 1 6 13, Galileo addressed
a letter to his pupil, the Abbe Castelli,
in which he endeavoured to shew that
there is as much difficulty in reconciling
the Ptolemaic as the Copernican system
of the world with the astronomical ex-

pressions contained in the Scriptures ,
and asserted, that the object of the Scrip-
tures not being to teach astronomy, suoh
expressions are there used as would be
intelligible and conformable to the vulgar
belief, without regard to the true struc-
ture of the universe ; which argument
he afterwards amplified in a letter ad-
dressed to Christina, Grand Duchess of
Tuscany, the mother of his patron
Cosmo. He discourses on this subject
with the moderation and good sense
which so peculiarly characterized him.
"I am," says he, "inclined to believe,
that the intention of the sacred Scriptures
is to give to mankind the information
necessary for their salvation, and which,
surpassing all human knowledge, can by
no other means be accredited than by
the mouth of the Holy Spirit. But I do
not hold it necessary to believe, that the
same God who has endowed us with
senses, with speech, and intellect, in-
tended that we should neglect the use of
these, and seek by other means for
knowledge which they are sufficient to
procure us ; especially in a science like
astronomy, of which so little notice is
taken in the Scriptures, that none of the
planets, except the sun and moon, and,
once or twice only, Venus under the
name of Lucifer, are so much as named
there. This therefore being granted,
methinks that in the discussion of natural
problems we ought not to begin at the
authority of texts of Scripture, but at
sensible experiments and necessary de-
monstrations : for, from the divine word,
the sacred Scripture and nature did
both alike proceed, and I conceive that,
concerning natural effects, that which
either sensible experience sets before
our eyes, or necessary demonstrations do
prove unto us, ought not upon any ac-
count to be called into question, much
less condemned, upon the testimony of
Scriptural texts, which may under their
words couch senses seemingly contrary
thereto.

" Again, to command the very pro-
fessors of astronomy that they of them-
selves see to the confuting of their own
observations and demonstrations, is to
enjoin a thing beyond all possibility of
doing ; for it is not only to command
them not to see that which they do see,
and not to understand that which they
do understand, but it is to order them to
seek for and to find the contraiy of that
which they happen to meet with. I would
entreat these wise and prudent fathers,
that they would with all diligence consi-

GALILEO.

47

der the difference that is between Opinion-
ative and demonstrative doctrines: to
the end that well weighing in their minds
with what force necessary inferences urge
us, they might the better assure them-
selves that it is not in the power of the
professors of demonstrative sciences to
change their opinions at pleasure, and
adopt first one side and then another;
and that there is a great difference be-
tween commanding a mathematician or
a philosopher, and the disposing of a
lawyer or a merchant ; and that the
demonstrated conclusions touching the
things of nature and of the heavens can-
not be changed with the same facility
as the opinions are touching what is
lawful or not in a contract, bargain, or
bill of exchange. Therefore, first let
these men apply themselves to examine
the arguments of Copernicus and others,
and leave the condemning of them as
erroneous and heretical to whom it be-
longeth ; yet let them not hope to find
such rash and precipitous determinations
in the wary and holy fathers, or in the
absolute wisdom of him who cannot err,
as those into which they suffer them-
selves to be hurried by some particular
affection or interest of their own. In
these and such other positions, which
are not directly articles of faith, certainly
no man doubts but His Holiness hath
always an absolute power of admitting
or condemning them, but it is not in
the power of any creature to make them
to be true or false, otherwise than of
their own nature, and in fact they are."
We have been more particular in ex-
tracting these passages, because it has
been advanced by a writer of high re-
putation, that the treatment which
Galileo subsequently experienced was
solely in consequence of his persisting in
the endeavour to prove that the Scrip-
tures were reconcileable with the Co-
pernican theory*, whereas we see here
distinctly that, for the reasons we have
briefly stated, he regarded this as a
matter altogether indifferent and beside
the question.

Galileo had not entered upon this
discussion till driven to it by a most
indecent attack, made on him from the

* Ce philosophe (Galilee) ne fut point persecute
comme bon astronome, mais comme mauvais theo-
logien. C'est son entetement a vsuloir concilier la
Bible avec Copernic qui lui donna des juges. Mais
vingt auteurs, surtout parmi les p-rotestans, ontecrit
quo Galilee fut persecute et imprisonne pour avqir
soutenu que la tcrre tourne autour du solei], que ce
systeme aetecondanne par 1'inquisition comme faux,
errone et contraire a la Bible, &c.— Bergier, Ency-
clopedic Methodique, Paris, 1790, Art. SCIENCES
HUMAINES.

pulpit, by a Dominican friar named.
Caccini, who thought it not unbecoming
his habit or religion to play upon the
words of a Scriptural text for the pur-
pose ^of attacking Galileo and his parti-
sans with more personality*. Galileo
complained formally of Caccini' s con-
duct to Luigi Maraffi the general of the
Dominicans, who apologised amply to
him, adding that he himself was to be
pitied for finding himself implicated in
all the brutal conduct of thirty or forty
thousand monks.

In the mean time, the inquisitors at
Rome had taken the alarm, and were
already, in 1615, busily employed in col-
lecting evidence against Galileo. Lorini,
a brother Dominican of Caccini, had
given them notice of the letter to Cas-
telli of which we have spoken, and the
utmost address was employed to get the
original into their hands, which attempt
however was frustrated, as Castelli had
returned it to the writer. Caccini was
sent for to Rome, settled there with the
title of Master of the Convent of St.
Mary of Minerva, and employed to put
the depositions against Galileo into
order. Galileo was not at this time
fully aware of the machinations against
him, but suspecting something of their
nature, he solicited and obtained per-
mission from Cosmo, towards the end of
1615, to make a journey to Rome, for
the purpose of more directly confronting
his enemies in that city. There was a
rumour at the time that this visit was
not voluntary, but that Galileo had been
cited to appear at Rome. A contempo-
rary declares that he heard this from
Galileo himself : at any rate, in a letter
which Galileo shortly afterwards wrote
to Picchena, the Grand Duke's secre-
tary, he expresses himself well satisfied
with the results of this step, whether
forced or not, and Querenghi thus de-
scribes to the Cardinal d'Este the public
effect of his appearance : " Your Emi-
nence would be delighted with Galileo if
you heard him holding forth, as he often
does, in the midst of fifteen or twenty,
all violently attacking him, sometimes in
one house, sometimes in another. But
he is armed after such fashion that he
laughs all of them to scorn — and even if
the novelty of his opinions prevents en-
tire persuasion, at least he convicts of
emptiness most of the arguments with
which his adversaries endeavour to over-
whelm him. He was particularly admi-

* Viri Galilsei, quid statis adspicientes in ccelora,
Acts I. II.

GALILEO.

rable on Monday last, in the house of
Signor Frederico Ghisilieri; and what
especially pleased me was, that before
replying to the contrary arguments-, he
amplified and enforced them with new
grounds of great plausibility, so as to
leave his adversanes in a more ridicu-
lous plight when he afterwards over-
turned them all."

Among the malicious stories which
were put into circulation, it had been
said, that the Grand Duke had with-
drawn his favour, which emboldened
many, who would not otherwise have
ventured on such open opposition, to
declare against Galileo. His appearance
at Rome, where he was lodged in the
palace of Cosmo's ambassador, and
whence he kept up a close correspon-
dence with the Grand Duke's family,
put an immediate stop to rumours of
this kind. In little more than a month
he was apparently triumphant, so far as
regarded himself ; but the question now
began to be agitated whether the whole
system of Copernicus ought not to be
condemned as impious and heretical.
Galileo again writes to Picchena, " so
far as concerns the clearing of my own
character, I might return home im-
mediately ; but although this new ques-
tion regards me no more than all those
who for the last eighty years have sup-
ported these opinions both in public and
private, yet, as perhaps I may be of
some assistance in that part of the dis-
cussion which depends on the knowledge
of truths ascertained by means of the
sciences which I profess, I, as a zealous
and Catholic Christian, neither can nor
ought to withhold that assistance which
my knowledge affords ; and this business
keeps me sufficiently employed." De
Lambre, whose readiness to depreciate
Galileo's merit we have already noticed
and lamented, sneeringly and ungrate-
fully remarks on this part of his life, that
" it was scarcely worth while to compro-
mise his tranquillity and reputation, in
order to become the champion of a
truth which could not fail every day to
acquire new partisans by the natural
effect of the progress of enlightened
opinions." We need not stop to con-
sider what the natural effects might
have been if none had at any time been
found who thought their tranquillity
worthily offered up in such a cause.

It has been hinted by several, and is
indeed probable, that Galileo's stay at
Rome rather injured the cause (so far
as provoking the inquisitorial censures
could injure it) which it was his earnest

desire to serve, for we cannot often
enough repeat the assertion, that it was
not the doctrine itself, so much as the
free, unyielding manner in which it was
supported, which was originally obnox-
ious. Copernicus had been allowed to
dedicate his great work to Pope Paul III.,
and from the time of its first appearance
under that sanction in 1543, to the year
1616, of which we are now writing, this
theory was left in the hands of mathe-
maticians and philosophers, who alter-
nately attacked and defended it without
receiving either support or molestation
from ecclesiastical decrees. But this
was henceforward no longer the case,
and a higher degree of importance was
given to the controversy from the reli-
gious heresies which were asserted to
be involved in the new opinions. We
have already given specimens of the so
called philosophical arguments brought
against Copernicus ; and the reader
may be curious to know the form of the
theological ones. Those which we se-
lect are taken from a work, which
indeed did not come forth till the time
of Galileo's third visit to Rome, but it is
relative to the matter now before us, as
it professed to be, and its author's party
affected to consider it, a complete refu-
tation of the letters to Castelli and the
Archduchess Christina*.

It was the work of a Jesuit, Melchior
Inchoffer, and it was greatly extolled by
his companions, " as differing so entirely
from the pruriency of the Pythagorean
writings." He quotes with approbation
an author who, first referring to the
first verse of Genesis for an argument
that the earth was not created till after
the heavens, observes that the whole
question is thus reduced to the exami-
nation of this purely geometrical diffi-
culty— In the formation of a sphere, does
the centre or circumference first come
into existence ? If the latter (which we
presume Melchior' s friend found good
reason for deciding upon), the conse-
quence is inevitable. The earth is in the
centre of the universe.

It may not be unprofitable to contrast
the extracts which we have given from
Galileo's letters on the same subject with
the following passage, which appears
one of the most subtle and argumen-

* Tractatus Syllepticns. Roma;, "1633. The
title-page of this remarkable production is decorated
with an emblematical figure, representing the earth
included in a triangle ; and in the three corner*,
grasping the globe with their fore feet, are placed
three bees, the arms of Pope Urban VIII. who
condemned Galileo and his writings. The motto
is " Hisjixa quiescit," ."Fixed by these it is at
rest."

GALILEO.

49

tative which is to be found in Melchior's
book. He professes to be enumerating;
and refuting the principal arguments
which the Copernicans adduced for
the motion of the earth. " Fifth argu-
ment. Hell is in the centre of the earth,
and in it is a fire tormenting the damned ;
therefore it is absolutely necessary that
the earth is moveable. The antecedent
is plain." (Inchoffer then quotes a
number of texts of Scripture on which,
according to} him, the Copernicans re-
lied in proof of this part of the argu-
ment.) "The consequent is proved:
because fire is the cause of motion,
for which reason Pythagoras, who,
as Aristotle reports, puts the place of
punishment in the centre, perceived
that the earth is animate and en-
dowed with action. I answer, even
allowing that hell is in the centre of the
earth, and a fire in it, I deny the conse-
quence : and for proof I say, if the ar-
gument is worth any thing, it proves
also that lime-kilns, ovens, and fire-grates
are animated and spontaneously move-
able. I say, even allowing that hell is
in the centre of the earth : for Gregory,
book 4, dial. chap. 42, says, that he dare
not decide rashly on this matter, although
he thinks more probable the opinion of
those who say that it is under the earth.
St. Thomas, in Opusc. 10, art. 31, says :
Where hell is, whether in the centre of
the earth or at the surface, does not
in my opinion, relate to any article of
faith ; and it is superfluous to be solici-
tous about such things, either in assert-
ing or denying them. And Opusc. 1 1 ,
art 24, he says, that it seems to him
that nothing should be rashly asserted
on this matter, particularly as Augustin
thinks that nobody knows where it is ;
but I do not, says he, think that it is in
the centre of the earth. 1 should be
loth, however, that it should be hence
inferred by some people that hell is in
the earth, that we are ignorant where hell
is, and therefore that the situation of the
earth is also unknown, and, in conclusion,
that it cannot therefore be the centre of
the universe. The argument shall be
retorted in another fashion : for if the
place of the earth is unknown, it cannot
be said to be in a great circle, so as to
be moved round the sun. Finally I say
that in fact it is known where the earth
is."

It is not impossible that some per-
sons adopted the Copernican theory,
from an affectation of singularity and
freethinking, without being able to give

very sound reasons for their change of
opinion, of whom we have an instance
in Origanus, the astrological instructor
of Wallenstein's famous attendant Seni,
who edited his work. His arguments
in favour of the earth's motion are
quite on a level with those advanced on
the opposite side in favour of its immo-
bility ; but we have not found any traces
whatever of such absurdities as these
having been urged by any of the leaders
of that party, and it is far more probable
that they are the creatures of Melchior's
own imagination. At any rate it is
worth remarking how completely he dis-
regards the real physical arguments,
which he ought, in justice to his cause,
to have attempted to controvert. His
book was aimed at Galileo and his ad-
herents, and it is scarcely possible that
he could seriously persuade himself that
he was stating and overturning argu-
ments similar to those by which Galileo
had made so many converts to the opi-
nions of Copernicus. Whatever may be
our judgment of his candour, we may at
least feel assured that if this had in-
deed been a fair specimen of Galileo's
philosophy, he might to the end of his
life have taught that the earth moved
round the sun, or if his fancy led him to
a different hypothesis, he might like the
Abbe Baliani have sent the earth spin-
ning round the stationary moon, and
like him have remained unmolested by
pontifical censures. It is true that Baliani
owned his opinion to be much shaken,
on observing it to be opposed to the de-
cree of those in whose hands was placed
the power of judging articles of faith.
But Galileo's uncompromising spirit of
analytical investigation, and the sober
but invincible force of reasoning with
which he beat down every sophism op-
posed to him, the instruments with which
he worked, were more odious than the
work itself, and the condemnation which
he had vainly hoped to avert was pro-
bably on his very account accelerated.

Galileo, according to his own story,
had in March 1616 a most gracious
audience of the pope, Paul V., which
lasted for nearly an hour, at the end of
which his holiness assured him, that the
Congregation were no longer in a hu-
mour to listen lightly to calumnies
against him, and that so long as he oc-
cupied the papal chair, Galileo might
think himself out of all danger. But
nevertheless he was not allowed to re-
turn home, without receiving formal
notice not to teach the opinions of Co-
E

50

GALILEO.

pernicus, that the sun is in the centre of
the system, and that the earth moves
about it, from that time forward, in any
manner. That these were the literal
orders given to Galileo will be presently
proved from the recital of them in the
famous decree against him, seventeen
years later. For the present, his letters
which we have mentioned, as well as one
of a similar tendency by Foscarini, a Car-
melite friar — a commentary on the book
of Joshua by a Spaniard named Diego
Zuniga — Kepler's Epitome of the Co-
pernican Theory— and Copernicus' sown
work, were inserted in the list of for-
bidden books, nor was it till four years
afterwards, in 1620, that, on reconsidera-
tion, Copernicus was allowed to be read
with certain omissions and alterations
then decided upon.

Galileo quitted Rome scarcely able
to conceal his contempt and indignation.
Two years afterwards this spirit had but
little subsided, for in forwarding to the
Archduke Leopold his Theory of the
Tides, he accompanied it with the fol-
lowing remarks : — " This theory occurred
to me when in Rome, whilst the theolo-
gians were debating on the prohibition
of Copernicus's book, and of the opi-
nion maintained in it of the motion of
the earth, which I at that time believed ;
until it pleased those gentlemen to sus-
pend the book, and declare the opinion
false and repugnant to the Holy Scrip-
tures. Now, as I know how well it be-
comes me to obey and believe the deci-
sions of my superiors, which proceed
out of more profound knowledge than
the weakness of my intellect can attain
to, this theory which 1 send you, which
is founded on the motion of the earth, I
now look upon as a fiction and a dream,
and beg your highness to receive it as
such. But, as poets often learn to prize
the creations of their fancy, so, in like
manner, do I set some value on this
absurdity of mine. It is true that when
I sketched this little work, I did hope
that Copernicus would not, after 80
years, be convicted of error, and I had
intended to develope and amplify it far-
ther, but a voice from heaven suddenly
awakened me, and at once annihilated
all my confused and entangled fancies."
It might have been predicted, from
the tone of this letter alone, that it would
not be long before Galileo would again
bring himself under the censuring notice
of the astronomical hierarchy, and in-
deed he had, so early as 1610, collected
some of the materials for the work which

caused the final explosion, and on which
he now employed himself with as little
intermission as the weak state of his
health permitted.

He had been before this time engaged
in a correspondence with the court of
Spain, on the method of observing lon-
gitudes at sea, for the solution of which
important problem Philip 111. had
ottered a considerable reward, an exam-
ple which has since been followed in our
own and other countries. Galileo had
no sooner discovered Jupiter's satellites,
than he recognized the use which might
be made of them for that purpose, and
devoted himself with peculiar assiduity
to acquiring as perfect a knowledge as
possible of their revolutions. The reader
will easily understand how they were to
be used, if their motion could be so well
ascertained as to enable Galileo at Flo-
rence to predict the exact times at which
any remarkable configurations would
occur, as, for instance, the times at which
any one of them would be eclipsed by
Jupiter. A mariner who in the middle
of the Atlantic should observe the same
eclipse, and compare the time of night
at which he made the observation (which
he might know by setting his watch by
the sun on the preceding day) with the
time mentioned in the predictions, would,
from the difference between the two,
learn the difference between the hour at
Florence and the hour at the place where
the ship at that time happened to be.
As the earth turns uniformly round
through 360° of longitude in 24 hours,
that is, through 1 5° in each hour, the
hours, minutes, and seconds of time
which express this difference must be
multiplied by 15, and the respective pro-
ducts will give the degrees, minutes,
and seconds of longitude, by which the
ship was then distant from Florence.
This statement is merely intended to
give those who are unacquainted with
astronomy, a general idea of the manner
in which it was proposed to use these
satellites. Our moon had already been
occasionally employed in the same way,
but the comparative frequency of the
eclipses of Jupiter's moons, and the
suddenness with which they disappear,
gives a decided advantage to the new
method. Both methods were embar-
rassed by the difficulty of observing the
eclipses at sea. In addition to this, it
was requisite, in both methods, that the
sailors should be provided with accurate
means of knowing the hour, wherever
they might chance to be, which was far

GALILEO.

51

from being: the case, for although (in
order not to interrupt the explanation)
we have above spoken of their watches,
yet the watches and clocks of that day
were not such as could be relied on suffi-
ciently, during the interval which must
necessarily occur between the two ob-
servations. This consideration led Ga-
lileo to reflect on the use which might
be made of his pendulum for this pur-
pose ; and, with respect to the other diffi-
culty, he contrived a peculiar kind of
telescope, with which he flattered him-
self, somewhat prematurely, that it would
be as easy to observe on ship-board as
on shore.

During his stay at Rome, in 1615,
and the following year, he disclosed
some of these ideas to the Conte di
Lemos, the viceroy of Naples, who had
been president of the council of the
Spanish Indies, and was fully aware
of the importance of the matter. Galileo
was in consequence invited to com-
municate directly with the Duke of
Lerma, the Spanish minister, and in-
structions were accordingly sent by
Cosmo, to the Conte Orso d'Elci, his
ambassador at Madrid, to conduct the
business there. Galileo entered warmly
into the design, of which he had no other
means of verifying the practicability;
for as he says in one of his letters to
Spain — " Your excellency may well be-
lieve that if this were an undertaking
which I' could conclude by myself, I
would never have gone about begging
favours from others ; but in my study
there are neither seas, nor Indies, nor
islands, nor ports, nor shoals, nor ships,
for which reason I am compelled to
share the enterprise with great person-
ages, and to fatigue myself to procure
the acceptance of that, which ought
with eagerness to be asked of me ; but
I console myself with the reflection that
1 am not singular in this, but that it
commonly happens, with the exception
of a little reputation, and that too often
obscured and blackened by envy, that
the least part of the advantage falls to
the share of the inventors of things,
which afterwards bring great gain, ho-
nours, and riches to others ; so that I
will never cease on my part to do every
thing in my power, and I am ready to
leave here all my comforts, my country,
my friends, and family, and to cross over
into Spain, to stay as long as I may be
wanted in Seville, or Lisbon, or wherever
it may be convenient, to implant the
knowledge of this method, provided that

due assistance and diligence be not want-
ing on the part of those who are to re-
ceive it, and who should solicit and foster
it." But he could not, with all his en-
thusiasm, rouse the attention of the
Spanish court. The negotiation lan-
guished, and although occasionally re-
newed during the next ten or twelve
years, was never brought to a satisfactory
issue. Some explanation of this other-
wise unaccountable apathy of the Spanish
court, with regard to the solution of a
problem which they had certainly much
at heart, is given in Nelli's life of Galileo ;
where it is asserted, on the authority of
the Florentine records, that Cosmo re-
quired privately from Spain, (in return
for the permission granted for Galileo to
leave Florence, m pursuance of this de-
sign,) the privilege of sending every year
from Leghorn two merchantmen, duty
free, to the Spanish Indies.

CHAPTER XII.

Controversy on Comets — Saggiatore —
Galileo's reception by Urban VIII —
His family.

THE year 1618 was remarkable for the
appearance of three comets, on which
almost every astronomer in Europe found
something to say and write. Galileo
published some of his opinions with
respect to them, through the medium of
Mario Guiducci. This astronomer de-
livered a lecture before the Florentine
academy, the heads of which he was
supposed to have received from Galileo,
who, during the whole time of the ap-
pearance of these comets, was confined
to his bed by severe illness. This essay
was printed in Florence at the sign of
The Medicean Stars.* What princi-
pally deserves notice in it, is the opinion
of Galileo, that the distance of a comet
cannot be safely determined by its paral-
lax, from which we learn that he inclined
to believe that comets are nothing but
meteors occasionally appearing in the
atmosphere, like rainbows, parhelia, and
similar phenomena. He points out the
difference in this respect between a fixed
object, the distance of which may be
calculated from the difference of direction
in which two observers (at a known dis-
tance from each other) are obliged to
turn themselves in order to see it, and
meteors like the rainbow, which are
simultaneously formed in different drops
of water for each spectator, so that two

* In Firenze nella Stamperia di Pietro Cecconcelli
alle stelle Medicee, 1619.

E2

GALILEO.

observers in different places are in fact
contemplating different objects. He
then warns astronomers not to engage
with too much warmth in a discussion
on the distance of comets before they
assure themselves to which of these two
classes of phenomena they are to be
referred. The remark is in itself per-
fectly just, although the opinion which
occasioned it is now as certainly known
to be erroneous, but it is questionable
whether the observations which, up to
that time, had been made upon comets,
were sufficient, either in number or qua-
lity, to justify the censure which has
been cast on Galileo for his opinion. The
theory, moreover, is merely introduced
as an hypothesis in Guiducci's essay.
The same opinion was for a short time
embraced by Cassini, a celebrated Italian
astronomer, invited by Louis XIV. to
the Observatory at Paris, when the
science was considerably more advanced,
and Newton, in his Principia, did not
think it unworthy of him to show on
what grounds it is untenable.

Galileo was become the object of ani-
mosity in so many quarters that none
of his published opinions, whether cor-
rect or incorrect, ever wanted a ready
antagonist. The champion on the pre-
sent occasion was again a Jesuit ; his
name was Oratio Grassi, who published
The Astronomical and Philosophical
Balance, under the disguised signature
of Lotario Sarsi.

Galileo and his friends were anxious
that his reply to Grassi should appear
as quickly as possible, but his health
had become so precarious and his fre-
quent illnesses occasioned so many in-
terruptions, that it was not until the au-
tumn of 1623 that II Saggiatore (or The
Assayer) as he called his answer, was
ready for publication. This was printed
by the Lvncean Academy, and as Cardi-
nal Mafrco Barberino, wno had just been
elected Pope, (with the title of Urban
VIII.) had been closely connected with
that society, and was also a personal
friend of Cesi and of Galileo, it was
thought a prudent precaution to dedicate
the pamphlet to him. This essay enjoys
a peculiar reputation among Galileo's
works, not only for the matter contained
in it, but also for the style in which it
is written ; insomuch that Andres*,
when eulogizing Galileo as one of the
earliest who adorned philosophical truths
with the graces and ornaments of lan-
guage, expressly instances the Saggia-

* Dell' Origine d'ogai Literatura : Parma, 1787.

tore, which is also quoted by Frisi and
Algarotti, as a perfect model of this sort
of composition. In the latter particular,
it is unsafe to interfere with the decisions
of an Italian critic ; but with respect to
its substance, this famous composition
scarcely appears to deserve its preemi-
nent reputation. It is a prolix and ra-
ther tedious examination of Grassi1 s
Essay; nor do the arguments seem so
satisfactory, nor the reasonings so com-
pact as is generally the case in Galileo's
other writings. It does however, like
all his other works, contain many very
remarkable passages, and the celebrity
of this production requires that we
should extract one or two of the most
characteristic.

The first, though a very short one, will
serve to shew the tone which Galileo
had taken with respect to the Coperni-
can system since its condemnation at
Rome, in 1616. "In conclusion, since
the motion attributed to the earth, which
I, as a pious and Catholic person, con-
sider most false, and not to exist,
accommodates itself so well to explain so
many and such different phenomena,
I shall not feel sure, unless Sarsi de-
scends to more distinct considerations
than those which he has yet produced,
that, false as it is, it may not just as
deludingly correspond with the pheno-
mena of comets."

Sarsi had quoted a story from Suidas
in support of his argument that motion
always produces heat, how the Babylo-
nians used to cook their eggs by whirl-
ing them in a sling ; to which Galileo
replies : " I cannot refrain from mar-
velling that Sarsi will persist in proving
to me, by authorities, that which at any
moment I can bring to the test of ex-
periment. We examine witnesses in
things which are doubtful, past, and
not permanent, but not in those things
which are 'done in our own presence.
If discussing a difficult problem were
like carrying a weight, since several
horses will carry more sacks of corn
than one alone will, I would agree that
many reasoners avail more than one ;
but discoursing is like coursing, and
not like carrying, and one barb by
himself will run farther than a hundred
Friesland horses. When Sarsi brings
up such a multitude of authors, it does
not seem to me that he in the least
degree strengthens his own conclusions,
but he ennobles the cause of Signor
Mario and myself, by she wing that we rea-
son better than many men of established
reputation. If Sarsi insists that I believe,

GALILEO.

53

on Suidas' credit, that the Babylonians
cooked eggs by swiftly whirling; them in
a sling, I will believe it ; but I must
needs say, that the cause of such an
effect is very remote from that to which
it is attributed, and to find the true
cause I shall reason thus. If an effect
does not follow with us which followed
with others at another time, it is be-
cause, in our experiment, something is
wanting which was the cause of the
former success ; and if only one thing
is wanting to us, that one thing is the
true cause. Now we have eggs, and
slings, and strong men to whirl them,
and yet they will not become cooked;
nay, if they were hot at first, they more
quickly become cold : and since nothing
is wanting to us but to be Babylonians,
it follows that being Babylonians is the
true cause why the eggs became hard,
and not the friction of the air, which is
what I wished to prove. — Is it possible
that in travelling post, Sarsi has never
noticed what freshness is occasioned on
the face by the continual change of
air ? and if he has felt it, will he rather
trust the relation by others, of what was
done two thousand years ago at Babylon,
than what he can at this moment verify
in his own person ? I at least will not
be so wilfully wrong, and so un-
grateful to nature and to God, that
having been gifted with sense and
language, I should voluntarily set less
value on such great endowments than
on the fallacies of a fellow man, and
blindly and blunderingly believe what-
ever I hear, and barter the freedom of
my intellect for slavery to one as liable
to error as myself."

Our final extract shall exhibit a sample
of Galileo's metaphysics, in which may
be observed the germ of a theory
very closely allied to that which was
afterwards developed by Locke and
Berkeley. — " I have now only to fulfil my
promise of declaring my opinions on the
proposition that motion is the cause of
heat, and to explain in what manner it
appears to me that it may be true. But
I must first make some remarks on that
•which we call heat, since I strongly
suspect that a notion of it prevails
which is very remote from the truth ; for
it is believed that there is a true acci-
dent, affection, and quality, really inherent
in the substance by which we feel our-
selves heated. This much I have to
say, that so soon as I conceive a material
or corporeal substance, I simultaneously
feel the necessity of conceiving that it

has its boundaries, and is of some shape
or other ; that, relatively to others, it is
great or small ; that it is in this or that
place, in this or that time ; that it is in
motion, or at rest ; that it touches, or
does not touch another body ; that it is
unique, rare, or common ; nor can I, by
any act of the imagination, disjoin it from
these qualities : but I do not find myself
absolutely compelled to apprehend it as
necessarily accompanied by such condi-
tions, as that it must be white or red,
bitter or sweet, sonorous or silent,
smelling sweetly or disagreeably ; and if
the senses had not pointed out these
qualities, it is probable that language
and imagination alone could never have
arrived at them. Because, I am in-
clined to think that these tastes, smells,
colours, &c., with regard to the subject
in which they appear to reside, are
nothing more than mere names, and
exist only in the sensitive body ; inso-
much that, when the living creature is
removed, all these qualities are carried
off and annihilated ; although we have
imposed particular names upon them,
and different from those of the other
first and real accidents, and would fain
persuade ourselves that they are truly
and in fact distinct. But I do not be-
lieve that there exists any thing in ex-
ternal bodies for exciting tastes, smells,
and sounds, but size, shape, quantity,
and motion , swift or slow ; and if ears,
tongues, and noses were removed, I am
of opinion that shape, number, and
motion would remain, but there would
be an end of smells, tastes, and sounds,
which, abstractedly from the living
creature, I take to be mere words."

In the spring following the publica-
tion of the " Saggiatore," that is to say,
about the time of Easter, in 1624, Gali-
leo went a third time to Rome to
compliment Urban on his elevation to
the pontifical chair. He was obliged to
make this journey in a litter ; and it ap-
pears from his letters that for some
years he had been seldom able to bear
any other mode of conveyance. In such
a state of health it seems unlikely that
he would have quitted home on a mere
visit of ceremony, which suspicion is
strengthened by the beginning of a letter
from him to Prince Cesi, dated in Oc-
tober, 1 623, in which he says : " I have
received the very courteous and prudent
advice of your excellency about the
time and manner of my going to Rome,
and shall act upon it ; and 1 will visit
you at Acqua Sparta, that I may bq

54

GALILEO.

completely informed of the actual state
of things at Rome." However this may
be, nothing could be more gratifying
than his public reception there. His
stay in Rome did not exceed two months,
(from the beginning of April till June,)
and during that time he was admitted
to six long and satisfactory interviews
with the Pope, and on his departure re-
ceived the promise of a pension for his
son Vincenzo, and was himself presented
with " a fine painting, two medals, one
of gold and the other of silver, and a
good quantity of agnus dei." He had
also much communication with several
of the cardinals, one of whom, Cardi-
nal Hohenzoller, told him that he had
represented to the pope on the subject
of Copernicus, that " all the heretics
were of that opinion, and considered it
as undoubted ; and that it would be
necessary to be very circumspect in
coming to any resolution : to which his
holiness replied, that the church had
not condemned it, nor was it to be con-
demned as heretical, but only as rash ;
adding, that there was no fear of any
one undertaking to prove that it must
necessarily be true. " Urban also ad-
dressed a letter to Ferdinand, who had
succeeded his father Cosmo as Grand
Duke of Tascany, expressly for the pur-
pose of recommending Galileo to him.
" For We find in him not only literary
distinction, but also the love of piety,
and he is strong in those qualities by
which pontifical good-will is easily ob-
tained. And now, when he has been
brought to this city to congratulate Us
on Our elevation, We have very lovingly
embraced him ; — nor can We suffer
him to return to the country whither
your liberality recalls him without an
ample provision of pontifical love. And
that you may know how dear he is to
Us, We have willed to give him this
honourable testimonial of virtue and
piety. And We further signify that every
benefit whicti you shall confer upon
him, imitating, or even surpassing your
father's liberality, will conduce to Our
gratification." Honoured with these un-
equivocal marks of approbation, Galileo
returned to Florence.

His son Vincenzo is soon afterwards
spoken of as being at Rome ; and it is
not improbable that Galileo sent him
thither on the appointment of his friend
and pupil, the Abbe Castelli, to be
mathematician to the pope. Vincenzo
had been legitimated by an edict of
Cosmo in 1619, and, according to Nelli,

married, in 1624, Sestilia, the daughter
of Carlo Bocchineri. There are no
traces to be found of Vincenzo' s mother
after 1610, and perhaps she died about
that time. Galileo's family by her con-
sisted of Vincenzo and two daughters,
Julia and Polissena, who both took the
veil in the convent of Saint Matthew
at Arcetri, under the names of Sister
Arcangiola and Sister Maria Celeste.
The latter is said to have possessed
extraordinary talents. The date of Vin-
cenzo's marriage, as given by Nelli,
appears somewhat inconsistent with the
correspondence between Galileo and
Castelli, in which, so late as 1629,
Galileo is apparently writing of his son
as a student under Castelli's superin-
tendence, and intimates the amount of
pocket-money he can afford to allow
him, which he fixes at three crowns a
month; adding, that "he ought to be
contented with as many crowns, as, at
his age, I possessed groats." Castelli
had given but an unfavourable account
of Vincenzp's conduct, characterizing
him as "dissolute, obstinate, and im-
pudent ;" in consequence of which be-
haviour, Galileo seems to have thought
that the pension of sixty crowns, which
had been granted by the pope, might be
turned to better account than by em-
ploying it on his son's education ; and
accordingly in his reply he requested
Castelli to dispose of it, observing that
the proceeds would be useful in assisting
him to discharge a great load of debt
with which he found himself saddled on
account of his brother's family. Besides
this pension, another of one hundred
crowns was in a few years granted by
Urban to Galileo himself, but it appears
to have been very irregularly paid, if at
all.

About the same time Galileo found
himself menaced either with the de-
privation of his stipend as extraordi-
nary professor at Pisa, or with the loss
of that leisure which, on his removal
to Florence, he had been so anxious
to secure. In 1629, the question was
agitated by the party opposed to him,
whether it were in the power of the
grand duke to assign a pension out of
the funds of the University, arising
out of ecclesiastical dues, to one who
neither lectured nor resided there. This
scruple had slept during nineteen years
which had elapsed since Galileo's esta-
blishment in Florence, but probably
those who now raised it reckoned upon
finding in Ferdinand II., then scarcely

GALILEO.

55

of age, a less firm supporter of Galileo
than his father Cosmo had been. But
the matler did not proceed so far ; for,
after full deliberation, the prevalent
opinion of the theologians and jurists
who were consulted appeared to be in
favour of this exercise of prerogative,
and accordingly Galileo retained his sti-
pend and privileges.

CHAPTKR XIII.

Publication of Galileo's ' System of the
World' — His Condemnation and Ab-
juration.

IN the year 1630, Galileo brought to its
conclusion his great work, " The Dia-
logue on the Ptolemaic and Copernican
Systems," and began to take the neces-
sary steps for procuring permission to
print it. This was to be obtained in the
first instance from an officer at Rome,
entitled the master of the sacred palace ;
and after a little negotiation Galileo
found it would be necessary for him
again to return thither, as his enemies
were still busy in thwarting his views
and wishes. Niccolo Riccardi, who at
that time filled the office of master of
the palace, had been a pupil of Galileo,
and was well disposed to facilitate his
plans ; he pointed out, however, some
expressions in the work which he
thought it necessary to erase, and,
with the understanding that this should
be done, he returned the manuscript to
Galileo with his subscribed approbation.
The unhealthy season was drawing near,
and Galileo, unwilling to face it, re-
turned home, where he intended to com-
plete the index and dedication, and then
to send it back to Rome to be printed
in that city, under the superintendence
of Federigo Cesi. This plan was discon-
certed by the premature death of that
accomplished nobleman, in August 1630,
in whom Galileo lost one of his steadiest
and most effective friends and pro-
tectors. This unfortunate event de-
termined Galileo to attempt to procure
permission to print his book at Florence.
A contagious disorder had broken out
in Tuscany with such severity as almost
to interrupt all communication between
Florence and Rome, and this was urged
by Galileo as an additional reason for
granting his request. Riccardi at first
seemed inclined to insist that the book
should be sent to him a second time,
but at last contented himself with in-
specting the commencement and conclu-
sion, and consented that (on its receiving
also a license from the inquisitor-

general 'at Florence, and from one or
two others whose names appear on the
title-page) it might be printed where
Galileo wished.

These protracted negotiations pre-
vented the publication of the work till
late in 1632; it then appeared, with a
dedication to Ferdinand, under the fol-
lowing title : — "A. Dialogue, by Galileo
Galilei, Extraordinary Mathematician
of the University of Pisa, and Principal
Philosopher and Mathematician of the
Most Serene Grand Duke of Tuscany ;
in which, in a conversation of four days,
are discussed the two principal Systems
of the World, the Ptolemaic and Co-
pernican, indeterminately proposing the
Philosophical Arguments as well on
one side as on the other." The begin-
ning of the introduction, which is ad-
dressed "To the discreet Reader," is
much too characteristic to be passed by
without notice. — " Some years ago, a
salutary edict was promulgated at
Rome, which, in order to obviate the
perilous scandals of the present age,
enjoined an opportune silence on the Py-
thagorean opinion of the earth's motion.
Some were not wanting, who rashly as-
serted that this decree originated, not in
a judicious examination, but in ill in-
formed passion ; and complaints were
heard that counsellors totally inexpe-
rienced in astronomical observations
ought not by hasty prohibitions to clip
the wings of speculative minds. My
zeal could not keep silence when I heard
these rash lamentations, and I thought
it proper, as being fully informed with
regard to that most prudent determi-
nation, to appear publicly on the theatre
of the world as a witness of the actual
truth. I happened at that time to be
in Rome : I was admitted to the au-
diences, and enjoyed the approbation of
the most eminent prelates of that court,
nor did the publication of that decree
occur without my receiving some prior
intimation of it.* Wherefore it is my
intention in this present work, to show
to foreign nations that as much is
known of this matter in Italy, and par-
ticularly in Rome, as ultramontane
diligence can ever have formed any
notion of, and collecting together all my
own speculations on the Copernican
system, to give them to understand that
the knowledge of all these preceded the
Roman censures, and that from this

* Delambre quotes this sentence from a passage
which is so obviously ironical throughout, as an in-
stance of Galileo's mis-statement of facts I — Hint,
de I'Astr. Mod., vol. i. p. 666.

56

GALILEO.

country proceed not only dogmas for
the salvation of the soul, but also inge-
nious discoveries for the gratification of
the understanding. With this object, I
have taken up in the Dialogue the Co-
pernican side of the question, treating it
as a pure mathematical hypothesis;
and endeavouring in every artificial
manner to represent it as having the
advantage, not over the opinion of the
stability of the earth absolutely, but
according to the manner in which that
opinion is defended by some, who in-
deed profess to be Peripatetics, but re-
tain only the name, and are contented
without improvement to worship sha-
dows, not philosophizing with their own
reason, but only from the recollection of
four principles imperfectly understood."
— This very flimsy veil could scarcely
blind any one as to Galileo's real views
in composing this work, nor does it
seem probable that he framed it with
any expectation of appearing neutral in
the discussion. It is more likely that he
flattered himself that, under the new go-
vernment at Rome, he was not likely to
be molested on account of the personal
prohibition which he had received in
1616, "not to believe or teach the motion
of the earth in any manner," provided
he kept himself within the letter of the
limits of the more public and general
order, that the Copernican system was
not to be brought forward otherwise
than as a mere mathematically conve-
nient, but in fact unreal supposition.
So long as this decree remained in force,
a due regard to consistency would com-
pel the Roman Inquisitors to notice an
unequivocal violation of it ; and this is
probably what Urban had implied in the
remark quoted by Hohenzoller to Gali-
leo.* There were not wanting circum-
stances which might compensate for the
loss of Cosmo and of Federigo Cesi ;
Cosmo had been succeeded by his
son, who, though he had not yet at-
tained his father's energy, showed him-
self as friendly as possible to Galileo.
Cardinal Bellarmine, who had been
mainly instrumental in procuring the
decree of 16 1 6, was dead ; Urban on the
contrary, who had been among the few
Cardinals who then opposed it as un-
called for and ill-advised, was now pos-
sessed of supreme power, and his recent
affability~s^eTned~~to~j)n)ve that the in-
creased difference in their stations had
not caused him to forget their early and
long-continued intimacy. It is probable
that Galileo would not have found him-

* Page 54.

self mistaken in this estimate of his
position, but for an unlucky circum-
stance, of which his enemies imme-
diately saw the importance, and which
they were not slow in making available
against him. The dialogue of Galileo's
work is conducted between three per-
sonages ; — Salviati and Sagredo, who
were two noblemen, friends of Galileo,
and Simplicio, a name borrowed from a
noted commentator upon Aristotle, who
wrote in the sixth century. Salviati is
the principal philosopher of the work ; it
is to him that the others apply for solu-
tions of their doubts and difficulties, and
on him the principal task falls of ex-
plaining the tenets of the Copernican
theory. Sagredo is only a half convert,
but an acute and ingenious one ; to him
are allotted the objections which seem
to have some real difficulty in them, as
well as lively illustrations and digres-
sions, which might have been thought
inconsistent with the gravity of Salviati' s
character. Simplicio, though candid
and modest, is of course a confirmed
Ptolemaist and Aristotelian, and is made
to produce successively all the popular
arguments of that school in support of
his master's system. Placed between
the wit and the philosopher, it may be
guessed that his success is very indiffer-
ent, and in fact he is alternately ridi-
culed and confuted at every turn. As
Galileo racked his memory and inven-
tion to leave unanswered no argument
which was or could be advanced against
Copernicus, it unfortunately happened,
that he introduced some which Urban
himself had urged upon him in their
former controversies on this subject;
and Galileo's opponents found means
to make His Holiness believe that
the character of Simplicio had been
sketched in personal derision of him.
We do not think it necessary to exone-
rate Galileo from this charge ; the ob-
vious folly of such an useless piece of
ingratitude speaks sufficiently for itself.
But self-love is easily irritated; and
Urban, who aspired to a reputation for
literature and science, was peculiarly sen-
sitive on this point. His own expres-
sions almost prove his belief that such
had been Galileo's design, and it seems
to explain the otherwise inexplicable
change which took place in his conduct
towards his old friend, on account of a
book which he had himself undertaken
to examine, and of which he had autho-
rised the publication.

One of the earliest notices of what was
approaching, is found in the dispatches,

GALILEO.

57

dated August 24, 1 632, from Ferdinand's
minister, Andrea Cioli, to Francesco
Nicolini, the Tuscan ambassador at the
court of Rome.

" I have orders to signify toYour Excel-
lency that His Highness remains greatly
astonished that a book, placed by the au-
thor himself in the hands of the supreme
authority in Rome, read and read again
there most attentively, and in which every
thing, not only with the consent, but at
the request of the author, was amended,
altered, added, or removed at the will of
his superiors, which was again subjected
here to the same examination, agreeably
to orders from Rome, and which finally
was licensed both there and here, and
here printed and published, should now
become an object of suspicion at the end
of two years, and the author and printer
be prohibited from publishing any more."
— In the sequel is intimated Ferdinand's
desire that the charges, of whatever
nature they might be, either against
Galileo or his book, might be reduced
to writing and forwarded to Florence,
that he might prepare for his justifi-
cation ; but this reasonable demand was
utterly disregarded. It appears to have
been owing to the mean subserviency of
Cioli to the court of Rome, that Ferdi-
nand refrained from interfering more
strenuously to protect Galileo. Cioli's
words are : " The Grand Duke is so en-
raged with this business of Galileo, that
I do not know what will be done. I
know, at least, that His Holiness shall
have no reason to complain of his mi-
nisters, or of their bad advice."*

A letter from Galileo's Venetian friend
Micanzio, dated about a month later,
is in rather a bolder and less formal
style : — " The efforts of your ene-
mies to get your book prohibited will
occasion no loss either to your reputa-
tion, or to the intelligent part of the
world. As to posterity, this is just one
of the surest ways to hand the book
down to them. But what a wretched
set this must be to whom every
good thing, and all that is founded in
nature, necessarily appears hostile and
odious ! The world is not restricted to
a single corner ; you will see the book
printed in more places and languages
than one ; and just for this reason, I
wish they would prohibit all good books.
My disgust arises from seeing myself
deprived of what I most desire of this
sort, I mean your other dialogues ; and
if, from this cause, I fail in having the

* Galuzzi. Storia di Toscana. Firenze, 1822.

pleasure of seeing them, I shall devote
to a hundred thousand devils these un-
natural and godless hypocrites."

At the same time, Thomas Campanella,
a monk, who had already distinguished
himself by an apology for Galileo (pub-
lished in 1622), wrote to him from
Rome : — " I learn with the greatest
disgust, that a congregation of angry
theologians is forming to condemn
your Dialogues, and that no single
member of it has any knowledge of ma-
thematics, or familiarity with abstruse
speculations. I should advise you to
procure a request from the Grand Duke
that, among the Dominicans and Je-
suits and Theatins, and secular priests
whom they are putting on this congre-
gation against your book, they should
admit also Castelli and myself." It
appears, from subsequent letters both
from Campanella and Castelli, that
the required letter was procured and
sent to Rome, but it was not thought
prudent to irritate the opposite party
by a request which it was then clearly
seen would have been made in vain.
Not only were these friends of Gali-
leo not admitted to the congrega-
tion, but, upon some pretext, Castelli
was even sent away from Rome, as if
Galileo's enemies desired to have as few
enlightened witnesses as possible of
their proceedings ; and on the contrary,
Scipio Chiaramonte, who had been long
known for one of the staunchest and
most bigoted defenders of the old sys-
tem, and who, as Montucla says, seems
to have spent a long life in nothing but
retarding, as far as he was able, the
progress of discovery, was summoned
from Pisa to complete their number.
From this period we have a tolerably
continuous account of the proceedings
against Galileo in the dispatches which
Nicolini sent regularly to his court.
It appears from them that Nicolini
had several interviews with the Pope,
whom he found highly incensed against
Galileo, and in one of the earliest he re-
ceived an intimation to advise the Duke
" not to engage himself in this matter
as he had done in the other business of
Alidosi,* because he would not get
through it with honour." Finding
Urban in this humour, Nicolini thought
it best to temporize, and to avoid the
appearance of any thing like direct op-
position. On the 15th of September,
probably as soon as the first report on

* Alidosi was a Florentine nobleman, whose estate
Urban wished to confiscate on a charge of heresy.— r
Galuzzi.

58

GALILEO.

Galileo's book had been made, Nicolini
received a private notice from the Pope,
" in especial token of the esteem in
which he held the Grand Duke," that he
was unable to do less than consign the
work to the consideration of the Inqui-
sition. Nicolini was permitted to com-
municate this to the Grand Duke pnly,
and both were declared liable to " the
usual censures" of the Inquisition in case
of divulging the secret.

The next step was to summon Galileo
to Rome, and the only answer returned to
all Nicolini's representations of his ad-
vanced age of seventy years, the very in-
firm state of his health, and the discom-
forts which he must necessarily suffer in
such a journey, and in keeping quaran-
tine, was that he might come at leisure,
and that the quarantine should be relaxed
as much as possible in his favour, but
that it was indispensably necessary that
he should be personally examined before
the Inquisition at Rome. Accordingly,
on the 14th of February, 1633, Nicolini
announces Galileo's arrival, and that he
had officially notified his presence to the
Assessor and Commissary of the Holy
Office. Cardinal Barberino, Urban's
nephew, who seems on the whole to
have acted a friendly part towards
Galileo, intimated to him that his most
prudent course would be to keep him-
self as much at home and as quiet as
possible, and to refuse to see any but
his most intimate friends. With this
advice, which was repeated to him from
several quarters, Galileo thought it best
to comply, and kept himself entirely se-
cluded in Nicolini's palace, where he was
as usual maintained at the expense of
the Grand Duke. Nelli quotes two let-
ters, which passed between Ferdinand's
minister Cioli and Nicolini, in which
the former intimated that Galileo's ex-
penses were to be defrayed only during
the first month of his residence at
Rome. Nicolini returned a spirited
answer, that in that case, after the time
specified, he should continue to treat
him as before at his own private cost.

The permission to reside at the am-
bassador's palace whilst his cause was
pending, was granted and received as an
extraordinary indulgence on the part of
the Inquisition, and indeed if we es-
timate the proceedings throughout
against Galileo by 'the usual practice of
that detestable tribunal, it will appear
that he was treated with unusual consi-
deration. Even when it became neces-
sary in the course of the inquiry to
examine him in person, which was in
the beginning of April, although his re-

moval to the Holy Office was then in-
sisted upon, yet he was not committed
to close or strictly solitary confinement.
On the contrary, he was honourably
lodged in the apartments of the Fiscal
of the Inquisition, where he was allowed
the attendance of his own servant, who
was also permitted to sleep in an adjoin-
ingroom.andto come and go at pleasure.
His table was still furnished by Nicolini.
But, notwithstanding the distinction with
which he was thus treated, Galileo was
annoyed and uneasy at being (though
little more than nominally) within the
walls of the Inquisition. He became
exceedingly anxious that the matter
should be brought to a conclusion, and
a severe attack of his constitutional
complaints rendered him still more fret-
ful and impatient. On the last day of
April, about ten days after his first ex-
amination, he was unexpectedly per-
mitted to return to Nicolini's house,
although the proceedings were yet far
from being brought to a conclusion.
Nicolini attributes this favour to Cardi-
nal Barberino, who, he says, liberated
Galileo on his own responsibility, in
consideration of the enfeebled state of
his health.

In the society of Nicolini and his
family, Galileo recovered something of
his courage and ordinary cheerful-
ness, although his return appears to
have been permitted on express condi-
tion of a strict seclusion ; for at the
latter end of May, Nicolini was obliged
to apply for permission that Galileo
should take that exercise in the open
air which was necessary for his health ;
on which occasion he was permitted to
go into the public gardens in a half-
closed carriage.

On the evening of the 20th of June,
rather more than four months after
Galileo's arrival in Rome, he was again
summoned to the Holy Office, whither
he went the following morning ; he was
detained there during the whole of
that day, and on the next day was
conducted in a penitential dress * to
the Convent of Minerva, where the
Cardinals and Prelates, his judges,
were assembled for the purpose of
passing judgment upon him, by which
this venerable old man was solemnly
called upon to renounce and ab-
jure, as impious and heretical, the opi-
nions which his whole existence had
been consecrated to form and strengthen.

* S' irrito il Papa, e lo fece abjurare, comparendo
il pover uome con uno straccio di camicia iiidosso,
che faceva compassione, MS. nella Bibl. Magliab.
Venturi.

GALILEO.

59

As we are not aware that this remark-
able record of intolerance and bigoted
folly has ever been printed entire in Eng-
lish, we subjoin a literal translation of
the whole sentence and abjuration.

The Sentence of the Inquisition on

Galileo.

" We, the undersigned, by the Grace of
God, Cardinals of the Holy Roman
Church, Inquisitors General through-
out the whole Christian Republic, Spe-
cial Deputies of the Holy Apostolical
Chair against heretical depravity,

" Whereas you, Galileo, son of the late
Vincenzo Galilei of Florence, aged^seven-
ty years, were denounced in 1615 to this
Holy Office, for holding as true a false
doctrine taught by many, namely, that
the sun is immoveable in the centre of
the world, and that the earth moves, and
also with a diurnal motion; also, for
having pupils whom you instructed in
the same opinions ; also, for maintain-
ing a correspondence on the same with
some German mathematicians ; also
for publishing certain letters on the
solar spots, in which you developed the
same doctrine as true ; also, for an-
swering the objections which were con-
tinually produced from the Holy Scrip-
tures, by glozing the said Scriptures
according to your own meaning ; and
whereas thereupon was produced the
copy of a writing, in form of a letter,
professedly written by you to a person
formerly your pupil, in which, follow-
ing the hypotheses of Copernicus, you
include several propositions contrary to
the true sense and authority of the Holy
Scripture : therefore this holy tribunal
being desirous of providing against the
disorder and mischief which was thence
proceeding and increasing to the detri-
ment of the holy faith, by the desire of
His Holiness, and of the Most Eminent
Lords Cardinals of this supreme and
universal Inquisition, the two proposi-
tions of the stability of the sun, and
motion of the earth, were qualified by
the Theological Qualifiers as follows :

" 1st. The proposition that the Sun is
in the centre of the world and immove-
able from its place, is absurd, philoso-
phically false, and formally heretical;
because it is expressly contrary to the
Holy Scripture.

" Idly. The proposition that the Earth
is not the centre of the world, nor im-
moveable, but that it moves, and also
with a diurnal motion, is also absurd,
philosophically false, and, theologically
considered, at least erroneous in faith.

" But whereas being pleased at that
time to deal mildly with you, it was de-
creed in the Holy Congregation, held
before His Holiness on the 25th day of
February, 1616, that His Eminence the
Lord Cardinal Bellarmine should enjoin
you to give up altogether the said false
doctrine ; if you should refuse, that you
should be ordered by the Commissary of
the Holy Office to relinquish it, not to
teach it to others, nor to defend it, nor
ever mention it, and in default of ac-
quiescence that you should be im-
prisoned ; and in execution of this de-
cree, on the following day at the pa-
lace, in presence of His Eminence the
said Lord Cardinal Bellarmine, after
you had been mildly admonished by the
said Lord Cardinal, you were com-
manded by the acting Commissary of the
Holy Office, before a notary and wit-
nesses, to relinquish altogether the said
false opinion, and in future neither to
defend nor teach it in any manner, nei-
ther verbally nor in writing, and upon
your promising obedience you were dis-
missed.

" And in order that so pernicious a
doctrine might be altogether rooted
out, nor insinuate itself farther to the
heavy detriment of the Catholic truth, a
decree emanated from the Holy Congre-
gation of the Index* prohibiting the
books which treat of this doctrine ; and
it was declared false, and altogether con-
trary to the Holy and Divine Scripture, j

" And whereas a book has since ap-
peared, published at Florence last year,
the title of which shewed that you were
the author, which title is : The Dialogue
of Galileo Galilei, on the two principal
systems of the world, the Ptolemaic and
Copernican ; and whereas the Holy
Congregation has heard that, in conse-
quence of the printing of the said book,
the false opinion of the earth's motion
and stability of the sun is daily gaining
ground ; the said book has been taken
into careful consideration, and in it has
been detected a glaring violation of the
said order, which had been intimated to
you ; inasmuch as in this book you have

* The Index is a list of books, the reading of
which is prohibited to Roman Catholics. This list,
in the early periods of the Reformation, was often
consulted by the curious, who were enlarging their
libraries ; and a story is current in England, that, to
prevent this mischief, the Index itself was inserted
in its own forbidden catalogue. The origin of this
story is, that an Index was published in Spain, par-
ticularizing the objectionable passages in such books
as were only partially condemned ; and although
compiled with the best intentions, this was found to
be so racy, that it became necessary to forbid the
circulation of this edition in subsequent lists.

60

GALILEO.

defended the "said opinion, already and
in your presence condemned ; although
in the said book you labour with many
circumlocutions to induce the belief that
it is left by you undecided, and in ex-
press terms probable : which is equally
a very grave error, since an opinion can
in no way be probable which has been
already declared and finally determined
contrary to the divine Scripture. There-
fore by Our order you have been cited to
this Holy Office, where, on your exami-
nation upon oath, you have acknow-
ledged the said book as written and
printed by you. You also confessed
that you began to write the said book
ten or twelve years ago, after the order
aforesaid had been given. Also, that
you demanded license to publish it, but
without signifying to those who granted
you this permission that you had been
commanded not to hold, defend, or teach
the said doctrine in any manner. You
also confessed that the style of the said
book was, in many places, so composed
that the reader might think the argu-
ments adduced on the false side to be so
worded as more effectually to entangle
the understanding than to be easily
solved, alleging in excuse, that you have
thus run into an error, foreign (as you
say) to your intention, from writing in
the form of a dialogue, and in conse-
quence of the natural complacency
which every one feels with regard to his
own subtilties, and in showing himself
more skilful than the generality of man-
kind in contriving, even in favour of
false propositions, ingenious and appa-
rently probable arguments.

" And, upon a convenient time being
given to you for making your defence,
you produced a certificate in the hand-
writing of His Eminence the Lord^Car-
dinalBellarmine, procured, as you said,
by yourself, that you might defend
yourself against the calumnies of your
enemies, who reported that you had ab-
jured your opinions, and had been pun-
ished by the Holy Office ; in which cer-
tificate it is declared, that you had not
abjured, nor had been punished, but
merely that the declaration made by
His Holiness, and promulgated by the
Holy Congregation of the Index, had
been announced to you, which de-
clares that the opinion of the motion of
the earth, and stability of the sun, is
contrary to the Holy Scriptures, and,
therefore, cannot be held or defended.
Wherefore, since no mention is there
made of two articles of the order, to wit,

the order ' not to teach/ and ' in any
manner,' you argued that we ought to
believe that, in the lapse of fourteen or
sixteen years, they had escaped your
memory, and that this was also the rea-
son why you were silent as to the order,
when you sought permission to publish
your book, and that this is said by you
not to excuse your error, but that it
may be attributed to vain-glorious am-
bition, rather than to malice. But this
very certificate, produced on your behalf,
has greatly aggravated yo'ur offence,
since it is therein declared that the said
opinion is contrary to the Holy Scripture,
and yet you have dared to treat of it,
to defend it, and to argue thai it is
probable ; nor is there any extenuation
in the licence artfully and cunningly
extorted by you, since you did not inti-
mate the command imposed upon you.
But whereas it appeared to Us that you
had not disclosed the whole truth with
regard to your intentions, We thought it
necessary to proceed to the rigorous exa-
mination of you, in which (without any
prejudice to what you had confessed,
and which is above detailed against you,
with regard to your said intention) you
answered like a good Catholic.

" Therefore, having seen and maturely
considered the merits of your cause,
with your said confessions and excuses,
and every thing else which ought to be
seen and considered, We have come to
the underwritten final sentence against
you.

" Invoking, therefore, the most holy
name of Our Lord Jesus Christ, and of
His Most Glorious Virgin Mother
Mary, by this Our final sentence, which,
sitting in council and judgment for the
tribunal of the Reverend Masters of
Sacred Theology, and Doctors of both
Laws, Our Assessors, We put forth in
this writing touching the matters and
controversies before Us, between The
Magnificent Charles Sincerus, Doctor
of both Laws, Fiscal Proctor of this
Holy Office of the one part, and you,
Galileo Galilei, an examined and con-
fessed criminal from this present writing
now in progress as above of the other
part, We pronounce, judge, and declare,
that you, the said Galileo, by reason of
these things which have been detailed
in the course of this writing, and which,
as above, you have confessed, have
rendered yourself vehemently suspected
by this Holy Office of heresy : that is
to say, that you believe arid hold the
false doctrine, and contrary to the Holy

GALILEO.

ft

and Divine Scriptures, namely, 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
finally decreed contrary to the Holy
Scripture, and consequently that you
have incurred all the censures and pe-
nalties enjoined and promulgated in the
sacred canons, and other general! and
particular constitutions against delin-
quents of this description. From which
it is Our pleasure that you be absolved,
provided that, first, with a sincere heart
and unfeigned faith, in Our presence,
you abjure, curse, and detest the said
errors and heresies, and every other
error and heresy contrary to the Ca-
tholic and Apostolic Church of Rome,
in the form now shown to you.

" But, that your grievous and per-
nicious error and transgression may
not go altogether unpunished, and that
you may be made more cautious in
future, and may be a warning to others
to abstain from delinquencies of this
sort, We decree that the book of the
dialogues of Galileo Galilei be prohibited
by a public edict, and We condemn you
to the formal prison of this Holy Office
for a period determinable at Our plea-
sure ; and, by way of salutary penance,
We order you, during the next three
years, to recite once a week the seven
penitential psalms, reserving to Our-
selves the power of moderating, com-
muting, or taking off the whole or part
of the said punishment and penance.

" And so We say, pronounce, and by
Our sentence declare, decree, and re-
serve, in this and in every other better
form and manner, which lawfully We
may and can use.

" So We, the subscribing Cardinals,
pronounce.

Felix, Cardinal di Ascoli,
Guido, Cardinal Bentivoglio,
Desiderio, Cardinal di Cremona,
Antonio, Cardinal S. Onofrio,
Berlingero, Cardinal Gessi,
Fabricio, Cardinal Verospi,
Martino, Cardinal Ginetti."
We cannot suppose that Galileo, even
broken down as he was with age and
infirmities, and overawed by the merci-
less tribunal to wjiose power he was
subjected, could without extreme reluc-
tance thus formally give the lie to his
whole life, and call upon God to witness
his renunciation of the opinions which

even his bigoted judges must have felt
that he still clung to in his heart.

We know indeed that his friends
were unanimous in recommending an
unqualified acquiescence in whatever
might be required, but some persons
have not been able to find an ade-
quate explanation of his submission,
either in their exhortations, or in the
mere dread of the alternative which
might await him in case of non-com-
pliance. It has in short been supposed,
although the suspicion scarcely rests
upon grounds sufficiently strong to war-
rant the assertion, that Galileo did not
submit to this abjuration until forced
to it, not merely by the apprehension,
but by the actual experience of personal
violence. The arguments on which this
horrible idea appears to be mainly
founded are the two following : First, the
Inquisitors declare in their sentence
that, not satisfied with Galileo's first
confession, they judged it necessary to
proceed " to the rigorous examination
of him, in which he answered like a good
Catholic.*" It is pretended by those
who are more familiar with inquisitorial
language than we can profess to be, that
the words il rigoroso esame, form the
official phrase for the application of the
torture, and accordingly they interpret
this passage to mean, that the desired
answers and submission had thus been
extorted from Galileo, which his judges
had otherwise failed to get from him.
And, secondly, the partisans of this opi-
nion bring forward in corroboration of
it, that Galileo immediately on his de-
parture from Rome, in addition to his
old complaints, was found to be afflicted
with hernia, and this was a common con-
sequence of the torture of the cord, which
they suppose to have been inflicted. It
is right to mention that no other trace
can be found of this supposed torturing
in all the documents relative to the
proceedings against Galileo, at least
Venturi was so assured by one who had
inspected the originals at Paris. t

* Giudicassimo esser necessario venir contro di
te al rigoroso esame nel quale rispondesti cattolica-
mente.

f The fate of these documents is curious ; after
being long preserved at Rome, they were, carried
away in 1809, by order of Buonaparte, to Paris,
where they remained till his first abdication. Just
before the hundred days, the late king of France,
wishing to inspect them, ordered that they should be
brought to his own apartments for that purpose. In
the hasty flight which soon afterwards followed, the
manuscripts were forgotten, and it is not known
what became of them. A French translation, begun
by Napoleon's desire, was completed only down to
the 30th of April, 1633, the date of Galileo's tirst re-
turn to Nicolini's palace.

GALILEO.

Although the arguments we have
mentioned appear to us slight, yet nei-
ther can we attach much importance to
the contrast which the favourers of the
opposite opinion profess to consider so in-
credible between the honourable manner
in which Galileo was treated throughout
the rest of the inquiry, and the suspected
harsh proceeding against him. Whe-
ther Galileo should be lodged in a pri-
son or a palace, was a matter of far
other importance to the Inquisitors and
to their hold upon public opinion, than
the question whether or not he should
be suffered to exhibit a persevering
resistance to the censures which they
were prepared to cast upon him. Nor
need we shrink from the idea, as we
might from suspecting of some gross
crime, on trivial grounds, one of hither-
to unblemished innocence and charac-
ter. The question may be disencum-
bered of all such scruples, since one
atrocity more or less can do little to-
wards affecting our judgment of the
unholy Office of the Inquisition.

Delambre, who could find so much to
reprehend in Galileo's former uncom-
promising boldness, is deeply penetrated
with the insincerity of his behaviour on
the present occasion. He seems to
have forgotten that a tribunal which
finds it convenient to carry on its in-
quiries in secret, is always liable to
the suspicion of putting words into
the mouth of its victims ; and if it were
worth while, there is sufficient internal
evidence that the language which Galileo
is made to hold in his defence and con-
fession, is rather to be read as the com-
position of his judges than his own. For
instance, in one of the letters which we
have extracted*, it may be seen that this
obnoxious work was already in forward
preparation as early as 1610, and yet he
is made to confess, and the circumstance
appears to be brought forward in aggra-
vation of his guilt, that he began to write
it after the prohibition which he had re-
ceived in 1616.

The abjuration was drawn up in the
following terms : —

The Abjuration of Galileo.

" I Galileo Galilei, son of the late Vin-
cenzo Galilei, of Florence, aged 70 years,
being brought personally to judgment,and
kneeling before you, Most Eminent and
Most Reverend Lords Cardinals, General
Inquisitors of the universal Christian re-

* Page 18.

public against heretical depravity, having
before my eyes the Holy Gospels, which
I touch with my own hands, swear, that
I hare always believed, and now believe,
and with the help of God will in future
believe, every article which the Holy
Catholic and Apostolic Church of Rome
holds, teaches, and preaches. But be-
cause 1 had been enjoined by this Holy
Office altogether to abandon the false
opinion which maintains that the sun is
the centre and immoveable, and forbid-
den to hold, defend, or teach, the said
false doctrine in any manner, and after
it had been signified to me that the said
doctrine is repugnant with the Holy
Scripture, I have "written and printed a
book, in which I treat of the same doc-
trine now condemned, and adduce rea-
sons with great force in support of the
same, without giving any solution, and
therefore have been judged grievously
suspected of heresy ; that is to say, that
I held and believed that the sun is the
centre of the world and immoveable,
and that the earth is not the centre and
moveable, Willing, therefore, to remove
from the minds of Your Eminences,
and of every Catholic Christian, this ve-
hement suspicion rightfully entertained
towards me, with a sincere heart and
unfeigned faith, I abjure, curse, and de-
test, the said errors and .heresies, and
generally every other error and sect con-
trary to the said Holy Church ; and I
swear, that I will never more in future
say or assert anything verbally, or in
writing, which may give rise to a simi-
lar suspicion of me : but if I shall know
any heretic, or any one suspected of
heresy, that I will denounce him to this
Holy Office, or to the Inquisitor and Or-
dinary of the place in which I may be.
I swear, moreover, and promise, that I
will fulfil, and observe fully, all the
penances which have been, or shall be
laid on me by this Holy Office. But if
it shall happen that I violate any of my
said promises, oaths, and protestations,
(which God avert !) I subject myself to
all the pains and punishments, which
have been decreed and promulgated by
the sacred canons, and other general
and particular constitutions, against de-
linquents of this description. So may
God help me, and his Holy Gospels,
which I touch with my own hands. I,
the above-named Galileo Galilei, have
abjured, sworn, promised, and bound
myself, as above, and in witness thereof
with my own hand have subscribed tliis
present writing of my abjuration, which

GALILEO.

I have .' recited word for word. At
Rome in the Convent of Minerva, 22d
June, 1633. I, Galileo Galilei, have ab-
jured as above with my own hand."

IL.is..-SaJd that Galileo, as he rose
from his knees, stamped on the ground,
and whispered to one of his friends, E
pur simuove — (It does move though).

Copies of Galileo's sentence and abju-
ration were immediately promulgated in
every direction, and the professors at
several universities received directions to
read them publicly. At Florence this
ceremony took place in the church of Sta.
Croce, whither Guiducci, Aggiunti, and
all others who were known in that city
as firm adherents to Galileo's opinions,
were specially summoned. The triumph
of the " Paper Philosophers" was so far
complete, and the alarm occasioned by
this proof of their dying power extended
even beyond Italy. " I have been told,"
writes Descartes from Holland to Mer-
senne at Paris, " that Galileo's system
was printed in Italy last year, but that
every copy has been burnt at Rome, and
himself condemned to some sort of pe-
nance, which has astonished me so much
that I have almost determined to burn
all my papers, or at least never to let
them be seen by any one. I cannot col-
lect that he, who is an Italian and even
a friend of the Pope, as I understand,
has been criminated on any other account
than for having attempted to establish
the motion of the earth. I know that
this opinion was formerly censured by
some Cardinals, but I thought I had
since heard, that no objection was now
made to its being publicly taught, even
at Rome."

The sentiments of all who felt them-
selves secured against the apprehension
of personal danger could take but one
direction, for, as Pascal well expressed
it in one of his celebrated letters to the
Jesuits — " It is in vain that you have
procured against Galileo a decree from
Rome condemning his opinion of the
earth's motion. Assuredly, that will
never prove it to be at rest ; and if we
have unerring observations proving that
it turns round, not all mankind toge-
ther can keep it from turning, nor them-
selves from turning with it."

The assembly of doctors of the Sor-
bonne at Paris narrowly escaped from
passing a similar sentence upon the
system of Copernicus. The question was
laid before them by .Richelieu, and it ap-
pears that their opinion was for a mo-
ment in fay our of confirming the Roman
decree. It is to be wished that the name

had been preserved of one of its mem-
bers, who, by his strong and philoso-
phical representations, saved that cele-
brated body from this disgrace.

Those who saw nothing in the punish-
ment of Galileo but passion and blinded
superstition, took occasion to- revert to
the history of a similar blunder of the
Court of Rome in the middle of the
eighth century. A Bavarian bishop,
named Virgil, eminent both as a man of
letters and politician, had asserted the
existence of Antipodes, which excited in
the ignorant bigots of his time no less
alarm than did the motion of the earth
in the seventeenth century. Pope Za-
chary, who was scandalized at the idea
of another earth," inhabited by another
race of men, and enlightened by another
sun and moon (for this was the shape
which Virgil's system assumed in his
eyes), sent out positive orders to his le-
gate in Bavaria. '* With regard to
Virgil, the philosopher, (I know not
whether to call him priest,) if he own
these perverse opinions, strip him of his
priesthood, and drive him from the
church and altars of God." But Virgil
had himself occasionally acted as legate,
and was .moreover too necessary to his
sovereign to be easily displaced. He
utterly disregarded these denunciations,
and during twenty-five years which
elapsed before his death, retained his
opinions, his bishopric of Salzburg, and
his political power. He was afterwards
canonized*.

Even the most zealous advocates of
the authority of Rome were embarrassed
in endeavouring to justify the treatment
which Galileo experienced. Tiraboschi
has attempted to draw a somewhat subtle
distinction between the bulls of the Pope
and the inquisitorial decrees which were
sanctioned and approved by him; he
dwells on the reflection that no one,
even among the most zealous Catholics,
has ever claimed infallibility as an attri-
bute of ;the Inquisition, and looks upon
it as a special mark of grace accorded to
the Roman Catholic Church, that during
the whole period in which most theolo-
gians rejected the opinions of Copernicus,
as contrary to the Scriptures, the head of
that Church was never permitted to com-
promise his infallible character by for-
mally condemning it t.

Whatever may be the value of this

* Annalium Bolorum, libri vii. Ingolstadii, 1554.

t La Chiesa non ha mai dichiarati eretici i soste-
nitori del Sistema Copernicano, e questa troppo ri-
gorosa censura non usci che dal tribunale della
Romana Inquisizione a cui niuno tra Cattolici ancor
piu zelanti ha mai attribuito U diritto dell' infalli-

64

GALILEO.

consolation, it can hardly be conceded,
unless it be at the same time admitted
that many scrupulous members of the
Church of Rome have been suffered to
remain in singular misapprehension of
the nature and sanction of the authority
to which Galileo had yielded. The words
of the bull of Sixtus V., by which the
Congregation of the Index was remo-
delled in 1588, are quoted by a pro-
fessor of the University of Louvain,
a zealous antagonist of Galileo, as fol-
lows : " They are to examine and ex-
pose the books which are repugnant
to the Catholic doctrines 'and Chris-
tian discipline, and after reporting on
them to us, they are to condemn them
by our authority.*" Nor does it ap-
pear 'that the learned editors of what
is commonly called the Jesuit's edi-
tion of Newton's "Principia" were of
opinion, that in adopting the Copernican
system they should transgress a mandate
emanating from any thing short of infal-
lible wisdom. The remarkable words
which they were compelled to prefix to
their book, show how sensitive the court
of Rome remained, even so late as 1742,
with regard to this rashly condemned
theory. In their preface they say :
" Newton in this third book supposes the
motion of the earth. We could riot
explain the author's propositions other-
wise than by making the same supposi-
tion. We are therefore forced to sus-
tain a character which is not our own ;
but we profess to pay the obsequious
reverence which is due to the decrees
pronounced by the supreme Pontiffs
against the motion of the earth."-{-

This coy reluctance to admit what
nobody any longer doubts has sur-
vived to the present time; for Bailli
informs us,$ that the utmost endea-
vours of Lalande, when at Rome, to
obtain that Galileo's work should be
erased from the Index, were entirely in-
effectual, in consequence of the decree
which had been fulminated against him ;
and in fact both it, and the book of
Copernicus, " Nisi Corrigatur," are still
to be seen on the forbidden list of 1828.

The condemnation of Galileo and his
book was not thought sufficient. Ur-

bilita. Anzi in cio ancora e d' ammirarsi la provi-
denza di Dip a favor della Chiesa, percioche in un
tempo in cni la maggior parte dei teologi ferma-
mente credavano che il Sistema Copernicano fosse
all* autorita delle sacre Carte contrario, pur non
pennise che dalla Chiesa si proferisse su cio un
solenne giudizio. — Stor. della Lett. Ital.

* Lib. Frpmondi Antaristarchus, Antwerpiae, 1631.

t Newtpni Principia, Colonise, 1760.

J Histoire de 1'Astronomie Moderce,

ban's indignation also vented itself upon
those who had been instrumental in ob-
taining the licence for him. The Inquisi-
tor at Florence was reprimanded ; Ric-
cardi, the master of the sacred palace,
and Ciampoli, Urban's secretary, were
both dismissed from their situations.
Their punishment appears rather ano-
malous and inconsistent with the pro-
ceedings against Galileo, in which it was
assumed that his book was not properly
licensed ; yet the others suffered on
account of granting that very licence,
which he was accused of having sur-
reptitiously obtained from them,, by con-
cealing circumstances with which they
were not bound to be otherwise ac-
quainted. Riccardi, in exculpation of
his conduct, produced a letter in the
hand-writing of Ciampoli, in which was
contained that His Holiness, in whose
presence the letter professed to be writ-
ten, ordered the licence to be given.
Urban only replied that this was a
Ciampolism ; that his secretary and Ga-
lileo had circumvented him ; that' he had
already dismissed Ciampoli, and that
Riccardi must prepare to follow him.

As soon as the ceremony of abju-
ration was concluded, Galileo was con-
signed, pursuant to his sentence, to
the prison of the Inquisition. Pro-
bably it was never intended that he
should long remain there, for at the end
of four days, he was reconducted on a
very slight representation of Nicolini to
the ambassador's palace, there to await
his further destination. Florence was
still suffering under the before-mentioned
contagion ; and Sienna was at last fixed
on as the place of his relegation. He
would have been shut up in some convent
in that city, if Nicolini had not recom-
mended as a more suitable residence, the
palace of the Archishop Piccolomini,
whom he knew to be among Galileo's
warmest friends. Urban consented to
the change, and Galileo finally left Rome
for Sienna in the early part of July.

Piccolomini received him with the ut-
most kindness, controlled of course by
the strict injunctions which were dis-
patched from Rome, not to suffer him
on any account to quit the confines of
the palace. Galileo continued at Sienna
in this state of seclusion till December
of the same year, when the contagion
having ceased in Tuscany, he applied for
permission to return to his villa at Arcetri.
This was allowed, subject to the same
restrictions under which he had been re-
siding with the archbishop.

GALILEO.

65

CHAPTER XIV.

Extracts from the Dialogues on the
System.

AFTER narrating- the treatment to
which Galileo was subject on account
of his admirable Dialogues, it will
not be irrelevant to endeavour, by a
few extracts, to convey some idea of
the style in which they are written.
It has been mentioned, that he is con-
sidered to surpass all other Italian
writers (unless we except Machiavelli)
in the purity and beauty of his lan-
guage, and indeed his principal fol-
lowers, who avowedly imitated his style,
make a distinguished group among the
classical authors of modern Italy. He
professed to have formed himself from
the .study of Ariosto, whose poems he
passionately admired, insomuch that he
could repeat the greater part of them,
as well as those of Berni and Petrarca,
all which he was in the frequent habit
of quoting in conversation. The fashion
and almost universal practice of that
day was to write on philosophical sub-
jects in Latin ; and although Galileo
wrote very passably in that language,
yet he generally preferred the use of
Italian, for which he gave his reasons in
the following characteristic manner : —

" I wrote in Italian because I wished
every one to be able to read what I
wrote ; and for the same cause I have
written my last treatise in the same
language: the reason which has induced
me is, that I see young men brought to-
gether indiscriminately to study to be-
come physicians, philosophers, &c., and
whilst many apply to such professions
who are most unfit for them, others who
would be competent remain occupied
either with domestic business, or with
other employments alien to literature ;
who, although furnished, as Ruzzante
might say, with ^decent set of brains, yet,
not being able to understand things
written in gibberish, take it into their
heads, that in these crabbed folios there
must be some grand hocus pocus of logic
and philosophy much too high up for them
to think of jumping at, I want them
to know, that as Nature has given eyes
to them just as well as to philosophers
for the purpose of seeing her works, she
has also given them brains for examin-
ing and understanding them."

The general structure of the dialogues
has been already described*; we shall

* See page 56.

therefore premise no more than the
judgment pronounced on them by a
highly gifted writer, to supply the de-
ficiencies of our necessarily imperfect
analysis.

" One forms a very imperfect idea of
Galileo, from considering the discoveries
and inventions, numerous and splendid
as they are, of which he was the undis-
puted author. It is by following his
reasonings, and by pursuing the train of
his thoughts, in his own elegant, though
somewhat diffuse exposition of them,
that we become acquainted with the
fertility of his genius — with the sagacity,
penetration, and comprehensiveness of
his mind. The service which he ren-
dered to real knowledge is to be esti-
mated, not only from the truths which
he discovered, but from the errors which
he detected — not merely from the sound
principles which he established, but from
the pernicious idols which he overthrew.
The dialogues on the system are written
with such singular felicity, that one reads
them at the present day, when the truths
contained in them are known and ad-
mitted, with all the delight of novelty,
and feels one's self carried back to the
period when the telescope was first di-
rected to the heavens, and when the
earth's motion, with all its train of con-
sequences, was proved for the first
time."*

The first Dialogue is opened by an at-
tack upon the arguments by which Aris-
totle pretended to determine a priori the
necessary motions belonging to different
parts of the world, and on his favourite
principle that particular motions belong
naturally to particular substances. Sal-
viati (representing Galileo) then objects
to the Aristotelian distinctions between
the corruptible elements and incorrupti-
ble skies, instancing among other things
the solar spots and newly appearing
stars, as arguments that the other hea-
venly bodies may probably be subjected
to changes similar to those which are
continually occurring on the earth, and
that it is the great distance alone which
prevents their being observed. After a
long discussion on this point, Sagredo
exclaims, " I see into the heart of Sim-
plicio, and perceive that he is much
moved by the force of these too conclu-
sive arguments; but methinks I hear
him say — ' Oh, to whom must we betake
ourselves to settle our disputes if Aris-
totle be removed from the chair ? What

* Playfair's Dissertation, Supp. Encyc. Brit.

66

GALILEO.

other author have we to follow in our
schools, our studies, and academies?
What philosopher has written on all the
parts of Natural Philosophy, and so
methodically as not to have overlooked
a single conclusion ? Must we then
desolate this fabric, by which so many
travellers have been sheltered ? Must
we destroy this asylum, this Prytaneum
wherein so many students have found
a convenient resting-place, where with-
out being exposed to the injuries of the
weather, one may acquire an intimate
knowledge of nature, merely by turning
over a few leaves ? Shall we level this
bulwark, behind which we are safe
from every hostile attack? I pity him
no less than I do one who at great ex-
pense of time and treasure, and with
the labour of hundreds, has built up a
very noble palace ; and then, because of
insecure foundations, sees it ready to
fail — unable to bear that those walls be
stripped that are adorned with so many
beautiful pictures, or to suffer those
columns to fall that uphold the stately
galleries, or to see ruined the gilded
roofs, the chimney-pieces, the friezes,
and marble cornices erected at so much
cost, he goes about it with girders and
props, with shores and buttresses, to
hinder its destruction."

Salviati proceeds to point out the
many points of similarity between the
earth and moon, and among others
which we have already mentioned, the
following remark deserves especial no-
tice:—

" Just as from the mutual and uni-
versal tendency of the parts of the earth
to form a whole, it follows that they all
meet together with equal inclination,
and that they may unite as closely as
possible, assume the spherical form ;
why ought we not to believe that the
moon, the sun, and other mundane
bodies are also of a round figure, from
no other; reason than from a common
instinct and natural concourse of all
their component parts ; of which if
by accident any one should be violently
separated from its whole, is it not rea-
sonable to believe that spontaneously,
and of its natural instinct, it would re-
turn? It may be added that if any
centre of the universe may be assigned,
to which the whole terrene globe if
thence removed would seek to return,
we shall find most probable that the sun
is placed in it, as by the sequel you shall
understand/'
Many who are but superficially ac-

quainted with the History of Astro-
nomy, are apt to suppose that New-
ton's great merit was in his being the
first to suppose an attractive force
existing in and between the different
bodies composing the solar system.
This idea is very erroneous ; Newton's
discovery consisted in conceiving and
proving the identity of the force with
which a stone falls, and that by which
the moon falls, towards the earth (on
an assumption that this force becomes
weaker in a certain proportion as the
distance increases at which it operates),
and in generalizing this idea, in apply-
ing it to all the visible creation, and
tracing the principle of universal gravi-
tation with the assistance of a most re-
fined and beautiful geometry into many
of its most remote consequences. But
the general notion of an attractive force
between the sun, moon, and planets,
was very commonly entertained before
Newton was born, and may be traced
back to Kepler, who was probably the
first modern philosopher who suggested
it. The following extraordinary pas-
sages from his "Astronomy" will shew
the nature of his conceptions on this
subject : —

"The true doctrine of gravity is
founded on these axioms : every corpo-
real substance, so far forth as it is cor-
poreal, has a natural fitness for resting
in every place where it may be situated
by itself beyond the sphere of influence
of its cognate body. Gravity is a mutual
affection between cognate bodies to-
wards union or conjunction (similar in
kind to the magnetic virtue), so that the
earth attracts a stone much rather than
the stone seeks the earth. Heavy bo-
dies (if in the first place we put the
earth in the centre of the world) are not
carried to the centre of the world in its
quality of centre of the world, but as to
the centre of a cognate round body,
namely the earth. So that wheresoever
the earth may be placed or whitherso-
ever it may be carried by its animal fa-
culty, heavy bodies will always be carried
towards it. If the earth were not round
heavy bodies would not tend from every
side in a straight line towards the centre
of the earth, but to different points from
different sides. If two stones were placed
in any part of the world near each other
and beyond the sphere of influence of a
third cognate body, these stones, like
two magnetic needles, would come to-
gether in the intermediate point, each
approaching the other by a space pro-

GALILEO.

67

portional to the comparative mass of the
other. If the moon and earth were not
retained in their orbits by their animal
force or some other equivalent, the earth
would mount to the moon by a fifty-
fourth part of their distance, and the
moon fall towards the earth through the
other fifty-three parts, and would there
meet, assuming however that the sub-
stance of both is of the same density. If
the earth should cease to attract its wa>-
ters to itself, all the waters of the sea
would be raised, and would flow to the
body of the moon*."

He also conjectured that the irregu-
larities in the moon's motion were
caused by the joint action of the sun
and earth, and recognized the mutual
action of the sun and planets, when he
declared the mass and density of the
sun to be so great that the united attrac-
tion of the other planets cannot remove
it from its place. Among these bold
and brilliant ideas, his temperament led
him to introduce others which show
how unsafe it was to follow his guidance,
and which account for, if they do not al-
together justify, the sarcastic remark of
Ross, that " Kepler's opinion that the
planets are moved round by the sunne,
and that this is done by sending forth a
magnetic virtue, and that the sun-beames
are like the teethe of a wheele taking
hold of the planets, are senslesse crotchets
fitter for a wheeler or a miller than a
philosopher." t Roberval took up Kep-
ler's notions, especially in the tract which,
he falsely attributed to Aristarchus, and
it is much to be regretted that Roberval
should deserve credit for anything con-
nected with that impudent fraud. The
principle of universal gravitation, though
not the varying proportion, is distinctly
assumed in it, as the following passages
will sufficiently prove: " In every single
particle of the earth, and the terrestrial
elements, is a certain property or acci-
dent which we suppose common to the
whole system of the world, by virtue of
which all its parts are forced together,
and reciprocally attract each other ; and
this property is found in a greater or
less degree in the different particles, ac-
cording to their density. If the earth
be considered by itself, its centres of
magnitude and virtue, or gravity, as we
usually call it, will coincide, to which
all its parts ^ tend in a straight line, as

* Astronomia Nova. Pragae. 1609.

f The new Planet no Planet, or the Earth no wan-
dering Star, except in the wandering heads of Gali-
leans. London, 1646.

well by their own exertion or gravity,
as by the reciprocal attraction of all the
rest," In a subsequent chapter, Roberval
repeats these passages nearly in the
same words, applying them to the whole
solar system, adding, that " the force of
this attraction is not to be considered
as residing in the centre itself, as some
ignorant people think, but in the whole
system whose parts are equally disposed
round the centre*". This very curious
work was reprinted in the third volume,
of the Reflexiones Physico-Mathematicce
of Mersenne, from whom Roberval pre-
tended to have received the Arabic ma-
nuscript, and who is thus irretrievably
implicated in the rforgery.t The last
remark, denying the attractive force to
be due to any property of the central
point, seems aimed at Aristotle, who,
in a no less curious passage, maintain-
ing exactly the opposite opinion, says,
" Hence, we may better understand
what the ancients have related, that
like things are wont to have a tendency
to each other. For this is not abso-
lutely true ; for if the earth were to be
removed to the place now occupied by
the moon, no part of the earth would
then have a tendency towards that place,
but would still fall towards the point
which the earth's centre now occupies.''^
Mersenne considered the consequences
of the attractive force of each particle
of matter so far as to remark, that if a
body were supposed to fall towards the
centre of the earth, it would be retarded
by the attraction of the part through
which it had already fallen.§ Galileo
had not altogether neglected to specu-
late on such a supposition, as is plain
from the following extract. It is taken
from a letter to Carcaville, dated from
Aicetri, in 1637. " I will say farther,
that I have not absolutely and clearly
satisfied myself that a heavy body
would arrive sooner at the centre of the
earth, if it began to fall from the dis-
tance only of a single yard, than another
which should start from the distance of
a thousand miles. I do not affirm this,
but I offer it as a paradox." f

It is very difficult to offer any satis-
factory comment upon this passage ; it
may be sufficient to observe that this
paradoxical result was afterwards de-

* Aristarchi Samii de Mundi Systemate. Parisiis
1644.

f See page 12.
I De Coelo.lib. iv. cap. 3.

§ Reflexiones Fhysico-Mathematicse, Pansiis,16±7»
If Yeutuvi.

68 GALILEO.

duced by Newton, as one of the conse-
quences of the general law with which all
nature is pervaded, but with which there
is no reason to believe that Galileo had
any acquaintance; indeed the idea is
fully negatived by other passages in this
same letter. This is one of the many
instances from which we may learn to
be cautious how we invest detached
passages of the earlier mathemati-
cians with a meaning which in many
cases their authors did not contem-
plate. The progressive development of
these ideas in the hands of Wallis,
Huyghens, Hook, Wren, and New-
ton, would lead us too far from our
principal subject. There is another
passage in the third dialogue connected
with this subject, which it may be as
well to notice in this place. " The
parts of the earth have such a pro-
pensity to its centre, that when it changes
its place, although they may be very
distant from the globe at the time of the
change, yet must they follow. An ex-
ample similar to this is the perpetual
sequence of the Medicean stars, although
always separated from Jupiter. The
same may be said of the moon, obliged
to follow the earth. And this may serve
for those simple ones who have difficulty
in comprehending how these two globes,
not being chained together, nor strung
upon a pole, mutually follow each other,
so that on the acceleration or retardation
of the one, the other also moves quicker
or slower."

The second Dialogue is appropriated
chiefly to the discussion of the diurnal
motion of the earth ; and the principal
arguments urged by Aristotle, Ptolemy,
and others, are successively brought
forward and confuted. The opposers of
the earth's diurnal motion maintained,
that if it were turning round, a stone
dropped from the top of a tower would
not fall at its foot ; but, by the rotation
of the earth to the eastward carrying
away the tower with it, would be left at
a great distance to the westward; it
was common to compare this effect to a
stone dropped from the mast-head of a
ship, and without any regard to truth
it was boldly asserted that this would
fall considerably nearer the stern than
the foot of the mast, if the ship were in
rapid motion. The same argument was
presented in a variety of forms, — such as
that a cannon-ball shot perpendicularly
upwards would not fall at the same
spot ; that if fired to the eastward it
would fly farther than to the westward ;

that a mark to the east or west would
never be hit, because of the rising or
sinking of the horizon during the flight
of the ball ; that ladies ringlets would all
stand out to the westward,* with other
conceits of the like nature : to which the
general reply is given, that in all these
cases the stone, or ball, or other body,
participates equally in the motion of the
earth, which, therefore, so far as regards
the relative motion of its parts, may be
disregarded. The manner in which this
is illustrated, appears in the following
extract from the dialogue : — Sagredo.
If the nib of a writing pen which was
in the ship during my voyage direct from
Venice to Alexandria, had had the power
of leaving a visible mark of all its path,
what trace, what mark, what line would
it have left? — "Simplicio. It would have
left a line stretched out thither from
Venice not perfectly straight, or to speak
more correctly, not perfectly extended in
an exact circular arc, but here and there
more and less curved accordingly as
the vessel had pitched more or less ; but
this variation in some places of one or
two yards to the right or left, or up or
down in a length of many hundred miles,
would have occasioned but slight altera-
tion in the whole course of the line, so
that it would have been hardly sensible,
and without any great error we may
speak of it as a perfectly circular arc. —
Sagred. So that the true and most
exact motion of the point of the pen
would also have been a perfect arc of a
circle if the motion of the vessel, ab-
stracting from the fluctuations of the
waves, had been steady and gentle ; and
if I had held this pen constantly in my
hand, and had merely moved it an inch
or two one way or the other, what alter-
ation would that have made in the true
and principal motion? — Simpl. Less
than that which would be occasioned in
a line a thousand yards long, by varying
here and there from perfect straightness
by the quantity of a flea's eye. — Sagred.
If then a painter on our quitting the
port had begun to draw with this pen
on paper, and had continued his draw-
ing till we got to Alexandria, he would
have been able by its motion, to produce
an accurate representation of many ob-
jects perfectly shadowed, and filled up on
all sides with landscapes, buildings, and
animals, although all the true, real, and
essential motion of the point of his pen
would have been no other but a very

•Jliccioli.

GALILEO.

69

long and very simple line ; and as to the
peculiar work of the painter, he would
have drawn it exactly the same if the
ship had stood still. Therefore, of the
very protracted motion of the pen, there
remain no other traces than those marks
drawn upon the paper, the reason of this
being that the great motion from Venice
to Alexandria was common to the paper,
the pen, and everything that was in the
ship ; but the trifling motion forwards
and backwards, to the right and left,
communicated by the painter's fingers
to the pen, and not to the paper, from
being peculiar to the pen, left its mark
upon the paper, which as to this mo-
tion was immoveable. Thus it is like-
wise true that in the supposition of the
earth's rotation, the motion of a falling
stone is really a long track of many
hundreds and thousands of yards ; and
if it could have delineated its course in
the calm air, or on any other surface,
it would have left behind it a very long
transversal line; but that part of all
this motion which is common to the
stone, the tower, and ourselves, is im-
perceptible by us and the same as if
not existing, and only that part remains
to be observed of which neither we nor
the tower partake, which in short is the
fall of the stone along the tower."

The mechanical doctrines introduced
into this second dialogue will be noticed
on another occasion ; we shall pass on
to other extracts, illustrative of the ge-
neral character of Galileo's reasoning : —
" Salviati. I did not say that the earth
has no principle, either" internal or ex-
ternal, of its motion of rotation, but I
do say that I know not which of the
two it has, and that my ignorance has
no power to take its motion away ; but
if this author knows by what principle
other mundane bodies, of the motion of
which we are certain, are turned round,
I say that what moves the Earth is
something like that by which Mars and
Jupiter, and, as he believes, the starry
sphere, are moved round ; and if he will
satisfy me as to the cause of their
motion, I bind myself to be able to
tell him what moves the earth. Nay
more ; I undertake to do the same if he
can teach me what it is which moves
the parts of the earth downwards. —
Simpl. The cause of this effect is no-
torious, and every one knows that it is
Gravity. — Salv. You are out, Master

ture of the thing, of which nature you
do not know one tittle more than you
know of the nature of the moving cause
of the rotation of the stars, except it be
the name which has been given to the
one, and made familiar and domestic,
by the frequent experience we have of it
many thousand times in a day ; but of
the principle or virtue by which a stone
falls to the ground, we really know no
more than we know of the principle which
carries it upwards when thrown into the
air, or which carries the moon round its
orbit, except, as I have said, the name
of gravity which we have peculiarly
and exclusively assigned to it ; whereas
we speak of the other with a more ge-
neric term, and talk of the virtue im-
pressed, and call it either an assisting or
an informing intelligence, and are con-
tent to say that Nature is the cause of
an infinite number of other motions."

Simplicio is made to quote a passage
from Schemer's book of Conclusions
against Copernicus, to the following ef-
fect : — " ' If the whole earth and water
were annihilated, no hail or rain would
fall from the clouds, but would only be
naturally carried round in a circle, nor
would any fire or fiery thing ascend,
since, according to the not improbable
opinion of these others, there is no fire
in the upper regions.' — Salv. The fore-
sight of this philosopher is most ad-
mirable and praiseworthy, for he is not
content with providing for things that
might happen during the common
course of nature, but persists in shew-
ing his care for the consequences of
what he very well knows will never
come to pass. Nevertheless, for the
sake of hearing some of his notable con-
ceits, I will grant that if the earth and
water were annihilated there would be
no more hail or rain, nor would fiery
matter ascend any more, but would con-
tinue a motion of revolution. What is
to follow ? What conclusion is the phi-
losopher going to draw ? — Simpl. This
objection is in the very next words —
4 Which nevertheless (says he) is con-
trary to experience and reason.' — Salv.
Now I must yield: since he has so
great an advantage over me as ex-
perience, with which I am quite unpro-
vided. For hitherto I have never hap-
pened to see the terrestial earth and
water annihilated, so as to be able to
observe what the hail and fire did in the

Simplicio ; you should say that every confusion. But does he.tell us for our in-
ane knows that it is called Gravity ; but formation at least what they did I—Simp.
I do not ask you the name but the na- No, he does not say any thing more. —

GALILEO.

Salv. I would give something to have
a word or two with this person, to ask
him whether, when this globe vanished,
it also carried away the common centre of
gravity, as I fancy it did, in which case
I take it that the hail and water would
remain stupid and confounded amongst
the clouds, without knowing what to do
with themselves. . . . And lastly, that I
may give this philosopher a less equivo-
cal answer, I tell him that I know as
much of what would follow after the
annihilation of the terrestrial globe, as
he could have known what was about
to happen in and about it, before it was
created."

Great part of the third Dialogue is
taken up with discussions on the paral-
lax of the new stars of 1572 and 1604,
in which Delambre notices that Galileo
does not employ logarithms in his cal-
culations, although their use had been
known since Napier discovered them in
1616 : the dialogue then turns to the an-
nual motion " first taken from the Sun
and conferred upon the Earth by Aris-
tarchus Samius, and afterwards by Co-
pernicus." Salviati speaks of his con-
temporary philosophers with great con-
tempt— " If you had ever been worn out
as I have been many and many a time
with hearing what sort of stuff is suf-
ficient to make the obstinate vulgar un-
persuadable, I do not say to agree with,
but even to listen to these novelties, I
believe your wonder at finding so few
followers of these opinions would greatly
fall off. But little regard in my judgment
is to be had of those understandings who
are convinced and immoveably persuaded
of the fixedness of the earth, by seeing
that they are not able to breakfast this
morning at Constantinople, and sup in
the evening in Japan, and who feel satis-
fied that the earth, so heavy as it is,
cannot climb up above the sun, and then
come tumbling in a breakneck fashion
down again ! " * This remark serves to
introduce several specious arguments
against the annual motion of the earth,
which are successively confuted, and it
is shewn how readily the apparent sta-
tions and retrogradations of the planets
are accounted for on this supposition.

* The notions commonly entertained of ' up' and
* down,' as connected with the observer's own situ-
ation, had long been a stumbling-block in the way
of the new doctrines. When Columbus held out the
certainty of arriving in India by sailing to the west-
ward on account of the earth's roundness, it was
gravely objected, that it might be well enough to
sail down to India, but that the chief difficulty would
consist in climbing up back again.

The following is one of the frequently
recurring passages in which Galileo,
whilst arguing in favour of the enor-
mous distances at which the theory of
Copernicus necessarily placed the fixed
stars, inveighs against the arrogance
with which men pretend to judge of mat-
ters removed above their comprehension.
" Simpl. All this is very well, and it is
not to be denied that the heavens may
surpass in bigness the capacity of our
imaginations, as also that God might
have created it yet a thousand times
larger than it really is, but we ought
not to admit anything to be created in
vain, and useless in the universe. Now
whilst we see this beautiful arrangement
of the planets, disposed round the earth
at distances proportioned to the effects
they are to produce on us for our be-
nefit, to what purpose should a vast
vacancy be afterwards interposed be-
tween the orbit of Saturn and the starry
spheres, containing not a single star, and
altogether useless and unprofitable ? to
what end? for whose use and advan-
tage ? — Salv. Methinks we arrogate too
much to ourselves, Simplicio, when we
will have it that the care of us alone
is the adequate and sufficient work and
bound, beyond which the divine wisdom
and power does and disposes of nothing.
I feel confident that nothing is omitted
by the Divine Providence of what con-
cerns the government of human affairs ;
but that there may not be other things
in the universe dependant upon His su-
preme wisdom, I cannot for myself, by
what my reason holds out to me, bring
myself to believe. So that when I am told
of the uselessness of an immense space
interposed between the orbits of the
planets and the fixed stars, empty and
valueless, I reply that there is teme-
rity in attempting by feeble reason to
judge the works of God, and in calling
vain and superfluous every part of the
universe which is of no use to us. — Sagr.
Say rather, and I believe you would say
better, that we have no means of know-
ing what is of use to us ; and I hold it
to be one of the greatest pieces of arro-
gance and folly that can be in this world
to say, because I know not of what use
Jupiter or Saturn are to me, that there-
fore these planets are superfluous ; nay
more, that there are no such things in
nature. To understand what effect is
worked upon us by this or that heavenly
body (since you will have it that all
their use must have a reference to us),
it would be necessary to remove it for a

GALILEO.

71

while, and then the effect which I find
no longer produced in me, I may say
that it depended upon that star. Besides,
who will dare say that the space which
they call too vast and useless between
Saturn and the fixed stars is void of
other bodies belonging to the universe.
Must it be so because we do not see
them : then I suppose the four Medi-
cean planets, and the companions of
Saturn, came into the heavens when we
first began to see them, and not before !
and, by the same rule, the other innu-
merable fixed stars did not exist before
men saw them. The nebulae were till
lately only white flakes, till with the
telescope we have made of them con-
stellations of bright and beautiful stars.
Oh presumptuous ! rather, Oh rash
ignorance of man ! "

After a discussion on Gilbert's Theory
of Terrestrial Magnetism, introduced by
the parallelism of the earth's axis, and of
which Galileo praises very highly both
the method and results, the dialogue
proceeds as follows : — " Simpl. It ap-
pears to me that Sig. Salviati, with a
fine circumlocution, has so clearly ex-
plained the cause of these effects, that
any common understanding, even though
unacquainted with science, may compre-
hend it : but we, confining ourselves to
the terms of art, reduce the cause of
these and other similar natural pheno-
mena to sympathy, which is a certain
agreement and mutual appetency arising
between things which have the same
qualities, just as, on the other hand, that
disagreement and aversion, with which
other things naturally repel and abhor
each other, we style antipathy. — Sagr.
And thus with these two words they are
able to give a reason for the great num-
ber of effects and accidents which we
see, not without admiration, to be pro-
duced in Nature. But it strikes me that
this mode of philosophising has a great
sympathy with the style in which one of
my friends used to paint : on one part
of the canvas he would write with
chalk — there I will have a fountain,with
Diana and her nymphs ; here some har-
riers ; in this corner I will have a hunts-
man, with a stag's head ; the rest may
be a landscape of wood and mountain ;
and what remains to be done may be
put in by the colourman : and thus he
flattered himself that he had painted the
story of Actaeon, having contributed
nothing to it beyond the names."

The fourth Dialogue is devoted en-
tirely to an examination of the tides, and

is a development and extension of the
treatise already mentioned to have
been sent to the Archduke Leopold,
in 1618*. Galileo was uncommonly
partial to his theory of the tides, from
which he thought to derive a direct
proof of the earth's motion in her
orbit ; and although his theory was
erroneous, it required a farther advance
in the science of motion than had
been attained even at a much later
period to point out the insufficiency of
it. It is well known that the problem of
explaining the cause of this alternate
motion of the waters had been consi-
dered from the earliest ages one of the
most difficult that could be proposed,
and the solutions with which different
inquirers were obliged to rest contented,
shew that it long deserved the name
given to it, of " the grave of human cu-
riosity!'." Riccioli has enumerated se-
veral of the opinions which in turn had
their favourers and supporters. One
party supposed the rise of the waters to
be occasioned by the influx of rivers into
the sea ; others compared the earth to
a large animal, of which the tides indi-
cated the respiration ; a third theory
supposed the existence of subterraneous
fires, by which the sea was periodically
made to boil ; others attributed the cause
of a similar change of temperature to
the sun and moon.

There is an unfounded legend, that
Aristotle drowned himself in despair of
being able to invent a plausible expla-
nation of the extraordinary tides in the
Euripus. His curiosity on the subject
does not appear to have been so acute
(judging from his writings) as this story
would imply. In one of his books he
merely mentions a rumour, that there
are great elevations or swellings of the
seas, which recur periodically, accord-
ing to the course of the moon. Lalande,
in the fourth volume of his Astronomy,
has given an interesting account of the
opinion of the connection of the tides
with the moon's motion. Pytheas of
Marseilles, a contemporary of Aristotle,
was the first who has been recorded as
observing, that the full tides occur at
full moon, and the ebbs at new moonj.
This is not quite correctly stated; for
the tide of new moon is known to be
still higher than the rise at the full, but
it is likely enough, that the seeming in-
accuracy should be attributed, not to

* See page 50. i Riccioli Almag. Nov.

K. Plutarch, De placit, Philos. lib. iii. c. 1?.

72

GALILEO.

Pytheas, but to his biographer Plutarch,
who, in many instances, appears to
have viewed the opinions of the old
philosophers through the mist of his
own prejudices and imperfect informa-
tion. The fact is, that, on the same
day when the tide rises highest, it also
ebbs lowest ; and Pytheas, who, according
to Pliny, had recorded a tide in Britain of
eighty cubits, could not have been
ignorant of this. Posidonius, as quoted
by Strabo, maintained the existence of
three periods of the tide, daily, monthly,
and annual, " in sympathy with the
moon." * Pliny, in his vast collection
of natural observations, not unaptly
styled the Encyclopaedia of the Antients,
has the following curious passages : —
'* The flow and ebb of the tide is very
wonderful ; it happens in a variety of
ways, but the cause is in the sun and
moont." He then very accurately de-
scribes the course of the tide during a
revolution of the moon, and adds:
" The flow takes place every day at a
different hour ; being waited on by the
star, which rises every day in a different
place from that of the day before, and
•with greedy' draught drags the seas with
it$." " When the moon is in the north,
and further removed from the earth, the
tides are more gentle than when digress-
ing to the south, she exerts her^force
with a closer effort^."

The College of Jesuits at Coimbra
appears to deserve the credit of first
clearly pointing out the true relation
between the tides and the moon, which
was also maintained a few years
later by Antonio de Dominis and
Kepler. In the Society's commentary
on Aristotle's book on Meteors, after
refuting the notion that the tides are
caused by the light of the sun and moon,
they say, " It appears more probable to
us, without any rarefaction, of which
there appears no need or indication,
that the moon raises the waters by some
inherent power of impulsion, in the same
manner as a magnet moves iron ; and
according to its different aspects and
approaches to the sea, and the obtuse
or acute angles of its bearing, at one time
to attract and raise the waters along
the shore, and then again to leave them
to sink down by their own weight, and

eix; ry fft^vr,. Geographic, lib. iii.

| Historia Naturalis, lit. ii. c, 97.

t Ut ancillante sidere, trahenteque secum avido
hausm maria.

§ Eadem Aquilonia, et a terris longius recedente,
mitiores qaam cum, in Austros digressa, propiore
nisuvim suam exercet.

to gather into a lower level.*" The
theory of Universal Gravitation seems
here within the grasp of these philo-
sophers, but unfortunately it did not
occur to them that possibly the same
attraction might be exerted on the earth
as well as the water, and that the tide
was merely an effect of the diminution
of force, owing to the increase of dis-
tance, with which the centre of the earth
is attracted, as compared with that
exerted on its surface. This idea, so
happily seized afterwards by Newton,,
might at once have furnished them with
a satisfactory explanation of the tide,
which is observed on the opposite side
of the earth as well as immediately
under the moon. They might have
seen that in the latter case the centre
of the earth is pulled away from the
water, just as in the former the water
is. pulled away from the centre of the
earth, the sensible effect to us being
in both cases precisely the same. For
want of this generalization, the inferior
tide as it is called presented a formi-
dable obstacle to this theory, and the
most plausible explanation that was
given was, that this magnetic virtue ra-
diated out from the moon was reflected,
by the solid heavens, and concentrated
again as in a focus on the opposite side
of the earth. The majority of modern-
astronomers who did not admit the
existence of any solid matter fit for
producing the effect assigned to it, found
a reasonable difficulty in acquiescing
in this explanation. Galileo, who men-
tions the Archbishop of Spalatro's book,
treated the theory of attraction by the
moon as absurd. " This motion of the
seas is local and sensible, made in an
immense mass of water, and cannot be
brought to obey light, and warmth, and
predominancy of occult qualities, and
such like vain fancies ; all which are so
far from being the cause of the tide, that
on the contrary the tide is the cause of
them, inasmuch as it gives rise to these-
ideas in brains which are more apt for
talkativeness and ostentation, than for
speculation and inquiry into the secrets
of Nature ; who, rather than see them-
selves driven to pronounce these wise,
ingenuous, and modest words — 1 do not
know, — will blurt out from their tongues
and pens all sorts of extravagancies."

Galileo's own theory is introduced by
the following illustration, \Mhich indeed

* Commentarii Collegii Conimbricensis. Colcmiaet

GALILEO.

73

probably suggested it, as he was in
the habit of suffering no natural phe-
nomena, however trivial in appearance,
to escape him. He felt the advantage
of this custom in being furnished on all
occasions with a stock of homely illus-
trations, to which the daily experience
of his hearers readily assented, and
which he could shew to be identical in
principle with the phenomena under
discussion. That he was mistaken in
applying his observations in the present
instance cannot be urged against the
incalculable value of such a habit.

" We may explain and render sensible
these effects by the example of one of
those barks which come continually
from Lizza Fusina, with fresh water
for the use of the city of Venice. Let
us suppose one of these barks to come
thence with moderate velocity along the
canal, carrying gently the water with
which it is filled, and then, either by
touching the bottom, or from some
other hindrance which is opposed to it,
let it be notably retarded ; the water
will not on that account lose like the
bark the impetus it has already ac-
quired, but will forthwith run on
towards the prow where it will sensibly
rise, and be depressed at the stern. If
on the contrary the said vessel in the
middle of its steady course shall receive
a new and sensible increase of velocity,
the contained water before giving into
it will persevere for some time in its
slowness, and will be left behind that is
to say towards the stern where con-
sequently it will rise, and sink at the
head. — Now, my masters, that which
the vessel does in respect of the water
contained in it, and that which the
water does in respect of the vessel con-
taining it, is the same to a hair as what
the Mediterranean vase does in respect
of the water which it contains, and that
the waters do in respect of the Medi-
terranean vase which contains them.
We have now only to demonstrate how,
and in what manner it is true that the
Mediterranean, and all other gulfs, and
in short all the parts of the earth move
with a motion sensibly not uniform,
although no motion results thence to
the whole globe which is not perfectly
uniform and regular."

This unequable motion is derived from
a combination of the earth's motion on
her axis, and in her orbit, the conse-
quence of which is that a point under
the sun is carried in the same direction
by the annual and diurnal velocities,

whereas a point on the opposite side of
the globe is carried in opposite direc-
tions by the annual and diurnal motions,
so that in every twenty-four hours the
absolute motion through space of every
point in the earth completes a cycle of
varying swiftness. Those readers who
are unacquainted with the mathematical
theory of motion must be satisfied with
the assurance that this specious repre-
sentation is fallacious, and that the
oscillation of the water does not in the
least result from the causes here as-
signed to it : the reasoning necessary to
prove this is not elementary enough to
be introduced here with propriety.

Besides the principal daily oscillation
of the water, there is a monthly ine-
quality in the rise and fall, of which the
extremes are called the spring and neap
tides : the manner in which Galileo
attempted to bring his theory to bear
upon these phenomena is exceedingly-
curious.

" It is a natural and necessary truth,
that if a body be made to revolve, the
time of revolution will be greater in a,
greater circle than in a less : this is
universally allowed, and fully confirmed
by experiments, such for instance as
these : — In wheel clocks, especially in
large ones, to regulate the going, the
workmen fit up a bar capable of revolv-
ing horizontally, and fasten two leaden
weights to the ends of it; and if the
clock goes too slow, by merely ap-
proaching these weights somewhat to-
wards the centre of the bar, they make
its vibrations more frequent, at which
time they are moving in smaller circles
than before*. — Or, if you fasten a weight
to a cord which you pass round a pulley
in the ceiling, and whilst the weight is
vibrating draw in the cord towards you,
the vibrations will become sensibly ac-
celerated as the length of the string
diminishes. Wre may observe the same
rule to hold among the celestial motions
of the planets, of which we have a
ready instance in the Medicean planets,
which revolve in such short periods
round Jupiter. We may therefore
safely conclude, that if the moon for
instance shall continue to be forced
round by the same moving power, and
were to move in a smaller circle, it
would shorten the time of its revolu-
tion. Now this very thing happens
in fact to the moon, which I have just
advanced on a supposition. Let us call

* See fig. 1, p. 96.

GALILEO.

to mind that we have already concluded
with Copernicus, that it is impossible to
separate the moon from the earth, round
which without doubt it moves in a
month : we must also remember that
the globe of the earth, accompanied
always by the moon, revolves in the
great circle round the sun in a year, in
which time the moon revolves round
the earth about thirteen times, whence
it follows that the moon is sometimes
near the sun, that is to say between
the earth and sun, sometimes far
from it, when she is on the outside of
the earth. Now if it be true that the
power which moves the earth and the
moon round the sun remains of the
same efficacy, and if it be true that the
same moveable, acted on by the same
force, passes over similar arcs of circles
in a time which is least when the circle
is smallest, we are forced to the conclu-
sion that at new moon, when in con-
junction with the sun, the moon passes
over greater arcs of the orbit round the
sun, than when in opposition at full
moon ; and this inequality of the moon
will be shared by the earth also. So
that exactly the same thing happens as
in the balance of the clocks ; for the
moon here represents the leaden weight,
which at one time is fixed at a greater
distance from the centre to make the
vibrations slower, and at another time
nearer to accelerate them."

Wallis adopted and improved this
theory in a paper which he inserted in
the Philosophical Transactions for 1666,
in which he declares, that the circular mo-
tion round the sun should be considered
as taking place at a point which is the
centre of gravity of the earth and moon.
" To the first objection, that it appears
not how two bodies that have no tie can
have one common centre of gravity, I
shall only answer, that it is harder to
show how they have it, than that they
have it*.M As Wallis was perfectly
competent from the time at which he
lived, and his knowledge of the farthest
advances of science in his time, to appre-
ciate the value of Galileo's writings, we
shall conclude this chapter with the
judgment that he has passed upon them
in the same paper. " Since Galileo, and
after him Torricelli and others have ap-
plied mechanical principles to the solv-
ing of philosophical difficulties, natural
philosophy is well known to have been
rendered more intelligible, and to have

» Phil. Trans., No. 16, August 1666.

made a much greater progress in less
than a hundred years than before for
many ages."

CHAPTER XV.

Galileo at Arcetri — Becomes Blind —
Moon's Librarian — Publication of
the Dialogues on Motion.

WE have already alluded to the imper-
fect state of the knowledge possessed
with regard to Galileo's domestic life
and personal habits; there is reason
however to think that unpublished
materials exist from which these outlines
might be in part filled up. Venturi in-
forms us that he had seen in the collec-
tion from which he derived a great part
of the substance of his Memoirs of
Galileo, about one hundred and twenty
manuscript letters, dated between the
years 1623 and 1633, addressed to him
by his daughter Maria, who with her sis-
ter had attached herself to the convent
of St. Matthew, close to Galileo's usual
place of residence. It is difficult not to
think that much interesting information
might be obtained from these, with respect
to Galileo's domestic character. The very
few published extracts confirm our fa-
vourable impressions of it, and convey
a pleasing idea of this his favourite
daughter. Even when, in her affec-
tionate eagerness to soothe her father's
wounded feelings at the close of his im-
prisonment in Rome, she dwells with
delight upon her hopes of being allowed
to relieve him, by taking on herself the
penitential recitations which formed a
part of his sentence, the prevalent feel-
ing excited in every one by the perusal
must surely be sympathy with the filial
tenderness which it is impossible to mis-
understand.

The joy she had anticipated in again
meeting her parent, and in compensat-
ing to him by her attentive affection the
insults of his malignant enemies, was
destined to be but of short duration.
Almost in the same month in which
Galileo returned ; to Arcetri she was
seized with a fatal illness ; and already
in the beginning of April, 1634, we
learn her death from the fruitless con-
dolence of his friends. He was deeply
and bitterly affected by this additional
blow, which came upon him when he
was himself in a weak and declining
state of health, and his answers breathe
a spirit of the most hopeless and gloomy
despondency.
In a letter written in. April to Boe-

GALILEO.

ehineri, his son's father-in-law, he says :
"The hernia has returned worse than
at first : my pulse is intermitting, ac-
companied with a palpitation of the
heart ; an immeasurable sadness and
melancholy ; an entire loss of appetite ;
I, am hateful to myself; and in short
I feel that I am called incessantly by
my dear daughter. In this state, I do
not think it advisable that Vincenzo
should set out on his journey, and leave
me, when every hour something may
occur, which would make it expedient
that he should be here." In this extre-
mity of ill health, Galileo requested leave
to go to Florence for the advantage of
medical assistance; but far from obtain-
ing permission, it was intimated that any
additional importunities would be no-
ticed by depriving him of the partial
liberty he was then allowed to enjoy.
After several years confinement at Ar-
cetri, during the whole of which time
he suffered from continual indisposi-
tion, the inquisitor Fariano wrote to
him in 1638, that the Pope permitted
his removal to Florence, for the purpose
of recovering his health ; requiring him
at the same time to present himself at
the Office of the Inquisition, where he
would learn the conditions on which this
favour had been granted. These were
that he should neither quit his house
nor receive his friends there; and so
closely was the letter of these instruc-
tions adhered to, that he was obliged to
obtain a special permission to go out to
attend mass during Passion week.
The strictness with which all personal
intercourse with his friends was inter-
rupted, is manifest from the result of
the following letter from the Duke of
Tuscany 's secretary of state to Nicolini,
his ambassador at Rome. " Signer
Galileo Galilei, from his great age and
the illnesses which afflict him, is in a
condition soon to go to another world ;
and although in this the eternal memory
of his fame and value is already secured,
yet his Highness is greatly desirous
that the world should sustain as little
loss as possible by his death ; that his
labours may not perish, but for the
public good may be brought to that per-
fection which he will not be able to give
them. He has in his thoughts many
things worthy of him, which he cannot
be prevailed on to communicate to any
but Father Benedetto Castelli, in whom
he has entire confidence. His Highness
wishes therefore that you should see
Castelli, and induce him to procure leave

to come to Florence for a few months
for this purpose, which his Highness
has very much at heart ; and if he ob-
tains permission, as his Highness hopes,
you will furnish him with money and
every thing else he may require for his
journey." Castelli, it will be remem-
bered, was at this time salaried by the
court of Rome. Nicolini answered
that Castelli had been himself to the
Pope to ask leave to go to Florence.
Urban immediately intimated his suspi-
cions that his design was to see Galileo,
and upon Castelli' s stating that certainly
it would be impossible for him to refrain
from attempting to see him, he received
permission to visit him in the company
of an officer of the Inquisition. At the
end of some months Galileo was re-
manded to Arcetri, which he never
again quitted.

In addition to his other infirmities, a
disorder which some years before had
affected the sight of his right eye re-
turned in 1636 ; in the course of the en-
suing year the other eye began to fail
also, and in a few months he became
totally blind. It would be difficult to
find any even among those who are the
most careless to make a proper use of
the invaluable blessing of sight, who
could bear unmoved to be deprived of it,
but on Galileo the loss fell with pe-
culiar and terrible severity ; on him who
had boasted that he would never cease
from using the senses which God had
given him, in declaring the glory of his
works, and the business of whose life
had been the splendid fulfilment of that
undertaking. "The noblest eye is
darkened," said Castelli, " which nature
ever made: an eye so privileged, and
gifted with such rare qualities, that it
may with truth be said to have seen,
more than all of those who are gone,
and to have opened the eyes of all who
are to come." His own patience and
resignation under this fatal calamity
are truly wonderful ; and if occasionally
a word of complaint escaped him, it was
in the chastened tone of the following ex-
pressions— " Alas ! your dear friend and
servant Galileo has become totally and
irreparably blind ; so that this heaven,
this earth, this universe, which with
wonderful observations I had enlarged
a hundred and thousand times beyond
the belief of by-gone ages, hencefor-
ward for me is shrunk into the narrow
space which I myself fill in it. — So it
pleases God : it shall therefore please
me also." Hopes were at first enter-

76

GALILEO.

tained by Galileo's friends, that the
blindness was occasioned by cataracts,
and that he might look forward to relief
from the operation of couching ; but it
very soon appeared that the disorder
was not in the humours of the eye, but
in a cloudiness of the cornea, the symp-
toms of which all external remedies
failed to alleviate.

As long as the power was left him, he
had indefatigably continued his astrono-
mical observations. Just before his
sight began to decay, he had observed a
new phenomenon in the moon, which is
now known by the name of the moon's
libration, the nature of which we will
shortly explain. A remarkable circum-
stance connected with the moon's mo-
tion is, that the same side is always
visible from the earth, showing that the
moon turns once on her own axis in ex-
actly the time of her monthly revolu-
tion.* But Galileo, who was by this
time familiar with the whole of the
moon's visible surface, observed that the
above-mentioned effect does not accu-
rately take place, but that a small part
on either side comes alternately forward
into sight, and then again recedes, ac-
cording to the moon's various positions
in the heavens. He was not long in de-
tecting one of the causes of this appa-
rent libratory or rocking motion. It is
partly occasioned by our distance as
spectators from the centre of the earth,
which is also the centre of the moon's
motion. In consequence of this, as
the moon rises in the sky we get an ad-
ditional view of the lower half, and lose
sight of a small part of the upper half
which was visible to us while we were
looking down upon her when low in the
horizon. The other cause is not quite so
simple, nor is it so certain that Galileo
adverted to it : it is however readily in-
telligible even to those who are unac-
quainted with astronomy, if they will re-
ceive as a fact that the monthly motion
of the moon is not uniform, but that she
moves quicker at one time than another,
whilst the motion of rotation on her own
axis, like that of the earth, is perfectly
uniform. A very. little reflection will
show that the observed phenomenon

* Frisi says that Galileo did not perceive this
conclusion (Elogio del Galileo) ; but see The Dial, on
the System, Dial. 1. pp. 61, 62, 85. Edit. 1744.
Plutarch says, £Ue Placitis Philos. lib. ii. c. 28,)
that the Pythagoreans believed the moon to have in-
habitants fifteen times as large as men, and that
their day is fifteen times as long as ours. It seems
probable, that the former of these opinions was en-
grafted on the latter, which is true, and implies a
2**&ejition of the fact ia the text.

will necessarily follow. If the moon did
not turn on her axis, every side of her
would be successively presented, in the
course of a month, towards the earth ;
it is the motion of rotation which tends
to carry the newly discovered parts out
of sight.

Let us suppose the moon to be in that
part of her orbit where she moves with
her average motion, and that she is
moving towards the part where she
moves most quickly. If the motion in
the orbit were to remain the same all
the way round, the motion of rotation
would be just sufficient at every point to
bring round the same part of the moon
directly in front of the earth. But since,
from the supposed point, the moon is
moving for some time round the earth
with a motion continually growing
quicker, the motion of rotation is not
sufficiently quick to carry out of sight
the entire part discovered by the
motion of translation. We therefore
get a glimpse of a narrow strip on
the side from which the moon is mov-
ing, which strip grows broader and
broader, till she passes the point where
she moves most swiftly, and reaches the
point of average swiftness on the oppo-
site side of her orbit. Her motion is
now continually growing slower, and
therefore from this point the motion of
rotation is too swift, and carries too
much out of sight, or in other words,
brings into sight a strip on the side
towards which the moon is moving.
This increases till she passes the point
of least swiftness, and arrives at the
point from which we began to trace her
course, and the phenomena are re-
peated in the same order.

This interesting observation closes
the long list of Galileo's discoveries in
the heavens. After his abjuration, he
ostensibly withdrew himself in a great
measure from his astronomical pur-
suits, and employed himself till 1636
principally with his Dialogues on Mo-
tion, the last work of consequence that
he published. In that year he entered
into correspondence with the Elzevirs^
through his friend Micanzio, on the pro-
ject of printing a complete edition of his
writings. Among the letters which
Micanzio wrote on the subject is one
intimating that he had enjoyed the gra-
tification, in his quality of Theologian
to the Republic of Venice, of refusing
his sanction to a work written against
Galileo and Copernicus. The temper
however in which this refusal was an-

GALILEO.

nounced, contrasts singularly with that
of the Roman Inquisitors. " A book was
brought to me which a Veronese Capu-
chin has been writing, and wished to
print, denying the motion of the earth.
I was inclined to let it go, to make the
world laugh, for the ignorant beast en-
titles every one of the twelve arguments
which compose his book, ' An irrefra-
gable and undeniable demonstration,'
and then adduces nothing but such
childish trash as every man of sense
has long discarded. For instance, this
poor animai understands so much geo-
metry and mathematics, that he brings
forward as a demonstration, that if the
earth could move, having nothing to
support it, it must necessarily fall. He
ought to have added that then we
should catch all the quails. But when
I saw that he speaks indecently of you,
and has had the impudence to put down
an account of what passed lately, say-
ing that he is in possession of the
whole of your process and sentence, I
desired the man who brought it to me
to go and be hanged. But you know the
ingenuity of impertinence ; I suspect he
will succeed elsewhere, because he is so
enamoured of his absurdities, that he be-
lieves them more firmly than his Bible."
After Galileo's condemnation at Rome,
he had been placed by the Inquisition in
the list of authors the whole of whose
writings, ' edita et edenda," were strictly
forbidden. Micanzio could not even ob-
tain permission to reprint the Essay on
Floating Bodies, in spite of his protes-
tations that it did not in any way relate
to the Copernican theory. This was the
greatest stigma with which the Inqui-
sition were in the habit of branding ob-
noxious authors; and, in consequence
of it, when Galileo had completed his
Dialogues on Motion, he found great
difficulty in contriving their publication,
the nature of which may be learned
from the account which Pieroni sent to
Galileo of his endeavours to print them
in Germany. He first took the manu-
script to Vienna, but found that every
book printed there must receive the ap-
probation of the Jesuits ; and Galileo's
old antagonist, Scheiner, happening to
be in that city, Pieroni feared lest he
should interfere to prevent the publi-
cation altogether, if the knowledge of it
should reach him. Through the inter-
vention of Cardinal Dietrich stein, he
therefore got permission to have it
printed at Olmutz, and that it should be
approved by a Dominican, so as to

keep the whole business a secret from
Scheiner and his party ; but during this
negociation the Cardinal suddenly died,
and Pieroni being besides dissatisfied
with the Olmutz type, carried back the
manuscript to Vienna, from which he
heard that Scheiner had gone into Sile-
sia. A new approbation was there pro-
cured, and the work was just on the
point of being sent to press, when the
dreaded Scheiner re- appeared in Vienna,
on which Pieroni again thought it ad-
visable to suspend the impression till his
departure. In the mean time his own
duty as a military architect in the Em-
peror's service carried him to Prague,
where Cardinal Harrach, on a former
occasion, had offered him the use of the
newly-erected University press. But
Harrach happened not to be at Prague,
and this plan like the rest became
abortive. In the meantime Galileo,
wearied with these delays, had engaged
with Louis Elzevir, who undertook to
print the Dialogues at Amsterdam.

It is abundantly evident from Galileo's
correspondence that this edition was
printed with his full concurrence, al-
though, in order to obviate further an-
noyance, he pretended that it was pirated
from a manuscript copy which he sent
into France to the Comte de Noailles, to
whom the work is dedicated. The
same dissimulation had been previously
thought necessary, on occasion of the
Latin translation of " The Dialogues on
the System," by Bernegger, which Gali-
leo expressly requested through his
friend Deodati, and of which he more
than once privately signified his appro-
bation, presenting the translator with a
valuable telescope, although he publicly
protested against its appearance. The
story which Bernegger introduced in his
preface, tending to exculpate Galileo
from any share in the publication, is
by his own confession a mere fiction.
Noailles had been ambassador at Rome,
and, by his conduct there, well deserved
the compliment which Galileo paid him
on the present occasion.

As an introduction to the account of
this work, which Galileo considered the
best he had ever produced, it will become
necessary to premise a slight sketch of
the nature of the mechanical philosophy
which he found prevailing, nearly as it
had been delivered by Aristotle, with the
same view with which we introduced spe-
cimens of the astronomical opinions cur-
rent when Galileo began to write on that
subject : they serve to show the nature

GALILEO.

and objects of the reasoning which he
had to oppose ; and, without some expo-
sition of them, the aim and value of
many of his arguments would be imper-
fectly understood and appreciated.

CHAPTER XVI.

State of the Science of Motion before
Galileo.

IT is generally difficult to trace any
branch of human knowledge up to
its origin, and more especially when,
as in the case of mechanics, it is
very closely connected with the im-
mediate wants of mankind. Little has
been told to us when we are in-
formed that so soon as a man might
wish to remove a heavy stone, " he
would be led, by natural instinct, to
slide under it the end of some long
instrument, and that the same instinct
would teach him either to raise the
further end, or to press it downwards, so
as to turn round upon some support
placed as near to the stone as possible*."

Montucla's history would have lost
nothing in value, if, omitting " this
philosophical view of the birth of the
art," he had contented himself with
his previous remark, that there can be
little doubt that men were familiar
with the use of mechanical contrivances
long before the idea occurred of enu-
merating or describing them, or even
of examining very closely the nature and
limits of the aid they are capable of af-
fording. The most careless observer
indeed could scarcely overlook that the
weights heaved up with a lever, or rolled
along a slope into their intended places,
reached them more slowly than those
which the workmen could lift directly
in their hands ; but it probably needed
a much longer time to enable them to
see the exact relation which, in these and
all other machines, exists between the
increase of the power to move, and the
decreasing swiftness of the thing moved.

In the preface to Galileo's Treatise on
Mechanical Science, published in 1592,
he is at some pains to set in a clear
light the real advantages belonging to
the use of machines, " which (says he)
I have thought it necessary to do, be-
cause, if I mistake not, I see almost all
mechanics deceiving themselves in the
belief that, by the help of a machine,
they can raise a greater weight than they
are able to lift by the exertion of the

* Histoire des Alatk^matiques, vol. i. p. 97.

same force without it. — Now if we take
any determinate weight, and any force,
and any distance whatever, it is beyond
doubt that we can move the weight to
that distance by means of that force ;
because even although the force may
be exceedingly small, if we divide the
weight into a number of fragments,
each of which is not too much for our
force, and carry these pieces one by one,
at length we shall have removed the
whole weight ; nor can we reasonably say
at the end of our work, that this great
weight has been moved and carried away
by a force less than itself, unless we add
that the force has passed several times
over the space through which the whole
weight has gone but once. From which
it appears that the velocity of the force
(understanding by velocity the space
gone through in a given time) has been
as many times greater than that of the
weight, as the weight is greater than
the force : nor can we on that ac-
count say that a great force is over-
come by a small one, contrary to nature :
then only might we say that nature is
overcome when a small force moves a
great weight as swiftly as itself, which
we assert to be absolutely impossible
with any machine either already or here-
after to be contrived. But since it may
occasionally happen that we have but a
small force, and want to move a great
weight without dividing it into pieces,
then we must have recourse to a ma-
chine by means of which we shall re-
move the given weight, with the given
force, through the required space. But
nevertheless the force as before will
have to travel over that very same space
as many times repeated as the weight sur-
passes its power, so that, at the end of
our work, we shall find that we have
derived no other benefit from our ma-
chine than that we have carried away
the same weight altogether, which if
divided into pieces we could have car-
ried without the machine, by the same
force, through the same space, in the
same time. This is one of the advan-
tages of a machine, because it often hap-
pens that we have a lack of force but
abundance of time, and that we wish to
move great weights all at once."

This compensation of force and time
has been fancifully personified by saying
that Nature cannot be cheated, and in
scientific treatises an mechanics, is
called the " principle of virtual velocities,"
consisting in the theorem that two
weights will balance each other on any

GALILEO.

machine, no matter how complicated or
intricate the connecting contrivances
may be, when one weight bears to the
other the same proportion that the
space through which the latter would
be raised bears to that through which
the former would sink, in the first instant
of their motion, if the machine were
stirred by a third force. The whole
theory of machines consists merely in
generalizing and following out this prin-
ciple into its consequences ; combined,
•when the machines are in a state of mo-
tion, with another principle equally
elementary, but to which our present
subject does not lead us to allude more
particularly.

The credit of making known the prin-
ciple of virtual velocities is universally
given to Galileo ; and so far deservedly,
Siat he undoubtedly perceived the im-
portance of it, and by introducing it
everywhere into his writings succeeded
in recommending it to others ; so that
five and twenty years after his death,
Borelli, who had been one of Galileo's
pupils, calls it " that mechanical prin-
ciple with which everybody is so fa-
miliar*," and from that time to the
present it has continued to be taught as
an elementary truth in most systems of
mechanics. But although Galileo had
the merit in this, as in so many other
cases, of familiarizing and reconciling
the world to the reception of truth, there
are remarkable traces before his time of
the employment of this same principle,
some of which have been strangely dis-
regarded. Lagrange assertsf that the
ancients were entirely ignorant of the
principle of virtual velocities, although
Galileo, to whom he refers it, dis-
tinctly mentions that he himself found
it in the writings of Aristotle. Montu-
cla quotes a passage from Aristotle's
Physics, in which the law is stated
generally, but adds that he did not
perceive its immediate application to the
lever, and other machines. The pas-
sage to which Galileo alludes is in
Aristotle's Mechanics, where, in dis-
cussing the properties of the lever, he
says expressly, " the same force will raise
a greater weight, in proportion as the
force is applied at a greater distance
from the fulcrum, and the reason, as I
have already said, is because it describes
a greater circle; and a weight which
is farther removed from the centre is
made to move through a greater space."$

* De vi Percussionis, Bcmoniae, 1667.
t Mec, Aaalyt. J Mechanica,

It is true, that in the last mentioned
treatise, Aristotle has given other rea-
sons which belong to a very different
kind of philosophy , and which may lead
us to doubt whether he fully saw the
force of the one we have just quoted.
It appeared to him not wonderful that so
many mechanical paradoxes (as he
called them) should be connected with
circular motion, since the circle itself
seemed of so paradoxical a nature.
" For, in the first place, it is made up of
an immoveable centre, and a moveable
radius, qualities which are contrary to
each other. 2dly. Its circumference is
both convex and concave. 3dly. The
motion by which it is described is both
forward and backward, for the describing
radius comes back to the place from
which it started. 4thly. The radius is
one; but every point of it moves in de-
scribing the circle with a different degree
of swiftness/'

Perhaps Aristotle may have borrowed
the idea of virtual velocities," contrast-
ing so strongly with his other physi-
cal notions, from some older writer;
possibly from Archytas, who, we are
told, was the first to reduce the science
of mechanics to methodical order ; *
and who by the testimony of his coun-
trymen was gifted with extraordinary
talents, although none of his works have
come down to us. The other principles and
maxims of Aristotle's mechanical phi-
losophy, which we shall have occasion
to cite, are scattered through his books
on Mechanics, on the Heavens, and in
his Physical Lectures, and will therefore
follow rather unconnectedly, though we
have endeavoured to arrange them with
as much regularity as possible.

After defining a body to be that which
is divisible in every direction, Aristotle
proceeds to inquire how it happens that
a body has only the three dimensions
of length, breadth, and thickness ; and
seems to think he has given a reason in
sayingthat, when we speak of two things,
we do not say " all," but " both," and
three is the first number of which we
say " all." t When he comes to speak
of motion, he says, "If motion is not
understood, we cannot but remain igno-
rant of Nature. Motion appears to be
of the nature of continuous quantities,
and in continuous quantity infinity first
makes its appearance ; so as to furnish
some with a definition who say that con-

* Diog. Laert. In vit. Archyt.
t De Coelo, lib. i. e. 1.^

80

GALILEO.

tinuous quantity is that which is infi-
. nitely divisible. — Moreover, unless there
v be time, space, and a vacuum, it is im-
possible that there should be motion*." —
Few propositions of Aristotle's physical
philosophy are more notorious than his
assertion that nature abhors a vacuum,
on which account this last passage is the
more remarkable, as he certainly did not
go so far as to deny the existence of
motion, and therefore asserts here the
necessity of that of which he afterwards
attempts to show the absurdity. — " Mo-
tion is the energy of what exists in power
so far forth as so existing. It is that
act of a moveable which belongs to its
power of moving." f After struggling
through such passages as the preceding
we come at last to a resting-place. — " It
is difficult to understand what motion
is." — When the same question was once
proposed to another Greek philosopher,
he walked away, saying, " I cannot tell
you, but I will show you ; " an answer
intrinsically worth more than all the sub-
tleties of Aristotle, who was not humble-
minded enough to discover that he was
tasking his genius beyond the limits
marked out for human comprehension.

He labours in the same manner and
with the same success to vary the
idea of space. He begins the next book
^vith declaring, that " those who say
there is a vacuum assert the existence
of space; for a vacuum is space, in
which there is no substance ;" and after
•a long and tedious reasoning concludes
that, " not only what space is, but also
whether there be such a thing, cannot
but be doubted."j Of time he is content
to say merely, that " it is clear that time
is not motion, but that without motion
there would be no time ; " § and there
is perhaps little fault to be found with
this remark, understanding motion in

* Phys. lib. i. c. 3.

-j- Lib. Hi. c. 2. The Aristotelians distinguished
between things as existing in act or energy (m^-
ytttt) and things in capacity or power (§i/va^/j).
For the advantage of those who may think the
distinction worth attending to, we give an illus-
tration of Aristotle's meaning, from a very acute and
learned commentator: — " It (motion) is something
more than dead capacity ; something less than per-
fect actuality ; capacity roused, and striving to quit
its latent character ; not the capable brass, nor yet
the actual statue, but the capacity in energy ; that is
to say, the brass in fusion while it is becoming the
statue and is not yet become."— " The bow moves
not because it may be bent, nor because it is bent;
but the motion lies between ; lies in an imperfect
and obscure union of the two together ; is the actu-
ality (if I may so say) even of capacity itself: im-
perfect and obscure, because such is capacity to
which it belongs."— Harris, Philosophical Arrange-

J Lib. iv. c. 1. § Lib. iv. c. 11.

the general sense in which Aristotle
here applies it, of every description of
change.

Proceeding after these remarks on the
nature of motion in general to the
motion of bodies, we are told that " all
local motion is either straight, circular, or
compounded of these two ; for these two
are the only simple sorts of motion.
Bodies are divided into simple and con-
crete ; simple bodies are those which
have naturally a principle of motion,
as fire and earth, and their kinds. By
simple motion is meant the motion of
a simple body." * By these expressions
Aristotle did not mean that a simple
body cannot have what he calls a
compound motion, but in that case he
called the motion violent or unnatu-
ral; this division of motion into na-
tural and violent runs through the
whole of the mechanical philosophy
founded upon his principles. " Circular
motion is the only one which can be
endless ;"f the reason of which is given
in another place : for " that cannot be
doing, which cannot be done; and
therefore it cannot be that a body should
be moving towards a point (i. e. the end
of an infinite straight line) whither no
motion is sufficient to bring it." $ Ba-
con seems to have had these passages
in view when he indulged in the reflec-
tions which we have quoted in page 14.
" There are four kinds of motion of one
thing by another: Drawing, Pushing,
Carrying, Rolling. Of these, Carrying
and Rolling may be referred to Drawing
and Pushing.^ — The prime mover and
the thing moved are always in contact."

The principle of the composition of
motions is stated very plainly : " when
a moveable is urged in two directions
with motions bearing any ratio to each
other, it moves necessarily in a straight
line, which is the diameter of the figure
formed by drawing the two lines of di-
rection in that ratio ;"|| and adds, in a
singularly curious passage, " but when
it is urged for any time with two motions
which have an indefinitely small ratio
one to another, the motion cannot be
straight, so that a body describes, a
curve, when it is urged by two motions
bearing an indefinitely small ratio one
to another, and lasting an indefinitely
small time.' ' •[

* De Coelo, lib. i. c. 2.
% De Ccelp, lib. i. c. 6.
|| Mechanica.

E«v $i iv tifitvi

f Phys. lib. viii. c. 8.
§ Phys. lib. vii. c. 2.

GALILEO.

81

He seemed on the point of discover-
ing some of the real laws of motion,
when he was led to ask — "Why are
bodies in motion more easily moved
than those which are at rest? — And'
why does the motion cease of things
cast into the air ? Is it that the force
has ceased which sent them forth, or is
there a struggle against the motion, or
is it through the disposition to fall, does it
become stronger than the projectile force,
or is it foolish to entertain doubts on this
question, when the body has quitted
the principle of its motion ? " A com-
mentator at the close of the sixteenth
century says on this passage : " They
fall because every thing recurs to its
nature; for if you throw a stone
a thousand times into the air, it
will never accustom itself to move
upwards.'' Perhaps we shall now find
it difficult not to smile at the idea we
may form of this luckless experimen-
talist, teaching stones to fly; yet it
may be useful to remember that it is
only because we have already collected
an opinion from the 'results of a vast
number of observations in the daily
experience of life, that our ridicule
would not be altogether misplaced, and
that we are totally unable to determine
by any kind of reasoning, unaccompa- v/
niecl by experiment, whether a stone
Thrown into the air would fall again to
the earth, or move for ever upwards, or
in any other conceivable manner and
direction.

The opinion which Aristotle held, that
motion must be caused by something in
contact with the body moved, led him
to his famous theory that falling bodies
are accelerated by the air through which
they pass. We will show how it was
attempted to explain this process when
we come to speak of more modern au-
thors. He classed natural bodies into
heavy and light, remarking at the same
time that it is clear that « there are
.some bodies possessing neither gravity
nor levity*." By light bodies he under-
stood those which have a natural ten-
dency to move from the earth, observing
that " that which is lighter is not al-
ways lightf." He maintained that the

x&ra, ftydtvx %govov, aSuvaiTov ivfaiav uvcci vnt
Qogxv. EOS.V yocp rivx Xoyov ivi%-6'/i &y wovcu nvt

ret

VOV

d s
—
dt

*DeCcelo,lib,i.c.3, fLib,iv.c,2

heavenly bodies were altogether devoid
of gravity ; and we have already had
occasion to mention his assertion, that
f a large body falls faster than a small
one in proportion to its weight*. With
this opinion may be classed another
great mistake, in maintaining that the
same bodies fall through different me- ,
diums, as air or water, with velocities ^
reciprocally proportional to their densi-
ties. By a singular inversion of expe-
rimental science, Cardan, relying on this
assertion, proposed in the sixteenth cen-
tury to determine the densities of air
and water by observing the different
times taken by a stone in falling through
themf. Galileo inquired afterwards why
the experiment should not be made with
a cork, which pertinent question put an
end to the theory.

There are curious traces still pre-
served in the poem of Lucretius of a
mechanical philosophy, of which the
credit is in general given to Democritus,
where many principles are inculcated
strongly at variance with Aristotle's no-
tions. We find absolute levity denied,
and not only the assertion that in a
vacuum all things would fall, but that *
they would fall with the same velocity ;
and the inequalities which we observe
are attributed to the right cause, the
impediment of the air, although the
error remains of believing the velocity
of bodies falling through the air to be
proportional to their weight^. Such
specimens of this earlier philosophy

* Phys., lib. iv. c. 8. f De Propprt.Basileae, 1570.
j " Nunc locus est, ut opinor, in his illud quoque

rebus

Confirmare tibi, nullam rem posse su§. vi
Corpoream sursum ferri,- sursumque meare. — •
Nee quom subsiliunt ignes ad tecta domorura,
Et celeri flamml degustant tigna trabeisque
Sponte sua facere id sine vi subicente putandum est.
— Nonne vides etiam quanta vi tigna trabeisque
Respuat humor aquae ? Nam quod magi' mersi-

mus altum

Directa et magna vi multi pressimus segre :—
Tarn cupide sursum revomit magis atque remittit
Plus ut parte foras emergant, exsiliantque :
•— Nee tamen haec, quantu'st in sedubitamus, opinor,
Quinvacuum per inane deorsum cuncta ferantur,
Sic igitur debent flammse quoque posse per auras
Aeris expresses sursum subsidere, quamquam
Pondera quantum in se est deorsum deducere pug-

nent.

— Quod si forte aliquis credit Graviora potesse
Corpora, quo citius rectum per Inane feruntur,
— Avius a vera longe ratione recedit.
Nam per Aquas quaecunque cadunt atque Aera

deorsum

Haec pro ponderibus casus celerare necesse 'st
Propterea quia corpus Aquae, naturaque tenuis
Aeris baud possunt aeque rem quamque morari :
Sed citius cedunt Gravioribus exsuperata.
At contra nulli de nulla parte, neque ullo
Tempore Inane potest Vacuum subsistere reii
Quin, sua quod natura petit, considere pergat :
Omnia qu& propter debent per Inane quietum
,3£que ponderibus non sequis concita ferri."

De Rerura Natura, lib, U, v. 184—239.
G

S2

GALILEO.

may well indispose us towards Aris-
totle, who was as successful in the
science of motion as he was in astro-
nomy in suppressing the knowledge
of a theory so much sounder than that
which he imposed so long upon the cre-
dulity of his blinded admirers.

An agreeable contrast to Aristotle's
mystical sayings and fruitless syllogisms
is presented in Archimedes' book on
Equilibrium, in which he demonstrates
very satisfactorily, though with greater
cumbrousness of apparatus than is now
thought necessary, the principal pro-
perties of the lever. This and the Trea-
tise on the Equilibrium of Floating
Bodies are the only mechanical works
which have reached us of this writer,
who was by common consent one of the
most accomplished mathematicians of
antiquity. Ptolemy the astronomer
wrote also a Treatise on Mechanics,
now lost, which probably contained
much that would be interesting in the
history of mechanics ; for Pappus says,
in the Preface to the Eighth Book of
his Mathematical Collections : " There
is no occasion for me to explain what
is meant by a heavy, and what by a
light body, and why bodies are carried
up and down, and in what sense these
very words ' up ' and * down ' are to be
taken, and by what limits they are
bounded ; for all this is declared in
Ptolemy's Mechanics."* This book of
Ptolemy's appears to have been also
known by Eutocius, a commentator of
Archimedes, who lived about the end of
the fifth century of our era ; he intimates
that the doctrines contained in it are
grounded upon Aristotle's ; if so, its loss
is less to be lamented. Pappus's own
book deserves attention for the enume-
ration which he makes of the mechanical
powers, namely, the wheel and axle, the
lever, pullies, the wedge and the screw.
He gives the credit to Hero and Philo
of having shown, in works which have
not reached us, that the theory of all
these machines is the same. In Pap-
pus we also find the first attempt to
discover the force necessary to support
a given weight on an inclined plane.
This in fact is involved in the theory
Of the screw ; and the same vicious
reasoning which Pappus employs on
this occasion was probably found in
those treatises which he quotes with
so much approbation. Numerous as
are the faults of his pretended demon-

• Math. Coll.Pisani, 16(52.

stration, it was received undoubtingly
for a long period.

The credit of first giving the true
theory of equilibrium on the inclined
plane is usually ascribed to Stevin, al-
though, as we shall presently show, with
very" little reason. Stevin supposed a
chain to be placed over two inclined
planes, and to hang down in the manner
represented in the figure. He then urged
that the chain would be in equilibrium ;
for otherwise, it would incessantly conti-
nue in motion, if there were any cause
why it should begin to move. This being
conceded, he remarks further, that the
parts A D and BD are also in equili-
brium, being exactly similar to each
other; and therefore
if they are taken
away, the remaining
parts A C and B C
will also be in equi-
librium. The weights
of these parts are
proportional to the
lengths AC and BC;
and hence Stevin
concluded that two
weights would balance on two inclined
planes, which are to each other as the
lengths of the planes included between
the same parallels to the horizon.* This
conclusion is the correct one, and there is
certainly great ingenuity in this contriv-
ance to facilitate the demonstration ; it
must not however be mistaken for an.
a priori proof, as it sometimes seems to
have been : we should remember that the
experiments which led to the principle
of virtual velocities are also necessary
to show the absurdity of supposing a
perpetual motion, which is made the
foundation of this theorem. That prin-
ciple had been applied directly to deter-
mine the same proportion in a work
written long before, where it has re-
mained singularly concealed from the
notice of most who have written on this
subject. The book bears the name of
Jordanus, who lived at Namur in the
thirteenth century ; but Commandine,
who refers to it in his Commentary on
Pappus, considers it as the work of an
earlier period. The author takes the
principle of virtual velocities for the
groundwork of his explanations, both
of the lever and inclined plane; the
latter will not occupy much space, and
in an historical point of view is too
curious to be omitted.

* (Euvres Math6mati<iues, Leyde. 1634,

GALILEO.

83

" Qucest. 10.— If two weights descend
bypaths of different obliquities, and the
proportion be the same of the weights
and the inclinations taken in the same
order, they will have the same descend-
ing force. By the inclinations, 1 do
not mean the angles, but the paths up
to the point in which both meet the same
perpendicular.* Let, therefore, e be
the weight upon d c, and h upon d a,
and let e be to h as d c to d a. I say
these weights, in this situation, are
equally effective. Take d k equally in-
clined with d c, and upon it a weight
equal to e, which call 6. If possible let
e descend to I, so as to raise h to m, and

take 6 n equal to h m or e I, and draw
the horizontal and perpendicular lines as
in the figure.

Then n z\n 6::d b:d k
and m h:m x::d a:d b
therefore n z : m x\ \d a : d k: :h : 6, and
therefore since e r is not able to raise
6 to n, neither will it be able to raise
h to m; therefore they will remain as
they are."t The passage in Italics
tacitly assumes the principle in ques-
tion. Tartalea, who edited Jorda-
nus's book in 1565, has copied this
theorem verbatim into one of his own
treatises, and from that time it appears
to have attracted no further attention.
The rest of the book is of an inferior
description. We find Aristotle's doc-
trine repeated, that the velocity of a
falling body is proportional to its weight ;
that the weight of a heavy body changes
with its form ; and other similar opinions.
The manner in which falling bodies are
accelerated by the air is given in detail.
" By its first motion the heavy body
will drag after it what is behind, and
move what is just below it ; and these
\vhen put in motion move what is next
to them, so that by being set in motion
they less impede the falling body. In

* This is not a literal translation, but by what
follows, is evidently the Author's meaning. His
•words are, "Proportionem igitur declination urn dico
uon angulorum, sed iinearum usque ad aequidis-
tantem resecationem in qu& aequaltter suinunt de
directo."

t Opusculum. De Ponderositate. Venetiis, 1565.

this manner it has the effect of being
heavier, and impels still more those
which give way before it, until at last
they are no longer impelled, but begin
to drag. And thus it happens that its
gravity is increased by their attraction,
and their motion by its gravity, whence
we see that its velocity is continually
multiplied."

In this short review of the state of
mechanical science before Galileo, the
name of Guido Ubaldi ought not to be
omitted, although his works contain
little or nothing original. We have
already mentioned Benedetti as having
successfully attacked some of Aristotle's
statical doctrines, but it is to be noticed
that the laws of motion were little if at
all examined by any of these writers.
There are a few theorems connected
with this latter subject in Cardan's ex-
traordinary book " On Proportions," but
for the most part false and contradictory.
In the seventy-first proposition of his
fifth book, he examines the force of the
screw in supporting a given weight, and
determines it accurately on the principle
of virtual velocities ; namely, that the
power applied at the end of the horizon-
tal lever must make a complete circuit
at that distance from the centre, whilst
the weight rises through the perpen-
dicular height of the thread. The very
next proposition in the same page is
to find the same relation between the
power and weight on an inclined plane ;
and although the identity of principle
in these two mechanical aids was well
known, yet Cardan declares the neces-
sary sustaining force to vary as the
angle of inclination of the plane, for no
better reason than that such an expres-
sion will properly represent it at the
two limiting angles of inclination, since
the force is nothing when the plane is
horizontal, and equal to the weight
when perpendicular. This again shows
how cautious we should be in attribut-
ing the full knowledge of general prin-
ciples to these early writers, on account
of occasional indications of their having
employed them.

CHAPTER XVII.
Galileo's theory of Motion — Extracts

from the Dialogues.
DURING Galileo's residence at Sienna,
when his recent persecution had ren-
dered astronomy an ungrateful, and in-
deed an unsafe occupation for his ever
active mind, he returned with increased
pleasure to the favourite employment of
G2

84

GALILEO.

his earlier years, an inquiry into the laws
and phenomena of motion. His manu-
script treatises on motion, written about
1590, which are mentioned by Venturi
to be in the Ducal library at Florence,
seem, from the published titles of the
chapters, to consist principally of objec-
tions to the theory of Aristotle ; a few
only appear to enter on a new field of
speculation. The llth, 13th, and 17th
chapters relate to the motion of bodies
on variously inclined planes, and of pro-
jectiles. The title of the 14th implies a
new theory of accelerated motion, and
the assertion in that of the 16th, that a
body falling naturally for however great
.a time would never acquire more than
an assignable degree of velocity, shows
that at this early period Galileo had
formed just and accurate notions of the
action of a resisting medium. It is
hazardous to conjecture how much he
might have then acquired of what we
should now call more elementary know-
ledge ; a safer course will be to trace
his progress through existing documents
in their chronological Older. In 1602
we find Galileo apologizing in a letter
addressed to his early patron the Mar-
chese Guido Ubaldi, for pressing again
upon his attention the isochronism of
the pendulum, which Ubaldi had re-
jected as false and impossible. It may
not be superfluous to observe that
Galileo's results are not quite accurate,
for there is a perceptible increase in the
x time occupied by the oscillations in
larger arcs ; it is therefore probable that
he was induced to speak so confidently
of their perfect equality, from attributing
the increase of time which he could not
avoid remarking to the increased resist-
ance of the air during the larger vibra-
tions. The analytical methods then
known would not permit him to dis-
cover the c\irious fact, that the time of
a total vibration is not sensibly altered
by this cause, except so far as it dimi-
nishes the extent of the swing, and thus
in fact, (paradoxical as it may sound)
renders each oscillation successively
more rapid, though in a very small
degree. He does indeed make the
same remark, that the resistance of the
air will not affect the time of the oscilla-
* tion, but that assertion was a conse-
quence of his erroneous belief that the
time of vibration in all arcs is the same.
Had he been aware of the variation, there
is no reason to think that he could have
perceived that this result is not affected
by it. In this letter is the first mention

of the theorem, that the times of fall
down all the chords drawn from the
lowest point of a circle are equal : and
another, from which Galileo afterwards
deduced the curious result, that it takes
less time to fall down the curve than
down the chord, notwithstanding the
latter is the direct and shortest course.
In conclusion he says, " Up to this point
I can go without exceeding the limits of
mechanics, but I have not yet been able
to demonstrate that all arcs are passed
in the same time, which is what I am
seeking." In 1604 he addressed the
following letter to Sarpi, suggesting the
false theory sometimes called Baliani's,
who took it from Galileo.

" Returning to the subject of motion,
in which I was entirely without a fixed
principle, from which to deduce the
phenomena I have observed, I have hit
upon a proposition, which seems natural
and likely enough ; and if 1 take it for
granted, I can show that the spaces
passed in natural motion are in the
double proportion of the times, and con-
sequently that the spaces passed in equal
times are as the odd numbers beginning
from unity, and the rest. The principle
is this, that the swiftness of the move-
able increases in the proportion of its
distance from the point whence it began
to move ; as for instance, — if a heavy
body drop from A towards
A - D, by the line A BCD, I
suppose the degree of velo-
city which it has at B to
bear to the velocity at C the
ratio of A B to AC. I shall
be very glad if your Rever-
ence will consider this, and
n _ tell me your opinion of it.
If we admit this principle,
not only, as I have said, shall
we demonstrate the other
D - conclusions, but we have
it in our power to show that
a body falling naturally, and another
projected upwards, pass through the
same degrees of velocity. For if the pro-
jectile be cast up from D to A, it is clear
that at D it has force enough to reach
A, and no farther ; and when it has
reached C and B, it is equally clear that
it is still joined to a degree of force
capable of carrying it to A : thus it is
manifest that the forces at D, C and B
decrease in the proportion of AB, A C,
and A D ; so that if, in falling, the degrees
of velocity observe the same proportion,
that is true which I have hitherto main-
tained and believed."

GALILEO.

85

We have no means of knowing how
early Galileo discovered the fallacy of
this reasoning. In his Dialogues on Mo-
tion, which contain the correct theory,
he has put this erroneous supposition
in the mouth of Sagredo, on which
Salviati remarks, " Your discourse has
so much likelihood in it, that our author
himself did not deny to me when I pro-
posed it to him, that he also had been
for some time in the same mistake.
But that which I afterwards extremely
wondered at, was to see discovered in
four plain words, not only the falsity,
but the impossibility of a supposition
carrying with it so much of seeming
truth, that although I proposed it to
many, I never met with any one but did
freely admit it to be so ; and yet it is as
false and impossible as that motion is
made in an instant : for if the velocities
are as the spaces passed, those spaces v
will be passed in equal times, and con-
sequently all motion must be instanta-
neous." The following manner of put-
ting this reasoning will perhaps make
the conclusion clearer. The velocity at
any point is the space that would be
passed in the next moment of time, if
the motion be supposed to continue the
same as at that point. At the beginning
of the time, when the body is at rest, the
motion is none ; and therefore, on this
theory, the space passed in the next
moment is none, and thus it will be seen
that the body cannot begin to move ac-
cording to the supposed law.

A curious fact, noticed by Guido
Grandi in his commentary on Galileo's
Dialogues on Motion, is that this false
law of acceleration is precisely that^
which would make a circular arc the
shortest line of descent between two
given points ; and although in general
Galileo only declared that the fall down
the arc is made in less time than down
the chord (in which he is quite correct),

of Galileo's second and correct theory,
that the spaces vary as the squares of
the times. He had been investigating
the curye of swiftest descent, and found
it to be a cycloid, the same curve in
which Huyghens had already proved
that all oscillations are made in accu-
rately equal times. " I think it," says
he, " worthy of remark that this iden-
tity only occurs on Galileo's supposition,
so that this alone might lead us to pre-
sume it to be the real law of nature.
For nature, which always does every-
thing in the very simplest manner, thus
makes one line do double work, whereas
on any other supposition, we must have
had two lines, one for equal oscillations,
the other for the shortest descent."*

Venturi mentions a letter addressed
to Galileo in May 1609 by Luca Valerio,
thanking him for his experiments on
the descent of bodies on inclined planes.
His method of making these experi-
ments is detailed in the Dialogues on
Motion : — " In a rule, or rather plank
of wood, about twelve yards long, half a
yard broad one way, and three inches
the other, we made upon the narrow
side or edge a groove of little more than
an inch wide : we cut it very straight,
and, to make it very smooth and sleek,
we glued upon it a piece of vellum, po-
lished and smoothed as exactly as pos-
sible, and in that we let fall a very hard,
round, and smooth brass ball, raising
one of the ends of the plank a yard or
two at pleasure above the horizontal

?lane. We observed, in the manner that
shall tell you presently, the time which
it spent in running down, and repeated
the same observation again and again
to assure ourselves of the time, in which
we never found any difference, no, not
so much as the tenth part of one beat
of the pulse. Having made and settled
this experiment, we let the same ball
descend through a fourth part only of

yet in some places he seems to assert 'Ahe length of the groove, and found the
that the circular arc is absolutely the measured time to be exactly half the
shortest line of descent, which is not former. Continuing our experiments
true. It has been thought possible that with other portions of the length, com-
the law, which on reflection he per- paring the fall through the whole with

the fall through half, two-thirds, three-
fourths, in short, with the fall through
any part, we found by many hundred'
experiments that the spaces passed over

ceived to be impossible, might have
originally recommended itself to him
from his perception that it satisfied his
prejudice in this respect.

John Bernouilli, one of the first ma-
thematicians in Europe at the beginning
of the last century, has given us a proof
that such a reason might impose even
on a strong understanding, in the follow-
ing argument urged by him in favour

were as the squares of the times, and
that this was the case in all inclinations
of the plank ; during which, we also re-

» Job. Bernoulli!, Opera Omnia, Lausannae, 1744.
torn. i. p. 192.

GALILEO.

marked that the times of descent, on
different inclinations, observe accurately
the proportion assigned to them farther
on, and demonstrated by our author.
As to the estimation of the time, we
hung up a great bucket full of water,
which by a very small hole pierced in
the bottom squirted out a fine thread
of water, which we caught in a small
glass during the whole time of the dif-
ferent descents: then weighing from
time to time, in an exact pair of scales,
the quantity of water caught in this way,
the differences and proportions of their
weights gave the differences and propor-
tions of the times ; and this with such
exactness that, as I said before, although
the experiments were repeated again and
again, they never differed in any degree
worth noticing." In order to get rid of
the friction, Galileo afterwards substi-
tuted experiments with the pendulum ;
but with all his care he erred very
widely in his determination of the space
through which a body would fall in l", if
the resistance of the air and all other im-
pediments were removed. He fixed it
at 4 braccia: Mersenne has engraved
the length of the * braccia ' used by Ga-
lileo, in his " Harmonie Universelle,"
from which it appears to be about 23£
English inches, so that Galileo's result
is rather less than eight feet. Mersenne's
own result from direct observation was
thirteen feet : he also made experiments
in St. Peter's at Rome, with a pendulum
325 feet long, the vibrations of which
were made in 10" ; from this the fall in
1" might have been deduced rather more
than sixteen feet, which is very close to
the truth.

From another letter also written in the
early part of 1609, we learn that Galileo
was then busied with examining the
strength and resistance " of beams of
different sizes and forms, and how much
weaker they are in the middle than at
the ends, and how much greater weight
they can support laid along their whole
length, than if sustained on a single
point, and of what form they should be
so as to be equally strong throughout."
He was also speculating on the motion
of projectiles, and had satisfied himself
that their motion in a vertical direction
is unaffected by their horizontal velo-
city ; a conclusion which, combined with
his other experiments, led him after-
wards to determine the path of a pro-
jectile in a non-resisting medium to be
parabolical.

Tartaleais supposed to have been the

first to remark that no bullet moves in a
horizontal line ; but his theory beyond
this point was very erroneous, for he
supposed the bullet's path through the
air to be made up of an ascending and
descending straight line, connected in
the middle by a circular arc.

Thomas Digges, in his treatise on the
Newe Science of Great Artillerie, came
much nearer the truth ; for he remarked*,
that " The bullet violentlye throwne
out of the peece by the furie of the
poulder hath two motions : the one vio-
lent, which endeuoreth to carry the bul-
let right out in his line diagonall, accord-
ing to the direction of the peece's axis,
from whence the violent motion proceed-
eth; the other naturall in the bullet
itselfe, which endeuoreth still to carrye
the same directlye downeward by a
right line perpendiculare to the horizon,
and which dooth though insensiblyeeuen
from the beginning by little and little
drawe it from that direct and diagonall
course." And a little farther he ob-
serves that " These middle curve arkes
of the bullet's circuite, compounded of
the violent and naturall motions of the
bullet, albeit they be indeed mere heli-
call, yet have they a very great resem-
blance of the Arkes Conical. And in
randons above 45° they doe much re-
semble the Hyperbole, and in all vnder
the Ellepsis. But exactly e they neuer
accorde, being indeed Spirall mixte and
Helicall."

Perhaps Digges deserves no greater
credit from this latter passage than the
praise of a sharp and accurate eye, for
he does not appear to have founded this
determination of the form of the curve
on any theory of the direct fall of bodies ;
but Galileo's arrival at the same result
was preceded, as we have seen, by a
careful examination of the simplest phe-
nomena into which this compound mo-
tion may be resolved. But it is time to
proceed to the analysis of his " Dialogues
on Motion," these preliminary remarks on
their subject matter having been merely
intended to show how long before their
publication Galileo was in possession of
the principal theories contained in
them.

Descartes, in one of his letters to Mer-
senne, insinuates that Galileo had taken
many things in these Dialogues from
him: the two which he especially in-
stances are the isochronism of the pen-
dulum, and the law of the spaces varying

« Pantometria, 1591.

GALILEO.

as the squares of the times.* Descartes
was born in 1596 : we have shown that
Galileo observed the isochronism of the
pendulum in 1583, and knew the law of
the spaces in 1604, although he was then
attempting to deduce it from an erro-
neous principle. As Descartes on more
than one occasion has been made to
usurp the credit due to Galileo, (in no in-
stance more glaringly so than when he
has been absurdly styled the forerunner of
Newton,) it will not be misplaced to men-
tion a few of his opinions on these sub-
jects, recorded in his letters to Mersenne
in the collection of his letters just cited :
— " 1 am astonished at what you tell
me of having found by experiment that
bodies thrown up in the air take neither
more nor less time to rise than to fall
again ; and you will excuse me if I say
that I look upon the experiment as a
very difficult one to make accurately.
This proportion of increase according to
the odd numbers 1, 3, 5, 7, &c., which
is in Galileo, and which I think I wrote
to you some time back, cannot be true, as
I believe I intimated at the same

do not believe that it generally happens,
but I allow it is not impossible that it
may happen occasionally." After this
the reader will know what value to
attach to the following assertion by the
same Descartes :— " I see nothing in
Galileo's books to envy him, and hardly
any thing which I would own as mine ;"
and then may judge how far Salisbury's
blunt declaration is borne out, " Where
or when did any one appear that durst
enter the lists" with our Galileus?
save only one bold and unfortunate
Frenchman, who yet no sooner came
within the ring but he was hissed out
again."*

The principal merit of Descartes must
undoubtedly be derived from the great
advances he made in what are generally
termed Abstract or Pure Mathematics ;
nor was he slow to point out to Mersenne
and his other friends the acknowledged
inferiority of Galileo to himself in this
respect. We have not sufficient proof
that this difference would have existed
if Galileo's attention had been equally
.directed to that object; the singular
•« elegance of some of his geometrical

time, unless we make two or three sup-
positions which are entirely false. One constructions indicates great talent for
is Galileo's opinion, that motion in- this as well as for his own more fa-
creases gradually from the slowest^ de- vourite speculations. But he was far
gree; and the other is, that the air -/more profitably employed: geometry
makes no resistance." In a later letter
to the same person he says, apparently
with some uneasiness, " I have been
revising my notes on Galileo, in which
I have not said expressly, that falling
bodies do not pass through every degree
of slowness, but I said that this cannot
be determined without knowing what
weight is ; which comes to the same
thing. As to your example, I grant
that it proves that every degree of velo-
city is infinitely divisible, but not that a

falling body actually passes through all
these divisions. — It is certain that a
stone is.not equally disposed to receive
a new motion or increase of velocity,
when it is already moving very quickly,
and when it is moving slowly. But I
believe that I am now able to determine
in what proportion the velocity of a stone
increases, not when falling in a vacuum,
but in this substantial atmosphere. —

and pure mathematics already far out-
stripped any useful application of their
results to physical science, and it was
the business of Galileo's life to bring up
the latter to the same level. He found
abstract theorems already demonstrated
in sufficient number for his purpose, nor
was there occasion to task his genius in
search of new methods of inquiry, till
all was exhausted which could be learned
from those already in use. The result
of his labours was that in the age imme-
diately succeeding Galileo, the study of
nature was no longer in arrear of the
abstract theories of number and mea-
sure ; and when the genius of Newton
pressed it forward to a still higher de-
gree of perfection, it became necessary
to discover at the same time more power-
ful instruments of investigation. This
alternating process has been successfully
continued to the present time ; the analyst

However I have now got my mind full of acts as the pioneer of the naturalist,

other things, and I cannot amuse myself so that the abstract researches, which at
with hunting this out, nor is it a matter ^"first have no value but in the eyes of

of much utility :" He afterwards returns those to whom an elegant formula, in

once more to the same subject : — " As its own beauty, is a source of pleasure

to what Galileo says, that falling bodies as real and as refined as a painting or

pass through every degree of velocity, I a statue, are often found to furnish the

* Lettres de Descartes. Paris, 1657. * Math. Coll. vol. ii,
•f Atti+* a«*i f» <v /«-* ^
w«/. m t /*• <t

88

GALILEO.

only means for penetrating into the
most intricate and concealed pheno-
mena of natural philosophy.

Descartes and Delambre agree in
suspecting that Galileo preferred the
dialogistic form for his treatises, because
it afforded a ready opportunity for him
to praise his own inventions : the reason
which he himself gave is, the greater
facility for introducing new matter and
collateral inquiries, such as he seldom
failed to add each time that he reperused
his work. We shall select in the first
place enough to show the extent of his
knowledge on the principal subject,
motion, and shall then allude .as well
as our limits will allow to the various
other points incidentally brought for-
ward.

The dialogues are between the same
speakers as in the " System of the
World ;" and in the first Simplicio gives
Aristotle's proof,* that motion in a va-
cuum is impossible, because according
to him bodies move with velocities in the
compound proportion of their weights
and the rarities of the mediums through
which they move. And since the density
of a vacuum bears no assignable ratio
to that of any medium in which motion
has been observed, any body which
should employ time in moving through
the latter, would pass through the same
distance in a vacuum instantaneously,
which is impossible. Salviati replies by
denying the axioms, and asserts that if
a cannon ball weighing 200 Ibs., and a
musket ball weighing half a pound, be
dropped together from a tower 200
yards high, the former will not antici-
pate the latter by so much as a foot;
*' and I would not have you do as some
are wont, who fasten upon some saying
of mine that may want a hair's breadth
of the truth, and under this hair they
seek to hide another man's blunder as
big as a cable. Aristotle says that an
iron ball weighing 1 00 Ibs. will fall from
the height of 1 00 yards while a weight
of one pound falls but one yard : I say
/ they will reach the ground together.
They find the bigger to anticipate the
less by two inches, and under these two
inches they seek to hide Aristotle's 99
yards." In the course of his reply to this
argument Salviati formally announces
the principle which is the foundation
of the whole of Galileo's theory of mo-
tion, and which must therefore be
quoted in his own words : — " A heavy

* Pbys. Lib. ir. c. 8.

body has by nature an intrinsic principle
of moving towards the common centre
of heavy things ; that is to say, to the
centre of our terrestrial globe, with a
motion continually accelerated in such
manner that in equal times there are
always equal additions of velocity. This
is to be understood as holding true only v/
when all accidental and external impe-
diments are removed, amongst which is
one that we cannot obviate, namely, the
resistance of the medium. This opposes
itself, less or more, accordingly as it is
to open more slowly or hastily to make
way for the moveable, which being by
its own nature, as I have said, continu-
ally accelerated, consequently encoun-
ters a continually increasing resistance
in the medium, until at last the velocity
reaches that degree, and the resistance
that power, that they balance each
other ; all further acceleration is pre-
vented, and the moveable continues ever
after with an uniform and equable mo-
tion." That such a limiting velocity is not
greater than some which may be exhi-
bited may be proved as Galileo suggested /
by firing a bullet upwards, which will in v
its descent strike the ground with less
force than it would have done if imme-
diately from the mouth of the gun ; for he
argued that the degree of velocity which
the air's resistance is capable of dimi-
nishing must be greater than that which
could ever be reached by a body falling
naturally from rest. " I do not think
the present occasion a fit one for ex-
amining the cause of this acceleration
of natural motion, on which the opinions
of philosophers are much divided ; some
referring it to the approach towards the
centre, some to the continual diminution
of that part of the medium remaining
to be divided, some to a certain extru-
sion of the ambient medium, which
uniting again behind the moveable
presses and hurries it forwards. All
these fancies, with others of the like sort,
we might spend our time in examining, >/
and with little to gain by resolving
them. It is enough for our author at
present that we understand his object to
be the investigation and examination of
some phenomena of a motion so acce-
lerated, (no matter what may be the
cause,) that the momenta of velocity,
from the beginning to move from rest,
increase in the simple proportion in
which the time hit-reuses, which is as
much as to say, that in equal times are
equal additions of velocity. And if it
shall turn out that the phenomena de-

GALILEO.

monstrated on this supposition are veri-
fied in the motion of falling and natu-
rally accelerated weights, we may thence
conclude that the assumed definition
does describe the motion of heavy bo-
dies, and that it is true that their acce-
leration varies in the ratio of the time
of motion."

When Galileo first published these
Dialogues on Motion, he was obliged
to rest his demonstrations upon another
principle besides, namely, that the velo-
city acquired in falling down all inclined
planes of the same perpendicular height
is the same. As this result was derived
directly from experiment, and from that

t ^ • , t /»• C^ L-

in the direction of the perpendicular
B N. Moreover let the straight line
B E drawn in the direction A B be taken
to represent the flow, or measure, of the
time, on which let any number of equal
parts B C, C D, D E, &c. be marked at
pleasure, and from the points C, D, E,
let lines be drawn parallel to B N ; in
the first of these let any part C I be
taken, and let D F be taken four times
as great as C I, E H nine times as
great, and so on, proportionally to the
squares of the lines B C, B D, B E, &c.,
or, as we say, in the double proportion
of these lines. Now if we suppose
that whilst by its equable horizontal

only, his theory was so far imperfect >/ motion the body moves from B to C, it
till he could show its consistency with also descends by its weight through C I,
the above supposed law of acceleration -A " ' * * ~ ~

When Viviani was studying with Galileo,
he expressed his dissatisfaction at this
chasm in the reasoning; the conse-
quence of which was, that Galileo, as
he lay the same night, sleepless through
indisposition, discovered the proof which
he had long sought in vain, and in-
troduced it into the subsequent edi-
tions. The third dialogue is princi-
pally taken up with theorems on the
direct fall of bodies, their times of descent
down differently inclined planes, which
in planes of the same height he deter-
mined to be as the lengths, and with
other inquiries connected with the same
subject, such as the straight lines of
shortest descent under different data,
&c.

The fourth dialogue is appropriated
to projectile motion, determined upon
the principle that the horizontal motion
will continue the same as if there were
no vertical motion, and the vertical mo-
tion as if there were no horizontal mo-
tion. " Let A B represent a horizontal

E D C B A.

N

line or plane placed on high, on which
let a body be carried with an equable
motion from A towards B, and the sup-
port of the plane being taken away at
B, let the natural motion downwards
due to the body's weight come upon it

at the end of the time denoted by B C
it will be at I. Moreover in the time
B D, double of B C, it will have fallen
four times as far, for in the first part of
the Treatise it has been shewn that the
spaces fallen through by a heavy body
vary as the squares of the times. Simi-
larly at the end of the time B E, or
three times B C, it will have fallen
through E H, and will be at H. And it
is plain that the points I, F, H, are in
the same parabolical line B I F H. The
same demonstration will apply if we
take any number of equal particles of
time of whatever duration."

The curve called here a Parabola by-
Galileo, is one of those which results
from cutting straight through a Cone,
and therefore is called also one of the
Conic Sections, the curious properties
of which curves had drawn the attention:
of geometricians long before Galileo
thus began to point out their intimate
connexion with the phenomena of mo-
tion. After the proposition we have
just extracted, he proceeds to anticipate
some objections to the theory, and ex-
plains that the course of a projectile-
will not be accurately a parabola for
two reasons ; partly on account of the
resistance of the air, and partly be-
cause a horizontal line, or one equi-
distant from the earth's centre, is not
straight, but circular. The latter cause
of difference will, however, as he says,
be insensible in all such experiments as
we are able to make. The rest of the
Dialogue is taken up with different con-
structions for determining the circum-
stances of the motion of projectiles, as
their range, greatest height, &c. ; and it
is proved that, with a given force of
projection, the range will be greatest
when a ball is projected at an elevation

90

GALILEO.

of 45°, the ranges of all angles equally
inclined above and below 45° corre-
sponding exactly to each other.

One of the most interesting subjects
discussed in these dialogues is the fa-
mous notion of Nature's horror of a
vacuum or empty space, which the old
school of philosophy considered as im-
possible to be obtained. Galileo's notions
of it were very different ; for although
he still unadvisedly adhered to the old
phrase to denote the resistance expe-
rienced in endeavouring to separate two
smooth surfaces, he was so far from
looking upon a vacuum as an impossi-
bility, that he has described an appa-
ratus by which he endeavoured to mea-
-sure the force necessary to produce one.
This consisted of a cylin-
der, into which is tightly
fitted a piston ; through
the centre of the piston
passes a rod with a coni-
cal valve, which, when
drawn down, shuts the
aperture closely, support-
ing a basket. The space between the
piston and cylinder being filled full of
water poured in through the aperture, the
valve is closed, the vessel reversed, and
weights are added till the piston is drawn
forcibly downwards. Galileo concluded
that the weight of the piston, rod, and
added weights, would be the measure of
the force of resistance to the vacuum
which he supposed would take place be-
tween the piston and lower surface of
the water. The defects in this appa-
ratus for the purpose intended are of no
consequence, so far as regards the pre-
sent argument, and it is perhaps need-
less to observe that he was mistaken in
supposing the water would not descend
with the piston. This experiment occa-
sions a remark from Sagredo, that he
had observed that a lifting - pump
would not work when the water in the
cistern had sunk to the depth of thirty-
five feet below the valve ; that he thought
the pump was injured, and sent for the
maker of it, who assured him that no
pump upon that construction would lift
water from so great a depth. This story
is sometimes told of Galileo, as if he
had said sneeringly on this occasion
that Nature's horror of a vacuum does
not extend beyond thirty-five feet ; but
itjs very plain that if he had made such
an observation, it would have been se-
riously ; and in fact by such a limi-
tation he deprived the notion of the
principal part of its absurdity. He evi-

dently had adopted the common notion
of suction, for he compares the column
of water to a rod of metal suspended
from its upper end, which may be length-
ened till it breaks with its own weight.
It is certainly very extraordinary that
he failed to observe how simply these phe-
nomena may be explained by a refer-
ence to the weight of the elastic atmo-
sphere, which he was perfectly well ac-
quainted with, and endeavoured by the
following ingenious experiment to de-
termine : — " Take a large glass flask
with a bent neck, and round its mouth
tie a leathern pipe with a valve in it,
through which water may be forced into
the flask with a syringe without suffer-
ing any air to escape, so that it will be
compressed within the bottle. It will be
found difficult to force in more than
about three-fourths of what the flask
will hold, which must be carefully
weighed. The valve must then be
opened, and just so much air will rush
out as would in its natural density oc-
cupy the space now filled by the water.
Weigh the vessel again ; the differ-
ence will show the weight of that quan-
tity of air*." By these means, which
the modern experimentalist will see were
scarcely capable of much accuracy, Ga-
lileo found that air was four hundred
times lighter than water, instead of ten
times, which was the proportion fixed
on by Aristotle. The real proportion is
about 830 times.

The true theory of the rise of water
in a lifting-pump is commonly dated
from Torricelli's famous experiment
with a column of mercury, in 1644,
when he found that the greatest height
at which it would stand is fourteen
times less than the height at which water
will stand, which is exactly the propor-
tion of weight between water and mer-
cury. The following curious letter from
Baliani, in 1630, shows that the original
merit of suggesting the real cause be-
longs to him, and renders it still more
unaccountable that Galileo, to whom it
was addressed, should not at once have
adopted the same view of the subject : —
" I have believed that a vacuum may
exist naturally ever since I knew that
the air has sensible weight, and that you
taught me in one of your letters how to
find its weight exactly, though I have
not yet succeeded with that experiment.
From that moment I took up the notion

* It has been recently proposed to determine the
density of high-pressure steam by a process analo-
gous to this.

GALILEO.

that it is not repugnant to the nature
of things that there should be a vacuum,
but merely that it is difficult to produce.
To explain myself more clearly : if we
allow that the air has weight, there is no
difference between air and water except
in degree. At the bottom of the sea
the weight of the water above me com-
presses everything round my body, and
it strikes me that the same thing must
happen in the air, we being placed at
the bottom of its immensity ; we do not
feel its weight, nor the compression
round us, because our bodies are made
capable of supporting it. But if we
were in a vacuum, then the weight of
the air above our heads would be felt.
It would be felt very great, but not infi-
nite, and therefore determinable, and it
might be overcome by a force propor-
tioned to it. In fact I estimate it to be
such that, to make a vacuum, I believe
we require a force greater than that of
a column of water thirty feet high*."

This subject is introduced by some ob-
servations on the force of cohesion, Ga-
lileo seeming to be of opinion that, al-
though it cannot be adequately ac-
counted for by " the great and principal
resistance to a vacuum, yet that per-
haps a sufficient cause may be found by
considering every body as composed of
very minute particles, between every
two of which is exerted a similar resist-
ance." This remark serves to lead to a
discussion on indivisibles and infinite
quantities, of which we shall merely ex-
tract what Galileo gives as a curious
paradox suggested in the course of it.
He supposes a basin to be formed by
scooping a hemisphere out of a cylinder,
and a cone to be taken of the same
depth and base as the hemisphere.
It is easy to show, if the cone and
scooped cylinder be both supposed
to be cut by the same plane, parallel to

the one on which both stand, that the
area of the'ring C D E F thus discovered
in the cylinder is equal to the area of the
corresponding circular section AB of the
cone, wherever the cutting plane is sup-

* Yeuturi, vol. ii.

posed to be*. He then proceeds with
these remarkable words : — ** If we raise
the plane higher and higher, one of these
areas terminates in the circumference of
a circle, and the other in a point, for
such are the upper rim of the basin and
the top of the cone. Now since in the
diminution of the two areas they to the
very last maintain their equality to one
another, it is in my thoughts proper to
say that the highest and ultimate terms f
of such diminutions are equal, and not
one infinitely bigger than the other. It
seems therefore that the circumference
of a large circle may be said to be equal
to one single point. And why may not
these be called equal if they be the last
remainders and vestiges left by equal
magnitudes $ ?"

We think no one can refuse to ad-
mit the probability, that Newton may
have found in such passages as these
the first germ of the idea of his prime
and ultimate ratios, which afterwards
became in his hands an instrument
of such power. As to the paradoxi-
cal result, Descartes undoubtedly has
given the true answer to it in saying
that it only proves that the line is not a
greater area than the point is. Whilst
on this subject, it may not be unin-
teresting to remark that something
similar to the doctrine of fluxions seems
to have been lying dormant in the minds
of the mathematicians of Galileo's era,
for Inchoffer illustrates his argument in
the treatise we have already mentioned,
that the Copernicans may deduce some
true results from what he terms their
absurd hypothesis, by observing, that
mathematicians may deduce the truth
that a line is length without breadth,
from the false and physically impossible
supposition that a point flows, and that
a line is the fluxion of a point §.

A suggestion that perhaps fire dis-
solves bodies by insinuating itself be-
tween their minute particles, brings on
the subject of the violent effects of heat
and light ; on which Sagredo inquires,
whether we are to take for granted that
the effect of light does or does not re-
quire time. Simplicio is ready with art
answer, that the discharge of artillery-
proves the transmission of light to be

* Galileo also reasons in the same way on the
equality of the solids standing on the cutting plane,
but one is sufficient for our present purpose.

t Gli altissimi e ultimi termini.

j Le ultimo reliquie e vestigie lasciate da grandezze
eguali.

§ Punctum fluere, et lineani esse fluxum puncti.
Tract. Syllept. Romae, 1633.

92

GALILEO.

instantaneous, to which Sagredo cau-
tiously replies, that nothing can be ga-
thered from that experiment except that
light travels more swiftly than sound ;
nor can we draw any decisive conclusion
from the rising of the sun. " Who can
assure us that he is not in the horizon
before his rays reach our sight?" Sal-
viati then mentions an experiment by
which he endeavoured to examine this
question. Two observers are each to be
furnished with a lantern: as soon as
the first shades his light, the second is to
discover his, and this is to be repeated
at a short distance till the observers are
perfect in the practice. The same thing
is to be tried at the distance of several
miles, and if the first observer perceive
any delay between shading his own light
and the appearance of his companion's,
it is to be attributed to the time taken
by the light in traversing twice the dis-
tance between them. He allows that he
, could discover no perceptible interval at
the distance of a mile, at which he had
tried the experiment, but recommends
that with the help of a telescope it should
be tried at much greater distances. Sir
Kenelm Digby remarks on this pas-
sage : " It may be objected (if there be
some observable tardity in the motion
of light) that the sunne would never be
truly in that place in which unto our
eyes he appeareth to be ; because that
it being seene by means of the light
•which issueth from it, if that light re-
quired tima to move in, the sunne (whose
motion is so swifte) would be removed
from the place where the light left it,
before it could be with us to give tidings
of him. To this I answer, allowing per-
adventure that it may be so, who
knoweth the contrary? Or what in-
convenience would follow if it be ad-
mitted * ?"

The principal thing remaining to be
noticed is the application of the theory
of the pendulum to musical concords
and dissonances, which are explained, in
the same manner as by Kepler in his
" Harmonices Mundi," to result from
the concurrence or opposition of vibra-
tions in the air striking upon the drum
of the ear. It is suggested that these
vibrations may be made manifest by
rubbing the finger round a glass set in
a large vessel of water ; "and if by pres-
sure the note is suddenly made to rise
to the octave above, every one of the

* " Treatise of the Nature of Bodies. London,
1665."

undulations which will be seen regu-
larly spreading round the glass, will
suddenly split into two, proving that
the vibrations that occasion the octave
are double those belonging to the sim-
ple note." Galileo then describes a
method he discovered by accident of
measuring the length of these waves more
accurately than can be done in the agi-
tated water. He was scraping a brass
plate with an iron chisel, to take out
some spots, and moving the tool rapidly
upon the plate, he occasionally heard a
hissing and whistling sound, very shrill
and audible, and whenever this occur-
red, and then only, he observed the
light dust on the plate to arrange itself
in a long row of small parallel streaks
equidistant from each other. In re-
peated experiments he produced differ-
ent tones by scraping with greater or
less velocity, and remarked that the
streaks produced by the acute sounds
stood closer together than those from
the low notes. Among the sounds pro-
duced were two, which by compari-
son with a viol he ascertained to differ
by an exact fifth ; and measuring the
spaces occupied by the streaks in both
experiments, he found thirty of the
one equal to forty-five of the other,
which is exactly the known proportion
of the lengths of strings of the same
material which sound a fifth to each
other *.

Salyiati also remarks, that if the
material be not the same, as for in-
stance if it be required to sound an
octave to a note on catgut, on a
wire of the same length, the weight of
the wire must be made four times as
great, and so for other intervals. " The
immediate cause of the forms of musi-
cal intervals is neither the length, the
tension, nor the thickness, but the pro-
portion of the numbers of the undula-
tions of the air which strike upon the
drum of the ear, and make it vibrate in
the same intervals. Hence we may
gather a plausible reason of the differ-
ent sensations occasioned to us by dif-
ferent couples of sounds, of which we
hear some with great pleasure, some
with less, and call them accordingly
concords, more or less perfect, whilst
some excite in us great dissatisfaction,
and are called discords. The disagree-
able sensation belonging to the latter

* This beautiful experiment is more easily tried by
drawing the bow of a violin across the edge of glass
strewed with fine dry sand. Those who wish to see more
on the subject may consult Chladni's ' Acoustique.'

GALILEO.

93

probably arises from the disorderly
manner in which the vibrations strike
the drum of the ear ; so that for in-
stance a most cruel discord would be
produced by sounding together two
strings, of which the lengths are to each
other as the side and diagonal of a
square, which is the discord of the false
fifth. On the contrary, agreeable con-
sonances will result from those strings
of which the numbers of vibrations made
in the same time are commensurable,
" to the end that the cartilage of the
drum may not undergo the incessant
torture of a double inflexion from the
disagreeing percussions." Something
similar may be exhibited to the eye by
hanging up pendulums of different
lengths : "if these be proportioned so
that the times of their vibrations cor-
respond with those of the musical con-
cords, the eye will observe with pleasure
their crossings and interweavings still
recurring at appreciable intervals ; but
if the times of vibration be incommen-
surate, the eye will be wearied and worn
out with following them."

The second dialogue is occupied en-
tirely with an investigation of the
strength of beams, a subject which does
not appear to have been examined by
any one before Galileo beyond Aris-
totle's remark, that long beams are
weaker, because they are at once the
weight, the lever, and the fulcrum ; and
it is in the development of this obser-
vation that the whole theory consists.
The principle assumed by Galileo as
the basis of his inquiries is, that the
force of cohesion with which a beam
resists a cross fracture in any section
may all be considered as acting at the
centre of gravity of the section, and that
it breaks always at the lowest point:
from this he deduced that the effect of
the weight of a prismatic beam in over-
coming the resistance of one end by
which it is fastened to a wall, varies .
directly as the square of the length, and
inversely as the side of the base. From
this it immediately follows, that if for
instance the bone of a large animal be
three times as long as the corresponding
one in a smaller beast, it must be nine
times as thick to have the same strength,
provided we suppose in both cases that
the materials are of the same consist-
ence. An elegant result which Galileo
also deduced from this theory, is that the
form of such a beam, to be equally strong
in every part, should be that of a para-
bolical prism, the vertex of the parabola

being the farthest removed from the
wall. As an easy mode of describing
the parabolic curve for this purpose, he
recommends tracing the line in which a
heavy flexible string hangs. This curve
is not an accurate parabola: it is now
called a catenary ; but it is plain from
the description of it in the fourth dia-
logue, that Galileo was perfectly aware
that this construction is only approxi-
mately true. In the same place he makes
the remark, which to many is so para-
doxical, that no force, however great, >
exerted in a horizontal direction, can
stretch a heavy thread, however slender,
into an accurately straight line.

The fifth and sixth dialogues were left
unfinished, and annexed to the former
ones by Viviani after Galileo's death :
the fragment of the fifth, which is on the
subject of Euclid's Definition of Ratio,
was at first intended to have formed a
part of the third, and followed the first
proposition on equable motion: the sixth
was intended to have embodied Galileo's
researches on the nature and laws of
Percussion, on which he was employed at
the time of his death. Considering these
solely as fragments, we shall not here
make any extracts from them.

. CHAPTER XVIII.

Correspondence on Longitudes. — Pen-
dulum Clock.

IN the spring of 1636, having finished
his Dialogues on Motion, Galileo re-
sumed the plan of determining the lon-
gitude by means of Jupiter's satellites.
Perhaps he suspected something of the
private intrigue which thwarted his
former expectations from the Spanish
government, and this may have induced
him on the present occasion to negotiate
the matter without applying for Ferdi-
nand's assistance and recommendation.
Accordingly he addressed himself to
Lorenz Real, who had been Governor
General of the Dutch possessions in
India, freely and unconditionally offer-
ing the use of his. theory to the States
General of Holland. Not long before,
his opinion had been requested by the
commissioners appointed at Paris to
examine and report on the practicability
of another method proposed by Morin,*
which consisted in observing the dis-
tance of the moon from a known star.
Morin was a French philosopher, prin-

* One of the Commissioners was the father of
Blaise Pascal,

94

GALILEO.

cipally known as an astrologer and zea-
lous Anti-Copernican ; but his name de-
serves to be recorded as undoubtedly one
of the first to recommend a method,
which, under the nwne of a Lunar dis-
tance, is now in universal practice.

The monthly motion of the moon is so
rapid, that her distance from a given star
sensibly varies in a few minutes even to
the unassisted eye ; and with the aid of
the telescope, we can of course appre-
ciate the change more accurately. Morin
proposed that the distances of the moon
from a number of fixed stars lying near
her path in the heavens should be be-
forehand calculated and registered for
every day in the year, at a certain hour,
in the place from which the longitudes
were to be reckoned, as for instance at
Paris. Just as in the case of the eclipses
of Jupiter's satellites, the observer, when
he saw that the moon had arrived at
the registered distance, would know the
hour at Paris : he might also make al-
lowance for intermediate distances.
Observing at the same instant the hour
on board his ship, the difference between
the two would show his position in re-
gard of longitude. In using this
method as it is now practised, several
modifications are to be attended to,
without which it would be wholly use-
less, in consequence of the refraction
of the atmosphere, and the proximity of
the moon to the earth. Owing to the
latter cause, if two spectators should at
the same instant of time, but in different
places, measure the distance of the
moon in the East, from a star still more
to the eastward, it would appear greater
to the more easterly spectator than to
the other observer, who as seen from
the star would be standing more di-
rectly behind the moon. The mode
of allowing for these alterations is taught
by trigonometry and astronomy.

The success of this method depends al-
together upon the exact knowledge which
we now have of the moon's course, and
till that knowledge was perfected it
would have been found altogether il-
lusory. Such in fact was the judgment
which Galileo pronounced upon it. " As
to Morin' s book on the method of find-
ing the longitude by means of the moon's
motion, I say freely that I conceive this
idea to be as accurate in theory, as
fallacious and impossible in practice. I
am sure that neither you nor any
one of the other four gentlemen can
doubt the possibility of finding the dif-
ference of longitude between two me-

ridians by means of the moon's motion^
provided we are sure of the following
requisites : First, an Ephemeris of the
moon's motion exactly calculated for
the first meridian from which the others
are to be reckoned ; secondly, exact in-
struments, and convenient to handle, in
taking the distance between the moon
and a fixed star ; thirdly, great prac-
tical skill in the observer ; fourthly, not
less accuracy in the scientific calcula-
tions, and astronomical computations ;
fifthly, very perfect clocks to number
the hours, or other means of knowing
them exactly, &c. Supposing, I say,
all these elements free from error, the
longitude will be accurately found ; but
I reckon it more easy and likely to err
in all of these together, than to be prac-
tically right in one alone. Morin ought
to require his judges to assign, at their
pleasure, eight or ten moments of dif-
ferent nights during four or six months
to come, and pledge himself to predict
and assign by his calculations the dis-
tances of the moon at those determined
instants from some star which would
then be near her. If it is found that
the distances assigned by him agree
with those which the quadrant or sex-
tant* will actually sho\v, the judges
would be satisfied of his success, or
rather of the truth of the matter, and
nothing would remain but to show that
his operations were such as could be
performed by men of moderate skill, and
also practicable at sea as well as on
land. I incline much to think that an
experiment of this kind would do much
towards abating the opinion and con-
ceit which Morin has of himself, which
appears to me so lofty, that I should
consider myself the eighth sage, if I
knew the half of what Morin presumes
to know.''

It is probable that Galileo was
biassed by a predilection for his own
method, on which he had expended
so much time and labour ; but the ob-
jections which he raises against Morin's
proposal in the foregoing letter are no
other than those to which at that period
it was undoubtedly open. With regard
to his own, he had already, in 1612,
given a rough prediction of the course
of Jupiter's satellites, which had been
found to agree tolerably well with sub-
sequent observations ; and since that

* These instruments were very inferior to those
now in use under the same name. See " Treatise on
Opt. Instrum."

GALILEO.

95

time, amid all his other employments,
he had almost unmtermittingly during
twenty-four years continued his obser-
vations, for the sake of bringing the
tables of their motions to as high a state
of perfection as possible. This was the
point to which the inquiries of the States
in their answer to Galileo's frank pro-
posal were principally directed. They
immediately appointed commissioners to
communicate with him, and report the
various points on which they required
information. They also sent him a
golden chain, and assured him that in
the case of the design proving success-
ful, he should have no cause to com-
plain of their want of gratitude and ge-
nerosity. The commissioners immedi-
ately commenced an active correspon-
dence with him, in the course of which
he entered into more minute details with
regard to the methods by which he
proposed to obviate the practical dif-
ficulties of the necessary observations.
• It is worth noticing that the secretary
to the Prince of Orange, who was mainly
instrumental in forming this commis-
sion, was Constantine Huyghens, father
of the celebrated mathematician of that
name, of whom it has been said that he
seemed destined to complete the disco-
veries of Galileo ; and it is not a little
remarkable, that Huyghens nowhere in
his published works makes any allusion
to this connexion between his father and
Galileo, not even during the discussion
that arose some years later on the sub-
ject of the pendulum clock, which must
necessarily have forced it upon his re-
collection.

The Dutch commissioners had chosen
one of their number to go into Italy for
the purpose of communicating person-
ally with Galileo, but he discouraged
this scheme, from a fear of its giving
umbrage at Rome. The correspondence
being carried on at so great a distance
necessarily experienced many tedious de-
lays, till in the very midst of Galileo's
labours to complete his tables, he was
seized with the blindness which we have
already mentioned. He then resolved
to place all the papers containing his
observations and calculations for this
purpose in the hands of Renieri, a for-
mer pupil of his, and then professor
of mathematics at Pisa, who under-
took to finish and to forward them into
Holland. Before this was done, a new
delay was occasioned by the deaths
which speedily followed each other of
every one of the four commissioners;

and for two or three years the cor-
respondence with Holland was entirely
interrupted. Constantine Huyghens,
who was capable of appreciating the
value of the scheme, succeeded after
some trouble in renewing it, but only
just before the death of Galileo himself,
by which of course it was a second
time broken off; and to complete the
singular series of obstacles by which the-
trial of this method was impeded, just
as Renieri, by order of the Duke of Tus-
cany, was about to publish the ephe-
meris and tables which Galileo had en-
trusted to him, and which the Duke
told Viviani he had seen in his pos-
session, he also was attacked with a
mortal malady ; and upon his death the
manuscripts were nowhere to be found,,
nor has it since been discovered what
became of them. Montucla has inti-
mated his suspicions that Renieri him-
self destroyed them, from a conscious-
ness that they were insufficient for the
purpose to which it was intended to ap-
ply them ; a bold conjecture, and one
which ought to rest upon something
more than mere surmise : for although it
may be considered certain, that the
practical value of these tables would be
very inconsiderable in the present ad-
vanced state of knowledge, yet it is
nearly as sure that they were unique at
that time, and Renieri was aware of
the value which Galileo himself had set
upon them, and should not be lightly
accused of betray ing his trust in so gross
a manner. In 1665, Borelli calculated
the places of the satellites for every day
in the ensuing year, which he professed
to have deduced (by desire of the Grand
Duke) from Galileo's tables;* but he
does not say whether or not these tables
were the same that had been in Renieri's
possession.

We have delayed till this opportunity
to examine how far the invention of the
pendulum clock belongs to Galileo. It
has been asserted that the isochronism
of the pendulum had been noticed by
Leonardo da Vinci, but the passage on
which this assertion is founded (as trans-
lated from his manuscripts by Venturi)
scarcely warrants this conclusion. '« A
rod which engages itself in the opposite
teeth of a spur-wheel can act like the
arm of the balance in clocks, that is to
say, it will act alternately, first on one
side of the wheel, then on the opposite

* Theoricae Mediceorum Planetarum, Florentise,
1666.

96

GALILEO.

one, without interruption." If Da
Vinci had constructed a clock on this
principle, and recognized the superiority
of the pendulum over the old balance,
he would surely have done more flian
merely mention it as affording an un-
intermitted motion "like the arm of the
balance." The use of the balance is
supposed to have been introduced at
least as early as the fourteenth century.
Venturi mentions the drawing and de-
scription of a clock in one of the manu-
scripts of the King's Library at Paris,
dated about the middle of the fifteenth
century, which as he says nearly re-
sembles a modern watch. The balance
is there called " The circle fastened to
the stem of the pallets, and moved by
the force with it.* In that singularly
wild and extravagant book, entitled
" A History of both Worlds," by Robert
Flud, are given two drawings of the
wheel-work of the clocks and watches
in use before the application of the pen-
dulum. An inspection of them will show
how little remained to be done when
the isochronism of the pendulum was
discovered. Fig. 1. represents "the

large clocks moved by a weight, such as
are put up in churches and turrets ;

• Circnlus affrxus virgaa paletorum qui cum e& de
vi movetur.

Jig. 2. the small ones moved by a
spring, such as are worn round the neck,
or placed on a shelf or table. The
use of the chain is to equalize the
spring, which is strongest at the begin-
ning of its motion."* This contrivance
of the chain is mentioned by Cardan, in
1570, and is probably still older. In
both figures the name given to the cross
bar, with the weight attached to it, is
" the time or balance (tempus sen libra-
tio) by which the motion is equalized."
The manner in which Huyghens first
applied the pendulum is shown in
Jig. 3.t The action in the old clocks of
the balance, or rake, as it was also called,
was by checking the motion of the
descending weight till its inertia was
overcome ; it was then forced round till
the opposite pallet engaged in the
toothed wheel. The balance was thus
suddenly and forcibly reduced to a
state of rest, and again set in motion,
in the opposite direction. It will be
observed that these balances wanted
the spiral spring introduced in all
modern watches, which has a pro-
perty of isochronism similar to that of
the pendulum. Hooke is generally
named as the discoverer of this pro-
perty of springs, and as the author of
its application to the improvement of
watches, but the invention is disputed
with him by Huyghens. Lahire asserts^
that the isochronism of springs was
communicated to Huyghens at Paris
by Hautefeuille, and that this was the
reason why Huyghens failed to obtain
the patent he solicited for the construc-
tion of spring watches. A great num-
ber of curious contrivances at this early
period in the history of Horology, may
be seen in Schott's Magia Naturae,
published at Nuremberg in 1664.

Galileo was early convinced of the im-
portance of his pendulum to the ac-
curacy of astronomical observations;
but the progress of invention is such
that the steps which on looking back
seem the easiest to make, are often those
which are the longest delayed. Galileo re-
cognized the principle of the isochronism
of the pendulum, and recommended it
as a measurer of time in 1583 ; yet fifty
years later, although constantly using it,
he had not devised a more convenient
method of doing so, than is contained in
the following description taken from
his "Astronomical Operations."

* Utriusque Cosmi Historia. Oppenhemii, 1617.
f Huygenii Opera. Lugduni, 1724.
t Memoires de 1' Academic, 171?.

GALILEO.

97

" A very exact time-measurer for mi-
nute intervals of time, is a heavy pendu-
lum of any size hanged by a fine thread,
which, if removed from the perpendicular
and allowed to swing freely, always com-
pletes its vibrations, be they great or
small, in exactly the same time/'*

The mode of finding exactly by means
of this the quantity of any time reduced
to hours, minutes, seconds, &c., which
are the divisions commonly used among
astronomers, is this : — " Fit up a pen-
dulum of any length, as for instance
about a foot long, and count pa-
tiently (only for once) the number
of vibrations during a natural day.
Our object will be attained if we know
the exact revolution of the natural
day. The observer must then fix a
telescope in the direction of any star,
and continue to watch it till it disap-
pears from the field of view. At that
instant he must begin to count the
vibrations of the pendulum, continuing
all night and the following day till the
return of the same star within the field
of view of the telescope, and its second
disappearance, as on the first night.
Bearing in recollection the total number
of vibrations thus made in twenty-four
hours, the time corresponding to any
other number of vibrations will be im-
mediately given by the Golden Rule."

A second extract out of Galileo's
Dutch correspondence, in 1637, will show
.the extent of his improvements at that
time: — " I come now to the second con-
trivance fpr increasing immensely the ex-
actness of astronomical observations. I
allude to my time-measurer, the precision
of which is so great, and such, that it
will give the exact quantity of hours,
minutes, seconds, and even thirds, if
their recurrence could be counted ; and
its constancy is such that two, four,
or six such instruments will go on
together so equably that one will not
differ from another so much as the
beat of a pulse, not only in an hour,
but even in a day or a month." —
" I do not make use of a weight hang-
ing by a thread, but a heavy arid solid
pendulum, made for instance of brass
or copper, in the shape of a circular
sector of twelve or fifteen degrees, the
radius of which may be two or three
palms, and the greater it is the less
trouble will there be in attending it.
This sector, such as I have described,-!
make thickest in the middle radius,

* See page 84.

tapering gradually towards the edges,
where I terminate it in a tolerably
sharp line, to obviate as much as pos-
sible the resistance of the air, which
is the sole cause of its retardation."
— [These last words deserve notice, be-
cause, in a previous discussion, Galileo
had observed that the parts of the
pendulum nearest the point of sus-
pension have a tendency to vibrate
quicker than those at the other end,
and seems to have thought erroneously
that the stoppage of the pendulum is
partly to be attributed to this cause.]
'—"This is pierced in the centre, through
which is passed an iron bar shaped like
those on which steelyards hang, termi-
nated below in an angle, and placed on
two bronze supports, that they may
wear away less during a long motion of
the sector. If the sector (when accu-
rately balanced) be removed several
degrees from its perpendicular position,
it will continue a reciprocal motion
through a very great number of vibra-
tions before it will stop ; and in order
that it may continue its motion as long
as is wanted, the attendant must occa-
sionally give it a smart push, to carry it
back to large vibrations." Galileo then
describes as before the method of count-
ing the vibrations in the course of a
day, and gives the rule that the lengths
of two similar pendulums will have the
same proportion as the squares of their
times of vibration. He then continues:
" Now to save the fatigue of the assist-
ant in continually counting the vibra-
tions, this is a convenient contrivance:
A very small and delicate needle extends
out from the middle of the circumfer-
ence of the sector, which in passing
strikes a rod fixed at one end ; this rod
rests upon the teeth of a wheel as light
as paper, placed in a horizontal plane
near the pendulum, having round it
teeth cut like those of a saw, that is to
say, with one side of each tooth perpen-
dicular to the rim of the wheel and
the other inclined obliquely. The rod
striking against the perpendicular side
of the tooth moves it, but as the same
rod returns against the oblique side, it
does not move it the contrary way, but
slips over it and falls at the foot of the
following tooth, so that the motion of
the wheel will be always in the same
direction. And by counting the teeth
you may see at will the number of teeth
passed, and consequently the number
of vibrations and of particles of time
elapsed, You nmy also fit to the axis

98

GALILEO.

of this first wheel a second, with a small
number of teeth, touching another
greater toothed wheel, &c. But it is su-
perfluous to point out this to you, who
have by you men very ingenious and
well skilled in making clocks and other
admirable machines ; and on this new
principle, that the pendulum makes its
great and small vibrations in the same
time exactly, they will invent contri-
vances more subtle than any I can
suggest; and as the error of clocks
consists principally in the disability of
workmen hitherto to adjust what we call
the balance of the clock, so that it may
vibrate regularly, my very simple pen-
dulum, which is not liable to any altera-
tion, affords a mean of maintaining the
measures of time always equal." The
contrivance thus described would be
somewhat similar to the annexed repre-
sentation, but it is almost certain that
no such instrument was actually con-
structed.

It must be owned that Galileo greatly
overrated the accuracy of his timekeeper";
and in asserting so positively that which
he had certainly not experienced, he
seems to depart from his own principles
of philosophizing. It will be remarked
that in this passage he still is of the
erroneous opinion, that all the vibra-
tions great or small of the same pen-
dulum take exactly the same time ; and
we have not been able to find any trace
of his having ever held a different opi-
nion, unless perhaps in the Dialogues,
where he says, " If the vibrations are
not exactly equal, they are at least in-
sensibly different." This is very much
at variance with the statement in the
Memoirs of the Academia del Cimento,
edited by their secretary Magalotti, on
the credit of which Galileo's claim to
the pendulum-clock chiefly rests. It
is there said that experience shows
that the smallest vibrations are rather
the quickest, "as Galileo announced after
the observation, which in 1583 he was
the first to make of their approximate

equality/' It is not possible immedi-
ately in connexion with so glaring a
misstatement, to give implicit credence
to the assertion in the next sentence,
that " to obviate this inconvenience*
Galileo was the first to contrive a clock,
constructed in 1649, by his son Vin-
cenzo, in which, by the action of a weight
or spring, the pendulum was con-
strained to move always from the same
height. Indeed it appears as if Maga-
lotti did not always tell this story in the
same manner, for he is referred to as the
author of the account given by Becher,
" that Galileo himself made a pendulum -
clock one of which was sent to Hol-
land," plainly insinuating that Huyghens
was a mere copyist.* These two ac-
counts therefore serve to invalidate
each other's credibility. Tiraboschit
asserts that, at the time he wrote, the
mathematical professor at Pisa was
in possession of the identical clock
constructed by Treffler under Vincen-
zo's directions ; and quotes a letter
from Campani, to whom it was shown
by Ferdinand," old, rusty, and unfinished
as Galileo's son made it before 1649."
Viviani on the other hand says that
Treffler constructed this same clock
some time after Vincenzo's death (which
happened in 1649), on a different prin-
ciple from Vincenzo's ideas, although he
says distinctly that he heard Galileo de-
scribe an application of the pendulum to
a clock similar to Huyghens' contrivance.
Campani did not actually see this clock
till 1659, which was three years after
Huyghens' invention, so that perhaps
Huyghens was too easily satisfied when,
on occasion of the answer which Ferdi-
nand sent to his complaints of the Me-
morie del Cimento he wrote to Bouil-
laud, " I must however believe, since
such a prince assures me, that Galileo
had this idea before me."

There is another circumstance almost
amounting to a proof that it was an after-
thought to attribute the merit of construct-
ing the pendulum-clock to Galileo, for on
the reverse of a medal struck by Viviani,
and inscribed " to the memory of his
excellent instructor,"^ is a rude exhibi-
tion of the principal objects to which
Galileo's attention was directed. The
pendulum is represented simply by a
weight attached to a string hanging on
the face of a rock. It is probable that,

* De nova Temporis dimetiendi ratione. Londini,
1630.

f StoriadellaLett. Ital.

* Museum Mazuchelliaimm, vol. ii. Tab. cvii, p. 29,

GALILEO.

99

in a design expressly intended to com-
memorate Galileo's s inventions, Viviani
would have introduced the timekeeper
in the most perfect form to which it had
been brought by him. Riccioli,* whose
industry was unwearied in collecting
every fact and argument which related in
any way to the astronomical and mecha-
nical knowledge and opinions of his time,
expressly recommends swinging a pen-
dulum, or perpendicular as it was often
called (only a few years before Huyghens'
publication), as much more accurate
than any clock. -'r Join to all these argu-
ments Huyghens1 positive assertion, that
if Galileo had conceivedany such idea, he
at least was entirely ignorant of it,| and
no doubt can remain that the merit of
the original invention (such as it was)
rests entirely with Huyghens. The step
indeed seems simple enough for a less
genius than his : tor the property of the
pendulum was known, and the conver-
sion of a rotatory into a reciprocating
motion was known ; but the connexion
of the one with the other having been
so long delayed, we must suppose that
difficulties existed where we are not now
able to perceive them, for Huyghens' im-
provement was received with universal
admiration.

There may be many who will con-
sider the pendulum as undeserving so
long a discussion ; who do not know
or remember that the telescope itself
has hardly done more for the preci-
sion of astronomical observations than
this simple instrument, not to mention
the invaluable convenience of an uni-
form and accurate timekeeper in the
daily intercourse of life. The patience
and industry of modern observers are
often the theme of well-merited praise,
but we must look with a still higher de-
gree of wonder on such men as Tycho-
Brahe and his contemporaries, who were
driven by the want of any timekeeper
on which they could depend to the most
laborious expedients, and who neverthe-
less persevered to the best of their abi-
lity, undisgusted either by the tedium of
such processes, or by the discouraging
consciousness of the necessary imper-
fection of .their most approved methods
and instruments.

The invariable regularity of the pen-
dulum's motion was soon made subser-
vient to ulterior purposes beyond that of

* AliTiagestum Novum, vol. i.
t Quovis horologin accuratius;.
j Clarorum Bel^aram ad Ant. Magliabech. Epis-
tolee. Florence, 1713, torn. i. p. 235.

merely registering time. We have seen
the important assistance it afforded in es-
tablishing the laws of motion ; and when
the theory founded on those laws was
extended and improved, the pendulum
was again instrumental, by a species of
approximate reasoning familiar to all
who are acquainted with physical in-
quiries, in pointing out by its minute
irregularities in different parts of the
earth, a corresponding change in the
weight of all bodies in those different
situations, supposed to be the conse-
quence of a greater distance from the
axis of the earth's rotation ; since that
would occasion the force of attraction
to be counterbalanced by an increased
centrifugal force. The theory which
kept pace with the constantly increasing
accuracy of such observations, proving
consistent in all trials of it, has left little
room for future doubts ; and in this
manner the pendulum in intelligent
hands became the simplest instrument
for ascertaining the form of the globe
which we inhabit. An English astro-
nomer, who corresponded with Kepler
under the signature of Brutius (whose
real name perhaps might be Bruce),
had already declared his belief in 1603,
that " the earth on which we tread is
neither round nor globular, but more
nearly of an oval figure."* There is
nothing to guide us to the grounds on
which he formed this opinion, which
was perhaps only a lucky guess. Kep-
ler's note upon it is : " This is not alto-
gether to be contemned."

A farther use of the pendulum is in
furnishing a general and unperishing
standard of measure. This application
is suggested in the third volume of the
' Reflections' of Mersenne, published in
1647, where he observes that it may be
best for the future not to divide time into
hours, minutes, and seconds, but to ex-
press its parts by the number of vibra-
tions of a pendulum of given length,
swinging through a given arc. It was
soon seen that it would be more con-
venient to invert this process, and to
choose as an unit of length the pendulum
which should make a certain number of
vibrations in the unit of time, naturally
determined by the revolution of the earth
on its axis. Our Royal Society took an
active part in these experiments, which
seem, notwithstanding their utility, to
have met from the first with much of
the same ridicule which was lavished

* Kepleri Epistolae.

H2

100

GALILEO.

upon them by the ignorant, when re-
cently repeated for the same purpose.
*' I contend," says Graunt* in a dedica-
tion to the Royal Society, dated 1662,
" against the envious schismatics of
your society (who think you do nothing
unless you presently transmute metals,
make butter and cheese without milk,
and, as their own ballad hath it, make
leather without hides), by asserting the
usefulness of even all your preparatory
and luciferous experiments, being not
the ceremonies, but the substance and
principles of useful arts. For I find in
trade the want of an universal measure,
and have heard musicians wrangle about
the just and uniform keeping of time in
their consorts, and therefore cannot with
patience hear that your labours about
vibrations, eminently conducing to both,
should be slighted, nor your pendula
called s\ving-swangs with scorn."t

CHAPTER XIX.

deta

ter of
ils — hi

is Death — Conclusion.

THE remaining years of Galileo's life
were spent at Arcetri, where indeed, even
if the Inquisition had granted his li-
berty, .his increasing age and infirmities
would probably have detained him. The
rigid caution with which he had been
watched in Florence was in great mea-
sure relaxed, ,and he was permitted to
see the friends who crowded round him
to express their respect and sympathy.
The Grand Duke visited him frequently,
and many distinguished strangers, such
as Gassendi and Deodati, came into
Italy solely for the purpose of testify-
ing their admiration of his character.
Among other visitors the name of Mil-
ton will be read with interest : we may
probably refer to the effects of this in-
terview the allusions to Galileo's disco-
veries, so frequently introduced into his
poem. Milton mentions in his ' Areo-
pagitica,' that he saw Galileo whilst in
Italy, but enters into no details of his
visit.

* Natural and Political Observations. London,
1664.

f See also Hudibras, Part II. Cant. III.
They're guilty by their own confessions
Of felony, and at the Sessions
Upon the bench I will so handle 'em,
That the vibration of this pendulum
Shall make all taylors' yards of one
Unanimous opinion ;
A thing he long has vaunted of,
But now shall make it put of proof.
Hudibras was certainly written before 1663 : ten
years later Huyghens speaks of the idea of SO employ-
ing the pendulum aaa common one.

Galileo was fond of society, and his
cheerful and popular manners rendered
him an universal favourite among those
who were admitted to his intimacy.
Among these, Viviani, who formed one
of his family during the three last years
of his life, deserves particular notice, on
account of the strong attachment and
almost filial veneration with which
he ever regarded his master and bene-
factor. His long life, which was pro-
longed to the completion of his 81st year
in 1703, enabled him to see the tri-
umphant establishment of the truths
on account of which Galileo had en-
dured so many insults; and even " in
his old age, when in his turn he had
acquired "a claim to the reverence
of a younger generation, our Royal So
ciety, who invited him among them in
1696, felt that the complimentary lan-
guage in which they addressed him as
the first mathematician of the age would
have been incomplete and unsatisfactory
without an allusion to the friendship
that gained him the cherished title of
" The last pupil of Galileo."*

Torricelli, another of Galileo's most ce-
lebrated followers, became a member of
his family in October, 1641: he first
learned mathematics from Castelli, and
occasionally lectured for him at Rome,
in which manner he was employed when
Galileo, who had seen his book ' On
Motion,' and augured the greatest suc-
cess from such a beginning, invited him
to his house — an offer which Torricelli
eagerly embraced, although he enjoyed
the advantages of it but for a short
time. He afterwards succeeded Galileo
in his situation at the court of Flo-
rence,t but survived him only a few
years.

It is from the accounts of Viviani and
Gherardini that we principally draw the
following particulars of Galileo's person
and character : — Signer Galileo was
of a cheerful and pleasant countenance,
especially in his old age, square built,
and well proportioned in stature, and
rather above the middle size. His
complexion was fair and sanguine, his
eyes brilliant, and his hair of a reddish
cast. His constitution was naturally

* The words of his diploma are : Galilaui in ma-
thematicis disciplinis discipulus, in aerumnis socius,
Italicum ingenium ita perpolivit optimis artibus ut
inter mathematicos sseculi nostri facile princeps per
orbem litterarium numeretur.— Tiraboschi.

t On this occasion the taste of the time showed
itself in the following anagram : — ,

Evangelista Torricellieus,
Kn yirescit Gulilwus alter.

GALILEO.

101

strong, but worn out by fatigue of mind
and body, so as frequently to be reduced
to a state of the utmost weakness. He
was subject to attacks of hypochondria,
and often molested by severe and dan-
gerous illnesses, occasioned in great
measure by his sleepless nights, the
whole of which he frequently spent
in astronomical observations. Curing
upwards of forty-eight years of his life,
he was tormented with" acute rheuma-
tic pains, suffering particularly on any
change of weather. He found himself
most free from these pains whilst re-
siding in the country, of which conse-
quently he became very fond : besides,
he used to say that in the country he
had greater freedom to read the book of
Nature, which lay there open before
him. His library was very small, but
well chosen, and open to the use of the
friends whom he loved to see assembled
round him, and whom he was accus-
tomed to receive in the most hospitable
manner. He ate sparingly himself; but
was particularly choice in the selection
of his wines, which in the latter part of
his life were regularly supplied out of
the Grand Duke's cellars. This taste
gave an additional stimulus to his agri-
cultural pursuits, and many of his leisure
hours were spent in the cultivation and
superintendence of his vineyards. It
should seem that he was considered a
good judge of wine ; for Viviani has pre-
served one of his receipts in a collection
of miscellaneous experiments. In it he
strongly recommends that for wine of
the first quality, that juice only should be
employed, which is pressed out by the
mere weight of the heaped grapes,
which would probably be that of the
ripest fruit. The following letter, written
in his 74th year, is dated, " From my
prison at Arcetri. — I am forced to
avail myself of your assistance and fa-
vour, agreeably to your obliging offers,
in consequence of the excessive chill of
the weather, and of old age, and from
having drained out my grand stock of a
hundred bottles, which I laid in two years
ago ; not to mention some minor parti-
culars during the last two months, which
I received from my Serene Master, the
Most Eminent Lord Cardinal, their
Highnesses the Princes, and the Most
Excellent Duke of Guise, besides
cleaning out two barrels of the wine of
this country. Now, I beg that with all
due diligence and industry, and with
consideration, and taking counsel with
the most refined palates, you will pro-

vide me with two cases, that is to say,
with forty flasks of different wines, the
most, exquisite that you can find : take
no thought of the expense, because I stint
myself so much in all other pleasures that
I can afford to lay out something at the
request of Bacchus, without giving
offence to his two companions Ceres and
Venus. You must be careful to leave out
neither Scillo nor Carino (I believe they
meant to call them Scylla and Charyb-
dis), nor the country of my master, Ar-
chimedes of Syracuse, nor Greek wines,
nor clarets, &c. &c. The expense I
shall easily be able to satisfy, but not the
infinite obligation."

In his expenditure Galileo observed a
just mean between avarice and profu-
sion : he spared no cost necessary for the
success of his many and various experi-
ments, and spent large sums in charity
and hospitality, and in assisting those in
whom he discovered excellence in any
art or profession, many of whom he
maintained in his own house. His tem-
per was easily ruffled, but still more
easily pacified. He seldom conversed
on mathematical or philosophical topics
except among his intimate friends ; and
when such subjects were abruptly
brought before him, as was often the
case by the numberless visitors he
was in the habit of receiving, he showed
great readiness in turning the conver-
sation into more popular channels, in
such manner however that he often
contrived to introduce something to
satisfy the curiosity of the inquirers.
His memory was uncommonly tena-
cious, and stored with a vast variety of old
songs and stories, which he was ire
the constant habit of quoting and allu-
ding to. His favourite Italian authors
were Ariosto, Petrarca, and Berni,
great part of whose poems he was
able to repeat. His excessive admira-
tion of Ariosto determined the side
which he took against Tasso in the
virulent and unnecessary controversy
which has divided Italy so long on the
respective merits of these two great
poets ; and he was accustomed to say that
reading Tasso after Ariosto was like
tasting cucumbers after melons. When
quite a youth, he wrote a great number
of critical remarks on Tasso's Geru-
salemme Liberata, which one of his
friends borrowed, and forgot to return.
For a long time it was thought that the
manuscript had perished, till the Abb6
Serassi discovered it, whilst collecting
materials for his Life of Tasso, pub-

102

GALILEO.

lishecl at Rome in 1785. Serassi being
a violent partizan of Tasso, but also un-
willing to lose the credit of the disco-
very, copied the manuscript, but without
any intention of publishing it, " till he
could find leisure for replying, properly
to the sophistical and unfounded attacks
of a critic so celebrated on other ac-
counts." He announced his discovery
as Tiaving been made " in one of the
famous libraries at Rome," which vague
indication he with some reason consi-
dered insufficient to lead to a second
discovery. On Serassi's death his copy
was found, containing a reference to the
situation of the original ; the criticisms
were published, and form the greatest
part of the last volume of the Milan
edition of Galileo's works. The manu-
script was imperfect at the time of this
second discovery, several leaves having
been torn out, it is not known by whom.
The opinion of the most judicious Ita-
lian critics appears to be, that it would
have been more for Galileo's credit if
these remarks had never been made pub-
lic : they are written in a spirit of flippant
violence, such as might not be extra-
ordinary in a common juvenile critic,
but which it is painful to notice from
the pen of Galileo. Two or three son-
nets are extant written by Galileo
himself, and in two instances he has not
scrupled to appropriate the conceits
of the poet he affected to under-
value.* It should be mentioned that
Galileo's matured taste rather receded
from the violence of his early prejudices,
for at a later period of his life he used
to shun comparing the two ; and when
forced to give an opinion he said, " that
Tasso's appeared the finer poem, but
that Ariosto gave him the greater plea-
sure." Besides these sonnets, there is
extant a short burlesque poem written
by him, " In abuse of Gowns," when,
on his first becoming Professor at Pisa,
he fpund himself obliged by custom to
wear his professional habit in every com-

Eany. It is written not without humour,
ut does not bear comparison with
Berni, whom he imitated.

There are several detached subjects
treated of by Galileo, which may be
noticed in this place. A letter by him
containing the solution of a problem in
Chances is probably the earliest no-

* Compare Son. ii. v. 8 & 9; and Son. iii. v. 2 & 3,
with Ger. Lib. c. iv. st. 76, and c. vii. st. 19.— The
author gladly owns his obligation for these remarks
To the )-in<!ne*s of Sig. Panizzi, Profesior of Italian
in the University of London.

tice extant of the application of ma-
thematics to that interesting subject :
the correspondence between Pascal and
Fermat, with which its history is gene-
rally made to begin, not having taken
place till at least twelve years later.
There can be little doubt after the clear
account of Carlo Dati, that Galileo was
the first to examine the curve called the
Cycloid, described by a point in the rim
of a wheel rolling on a straight line,
which he recommended as a graceful
form for the arch of a bridge at Pisa. He
even divined that the area contained be-
tween it and its base is exactly three
times that of the generating circle. He
seems to have been unable to verify this
guess by strict geometrical reasoning,
for Viviani tells an odd story, that in
order to satisfy his doubts he cut out
several large cycloids of pasteboard, but
finding the weight in every trial to be
rather less than three times that of the
circle, he suspected the proportion to be
irrational, and that there was some
error in his estimation ; the inquiry he
abandoned was afterwards resumed with
success by his pupil Torricelli.*

The account which Lagalla gives of
an experiment shown in his presence
by Galileo, carries the observation of
the phosphorescence of the Bologna
stone at least as far back as 1612.t
Other writers mention the name of an
alchymist, who according to them dis-
covered it accidentally in 1603. Cesi,
Lagalla, and one or two others, had
passed the night at Galileo's house, with
the intention of observing Venus and
Saturn; but, the night being cloudy,
the conversation turned on other matters,
and especially on the nature of light,
" on which Galileo took a small wooden
box at daybreak before sunrise, and
showed us some small stones in it, desir-
ing us to observe that they were not in
the least degree luminous. Having then
exposed them for some time to the twi-
light, he shut the window again ; and in
the midst of the dark room showed us
the stones, shining and glistening with
a faint light, which we saw presently
decay and become extinguished." In
1640, Liceti attempted to refer the
effect of the earthshine upon the
moon to a similar phosphorescent qua-
lity of that luminary, to which Galileo,
then aged 76, replied by a long and able
letter, enforcing the true explanation he
had formerly given.

* Lettera di Timauro Antiate. Firenze, 1663.
•j- De phaenomenis in orbe Lunae. Venetiis, 1612;

GALILEO.

103

Although quite blind, and nearly deaf,
the intellectual powers of Galileo re-
mained to the end of his life ; but he oc-
casionally felt that he was overworking
himself, and used to complain to his friend
Micanzio that he found his head too busy
for his body. " I cannot keep my rest-
less brain from grinding on, although
with great loss of time; for whatever
idea comes into my head with respect
to any novelty, drives out of it what-
ever t had been thinking of just be-
fore." He was busily engaged in consi-
dering the nature of the force of percus-
sion, and Torricelli was employed in
arranging his investigations for a conti-
nuation of the ' Dialogues on Motion,'
when he was seized with an attack
of fever and palpitation of the heart,
which, after an illness of two months,
put an end to his long, laborious, and
useful life, on the 8th of January, 1642,
just one year before his great successor
Newton was born.

The malice of his enemies was scarcely
allayed by his death. His right of making
a will was disputed, as having died a
prisoner to the Inquisition, as well as
his right to burial in consecrated ground.
These were at last conceded, but Urban
anxiously interfered to prevent the design
of erecting a monument to him in the
church of Santa Croce, in Florence, for
which a large sum had been subscribed.
His body was accordingly buried in an
obscure corner of the church, which for
upwards of thirty years after his death
was unmarked even by an inscription to
his memory. It was not till a century
later that the splendid monument was
erected which now covers his and
Viviani's remains. When their bodies
were disinterred in 1737 for the purpose
of being removed to their new resting-
place, Capponi, the president of the
Florentine Academy, in a spirit of spu-
rious admiration, mutilated Galileo's
body, by removing the thumb and fore-
finger of the right-hand, and one of the
vertebrae of the back, which are still pre-
served in some of the Italian museums.
The monument was put up at the ex-
pense of his biographer, Nelli, to whom
Viviani's property descended, charged
with the condition of erecting it. Nor
was this the only public testimony which
Viviani gave of his attachment. The
medal which he str uck in honour o f Galileo
has already been mentioned; he also,
as soon as it was safe to do so, covered
every side of the house in which he
lived with laudatory inscriptions to the

same effect. A bust of Galileo was
placed over the door, and two bas-reliefs
on each side representing some of his
principal discoveries. Not less than
five other medals were struck in honour
of him during his residence at Padua
and Florence, which are all engraved in
Venturi's Memoirs.

There are several good portraits
of Galileo extant, two of which, by
Titi and Subtermanns, are engraved
in Nelli' s Life of Galileo. Another
by Subtermanns is in the Florentine
Gallery, and an engraving from a copy
of this is given by Venturi. There is
also a very fine engraving from the
original picture. An engraving from
another original picture is in the fron-
tispiece of the Padua edition of his
works. Salusbury seems in the fol-
lowing passage to describe a portrait
of Galileo painted by himself: " He did
not contemn the other inferior arts, for
he had a good hand in sculpture and
carving ; but his particular care was to
paint well. By the pencil he described
what his telescope discovered ; in one
he exceeded art, in the other, nature.
Osorius, the eloquent bishop of Sylya,
esteems one piece of Mendoza the wise
Spanish minister's felicity, to have been
this, that he was contemporary to Titian,
and that by his hand he was drawn in a
fair tablet. And Galilaeus, lest he should
want the same good fortune, made so
great a progress in this curious art, that
he became his own Baonarota; and
because there was no other copy worthy
of his pencil, drew himself." No other
author makes the slightest allusion to
such a painting ; and it appears more
likely that Salusbury should be mis-
taken than that so interesting a portrait
should have been entirely lost sight of.
Galileo's house at Arcetri was stand-
ing in 1821, when Venturi visited it,
and found it in the same state in which
Galileo might be supposed to have left
it. It is situated nearly a mile from
Florence, on the south-eastern side, and
about a gun-shot to the north-west of
the convent of St. Matthew. Nelli
placed a suitable inscription over the
door of the house, which belonged in
1821 to a Signor Alimarl*

Although Nelli's Life of Galileo dis-
appointed the expectations that had
been formed of it, it is impossible for
any admirer of Galileo not to feel the
greatest degree of gratitude towards

* Veaturi.

104

GALILEO.

him, for the successful activity with
which he rescued so many records of
the illustrious philosopher from destruc-
tion. After Galileo's death, the prin-
cipal part of his books, manuscripts,
and instruments, were put into the
charge of Viviani, who was himself at
that time an object of great suspicion ;
most of them he thought it prudent to
conceal, till the superstitious outcries
against Galileo should be silenced. At
Viviani's death, he left his library, con-
taining a very complete collection of the
works of all the mathematicians who
had preceded him (and amongst them
those of Galileo, Torricelli, and Castelli,
all which were enriched with notes and
additions by himself), to the hospital of
St. Mary at Florence, where an extensive
library already existed. The directors of
the hospital sold this unique collection
in 1781, when it became entirely dis-
persed. The manuscripts in Viviani's
possession passed to his nephew, the
Abbe Panzanini, together with the por-
traits of the chief personages of the Gali-
lean school, Galileo's instruments, and,
among other curiosities, the emerald ring
which he wore as a member of the Lyn-
cean Academy. A great number of these
books and manuscripts were purchased at
different times by Nelli, after the death
of Panzanini, from his relations, who
were ignorant or regardless of their
value. One of his chief acquisitions
was made by an extraordinary accident,
related by Tozzetti with the following
details, which we repeat, as they seem
to authenticate the story : — " In the
spring of 1739, the famous Doctor Lami
went out according to his custom to
breakfast with some of his friends at the
inn of the Bridge, by the starting-place ;
and as he and Sig. Nelli were passing
through the market, it occurred to
them to buy some Bologna sausages
from the pork-butcher, Cioci, who was
supposed to excel in making them. They
went into the shop, had their sausages
cut off and rolled in paper, which Nelli
put into his hat. On reaching the inn,
and calling for a plate to put them in,
Nelli observed that the paper in which
they had been rolled was one of Galileo's
letters. He cleaned it as well as he
could with his napkin, and put it into
his pocket without saying a word to
Lami ; and as soon as he returned into
the city, and could get clear of him, he
flew to "the shop of Cioci, who told
him that a servant whom he did not
know bi ought him from time to time,

similar letters,whichhe bought by weight
as waste paper. Nelli bought all that
remained, and on the servant's next
reappearance in a few days, he learned
the quarter whence they came, and
after some time succeeded at a small
expense in getting into his own posses-
sion an old corn-chest, containing all
that still remained of the precious trea-
sures which Viviani had concealed in it
ninety years before."*

The earliest biographical notice of
Galileo is that in the Obituary of
the Mercurio Italico, published at
Venice in 1647, by Vittorio Siri. It
is very short, but contains an exact
enumeration of his principal works and
discoveries. Rossi, who wrote under
the name of Janus Nicius Erythraeu*?,
introduced an account of Galileo in his
Pinacotheca Imaginum Illustrium, in
which the story of his illegitimacy first
made its appearance. In 1664, Salus-
bury published a life of Galileo in the
second volume of his Mathematical
Collections, the greater part of which
is a translation of Galileo's principal
works. Almoit the whole edition of
the second volume of Salisbury's
book was burnt in the great fire of
London. Chauffepi6 says that only one
copy is known to be extant in England :
this is now in the well-known library of
the Earl of Macclesfield, to whose kind-
ness the author is much indebted for the
use he has been allowed to make of this
unique volume. A fragment of this
second volume is in the Bodleian Li-
brary at Oxford. The translations in the
preceding pages are mostly founded upon
Salusbury's version. Salisbury's ac-
count, although that of an enthusiastic
admirer of Galileo, is too prolix to be
interesting : the general style of the per-
formance may be guessed from the title
of the first chapter — ' Of ..Man in gene-
ral, and how he excelleth all the other
Animals.' After informing his readers
that Galileo was born at Pisa, he pro-
ceeds : — " Italy is affirmed to have been
the first that peopled the world after
the universal deluge, being governed by
Janus, Cameses, and Saturn, &c." His
description of Galileo's childhood is
somewhat quaint. " Before others had
left making of dirt pyes, he was framing
of diagrams ; and whilst others were
whipping of toppes, he was considering
the cause of their motion." It is on the

* Xotizie sul Ingrandimento dello Scienze Fisiche.
Fireoze, 1780.

GALILEO.

105

whole tolerably correct, especially if we
take into account that Salusbury had
not yet seen Viviani's Life, though com-
posed some years earlier.

The Life of Galileo by Viviani was
first written as an outline of an intended
larger work, but this latter was never
completed. This sketch was published
in the Memoirs of the Florentine Aca-
demy, of which Galileo had been one of
the annual presidents, and afterwards
prefixed to the complete editions of Gali-
leo's works ; it is written in a very
agreeable and flowing style, and has
been the groundwork of most subse-
quent accounts. Another original me-
moir by Niccolo Gherardini, was pub-
lished by Tozzetti. A great number
of references to authors who have
treated of Galileo is given by Sach
in his Onomasticon. An approved
Latin memoir by Brenna is in the
first volume of Fabroni's Vitae Ita-
lorum Illustrium ; he has however
fallen into several errors : this same
work contains the lives of several of his
principal followers.

The article in Chauffepie's Continua-
tion of Bayle's Dictionary does not con-
tain anything which is not in the earlier
accounts.

Andres wrote an essay entitled ' Sag-
gio sulla Filosofi a del Galileo,' published
at 'Mantua 1776; and Jagemann pub-
lished his * Geschichte des Leben des
Galileo1 at Leipzig, in 1787;* neither
of these the author has been able to
meet with. An analysis of the latter
may be seen in Kastner's ' Geschichte
der Mathematik, Gottingen, 1800,' from
which it does not appear to contain
any additional details. The ' Elogio del
Galileo' by Paolo Frisi, first published
at Leghorn in 1775, is, as its title ex-
presses, rather in the nature of a pa-
negyric than of a continuous biogra-
phical account. It is written with
very great elegance and intimate
knowledge of the subjects of which
it treats. Nelli gave several curious
particulars with respect to Galileo in his
' Saggio di Storia Letteraria Fiorentina,
Lucca, 1759;' and in 1793 published
his large work entitled ' Vita e Com-
mercio Letterario di Galileo Galilei.' So
uninteresting a book was probably never
written from such excellent materials.
Two thick quarto volumes are filled with
repetitions of the accounts that were
already in print, the bulky preparation

* Venturi.

of which compelled the author to forego
the publication of the vast collection of
original documents which his unwearied
zeal and industry had collected. This
defect has been in great measure sup-
plied by Venturi in 1818 and 1821, who
has not only incorporated in his work
many of Nelli' s manuscripts, but has
brought together a number of scattered
notices of Galileo and his writings from
a variety of outlying sources — a ser-
vice which the writer is able to appre-
ciate from having gone through th«
greatest part of the same labour before
he was fortunate enough to meet with
Venturi' s book. Still there are many
letters cited by Nelli, which do not ap-
pear either in his book or Venturi's...
Carlo Dati, in 1663, quotes " the regis-
ters of Galileo's correspondence arranged
in alphabetical order, in ten large vo-
lumes."* The writer has no means of
ascertaining what collection this may
have been ; it is difficult to suppose that
one so arranged should have been lost
sight of. It is understood that a life of
Galileo is preparing at this moment in
Florence, by desire of the present Grand
Duke, which will probably throw much
additional light on the character and me-
rits of this great and useful philosopher.

The first editions of his various trea-
tises, as mentioned by Nelli, are given
below. Clement, in his ' Bibliotheque
Curieuse,' has pointed out such among
them, and the many others which have,
been printed, as have become rare.

The Florentine edition is the one used
by the Academia della Crusca for their
references ; for which reason its paging
is marked in the margin of the edition
of Padua, which is much more complete,
and is the one which has been on the
present occasion principally consulted.

The latter contains the Dialogue on the
System, which was not suffered to be
printed in the former editions. The
twelve first volumes of the last edition of
Milan are a mere transcript of that of
Padua: the thirtee-nth contains in addi-
tion the Letter to the Grand Duchess,
the Commentary on Tasso, with some
minor pieces . A complete edition is still
wanted, embodying all the recently dis-
covered documents, and omitting the
verbose commentaries, which, however
useful when they were written, now
convey little information that cannot be
more agreeably and more profitably
learned in treatises of a later date.

* Lettera di Timauro Antiate.

106

GALILEO.

Such was the life, and such were the
pursuits, of this extraordinary man.
The numberless inventions of his acute
industry ; the use of the telescope, and
the brilliant discoveries to which it led ;
the patient investigation of the laws of
weight and motion ; must all be looked
upon as forming but a part of his real
merits, as merely particular demonstra-
tions of the spirit in which he every-
where withstood the despotism of igno-
rance, and appealed boldly from tradi-
tional opinions to the judgments of
reason and common sense. He claimed
and bequeathed to us the. right of
exercising our faculties in examining
the beautiful creation which surrounds

us. Idolized by his friends, he deserved
their affection "by numberless acts of
kindness ; by his good humour, his
affability, and by the benevolent gene-
rosity with which he devoted himself
and a great part of his limited income
to advance their talents and fortunes.
If an intense desire of being useful is
everywhere worthy of honour; if its
value is immeasurably increased, when
united to genius of the highest order ;
if we feel for one who, notwithstanding
such titles to regard, is harassed by cruel
persecution, — then none deserve our
sympathy, our admiration, and our gra-
titude, more than Galileo.

List of Galileo's Works.

Le Operazioni del Compasso Geom. e Milit.
Difesa di Gal. Galilei contr. all. cal. et impost, di Bald. Capra
Sydereus Nuucius .....

Discorso int. alle cose che stanno in su 1' Acqua . .

Novantiqua SS. PP. Doctrina de S. Scripturse Testimoniis .
Istoria e Demostr. int. alle Macchie Solari

Risp. alle oppos. del S. Led. delle Colombe e del S. Vine, di Grazia
Discorso delle Comete di Mario Guiducci . ,

Dialogo sopra i due Massimi Sistemi del Moudo .

Discorso e Demostr. intorno alle due nuove Scienze
Delia Scienza Meccanica .....

Trattato della Sfera .....

Discorso sopra il Flusso e Reflusso. (Scienze Fisiche di Tozzetti.)
Considerazioni sul Tasso .....
Trattato della Fortificazione. (Memorie di Venturi.)

The editions of his collected works (in which is contained much that was
published separately) are —

Opere di Gal. Galilei, Line. Nob. Fior. &c. . Bologna, 1G5G.

Opere di Gal. Galilei, Nob. Fior. Accad. Line. &c. . Firenze, 1718.
Opere di Gal. Galilei •'•';'*•' '•' : Paclova, 1744.

Padova,

1606.

Fol.

Venezza,

1607.

4 to.

Venetiis,

1610.

4to.

Firenze,

1612.

4to.

Argent,

1612.

4to.

Roma,

1613.

4to.

Firenze,

1615.

4to.

Firenze,

1619.

4 to.

Firenze,

1632.

4to.

Leida,

1638.

4 to.

Ravenna,

1649.

4to.

Roma,

1655.

4to.

Firenze,

1780.

4to.

Roma,

1793.

Modena,

1818.

4to.

much that was

never

Opere di Gal. Galilei

4to.
4to.
4to.
Milano, 1811. 13 vols. 8vo.

2 vols.

3 vols.

4 vols.

CORRECTIONS.

Page Co . Line.
512, Add : Hia instructor was the celebrated botanist, Andreas Ceesalpinus, who was professor

of medicine at Pisa from 1567 to 1592. Hist. Acad. Pisan. ; Pisis, 1/91.
8 2 18, Add: According to Kiistner, his German name was Wursteisen.
8 2 21, for 1588 read 1586.
15 1 57, for 1632 read 1630.

17 1 29. Salusbury alludes to the instrument described and figured in "The Use of the Sector,
Crosse Staffe, and other Instruments. London, 1624." It is exactly Galileo's Compass.
17 1 52, for Burg, a German, read Burgi, a Swiss.
27 2 17. The author here called Brutti was an Englishman : his real name, perhaps, was Bruce.

See p. 99.

50 1 14. Kepler's Epitome was not published till 1619 : it was then inserted in the Index.
73 1 60, for under read turned from.
[60 1 50, for any read an indefinitely small.

LIFE OF KEPLER.

CHAPTER I.

Introduction — Birth and Education of
Kepler — He is appointed Astronomi-
cal Professor at Gratz — Publishes
the * Mysterium Cosmographicum."

IN the account of the life and discoveries
of Galileo, we have endeavoured to in-
culcate the safety and fruitfulness of the
method followed by that great reformer
in his search after physical truth. As
his success furnishes the best instance
of the value of the inductive process, so
the failures and blunders of his adversa-
ries supply equally good examples of the
dangers and the barrenness of the oppo-
site course. The history of JOHN KEP-
LER might, at the first view, suggest con-
clusions somewhat inconsistent with this
remark. Every one who is but mode-
rately acquainted with astronomy is
familiar with the discoveries which that
science owes to him ; the manner in
which he made them is, perhaps, not so
generally known. This extraordinary
man pursued, almost invariably, the
hypothetical method. His life was passed
in speculating on the results of a few
principles assumed by him, from very
precarious analogies, as the causes of
the phenomena actually observed in
Nature. We nevertheless find that he
did, in spite of this imphilosophical me-
thod, arrive at discoveries which have
served as guides to some of the most
valuable truths of modern science.

The difficulty will disappear if we
attend more closely to the details of
Kepler's investigations. We shall per-
ceive that to an unusual degree of
rashness in the formation of his sys-
tems, he added a quality very rarely
possessed by philosophers of the hypo-
thetical school. One of the greatest in-
tellectual vices of the latter was a wilful
blindness to the discrepancy of facts
from their creed, a perverse and obsti-
nate resistance to physical evidence,
leading not unfrequently to an attempt
at disguising the truth. From this be-
setting sin of the school, which from an
intellectual fault often degenerated into
a moral one, Kepler was absolutely free.

Scheme after scheme, resting originally
upon little beyond his own glowing ima-
gination, but examined and endeared by
the 'ceaseless labour of years, was unhe-
sitatingly sacrificed, as soon as its in-
sufficiency became indisputable, to make
room for others as little deserving sup-
port. The history of philosophy affords
no more remarkable instance of sincere
uncompromising love of truth. To this
virtue he owed his great discoveries : it
must be attributed to his unhappy me-
thod that he made no more.

In considering this opinion upon the
real nature of Kepler's title to fame, it
ought not to be forgotten that he has ex-
posed himself at a disadvantage on which
certainly very few philosophers would
venture. His singular candour allowed
him to comment upon his own errors with
the same freedom as if scrutinizing the
work of a stranger ; careless whether the
impression on his readers were favour-
able or otherwise to himself, provided it
was instructive. Few writers have spoken
so much, and so freely of themselves, as
Kepler. He records, on almost every
occasion, the train of thought by which
he was led to each of the discoveries
that eventually repaid his persever-
ance ; and he has thus given us "a
most curious and interesting view of the
workings of a mind of great, though ec-
centric power. " In what follows," says
he (when introducing a long string of
suppositions, of which he had already
discovered the fallacy), " let the reader
pardon my credulity, whilst working
out all these matters by my own inge-
nuity. For it is my opinion that the oc-
casions by which men have acquired
a knowledge of celestial phenomena
are not less admirable than the disco-
veries themselves.'" Agreeing altogether
with this opinion in its widest application,
we have not scrupled, in the following
sketch, to introduce at some length an
account even of Kepler's erroneous spe-
culations ; they are in themselves very
amusing, and will have the additional
utility of proving the dangerous ten-
dency of his method ; they will show by
how many absurd theories, and how

KEPLER.

many years of 'wasted labour, his real
discoveries and services to science lie
surrounded.

JOHN KEPLER was born (as we are as-
sured by his earliest biographer Hantsch)
in long. 29° 7', lat. 48° 54', on the 21 st day
of December, 1571. On this spot stands
the imperial city of Weil, in the duchy of
"Wirtemberg. His parents were Henry
Kepler and Catherine Guldenmann,bpth
of noble, though decayed families.
Henry Kepler, at the time of his mar-
riage, was a petty officer in the Duke of
"Wirtemberg's service ; and a few years
after the birth of his eldest son John,
he joined the army then serving in the
Netherlands. His wife followed him,
leaving their son, then in his fifth
year, at Leonberg, under the care of his
grandfather. He was a seven months
child, very weak and sickly ; and after
recovering with difficulty from a severe
attack of small-pox, he was sent to
school in 1577. Henry Kepler's limited
income was still farther reduced on his
return into Germany, the following year,
in consequence of the absconding of
one of his acquaintance, for whom he
Jiad incautiously become surety. His
circumstances were 'so much nar-
rowed by this misfortune, that he was
obliged to sell his house, and nearly all
that'he possessed, and for several years
he supported his family by keeping a
tavern at Elmendingen. This occasioned
great interruption to young Kepler's
education ; he was taken from school,
and employed in menial services till
his twelfth year, when he was again
placed in the school at Elmendingen.
In the following year he was again
seized wkh a violent illness, so that
his life was almost despaired of. In
1586, he was admitted into the monastic
school of Maulbronn, where the cost of
his education was defrayed by the Duke
of Wirtemberg, This school was one
of those established on the suppression
of the monasteries at the Reformation,
and the usual course of education fol-
lowed there required that the students,
after remaining a year in the superior
classes, should offer themselves for ex-
lamination at the college of Tubingen
for the degree of bachelor: they then
returned to their school with the title
of veterans ; and after completing the
studies taught there, they were admitted
as resident students at Tubingen, pro-
ceeded in about a year to the degree of
master, and were then allowed to com-
mence their course of theology. The

three years of Kepler's life following his
admission to Maulbronn, were marked
by periodical returns of several of the dis-
orders which had well nigh proved fatal
to him in his childhood. During the same
time disagreements arose between his
parents, in consequence of which his
father quitted his home, and soon after
died abroad. After his father's depar-
ture, his mother also quarrelled with her
relations, having been treated, says
Hantsch, " with a degree of barbarity
by her\ husband and brother-in-law
that was hardly exceeded even by her
own perverseness :" one of his bro-
thers died, and the family-affairs were
in the greatest confusion. Notwith-
standing these disadvantages, Kepler
took his degree of master in August 1591,
attaining the second place in the annual
examination. The first name on the
list was John Hippolytus Brentius.

Whilst he was thus engaged at Tu-
bingen, the astronomical lectureship at
Grate, the chief town of Styria, be-
came vacant by the death of George
Stadf, and the situation was offered to
Kepler. Of this first occasion of turn-
ing his thoughts towards astronomy, he
has himself given the following account :
" As soon as I was of an age to feel the
charms of philosophy, I embraced every
part of it with intense desire, but paid
no especial regard to astronomy. I had
indeed capacity enough for it, and learn-
ed without difficulty the geometrical
and astronomical theorems occurring in
the usual course of the school, being
well grounded in figures, numbers, and
proportions. But those were compulsory
studies — there was nothing to show a
particular turn for astronomy. I was
educated at the expense of the Duke of
Wirtemberg, and when I saw such of
my companions as the duke selected to
send abroad shrink in various ways from
their employments, out of fondness for
home,. I, who was more callous, had
early made up my mind to go with the
utmost readiness whithersoever I might
be sent. The first offering itself was.
an astronomical post, which I was in.
fact forced to accept by the authority of
my tutors ; not that I was alarmed, in
the manner I had condemned in others,
by the remoteness of the situation, but
by the unexpected and contemptible
nature of the office, and by the slightness
of my information in this branch of phi-
losophy. I entered on it, therefore, bet-
ter furnished with talent than knowledge :
with many protestations that I was

KEPLER.

not abandoning my claim to be provided
for in some other more brilliant pro-
fession. What progress I made in the
first two years of my studies, may be
seen in my ' Mysterium Cosmogra-
phicurn ;' and the encouragement given
me by my tutor, Mastlin, to take up the
science of astronomy, may be read in the
same book, and in his letter which is
prefixed to the ' Narrative of Rheticus.'
I looked on that discovery as of the
highest importance, and still more so,
because I saw how greatly it was ap-
proved by Mastlin."

The nature of the singular work to
which Kepler thus refers with so much
complacency, will be best shown by
quoting some of the most remarkable parts
of it, and especially the preface, in which
he briefly details some of the theories
he successively examined and rejected,
before detecting (as he imagined he had
here done) the true cause of the number
and order of the heavenly bodies. The
other branches of philosophy with which
he occupied himself in his younger years,
were those treated by Scaliger in his
* Exoteric Exercises,' to the study of
which book Kepler attributed the for-
mation of many of his opinions ; and he
tells us that he devoted much time " to
the examination of the nature of heaven,
of souls, of genii, of the elements, of the
essence of fire, of the cause of fountains,
the ebb and flow of the tide, the shape
of the continents, and inland seas, and
things of this sort." He also says, that
by his first success with the heavens, his
hopes were greatly inflamed of discover-
ing similar analogies in the rest of the
visible world, and for this reason, named
his book merely a Prpdromus, or Fore-
runner, meaning, at some future period,
to subjoin the Aftercomer, or Sequel.
But this intention was never fulfilled;
either his imagination failed him, or,
what is more likely, the laborious calcu-
lations in which his astronomical theories,,
engaged him, left him little time for
turning his attention to objects uncon-
nected with his first pursuit.

It is seldom that we are admitted to
trace the progress of thought in those
who have distinguished themselves by
talent and originality ; and although the
whole of the following speculations be-
gin and end in error, yet they are so
characteristic, and exhibit such an extra-
ordinary picture of the extravagances
into which Kepler's lively imagination
•was continually hurrying him, that we
cannot refrain from citing nearly the

whole preface. From it, better than from
any enumeration of peculiarities, the
reader will at once apprehend the nature
of his disposition.

" When I was attending the celebrated
Mastlin, six years ago, at Tubingen,
I was disturbed by the manifold incon-
veniences of the common theory of the
universe, and so delighted with Coper-
nicus, whom Mastlin was frequently in
the habit of quoting with great respect,
that I not only often defended his pro-
positions in the physical disputations of
the candidates, but also wrote a correct
essay on the primary motion, maintain-
ing, that it is caused by the rotation of
the earth. And I was then at that point
that I attributed to the earth the motion
of the sun on physical (or, if you will,
on metaphysical) grounds, as Copernicus
had done for mathematical reasons.
And, by this practice, I came by de-
grees, partly from Miistlin's instructions,
and partly from my own efforts, to un-
derstand the superior mathematical con-
venience of the system of Copernicus
beyond Ptolemy's. This labour might
have been spared me, by Joachim Rhe-
ticus, who has shortly and clearly ex-
plained everything in his first Narra-
tive. While incidentally engaged in
these labours, in the intermission of
my theology, it happened conveniently
that I succeeded George Stadt in his
situation at Gratz, where the nature of
my office connected me more closely
with these studies. Everything I had
learned from Mastlin, or had acquired
of myself, was there of great service
to me in explaining the first elements of
astronomy. And, as in Virgil, ' Fama
mobilitate viget, viresque acquirit eitn-
do,' so it was with me, that the diligent
thought on these things was the occasion
of still further thinking : until, at last,
in the ye'ar 1595, when I had some in-
termission of my lectures allowed me, I
brooded with the whole energy of my mind
on this subject. There were three things
in particular, of which I pertinaciously
sought the causes why they aye not
other than they are : the number, the
size, and the motion of the orbits. I
attempted the thing at first with num-
bers, and considered whether one of the
orbits might be double, triple, quadru-
ple, or any other multiple of the others,
and how much, according to Coper-
nicus, each differed from the rest. I
spent a great deal of time in that labour,
as if it were mere sport, but could find
no equality either in the proportions or

KEPLER.

the differences, and I gained nothing
from this beyond imprinting deeply in
my memory the distances as assigned
by Copernicus ; unless, perhaps, reader,
this record of my various attempts may
force your assent, backwards and for-
wards, as the waves of the sea; until
tired at length, you will willingly repose
yourself, as in a safe haven, on the rea-
sons explained in this book. However,
I was comforted in some degree, and my
hopes of success were supported as well
by other reasons which will follow pre-
sently, as by observing that the motions
in every case seemed to be connected
with the distances, and that where there
was a great gap bet ween the orbits, there
was the same between the motions. And
I reasoned, that if God had adapted
motions to the orbits in some relation to
the distances, it was probable that he
had also arrayed the distances them-
selves in relation to something else.

" Finding no success by this method,
I tried another, of singular auda-
city. I inserted a new planet between
Mars and Jupiter, and another between
Venus and Mercury, both of which I
supposed invisible, perhaps on account
of their smallness, and I attributed to
each a certain period of revolution.* I
thought that I could thus contrive some
equality of proportions, increasing be-
tween every two, from the sun to the
fixed stars. For instance, the Earth is
nearer Venus in parts of the terrestrial
orbit, than Mars is to the Earth in parts
of the orbit of Mars. But not even the
interposition of a new planet sufficed for
the enormous gap between Mars and
Jupiter ; for the proportion of Jupiter
to the new planet was still greater than
that of Saturn to Jupiter. And although,
by this supposition, I got some sort of a
proportion, yet there was no reasonable
conclusion, no certain determination of the
number of the planets either towards the
fixed stars, till we should get as far as
them, nor ever towards the Sun, be-
cause the division in this proportion of
the residuary space within Mercury
might be continued without end. Nor

* The following scrupulous note added by Kepler
in 1621 to a subsequent edition of this work, de-
serves to be quoted. It shows how entirely superior
he was to the paltriness of attempting to appropriate
the discoveries of others, of which many of his con-
temporaries had exhibited instances even on
slighter pretences than this passage might have
afforded him. The note is as follows : " Not cir-
culating round Jupiter like the Jfedicoean stars. lie
not deceived. I never had them in rny thoughts,
but, like the other primary planets, including the
sun in the centre of tli€ system within their orbits."

could I form any conjecture, from the
mobility of particular numbers, why,
among an infinite number, so few should
be moveable. The opinion advanced
by Rheticus in his Narrative is impro-
bable, where he reasons from the sanctity
of the number six to the number of the
six moveable heavens ; for he who is in-
quiring of the frame of the world itself,
must not derive reasons from these
numbers, which have gained importance
from things of later date.

" I sought again, in another way, whe-
ther the distance of every planet is not
as the residuum of a sine ; and its mo-
tion as the residuum of the sine of the
complement in the same quadrant.

" Conceive the square A B to be con-
structed, whose side A. C is equal to the
sernidiameter of the universe. From the
angle B opposite to A the place of the
sun, or centre of the world, describe the
quadrant D C with the radius B C.
Then in A C, the true radius of the
world, let the sun, fixed stars, and pla-
nets be marked at their respective dis-
tances, and from these points draw lines
parallel toB C, meeting the quadrant. I
imagined the moving force acting on
each of the planets to be in the propor-
tion of these parallels. In the line of the
sun is infinity, because A D is touched,
and not cut, by the quadrant : therefore
the moving force is infinite in the sun,
as deriving no motion except from its
own act. In Mercury the infinite line
is cut off at K, and therefore at this
point the motion is comparable with the
others. In the fixed stars the line is
altogether lost, arid compressed into a
mere point C ; therefore at that point
there is no moving force. This was the
theorem, which was to be tried by cal-

KEPLER.

dilation ; but if any one will reflect
that two things were wanting to me,
first, that I did not know the size of the
Sinus Totus, that is, the radius of the
proposed quadrant ; secondly, that the
energies of the motions were not thus
expressed otherwise than in relation one
to another ; whoever, I say, well consi-
ders this, will doubt, not without reason,
as to the progress I was likely to make
in this difficult course. And yet, with
unremitting labour, and an infinite re-
ciprocation of sines and arcs, I did
get so far as to be convinced that this
theory could not hold.

" Almost the whole summer was lost
in these annoying labours ; at last, by a
trifling accident, I lighted more nearly
on the truth. I looked on it as an in-
terposition of Providence, that I should
obtain by chance, what I had failed to
discover with my utmost exertions ; and
I believed this the more, because I
prayed constantly that I might succeed,
if Copernicus had really spoken the
truth. It happened on the 9th or 1 9th *
day of July, in the year 1595, that,
having occasion to show, in my lecture-
room, the passages of the great con-
junctions through eight signs, and how
they pass gradually from one trine as-
pect to another, I inscribed in a circle

A Scheme of the
great Conjunctions of
SATURN & JUPITER,
their leaps through eight
Signs, and their passa-
ges through all the
four Triplicities
of the Zodiac.

a great number of triangles, or quasi-
triangles, so that the end of one was
made the beginning of another. In this
manner a smaller circle was shadowed
out by the points in which the lines
crossed each other.

" The radius of a circle inscribed in
a triangle is half the radius of that
described about it; therefore the pro-

* This inconvenient mode of dating was neces-
sary before the new or Gregorian style was uni-
versally adopted.

portion between these two circles struck
the eye as almost identical with that
between Saturn and Jupiter, and the
triangle is the first figure, just as Sa-
turn and Jupiter are the first planets.
On the spot I tried the second distance
between Jupiter and Mars with a square,
the third with a pentagon, the fourth
with a hexagon. And as the eye again
cried out against the second distance
between Jupiter and Mars, I combined
the square with a triangle and a pen-
tagon. There would be no end of men-
tioning every trial. The failure of this
fruitless attempt was the beginning of
the last fortunate one ; for I reflected,
that in this way I should never reach
the sun, if I wished to observe the same
rule throughout ; nor should I have
any reason why there were six, rather
than twenty or a hundred moveable
orbits. And yet figures pleased me, as
being quantities, and as having existed
before the heavens; for quantity was
created with matter, and the heavens
afterwards. But if (this was the current
of my thoughts), in relation to the quan-
tity and proportion of the six orbits, as
Copernicus has determined them among
the infinite ether figures, five only could
be found having peculiar properties above
the rest, my business would be done.
And then again it struck me, what have
plane figures to do among solid orbits ?
Solid bodies ought rather to be intro-
duced. This, reader, is the invention
and the whole substance of this little
work; for if any one, though but mo-
derately skilled in geometry, should
hear these words hinted, the five regular
solids will directly occur to him with
the proportions of their circumscribed
and inscribed spheres: he has imme-
diately before his eyes that scholium of
Euclid to the 18th proposition of his
13th Book, in which it is proved to be
impossible that there should be, or be
imagined, more than five regular bodies.
" What is worthy of admiration (since
I had then 'no proof of any prerogatives
of the bodies with regard to their order)
is, that employing a conjecture which
was far from being subtle, derived from
the distances of the planets, I. should at
once attain my end so happily in arrang-
ing them, that I was not able to change
anything afterwards with the utmost ex-
ercise of my reasoning powers. In me-
mory of the event, I write down here for
you the sentence, just as it fell from me,
and in the words in which it was that
moment conceived :— The Earth is the

6

KEPLER.

circle, the measurer of all ; round it de-
scribe a dodecahedron, the circle in-
cluding this will be Mars. Round Mars
describe a tetrahedron, the circle includ-
ing this will be Jupiter. Describe a
cube round Jupiter, the circle including

this will be Saturn. Now, inscribe in
the Earth an icosaedron, the circle in-
scribed in it will beVenus. Inscribe an
octaedron in Venus, the circle inscribed
in it will be Mercury. This is the reason
of the number of the planets.

" This was the cause, and such the suc-
cess, of my labour : now read my propo-
sitions in this book. The intense plea-
sure 1 have received from this discovery
never can be told in words. I regretted
no more the time wasted ; I tired of no
labour; I shunned no toil of reckoning ;
days and nights I spent in calculations,
until I could see whether this opinion
would agree with the orbits of Coper-
nicus, or whether my joy was to vanish
into air. I willingly subjoin that senti-
ment of Archytas, as given by Cicero :
' If I could mount up into heaven, and
thoroughly perceive the nature of the
world, "and beauty of the stars, that ad-
miration would be without a charm for
me, unless I had some one like you,
reader, candid, attentive, and eager for
knowledge, to whom to describe it.' If

you acknowledge this feeling, and are
candid, you will refrain from blame, such
as not without cause I anticipate ; but
if, leaving that to itself, you fear lest
these things be not ascertained, and
that I have shouted triumph before vic-
tory, at least approach these pages, and
learn the matter in consideration : you
will not find, as just now, new and un-
known planets interposed ; that boldness
of mine is not approved, but those old
ones very little loosened, and so furnished
by the interposition (however absurd you
may think it) of rectilinear figures, that
in future you may give a reason to the
rustics when they ask for the hooks
which keep the skies from falling. —
Farewell."

In the third chapter Kepler mentions,
that a thickness must be allowed to

KEPLER. 7

each orb sufficient to include the greatest parison with the real distances are as
and least distance of the planet from the follows : —
sun. The form and result of his com-

Book V.

If the
inner
surface
of the

Saturn
Jupiter
Mars
Earth

be taken at
1000, then

the outer
e

1 Jupiter = 577
Mars = 333
Earth = 79")
Venus = 795

1 According to
Copernicus
they are

i635 Ch. 9
333 — 14
757 — 19
794 — 21,22

orbit of

Venus

one 01

Mercury = 577

723 — 27

It will he observed, that Kepler's re-
sults were far from being entirely satis-
factory ; but he seems to have flattered
himself, that the differences might be
attributed to erroneous measurements.
Indeed, the science of observation was
then so much in its infancy, that such
an assertion might be made without in-
curring much risk of decisive refutation.
• Kepler next endeavoured to deter-
mine why the regular solids followed in
Ihis rather than any other order; and
his imagination soon created a variety of
assential distinctions between the cube,
pyramid, and dodecahedron, belonging
to the superior planets, and the other two.

The next question examined in the
t>pok, is the reason why the zodiac is
divided into 3GO degrees;" and on this
subject, he soon becomes enveloped in
a variety of subtle considerations, (not
very intelligible in the original, and still
more difficult to explain shortly to others
unacquainted with it,) in relation to the
divisions of the musical scale ; the origin
of which he identifies with his five fa-
vourite solids. The twentieth chapter
is appropriated to a more interesting
inquiry, containing the first traces of
his finally successful researches into the
proportion between the distances of the
planets, and the times of their motions
round the sun. He begins with the
generally admitted fact, that the more
distant planets move more slowly ; but
in order to show that the proportion,
whatever it may be, is not the simple
one of the distances, he exhibits the
following little Table :—

<?

D. Scr.

%

<?

4j

$

S

10759.12

D. Scr.

%

3
£

6151)

4382.37

D.Scr.

1785

1282

686.59

D.Scr.

1174

843

482

3(55.15

D.Scr.

?

844

COS

325

202.30

224.42

D.Scr.

5

434

312

1(57

>135

115

87. 5 S

At the head of each vertical column
is placed the real time (in days and sex-
agesimal parts) of the revolution of the

planet placed above it, and underneath
the days due to the other inferior pla-
nets, if they observed the proportion of
distance. Hence it appears that this
proportion in every case gives a time
greater than the truth ; as for instance,
if the earth's rate of revolution were to
Jupiter's in the proportion of their dis-
tances, the second column shows thafc
the time of her period would be 843 in-
stead of 3G5| days ; so of the rest. His
next attempt was to compare them by
two by two, in which he found that he
arrived at a proportion something like
the proportion of the distances, although
as yet far from obtaining it exactly. This
process amounts to taking the quotients
obtained by dividing the period of each
planet by the period of the one next
beyond. »

9.27 ^ be successively
0 ,- I taken to consist of I
^61 1000 equal parts,
6.59 V the periods of J

the planet next
below will contain I
of those parts in I

But if the distance of each planet in
succession be taken to consist of
1000 equal parts, the distance of
the next below will contain, ac-
cording to Copernicus, in ^ $ 500

From this table he argued that to make
the proportions agree, we must assume
one of two things, " either that the
moving intelligences of the planets are
weakest in those which are farthest from
the Sun, or that there is one moving
intelligence in the Sun, the common
centre forcing them all round, but those
most violently which are nearest, and
that it languishes in some sort, and
grows weaker at the most distant, be-
cause of the remoteness and the atte-
nuation of the virtue."

We stop here to insert a note added
by Kepler to the later editions, and
shall take advantage of the same in-
terruption to warn the reader not to
confound this notion of Kepler with the
theory of a gravitating force towards the
Sun, in the sense in which we now use
those words. According to our theory,
the effect of the presence of the Sun
upon the planet is to pull it towards the

KEPLER.

centre in a straight line, and the'effect of
the motion thus produced combined with
the motion of the planet, which if un-
disturbed would be in a straight line
inclined to the direction of the radius, is,
that it describes a curve round the Sun.
Kepler considered his planets as per-
fectly quiet and unwilling to move when
left alone ; and that this virtue supposed
by him to proceed in every direction out
of the Sun, swept them round, just as the
sails of a windmill would carry round
anything which became entangled in
them. In other parts of his works
Kepler mentions having speculated on
a real attractive force in the centre ; but
as he knew that the planets are not
always at the same distance from the
Sun, and conceived erroneously, that to
remove them from their least to their
greatest distance a repulsive force must
be supposed alternating with an attrac-
tive one, he laid aside this notion as
improbable. In a note he acknowledges
that when he wrote the passage just
quoted, imbued as he then was with
Scaliger's notions on moving intelli-
gences, he literally believed " that each
planet was moved by a living spirit, but
afterwards came to look on'the moving
cause as a corporeal though immaterial
substance, something in the nature of
light which is observed to diminish simi-
larly at increased distances." He then
proceeds as follows in the original text.
" Let us then assume, as is very pro-
bable, that motion is dispensed by the
sun in the same manner as light. The
proportion in which light emanating
from a centre is diminished, is taught
by optical writers : foj there is the same
quantity of light, or of the solar rays, in
the small circles as in the large; and
therefore, as it is more condensed in the
former, more attenuated in the latter, a
measure of the attenuation may be de-
rived from the proportion of the circles
themselves, both in the case of light and
of the moving virtue. Therefore, by how
much the orbit of Venus is greater than
that of Mercury, in the same proportion
will the motion of the latter be stronger,
or mere hurried, or more swift, or more
powerful, or by whatever other word
you like to express the fact, than that of
the former. But a larger orbit would
require a proportionably longer time of
revolution, even though the moving force
were the same. Hence it follows that
the one cause of a greater distance of
the planet from the Sun, produces a
double effect in increasing the period,

and conversely the increase of the pe-
riods will be double the difference of the
distances. Therefore, half the incre-
ment added to the shorter period ought
to give the true proportion of the dis-
tances, so that the sum should represent
the distance of the superior planet, on
the same scale on which the shorter
period represents the distance of the^ in-
terior one. For instance, the period of
Mercury is nearly 88 days ; that of Ve-
nus is 224f, the difference is 13623: half
of this is 683% which, added to 88, gives
156i. The mean distance of Venus
ought, therefore, to be, in proportion to
that of Mercury, as 156± to 88. If this be
done with all the planets, we get. the fol-
lowing results, taking successively, as be-
fore, the distance of each planet at 1000.

The distance iin 1£ 574 But accordr(572

parts of which ^ 274 in? *° c°- 290

the distance of U fiq, pernicus J ( . .g

the next superior Hf they are ) ™

planet contains ¥ <G2 respectively

1000, is at

<G2
563

500

As you see, we have now got nearer
the truth."

Finding that this theory of the rate
of diminution would not bring him quite
close to the result he desired to find,
Kepler immediately imagined another.
This latter occasioned him a great deal
of perplexity, and affords another of
the frequently recurring instances of
the waste of time and ingenuity ^ occa-
sioned by his impetuous and precipitate
temperament. Assuming the distance
of any planet, as for instance of Mars,
to be the unit of space, and the virtue at
that distance to be the unit of force, he
supposed that as many particles as the
virtue at the Earth gained upon that of
Mars, so many particles of distance did
the Earth lose. He endeavoured to de-
termine the respective positions of the
planets upon this theory, by the rules of
false position, but was. much astonished
at finding the same exactly as on his
former hypothesis. The fact was, as he
himself discovered, although not until
after several years, that he had become
confused in his calculation ; and when
half through the process, had retraced
his steps so as of course to arrive again
at the numbers from which he started,
and which he had taken from his former
results. This was the real secret of the
identity of the two methods; and if,
when he had taken the distance of Mars
at 1000, instead of assuming the distance
of the earth at 694, as he did, he had
taken any other number, and operated
upon it in the same manner, he would

KEPLEP.

have had the same reason for relying on
the accuracy of his supposition. As it
was, the result utterly confounded him ;
and he was obliged to leave it with the
remark, that " the two theories are thus
proved to be the same in fact, and only
different in form ; although how that
can possibly be, I have never to this
day been able to understand." — His
perplexity was very reasonable ; they
are by no means the same ; it was only
his method of juggling with the figures
which seemed to connect them.

Notwithstanding all its faults, the
genius and unwearied perseverance dis-
played by Kepler in this book, immedi-
ately ranked him among astronomers of
the first class ; and he received the most
flattering encomiums from many of the
most celebrated ; among others, from
Galileo and Tycho Brahe, whose opinion
he invited upon his performance. Galileo
contented himself with praising in ge-
neral terms the ingenuity and good faith
which appeared so conspicuously in it.
Tycho Brahe entered into a more de-
tailed criticism of the work, and, as
Kepler shrewdly remarked, showed how
highly he thought of it by advising him
to try to adapt something of the same
kind to the Tychonic system. Kepler
also sent a copy of his book to the
imperial astronomer, Raimar,. with a
complimentary letter, in which he exalted
him above all other astronomers of the
age. Raimar had surreptitiously ac-
quired a notion of Tycho Brahe's theory,
and published it as his own ; and Tycho,
in his letter, complained of Kepler's ex-
travagant flattery. This drew a long
apologetical reply from Kepler, in which
he attributed the admiration he had ex-
pressed of Raimar to his own want of
information at that time, having since
met with many things in Euclid and
Regiomontanus, which he then believed
original in Raimar. With this explana-
tion, Tycho professed himself perfectly
satisfied.

CHAPTER II.

Kepler's Marriage — He joins Tycho
Brahe at Prague — Is appointed Im-
perial Mathematician — Treatise on
the New Star.

THE publication of this extraordinary
book, early as it occurs in the history
of Kepler's life, was yet preceded by his
marriage. He had contemplated this
step so early as 1592; but that suit
having been broken off, he paid his ad-

dresses, in 1596, to Barbara Muller von
Muhleckh. This lady was already a
widow for the second time, although two
years younger than Kepler himself. 0 n
occasion of this alliance he was required
to prove the nobility of his family, and
the delay consequent upon the inquiry
postponed the marriage till the follow*-
ing year. He soon became involved
in difficulties in consequence of this
inconsiderate ^engagement: his wife's
fortune was less than he had been led
to expect, and he became embroiled on
that account with her relations. Still
more serious inconvenience resulted to
him from the troubled state in which the
province of Styria was at that time,
arising out of the disputes in Bohe-
mia and the two great religious parties
into which the empire was now divided,
the one headed by Rodolph, the feeble
minded emperor, — the other by Matthias,
his ambitious and enterprising brother.

In the year following his marriage, he
thought it prudent, on account of some
opinions he had unadvisedly promul-
gated, (of what nature does not very
distinctly appear,) to withdraw himself
from Gratz into Hungary. Thence he
transmitted several short treatises to his
friend Zehentmaier, at Tubingen — " On
the Magnet," " On the Cause of the
Obliquity of the Ecliptic," and '" On the
Divine Wisdom, as shown in the Crea-
tion." Little is known of these works
beyond the notice taken of them in Ze-
hentmaier's answers. Kepler has himself
told us, that his magnetic philosophy
was built upon the investigations of
Gilbert, of whom he always justly spoke
with the greatest respect.

About the same time a more violent
persecution had driven Tycho Brahe from
his observatory of Uraniburg, in the little
island of Hueen, at the entrance of the
Baltic. This had been bestowed on him
by the munificence of Frederick I. of
Denmark, who liberally furnished him
with every means of prosecuting his
astronomical observations. After Fre-
derick's death, Tycho found himself un-
able to withstand the party which had
constantly opposed him, and was forced,
at a great loss and much inconvenience,
to quit his favourite island. On the in-
vitation of the emperor, Rudolph II.,.
he then betook himself, after a short
stay at Hamburg, to the castle of Be-
nach, near Prague, which was assigned
to him with an annual pension of three
thousand florins, a truly munificent pro-
vision in those times and that country.
12

10

KEPLER.

Kepler had been eager to see Tycho
Brahe since the latter had intimated
that his observations had led him to a
more accurate determination of the ex-
centricities of the orbits of the planets.
By help of this, Kepler hoped that his
theory might be made to accord more
nearly with the truth ; and on learning
that Tycho was in Bohemia, he imme-
diately set out to visit him, and arrived
at Prague in January, 1600. From
thence he wrote a second letter to Tycho,
not having received the answer to his
former apology, aj;am excusing himself
for the part he had appeared to take with
Raimar against him. Tycho replied im-
mediately in the kindest manner, and
begged he would repair to him directly :
— " Come not as a stranger, but as a
very welcome friend ; come and share
in my observations with such instru-
ments as I have with me, and as a
dearly beloved associate." During his
stay of three or four months at Benach,
it was settled that Tycho should apply to
the emperor, to procure him the situation
of assistant in the observatory. Kep-
ler then returned to Gratz, having pre-
viously received an intimation, that he
might do so in safety. The plan, as it
had been arranged between them was,
that a letter should be procured from
the emperor to the states of Styria,
requesting that Kepler might join Tycho
Brahe for two years, and retain his
.salary during that time: a hundred
florins were to be added annually by
the emperor, on account of the greater
dearness of living at Prague. But
before everything was concluded, Kep-
ler finally threw up his situation at
Gratz, in consequence of new dissen-
sions. Fearing that this would utterly
put an end to his hopes of connecting
himself with Tycho, he determined to
.revive his claims on the patronage of the
Duke of Wirtemberg. With this view
he entered into correspondence with
Mastlin and some of his other friends
at Tubingen, intending to prosecute
his medical studies, and offer himself
for the professorship of medicine in
that university. He was dissuaded from
this scheme by the pressing instances
of Tycho, who undertook to exert
•himself in procuring a permanent set-
tlement for him from the emperor,
.and assured him, even if that attempt
should fail, that the language he had
used when formerly inviting him to
visit him at Hamburg, should not be
forgotten. In consequence of this en-

couragement," Kepler abandoned his
former scheme, and travelled again
with his wife to Prague. He was
detained along time on the road by
violent illness, and his money became
entirely exhausted. On this he wrote
complainingly to Tycho, that he was
unable without assistance to travel even
the short distance which still separated
them, far less to await much longer the
fulfilment of the promises held out to
him.

By his subsequent admissions, it ap-
pears that for a considerable time he
lived entirely on Tycho' s bounty, and by
way of return, he wrote an essay against
Raimar, and against a Scotchman named
Liddell, professor at Rostoch and Helm-
stadt, who, like Raimar, had appropri-
ated to himself the credit of the Ty-
chonic system. Kepler never adopted
this theory, and indeed, as the question
merely regarded priority of invention,
there could be no occasion, in the dis-
cussion, for an examination of its prin-
ciples.

This was followed by a transaction,
not much to Kepler's credit, who in the
course of the following year, and during a
second absence from Prague, fancied that
he had some reason to complain of Ty-
cho's behaviour, and wrote him a violent
letter, filled with reproaches and insults.
Tycho appears to have behaved in this
affair with great moderation : professing
to be himself occupied with the marriage
of his daughter, he gave the care of reply-
ing to Kepler's charges, to Ericksen, one
of his assistants, who, in a very kind and
temperate letter, pointed out to him the
ingratitude of his behaviour, and the
groundlessness of his dissatisfaction. His
principal complaint seems to have been,
that Tycho had not sufficiently supplied
his wife with money during his absence.
Ericksen's letter produced an immediate
and entire change in Kepler's temper,
and it is only from the humble recanta-
tion which he instantaneously offered
that we learn the extent of his previous
violence. " Most noble Tycho," these
are the words of his letter, " how shall
1 enumerate or rightly estimate your
benefits conferred on me ! For two
months you have liberally and gratui-
tously maintained me, and my whole
family ; you have provided for all my
wishes ; you have done me every pos-
sible kindness ; you have communicated
to me everything you hold most dear ;
no one, by word o'r deed, has intention-
ally injured me in any thing: in short,

KEPLER.

11

not to your children, your wife, or your-
self have you shown more indulgence
than to me. This being so, as I am
anxious to put upon record, I cannot
reflect without consternation that I
should have been so given up by God to
my own intemperance, as to shut my
eyes on all these benefits ; that, instead of
modest and respectful gratitude, I should
indulge for three weeks in continual mo-
roseness towards all your family, in head-
long passion, and the utmost insolence
towards yourself, who possess so many
claims on my veneration from your noble
family, your extraordinary learning, and
distinguished reputation. Whatever I
have said or written against the person,
the fame, the honour, and the learning
of your excellency ; or whatever, in any
other way, I have injuriously spoken or
written, (if they admit no other more fa-
vourable interpretation,) as to my grief I
have spoken and written many things,
and more than I can remember ; all and
everything I recant, and freely and ho-
nestly declare and profess to be ground-
less, false, and incapable of proof." Hoff-
mann, the president of the states of
Styria, who had taken Kepler to Prague
on his first visit, exerted himself to per-
fect the reconciliation, and this hasty
quarrel was entirely passed over.

On Kepler's return to Prague, in
September, 1601, he was presented to
the Emperor by Tycho, and honoured
•with the title of Imperial Mathematician,
on condition of assisting Tycho in his
calculations. Kepler desired nothing
more than this condition, since Tycho
was at that time probably the only per-
son in the world who possessed obser-
vations sufficient for the reform which
he now began to meditate in the theory
of astronomy. Rudolph appears to have
valued both Tycho Brahe and Kepler as
astrologers rather than astronomers ; but
although unable to appreciate rightly the
importance of the task they undertook,
of compiling a new set of astronomical
tables founded upon Tycho's observa-
tions, yet his vanity was flattered with
the prospect of his name being con-
nected with such a work, and he made
liberal promises to defray the expense of
the new Hudolphine Tables. Tycho's
principal assistant at this time was
Longomontanus, who altered his name
to this form, according to the prevalent
fashion of giving to every name a Latin
termination. Lomborg or Longbierg
•was the name, not of his family, but
of the village in Denmark, where he was

born, just as Miiller was seldom called
by any other name than Regiomontanus,
from 'his native town Konigsberg, as
George Joachim Rheticus was so sur-
named from Rhetia, the country of the
Grisons, and as Kepler himself was
sometimes called Leonmontanus, from
Leonberg, where he passed his in-
fancy. It was agreed between Longo-
montanus and Kepler, that in discuss-
ing Tycho's observations, the former
should apply himself especially to the
Moon, and the latter to Mars, o*n which
planet, owing to its favourable position,
Tycho was then particularly engaged.
The nature of these labours will be ex-
plained when we come to speak of the
celebrated book " On the Motions of
Mars."

This arrangement was disturbed by
the return of Longomontanus into Den-
mark, where he had been offered an as-
tronomical professorship, and still more
by the sudden death of Tycho Brahe
himself in the following October. Kep-
ler attended him during his illness, and
after his death undertook -to arrange
some of his writings. But, in conse-
quence of a misunderstanding between
him and Tycho's family, the manuscripts
were taken out of his hands ; and when,
soon afterwards, the book appeared,
Kepler complained heavily that they had
published, without his consent or know-
ledge, the notes and interlineations added
by him for his own private guidance
whilst preparing it for publication.

On Tycho's death, Kepler succeeded
him as principal mathematician to the
emperor; but although he was thus
nominally provided with a liberal salary,
it was almost always in arrear. The
pecuniary embarrassments in which he
constantly found himself involved, drove
him to the resource of gaining a liveli-
hood by casting nativities. His peculiar
temperament rendered him not averse
from such speculations, and he enjoyed
considerable reputation in this line, and
received ample remuneration for his pre-
dictions. But although he did not scruple,
when consulted, to avail himself in this
manner of the credulity of his contem-
poraries, he passed over few occasions
in his works of protesting against the
futility of this particular genethliac as-
trology. His own astrological creed was
in a different strain, more singular, but
not less extravagant. We shall defer en-
tering into any details concerning it, till
we come to treat of his book on Har-
monics, in which he has collected and

12

KEPLEP.

recapitulated the substance of his scat-
tered opinions on this strange subject.

His next works deserving notice are
those published on occasion of the new
star which shone out with great splen-
dour in 1 604, in the constellation Cassio-
peia *. Immediately on its appearance,
Kepler wrote a short account of it in
German, marked with all the oddity
which characterises most of his pro-
ductions. We shall see enough of his
astronomical calculations when we come
to his book on Mars ; the following
passage will probably be found more
amusing.

After comparing this star with that of
1572, and mentioning that many persons
who had seen it maintained this to be
the brighter of the two, since it was nearly
twice the size of its nearest neighbour,
Jupiter, he proceeds as follows : —
" Yonder one chose for its appearance
a time no way remarkable, and came
into the world quite unexpectedly, like
an enemy storming a town, and break-
ing into the market-place before the
citizens are *aware of his approach;
but ours has come exactly in the year
of which astrologers have -written so
much about the fiery trigon that hap-
pens in it t ; just in the month in which
(according to Cyprian) Mars comes up
to a very perfect conjunction with the
other two superior planets ; just in
the day when Mars has joined Jupiter,
and just in the place where this con-
junction has taken place. Therefore the
apparition of this star is not like a secret
hostile irruption, as was that one of 1 572,
but the spectacle of a public triumph, or
the entry of a mighty potentate ; when
the couriers ride in some time before,
to prepare his lodgings, and the crowd
of young urchins begin to think the
time over-long to wait : then roll in, one
after another, the ammunition, and mo-
ney, and baggage waggons, and presently
the trampling of horse, and the rush of
people from every side to the streets and
windows; and when the crowd have
gazed with their jaws all agape at the
troops of knights; then at last, the
trumpeters, afld archers, and lackeys, so
distinguish the person of the monarch,
that there is no occasion to point him
out, but every one cries out of his own
accord— * Here we have him!'— What
it may portend is hard to determine, and

* See Life of Galileo, p. 16.
t The fiery trigon occurs about once in every
800 years, when Saturn, Jupiter, and Mars are in
the three fiery signs, Aries, Leo, and Sagittarius.

thus much only is certain, that it comes
to tell mankind either nothing at all, or
high and weighty news, quite beyond
human sense and understanding. It
will have an important influence on
political and social relations; not indeed
by its own nature, but, as it were, acci-
dentally through the disposition of man-
kind. First, it portends to the book-
sellers great disturbances, and tolerable
gains ; for almost every Theologus, Phi'
losophicus, Medicus, and Mathematicus*
or whoever else, having no laborious oc-
cupation intrusted to him, seeks his plea-
sure in studiis, will make particular re-
marks upon it, and will wish to bring these
remarks to the light. Just so will others,
learned and -unlearned, wish to know its
meaning, and they will buy the authors
who profess to tell them. I mention
these things merely by way of example,
because, although thus much can be
easily predicted without great skill, yet
may it happen just as easily, and in the
same manner, that the vulgar, or whoever
else is of easy faith, or it may be, crazy,
may wish to exalt himself into a great
prophet ; or it may even happen that
some powerful lord, who has good foun-
dation and beginning of great dignities,
will be cheered on by this phenomenon
to venture on some new scheme, just as
if God had set up this star in the dark-
ness merely to enlighten them."

It would hardly be supposed, from the
tenor of this last passage, that the writer
of it was not a determined enemy to
astrological predictions of every descrip-
tion. In 1602 he had published a dis-
putation, not now easily met with, " On
the Principles of Astrology," in which
it seems that he treated the professed
astrologers with great severity. The
essence of this book is probably con-
tained in the second treatise on the
new star, which he published in 1606*.
In this volume he inveighs repeatedly
against the vanity and worthlessness of
ordinary astrology, declaring at the same
time, that the professors of that art know
that this judgment is pronounced by one
well acquainted with its principles. " For
if the vulgar are to pronounce who is
the best astrologer, my reputation is
known to be of the highest order ; if they

* The copy of this work in the British Museum
is Kepler's presentation copy to our James I. On
the blank leaf, opposite the title-page, is the follow-
ing inscription, apparently in the author's hand-
writing :—" Regi philosophanti, philosophus ser-
viens, Platoni Diogenes, Britannias tenenti, Pragae
stipem mendicans ab Alexandro, e dolio conduc-
titio, hoc stium philosophema misit et coimnen-
darit,"

KEPLER.

13

prefer the judgment of the learned, they
are already condemned. Whether they
stand with me in the eyes of the popu-
lace, or I fall with them before the
learned, in both cases I am in their
ranks ; I am on a level with them ; T
cannot be renounced."

The theory which Kepler proposed
to substitute is intimated shortly in
the following passage: " I maintain
that the colours and aspects, and con-
junctions of the planets, are impressed
on the natures or faculties of sub-
lunary things, and when they occur,
that these are excited as well in forming
as in moving the body over whose
motion they preside. Now let no one
conceive a prejudice that I am anxiously
seeking to mend the deplorable and hope-
less cause of astrology by far-fetched
subtilties and miserable quibbling. I do
not value it sufficiently, nor have I ever
shunned having astrologers for my ene-
mies. But a most unfailing experience
(as .far as can be hoped in natural phe-
nomena) of the excitement of sublunary
natures by the conjunctions and aspects
of the planets, has instructed and com-
pelled my unwilling belief."

After exhausting other topics sug-
gested by this new star, he examines the
different opinions on the cause of its ap-
pearance. Among others he mentions
the Epicurean notion, that it was a for-
tuitous concourse of atoms, whose ap-
pearance in this form was merely one of
the infinite number of ways in which,
since the beginning of time, they have
been combined. Having descanted for
some time on this opinion, and declared
himself altogether hostile to it,Kepler pro-
ceeds as follows : — " When I was a youth,
with plenty of idle time on my hands,
I was much taken with the vanity, of
which some grown men are not ashamed,
of making anagrams, by transposing the
letters of my name, written in Greek,
so as to make another sentence : out of

Lwavvjjj KssrX^oj I made "Slipway x.dtf'/iXo;'* ',

in Latin, out of Joannes Keplerus came
Serpens in akule&\. But not being satis-
fied with the meaning of these words,
and being unable to make another, I
trusted the thing to chance, and taking
out of a pack of playing cards as many
as there were letters in the name, I wrote
one upon each, and then began to shuffle
them, and at each shuffle to read them
in the order they came, to see if any
meaning came of it, Now, may all the
Epicurean gods and goddesses confound

* The tapster of the Sirens,
t A serpent in his sting.

this same chance, which, although I
spent a good deal of time over it, never
showed me anything like sense even from
a distance *. So 1 gave up my cards to
the Epicurean eternity, to be carried away
into infinity, and, it is said, they are still
flying about there, in the utmost confu-
sion among the atoms, and have never
yet come to any meaning. I will tell
these disputants, my opponents, not my
own opinion, but my wife's. Yesterday,
when weary with writing, and my mind
quite dusty with considering these atoms,
1 was called to supper, and a salad I
had asked for was set before me. It
seems then, said I aloud, that if pewter
dishes, leaves of lettuce, grains of salt,
drops of water, vinegar, and oil, and
slices of egg, had been flying about in
the air. from all eternity, it might at last
happen by chance that there would come
a salad. Yes, says my wife, but not so
nice and well dressed as this of mine is."

CHAPTER III.

Kepler publishes his Supplement to

Vitellion — Theory of Refraction.
DURING several years Kepler remained,
as he himself forcibly expressed it,
begging his bread from the emperor at
Prague, and the splendour of his nomi-
nal income served only to increase his
irritation, at the real neglect under
which he nevertheless persevered in his
labours. His family was increasing,
and he had little wherewith to support
them beyond the uncertain proceeds of
his writings and nativities. His salary
was charged partly on the states of Si-
lesia, partly on the imperial treasury ;
but it was in vain that repeated orders
were procured for the'payment of the
arrears due to him. The resources of
the empire were drained by the constant
demands of an engrossing war, and
Kepler had not sufficient influence to
enforce his claims against those who
thought even the smallest sum bestowed
upon him ill spent, in fostering profit-
less speculations. In consequence of
this niggardliness, Kepler was ^forced to
postpone the publication of the Rudol-
phine Tables, which he was engaged in
constructing from his own and Tycho
Brahe's observations, and applied him-
self to other works of a less costly de-
scription. Among these may be men-

* In one of his anonymous writings Kepler has
anagrammatized his name, Joannes Keplerus, in a
variety of other forms, probably selected from the
luckiest of his shuffles :— " Kleopas Herennius,
tielenor Kapuensis, Raspinus Enkeleo, Kanones
Pueriles,"

14

KEPLER.

tioned a " Treatise on Comets," written
on occasion of one which appeared in
3607 : in this h? suggests that they are
planets moving in straight lines. The
book published in 1G04, which he en-
titles " A Supplement to Vitellion,"
may be considered as containing the
first reasonable and consistent theory of
optics, especially in that branch of
it usually termed dioptrics, which re-
lates to the theory of vision through trans-
parent substances. In it was first ex-
plained the true use of the different parts
of the eye, to the knowledge of which
Baptista Porta had already approached
very nearly, though he stopped short of
the accurate truth. Kepler remarked
the identity of the mechanism in the eye
\vith that beautiful invention of Porta's,
the camera obscura ; showing, that the
light which falls from external objects on
the eye is refracted through a transpa-
rent substance, called, from its form and
composition, the crystalline lens, and
makes a picture on the fine net- work of
nerves, called the retina, which lies at the
back of the eye. The manner in which
the existence of this coloured picture on
the retina causes to the individual the
sensation of sight, belongs to a theory not
purely physical ; and beyond this point
Kepler did not attempt to go.

The direction into which rays of light
(as they are usually called) are bent or
refracted in passing through the air and
other transparent substances or me-
diums, is discussed in this treatise at
great length. Tycho Brahe had been the
first astronomer who recognized the
necessity of making some allowance on
this account in the observed heights of
the stars. A long controversy arose on
this subject between Tycho Brahe and
Rothman,' the astronomer at Hesse
Cassel, a man of unquestionable talent,
but of odd and eccentric habits. Neither
was altogether in the right, although
Tycho had the advantage in theargument.
He failed however to "establish the true
law of refraction, and Kepler has devoted
a chapter to an examination of the same
question. It is marked by precisely the
same qualities as those appearing so
conspicuously in his astronomical writ-
Ings : — great' ingenuity ; wonderful per-
severance ; bad philosophy. That this
may not be taken solely upon assertion,
some samples of it are subjoined. The
writings of the authors of this period
are little read or known at the present
day ; and it is only by copious extracts
that any accurate notion can be forrrted
of the nature and value of their labours.

The following tedious specimen of Kep-
ler's mode of examining physical pheno-
mena is advisedly selected to contrast
with his astronomical researches : though
the luck and consequently the fame that
attended his divination were widely dif-
ferent on the two occasions, the method
pursued was the same. After comment-
ing on ,the points of difference between
Rothman and Tycho Brahe, Kepler pro-
ceeds to enumerate his own endeavours
to discover the law of refraction.

" I did not leave untried whether,
by assuming a horizontal refraction
according to the density of the medium,,
the rest would correspond with the sines
of the distances from the vertical direc-
tion, but calculation proved that it wras
not so : and indeed there was no occa-
sion to have tried it, for thus the refrac-
tions would increase according to the
same law in all mediums, which is con-
tradicted by experiment.

" The same kind of objection may be
brought against the cause of refraction
alleged by^Alhazen and Vitellion. They
say that "the light seeks to be compen-
sated for the loss sustained at the ob-
lique impact ; so that in proportion as
it is enfeebled by striking against the
denser medium, in the same degree does
it restore its energy by approaching the
perpendicular, that it may strike the bot-
tom of the denser medium with greater
force ; for those impacts are most for-
cible which are direct. And they add
some subtle notions, I know not what,
how the motion of obliquely incident
light is compounded of a motion perpen-
dicular and a motion parallel to the dense
surface, and that this compound motion
is not destroyed, but only retarded by
meeting the denser medium.

" I tried another way of measuring the
refraction, which should include the den-
sity of the medium and the incidence :

for, since a denser medium is the causa
of refraction, it seems to be the same
thing as if we were to prolong the depth
of the medium in which the rays are re-

KEPLER.

fracted into as much space as would be
filled by the denser medium under the
force of the rarer one.

" Let A be the place of the light, B C
the surface of the denser medium, D E
its bottom . Let A B , A G, A F be rays
falling obliquely, which would arrive at
D, I, H, if the medium were uniform.
But because it is denser, suppose the
bottom to be depressed to K L, deter-
mined by this that there is as much of
the denser matter contained in the space
DC as of the rarer in LG : and thus, on
the sinking of the whole bottom DE, the
points D, I, H, E will descend vertically
to L, M, N, K. Join the points B L,
GM, FN, cutting D E in O,P, Q ;
the refracted rays will be A B O, A G P,
AFQ."— ''This method is refuted by
experiment ; it gives the refractions near
the perpendicular A C too great in re-
spect of those near the horizon. Who-
ever has leisure may verify this, either
by calculation or compasses. It may be
added that the reasoning itself is not
very sure-footed, and, whilst seeking to
measure other things, scarcely takes in
and comprehends itself." This reflec-
tion must not be mistaken for the dawn
of suspicion that his examination of phi-
losophical questions began not altogether
at the right end : it is merely an acknow-
ledgment that he had not yet contrived a
theory with which he was quite satisfied
before it was disproved by experiment.

After some experience of Kepler's
miraculous good fortune in seizing truths
across the wildest and most absurd theo-
ries, it is not easy to keep clear of the op-
posite feeling of surprise whenever any of
his extravagancies fail to discover to him
some beautiful law of nature. But we
must follow him as he plunges deeper in
this unsuccessful inquiry ; and the reader
must remember, in order fully to appre-
ciate this method of philosophizing, that
it is almost certain that Kepler laboured
upon every one of the gratuitous sup-
positions that he makes, until positive
experiment satisfied him of their incor-
rectness.

" I go on to other methods. Since
density is clearly connected with the
cause of the refractions, and refraction
itself seems a kind of compression of
light, as it were, towards the perpendi-
cular, it occurred to me to examine whe-
ther there was the same proportion be-
tween the mediums in respect of density
and the parts of the bottom illuminated
by the light, when let into a vessel, first
empty, and afterwards filled with water.

This mode branches out into many : for
the proportion may be imagined, either
in the straight lines, as if one should
say that the line E Q, illuminated by
refraction, is to EH illuminated directly,
as the density of the one medium is
to that of the other— Or another may
suppose the proportion to be between
FC and FH— Or it may be conceived
to exist among surfaces, or so that
some power of E Q should be to some
power of E H in this proportion, or
the circles or similar figures described
on them. In this manner the proportion-
of E Q to E P would be double that of
E H to El — Or the proportion may be
conceived existing among the solidities
of the pyramidal frustums FHEC,
FQEC— Or, since the proportion of
the mediums involves a threefold con-
sideration, since they have density in
length, breadth, and thickness, 1 pro-
ceeded also to examine the1 cubic propor-
tions among the lines E Q, EH.

" I also considered other lines. From
any of the points of refraction as GV
let a perpendicular GY be dropped upon/
the bottom. It may become a question
whether possibly the triangle I G Y,
that, is, the base I Y, is divided by the
refracted ray G P, in the proportion of
the densities of the mediums.

" I have put all these methods here
together, because the same remark dis-
proves them all. For, in whatever manner,
whether as line, plane, or pyramid, E I
observes a given proportion to E P, or
the abbreviated line Y I to YP, namely,
the proportion of the mediums, it is sure
that E I, the tangent of the distance of
the point A from the vertex, will be-
come infinite, and will, therefore make
E P or Y P, also infinite. Therefore,
I G P, the angle of refraction, will be
entirely lost ; and, as it approaches the
horizon, will gradually become less and
less, which is contrary to experiment.

" I tried again whether the images
are equally removed from their points'
of refraction, and whether the ratio of
the densities measures the least dis-
tance. For instance, supposing E to
be the imaije, C the surface of the water,
K the bottom, and C E to C K in the
proportion of the densities of the me
diums. Now, let F, G, B, be three
other points of refraction and images at
S, T, V, and let C E be equal to F S, GT,
and B V. But according to this rule an
image E would still be somewhat raised
in the perpendicular A K, which is con-
trary to experiment, not to mention other

16

KEPLER.

contradictions. Thirdly, whether the
proportion of the mediums holds be-
tween F H and F X, supposing H to be
the place of the image? Not at all.
For so, C E would be in the same pro-
portion to C K, so that the height of
the image would always be the same,
which we have just refuted. Fourthly,
•whether the raising of the image at E is
to the raising at H, as CEtoFH?
Not in the least; for so the images
either would never begin to be raised, or,
having once begun, would at last be
infinitely raised, because FH at last
becomes infinite. Fifthly, whether the
images rise in proportion to the sines of
the inclinations ? Not at all ; for so the
proportion of ascent would be the same
in all mediums. Sixthly, are then the
images raised at first, and in perpen-
dicular radiation, according to the pro-
portion of the mediums, and do they
subsequently rise more and more ac-
cording to the sines of the inclinations ?
For so the proportion would be com-
pound, and would become different in
different mediums. There is nothing in
it: for the calculation disagreed with
experiment. And generally it is in vain
to have regard to the image or the place
of the image, for that very reason, that
it is imaginary. For there is no con-
nexion between the density of the me-
dium or any real [quality or refraction of
the light, and an accident of vision, by
an error of which the image happens.

" Up to this point, therefore, I had fol-
lowed a nearly blind mode of inquiry, and
had trusted to good fortune ; but now
I opened the other eye, and hit upon a
sure method, for I pondered the fact,
that the image of a thing seen under
water approaches closely to the true
ratio of the refraction, and almost mea-
sures it ; that it is low if the thing is
viewed directly from above ; that by de-
grees it rises as the eye passes towards
the horizon of the water. Yet, on the
other hand, the reason alleged above,
proves that the measure is not to be
sought in the image, because the image
is not a thing actually existing, but arises
from a deception of vision which is
purely accidental. By a comparison of
these conflicting arguments, it occurred
to me at length, to seek the causes them-
selves of the existence of the image un-
der water, and in these causes the mea-
sure of the refractions. This opinion
was strengthened in me by seeing that
opticians had not rightly pointed out the
cause of the image which appears both

in mirrors and in water. And this was
the origin of that labour which I under-
took in the third chapter. Nor, indeed,
was that labour trifling, whilst hunting
down false opinions of all sorts among
the principles, in a matter rendered so
intricate by the false traditions of optical
writers ; whilst striking out half a dozen
different paths, and beginning anew the
whole business. How often did it hap-
pen that a rash confidence made me look
upon that which I sought with such
ardour, as at length discovered !

" At length I cut this worse than
Gordian knot of catoptrics by analogy
alone, by considering what happens in
mirrors, and what must happen analo-
gically in water. In mirrors, the image
appears at a distance from the real place
of the object, not being itself material,
but produced solely by reflection at the
polished surface. "Whence it followed
in water also, that the images rise and
approach the surface, not according to
the law of the greater or less density in
the water, as the view is J less or more
oblique, but solely because of the re-
fraction of the ray of light passing
from the object to the eye. On which
assumption, it is plain that every attempt
I had hi!herto made to measure refrac-
tions by the image, and its elevation,
must fall to the ground. And this be-
came more evident when I discovered
the true reason why the image is in the
same perpendicular line with the object
both in mirrors and in dense mediums.
When I had succeeded thus far by
analogy in this most difficult investiga-
tion, as to the place of the image, I be-
gan to follow out the analogy further, led
on by the strong desire of measuring
refraction. For I wished to get hold of
some measure of some sort, no matter
how blindly, having no fear but that so
soon as the measure should be accurately
known, the cause would plainly appear.
I went to work as follows. In convex
mirrors the image is diminished, and just
so in rarer mediums ; in denser mediums
it is magnified, as in concave mirrors.
In convex mirrors the central parts of
the image approach, and recede in con-
cave farther than towards the circumfe-
rence ; the same thing happens in different
mediums, so that in water the bottom
appears depressed, and the surrounding
parts elevated. Hence it appears that a
denser medium corresponds with a con-
cave reflecting surface, and a rarer one
with a convex one : it was clear, at the
same time, that the plane surface of the

KEPLER.

17

water affects a property of curvature. I
was, therefore, to excogitate causes
consistent with its having this effect 'of
curvature, and to see if a reason could
be given, why the parts of the water
surrounding the incident perpendicular
should represent a greater density than
the parts just under the perpendicular.
And so the thing came round again to
my former attempts, which being refuted
by reason and experiment, I was forced
to abandon the search after a cause. I
then proceeded to measurements."

Kepler then endeavoured to connect
his measurements of different quantities
of refraction with the conic sections, and
was tolerably well pleased with some of
his results. They were however not
entirely satisfactory, on which he breaks
off with the following sentence : " Now,
reader, you and I have been detained
sufficiently long whilst I have been at-
tempting to collect into one faggot the
measure of different refractions : I ac-
knowledge that the cause cannot be con-
nected with this mode of measurement :
for what is there in common between
refractions made at the plane surfaces of
transparent mediums,' and mixtilinear
conic sections ? Wherefore, quod Deus
benevortat, we will now have had enough
of the causes of this measure ; and al-
though, even now, we are perhaps err-
ing something from the truth, yet it is
better, by working on, to show our in-
dustry, than our laziness by neglect."

Notwithstanding the great length of
this extract, we must add the concluding
paragraph of the Chapter, directed, as
we are told in the margin, against the
" Tychonomasticks :" —

" I know how many blind men at this
day dispute about colours, and how they
long for some one to give some assist-
ance by argument to their rash insults
of Tycho, and attacks upon this whole
matter of refractions ; who, if they had
kept to themselves their puerile errors
and naked ignorance, might have escaped
censure ; for that may happen to many
great men. But since they venture forth
publicly, and with thick books and sound-
ing titles, lay baits for the applause of
the unwary, (for now-a-days there is
more danger from the abundance of bad
books, than heretofore from the lack of
good ones,) therefore let them know that
a time is set for them publicly to amend
their own errors. If they longer delay
doing this, it shall be open, either to me
or any other, to do to these unhappy
meddlers in geometry as they have taken
upon themselves to do with respect to men

of the highest reputation. And although
this labour will be despicable, from the
vile nature of the follies against which it
will be directed, yet so much more ne-
cessary than that which they have un-
dertaken against others, as he is a greater
public nuisance, who endeavours to
slander good and necessary inventions,
than he who fancies he has found what
is impossible to discover. Meanwhile,
let them cease to plume themselves on
the silence which is another word for
their own obscurity."1

Although Kepler failed, as we have
seen, to detect the true law of refraction,
(which was discovered some years later
by Willibrord Snell, a Flemish mathe-
matician,) there are many things well
deserving notice in his investigations.
He remarked, that the quantity of re-
fraction would alter, if the height of the
atmosphere should vary ; and also, that
it would be different at different tempe-
ratures. Both these sources of varia-
tion are nown constantly taken into ac-
count, the barometer and thermometer
fiving exact indications of these changes,
here is also a very curious passage in
one of his letters to Bregger, written in
1605, on the subject of the colours in
the rainbow. It is in these words :—
" Since every one sees a different rain-
bow, it is possible that some one may
see a rainbow in the very place of my
sight. In this case, the medium is co-
loured at the place of my/vision, to which
the solar ray comes to me through
water, rain, or aqueous vapours. For
the rainbow is seen when the sun is
shining between rain, that is to say, when
the sun also is visible. Why then do
I. not see the sun green, yellow, red, and
blue, if vision takes place according to
the mode1 of illumination ? I will say
something for you to attack or examine.
The sun's rays are not coloured, except
with a definite quantity of refraction.
Whether you are in the optical cham-
ber, or standing opposite glass globes',
or walking in the morning dew, every-
where it is obvious that a certain and de-
finite angle is observed, under which,
when seen in dew, in glass, in water, the
sun's splendour appears coloured, and
under no other angle. There is no
colouring by mere reflexion, without the
refraction of a denser medium." How
closely does Kepler appear, in this pas-
sage, to approach the discovery which
forms not the least part of Newton's
fame !

We also find in this work a defence of
the opinion that the planets are lumi

18

KEPLER.

nous of themselves ; on the ground that
the inferior planets would, on the contrary
supposition, display phases like those of
the moon when passing between us and
the sun. 1 he use of the telescope was
not then known; and, when some years
later the form of the disk of the planets
was more clearly defined with their
assistance, Kepler had the satisfaction
of finding his assertions verified by the
discoveries of Galileo, that these changes
do actually take place. In another of
his speculations, connected with the same
subject, he was less fortunate. In 1607
a black spot appeared on the face of sun,
such as may almost always be seen with
the assistance of the telescope, although
they are seldom large enough to be visible
to the unassisted eye. Kepler saw it for
a short time, and mistook it for the planet
Mercury, and with his usual precipi-
tancy hastened to publish an account of
his observation of this rare phenomenon.
A few years later, Galileo discovered with
his glasses, a great number of similar
spots ; and Kepler immediately retracted
the opinion announced in his treatise,
and acknowledged his belief that previous
accounts of the same occurrence which
he had seen in old authors, and which
he had found great difficulty in recon-
ciling with his more accurate knowledge
of the motions of Mercury, were to be
referred to a like mistake. On this occa-
sion of the invention of the telescope,
Kepler's candour and real love of truth
appeared in a most favourable light.
Disregarding entirely the disagreeable
necessity, in consequence of the dis-
coveries of this new instrument, of retract-
ing several opinions which he had main-
tained with considerable warmth, he
ranged himself at once on the side of Gali-
leo, in opposition to the bitter and deter-
mined hostility evinced by most of those
whose theories were endangered by the
new views thus offered of the heavens.
Kepler's quarrel with his pupil, Horky, on
this account, has been mentioned in the
" Life of Galileo ;" and this is only a se-
lected instance from the numerous occa.-
sions on which he espoused the same
unpopular side of the argument He
published a dissertation to accompany
Galileo's " Intelligencer of the Stars,"
in which he warmly expressed his ad-
miration of that illustrious inquirer into
nature. His conduct in this respect was
the more remarkable, as some of his most
intimate friends had taken a very opposite
view of Galileo's merit, and seem to
have laboured much to disturb their mu-
tual regard : Mastlin especially, Kepler's

early instructor, seldom mentioned to him
the name of Galrleo, without some con-
temptuous expression of dislike. These
statements have rather disturbed ,the
chronological order of the account of
Kepler's works. We now return to the
year 1609, in which he published his
great and extraordinary book, ** On the
Motions of Mars ;" a work which holds
the intermediate place, and is in truth
the connecting link, between the disco-
veries of Copernicus and Newton.

CHAPTER IV.
Sketch of the Astronomical Theories.

before Kepler.

KEPLER had begun to labour upon
these commentaries from the moment
when he first made Tycho's acquaint-
ance ; and it is on this work that his re-
putation should be made mainly to rest.
It is marked in many places with his
characteristic precipitancy, and indeed
one of the most important discoveries
announced in it (famous among astro-
nomers by the name of the Equable
Description of Areas) was blundered upon,
by a lucky compensation of errors, of
the nature of which Kepler remained
ignorant to the very last. Yet there is
more of the inductive method in this than
in any of his other publications ; and the
unwearied perseverance with which he ex-
hausted years in hunting down his often
renewed theories, till at length he seemed
to arrive at the true one, almost by having
previously disproved every other, excites
a feeling of astonishment nearly ap-
proaching to awe. It is wonderful how
he contrived to retain his vivacity and
creative fancy amongst the clouds of
figures which he conjured up round him ;
for the slightest hint or shade of proba-
bility was sufficient to plunge him into
the midst of the most laborious compu-
tations. He was by no means an accu-
rate calculator, according to the follow-
ing character which he has given of him-
self: — " Something of these delays must
be attributed to my own temper, for non
omnia possumus omnes, and I am totally
unable to observe any order; what I do
suddenly, I do confusedly, and if I pro-
duce any thing well arranged, it has been
done ten times over. Sometimes an
error of calculation committed by hurry ^
delays me a great length of time. I
could indeed publish an infinity of things,
for though my reading is confined,
my imagination is abundant, but I grow
dissatisfied with such confusion : I get
disgusted and out of humour, and either
throw them away, or put them aside to

KEPLER.

19

l>e looked at again ; or, in other words,
to be written again, for that is generally
the end of it. I entreat you, my friends,
not to condemn me for ever to grind in
the mill of mathematical calculations :
allow me some time for philosophical
speculations, my only delight."

He was very seldom able to afford
the expense of maintaining an assist-
ant, and was forced to go through most
of the drudgery of his calculations by
himself; and the most confirmed and
merest arithmetician could not have
toiled more doggedly than Kepler did in
the work of which we are about to speak.

In order that the language of his as-
tronomy may be understood, it is neces-
sary to mention briefly some of the older
theories. When it had been discovered
that the planets did not move regularly
round the earth, which was supposed to
be fixed in the centre of the world, a me-
chanism was contrived by which it was
thought that the apparent irregularity
could be represented, and yet the prin-
ciple of uniform motion, which was ad-
hered to with superstitious reverence,
might be preserved. This, in its sim-
plest form, consisted in supposing the
planet to move uniformly in a small
circle, called an epicycle, the centre of
which moved with an equal angular
motion in the opposite direction round
the earth*. The circle D d, described
by D, the centre of the epicycle, was
called the deferent. For instance, if the
planet was supposed to be at A when
the centre of the epicycle was at D, its

position, when the centre of the epicycle
had removed to d, would be at p, found
by drawing dp parallel to D A. Thus,
the angle a dp, measuring the motion of
the planet in its epicycle, would be equal

* By " the opposite direction" is meant, that
while the motion in the circumference of one
circle appeared, as viewed from its centre, to be
from left to right, the other, viewed from its centre,
appeared from right to left. This must be under-
stood whenever these or similar expressions are
repeated.

to DEd, the angle described by the
centre of the epicycle in the deferent.
The angle pE d between Ejo, the direc-
tion in which a planet so moving would
be seen from the earth, supposed to be
at E, and E d the direction in which it
would have been seen had it been mov-
ing in the centre of the deferent, was
called the equation of the orbit, the
word equation, in the language of astro-
nomy, signifying what must be added
or taken from an irregularly varying
quantity to make it vary uniformly.

As the accuracy of ^observations in-
creased, minor irregularities were dis-
covered, which were attempted to be
accounted for by making a second
deferent of the epicycle, and making
the centre of a second epicycle revolve
in the circumference of the first, and
so on, or else by supposing the revo-
lution in the epicycle not to be com-
pleted in exactly the time in which its
centre is carried round the deferent.
Hipparchus was the first to make a re-
mark by which the geometrical repre-
sentation of these inequalities was consi-
derably simplified. In fact, if EC be
taken equal to p d, Cd will be a paral-
lelogram, and consequently Cp equal
to E d, so that the machinery of the
first deferent and epicycle amounts to
supposing that Ihe planet revolves uni-
formly in a circle round the point C,
not coincident with the place of the
earth. This was consequently called
the excentric theory, in opposition to
the former or concentric one, and was
received as a great improvement. As
the point d is not represented by this
construction, the equation to the orbit
was measured by the angle CpE,
which is equal top Ed. It is not ne-
cessary to give any account of the man-
ner in which the old astronomers de-
termined the magnitudes and positions
of these orbits, either in the concentric
or excentric theory, the present object
being little more than to explain the
meaning of the terms it will be neces-
sary to use in describing Kepler's in-
vestigations.

To explain the irregularities observed
in the other planets, it became neces-
sary to introduce another hypothesis, in
adopting which the severity of the prin-
ciple of uniform motion was somewhat
relaxed. The machinery consisted partly
of an excentric deferent round E, the
earth, and on it an epicycle, in which the
planet revolved uniformly ; but the centre
of the epicycle, instead of revolving uni-
formly round C, the centre of the deferent,

KEPLER.

as it had hitherto been made to do, was
supposed to move in its circumference
with an uniform angular motion round
a third point, Q ; the necessary effect of
which supposition was, that the linear
motion of the centre of the epicycle
ceased to be uniform. There were thus
three points to be considered within the
deferent ; E, the place of the earth ;
C, the centre of the deferent, and some-
times called the centre of the orbit ; and
Q, called the centre of the equant, be-
cause, if any circle were described round
Q, the planet would appear to a spec-
tator at Q, to be moving equably in it.
It was long uncertain what situation
should be assigned to the centre of the
equant, so as best to represent the ir-
regularities to a spectator on the earth,
until Ptolemy decided on placing it (in
every case but that of Mercury, the
observations on which were very doubt-
ful) so that C, the centre of the orbit, lay
just half way in the straight line, joining
Q, the centre of equable motion, and E,
the place of the earth. This is the famous
principle, known by the name of the
bisection of the excentricity.

The first equation required for the
planet's motion was thus supposed to be
due to the displacement of E, the earth,
from Q, the centre of uniform motion,
which was called the excentricity of the
equant : it might be represented by the
angle d E M, drawing E M parallel to
Q d ; for clearly M "would have been
the place of the centre of the epicycle
at the end of a time proportional to
D d, had it moved with an equable angu-
lar motion round E instead of Q. This
angle dE M, or its equal Erf Q, was called
the equation of the centre (i. e. of the
centre of the epicycle) ; and is clearly
greater than if E Q, the excentri-
city of the equant, had been "no greater
than E C, called the excentricity of the
orbit. The second equation was mea-
sured by the angle subtended at E by d,
the centre of the epicycle, and p the

planet's place in its circumference : it was
called indifferently the equation of the
orbit, or of the argument. In order to
account for the apparent stations and
retrogradations of the planets, it be-
came necessary to suppose that many
revolutions in the latter were completed
during one of the former. The va-
riations of latitude of the planets were
exhibited by supposing not only that the
planes of their deferents were oblique to
the plane of the ecliptic, and that the
plane of the epicycle was also oblique to
that of the deferent, but that the inclination
of the two latter was continually chang-
ing, although Kepler doubts whether
this latter complication was admitted by
Ptolemy. In the inferior planets, it was
even thought necessary to give to the
plane of the epicycle two oscillatory mo-
tions on axes at right angles to each
other.

The astronomers at this period
were much struck with a remarkable
connexion between the revolutions of
the superior planets in their epicycles,
and the apparent motion of the sun; for
when in conjunction with the sun, as
seen from the earth, they were always
found to be in the apogee, or point of
greatest distance from the earth, of their
epicycle ; and when in opposition to the
Sun, they were as regularly in the peri-
gee, or point of nearest approach of the
epicycle. This correspondence between
two phenomena, which, according to
the old astronomy, were entirely uncon-
nected, was very perplexing, and it seems
to have been one of the facts which led
Copernicus to substitute the theory of
the earth's motion round the sun.

As time wore on, the superstructure
ofexcentrics and epicycles, which had
been strained into representing the ap-
pearances of the heavens at a particular
moment, grew out of shape, and the
natural consequence of such an artifi-
cial system was, that it became next to
impossible to foresee what ruin might
be produced in a remote part of it "by
any attempt to repair the derangements
and refit the parts to the changes, as
they began to be remarked in any par-
ticular point. In the ninth century of
our era, Ptolemy's tables were already
useless, and all those that were con-
trived with unceasing toil to supply
their place, rapidly became as unser-
viceable as they. Still the triumph of
genius was seen in the veneration that
continued to be paid to the assump-
tions of Ptolemy and Hipparchus ; and
even when the great reformer, Coper-

KEPLER.

21

nicus, appeared, he did not for along
time intend to do more than slightly
modify their principles. That which he
found difficult in the Ptolemaic system,
was none of the inconveniences by which,
since the establishment of the new sys-
tem, it has become common to demon-
strate the inferiority of the old one ; it
was the displacement of the centre of
the equant from the centre of the orbit
that principally indisposed him against
it, and led him to endeavour to represent
the appearances by some other combina-
tions of really uniform circular motions.
There was an old system, called the
Egyptian, according to which Saturn,
Jupiter, Mars, and the Sun circulated
round the earth, the sun carrying with
it, as two moons or satellites, the other
two planets, Venus and Mercury. This
system had never entirely lost credit :
it had been maintained in the fifth cen-
tury by Martianus Capella*, and in-
deed it was almost sanctioned, though
not formally taught, by Ptolemy himself,
when he made the mean motion of the
sun the same as that of the centres of
the epicycles of both these planets. The
remark which had also been made by the
old astronomers, of the .connexion be-
tween the motion of the sun and the revo-
lutions of the superior planets in their
epicycles, led him straight to the expec-
tation that he might, perhaps, produce the
uniformity he sought by extending the
Egyptian system to these also, and this
appears to have been the shape in which
his reform was originally projected.
It was already allowed that the centre of
the orbits of all the planets was not coin-
cident with the earth, but removed from
it by the space E C. This first change
merely made E C the same for all the
planets, and equal to the mean distance
of the earth from the sun. This sys-
tem ^afterwards acquired great cele-
brity through its adoption by Tycho
Brahe, who believed it originated with
himself. It might perhaps have been
at this period of his researches, that
Copernicus was struck with the pas-
sages in the Latin and Greek authors,
to which he refers as testifying the ex-
istence of an old belief in the motion
of the earth round the sun. He im-
mediately recognised how much this
alteration would further his princi-
ples of uniformity, by referring all the

* Venus Mercuriusque, licet ortus occasusque
quotidianos ostendunt, tamen eorum circuli terras
omnino non ambiunt, sed circa solem laxiore am-
bitu circulantur. Denique circulorura suorum
centron in sole constituunt. — De Nuptiis Philolo-
gise et Mercurii. Vicentije. 1499.

planetary motions to one centre, and
did not hesitate to embrace it. The idea
of explaining the daily and principal
apparent motions of the heavenly bodies
by the revolution of the earth on its
axis, would be the concluding change,
and became almost a necessary con-
sequence of his previous improvements,
as it was manifestly at variance with
his principles to give to all the pla-
nets and starry worlds a rapid daily
motion round the centre of the earth,
now that the latter was removed from
its former supposed post in the centre of
the universe, and was itself carried with
an annual motion round another fixed
point.

The reader would, however, form an
inaccurate notion of the system of Co-
pernicus, if he supposed that it com-
prised no more than the theory that
each planet, including the earth among'
them, revolved in a simple circular orbit
round the sun. Copernicus was too well
acquainted with the motions of the hea-
venly bodies, not to be aware that such
orbits would not accurately represent
them ; the motion he attributed to the
earth round the sun, was at first merely
intended to account for those which
were called the second inequalities of the
planets, according to which they ap-
pear one while to move forwards, then
backwards, and at intermediate periods,
stationary, and which thenceforward
were also called the optical equations,,
as being merely an optical illusion.
With regard to what were called the
first inequalities, or physical equations,
arising from a real inequality of motion,,
he still retained the machinery of the
deferent and epicycle ; and all the al-
teration he attempted in the orbits of
the superior planets was an| extension
of the concentric theory to supply the
place of the equant, which he considered
the blot of the system. His theory for
this purpose is shown in the accompany-
ing diagram, where S represents the sun,.

D d, the deferent or mean orbit of the

KEPLER.

planet, on \vhich revolves the centre of
the great epicycle, whose radius, D F,
\vas taken at | of Ptolemy's excentricity
of the equant ; and round the circum-
ference of this revolved, in the opposite
direction, the centre of the little epicycle,
\vhose radius, F P, \vas made equal to
the remaining £ of the excentricity of the
•equant.

The planet P revolved in the circum-
ference^of the little epicycle, in the same
direction with the centre of the great epi-
cycle in the circumference of the defe-
rent, but with a double angular velocity.
The planet was supposed to be in the
perigee of the little epicycle, when its
centre was in the apogee of the greater ;
•and whilst, for instance, D moved equably
though the angle DSd, F moved through
h d f= D S d, and P through r f p =

It is easy to show that this construc-
tion gives nearly the same result as
Ptolemy's ; for the deferent and great
epicycle have been already shown ex-
actly equivalent to an excentric circle
round S, and indeed Copernicus latterly
so represented it: the effect of his con-
struction, as given above, may therefore
be reproduced in the following simpler
form, in which only the smaller epicycle
is retained :

In this construction, the place of the
"planet is found at the end of any time
proportional to F /, by drawing / r
parallel to SF, and taking rfp = 2 F of.
Hence it is plain, if we take O Q, equal
to F P, (already assumed equal to £ of
Ptolemy's excentricity of the equant,)
since S O is equal to f cf the same,
that S Q is the whole of Ptolemy's ex-
centricity of the equant ; and therefore,
that Q is the position of the centre of
his equant. It is also plain if we join
Qp, since rfp = 2Fo/, and oQ =
.fp,'\ that p Q is parallel to fo, and,
therefore, p Q P is proportional to the
time ; so that the planet moves uni-
formly about the same point Q, as in
•Plolwiry's theory ; and if we bisect S Q

in C, which is the position of tVie centre
of Ptolemy's deferent, the planet will,
according to Copernicus, move very
nearly, though not exactly, in the same
circle, whose radius is C P, as that
given by the simple excentric theory.

The explanation offered by Coperni-
cus, of the motions of the inferior pla-
nets, differed again in form from that of
the others. He here introduced what
was called a hypocycle, which, in fact,
was nothing but a deferent not including
the sun, round which the centre of the
orbit revolved. An epicycle in addition
to the hypocycle was introduced into
Mercury's orbit. In this epicycle he
was not supposed to revolve, but to
librate, or move up and down in its
diameter. Copernicus had recourse to
this complication to satisfy an erroneous
assertion of Ptolemy with regard to some
of Mercury's inequalities. He also re-
tained the oscillatory motions ascribed
by Ptolemy to the planes of the epicy-
cles, in order to explain the unequal
latitudes observed at the same distance
from the nodes, or intersections of the
orbit of the planet with the ecliptic. Into
this intricacy, also, he was led by placing
too much confidence in Ptolemy's obser-
vations, which he was unable to satisfy
by an unvarying obliquity. Other very
important errors, such as his belief that
the line of nodes always coincided with
the line of apsides, or places of greatest
and least distance from the central body,
(whereas, at that time, in the case of
Mars, for instance, they were nearly 90°
asunder,) prevented him from accurately
representing many of the celestial phe-
nomena.

These brief details may serve to show
that the adoption or rejection of the
theory of Copernicus was not altogether
so simple a question as sometimes it
may have been considered. It is, how-
ever, not a little remarkable, while it is
strongly illustrative of the spirit of the
times, that these very intricacies, with
which Kepler's theories have enabled us
to dispense, were the only parts of the
system of Copernicus that were at first
received with approbation. His theory
of Mercury, especially, was considered
a masterpiece of subtle invention.
Owing to his dread of the urifavourable
judgment he anticipated on the main
principles of his system, his work re-
mained unpublished during forty years,
and was at last given to the world only
just in time to allow Copernicus to re-
ceive the first copy of it a few hours
before his death.

KEPLER.

CHAPTER V.

Account of the Commentaries on the
motions of Mars — Discovery of the
Law of 'the equable description of
' A reas, and of Elliptic Orbits.
WE may now proceed to examine Kep-
ler's innovations, but it would be doing
injustice to one of the brightest points
of his character, not to preface them by
his own animated exhortation to his
readers. " If any one be too dull to com-
prehend the science of astronomy, or too
feeble-minded to believe in Copernicus
without prejudice to his piety, my advice
to such a one is, that he should quit the
astronomical schools, and condemning,
if he has a mind, any or all of the theories
of philosophers, let him look to his own
affairs, and leaving this worldly travail,
let him go home and plough his fields:
and as often as he lifts up to this goodly
heaven those eyes with which alone he
is able to see, let him pour out his
heart in praises and thanksgiving to
God the Creator ; and let him not fear
but he is offering a worship not less ac-
ceptable than his to whom God has
granted to see yet more clearly with the
eyes of his mind, and who both can and
will praise his God for what he has so
discovered."

Kepler did not by any means under-
rate the importance of his labours, as is
sufficiently shewn by the sort of collo-
quial motto which he prefixed to his
work. It consists in the first instance
of an extract from the writings of the
celebrated and unfortunate Peter Ramus.
This distinguished philosopher was pro-
fessor of mathematics in Paris, and in
the passage in question, after calling on
his contemporaries to turn their thoughts
towards the establishment of a system of
Astronomy unassisted by any hypo-
thesis, he promised as an additional in-
ducement to vacate his own chair in fa-
vour of any one who should succeed in
this object. Ramus perished in the
massacre of St. Bartholomew, and Kepler
apostrophizes him as follows : — " It is
well, Ramus, that you have forfeited your
pledge, by quitting your life and profes-
sorship together :"for if you still held it,
I would certainly claim it as of right be-
longing to me on account of this work,
as I could convince you even with your
own logic." It was rather bold in Kepler
to assert his claim to a reward held out
for a theory resting on no hypothesis, by
light of a work filled with hypotheses of
the most startling description ; but ot"

the vast importance of this book there
can be no doubt ; and throughout the
many wild and eccentric ideas to which
we are introduced in the course of it, it
is fit always to bear in mind that they
form part of a work which is almost the
basis of modern Astronomy."

The introduction contains a curious
criticism of the. commonly-received
theory of gravity, accompanied with
a declaration of Kepler's own opinions
on the same subject. Some of the most
remarkable passages in it have been
already quoted in the life of Galileo ; but,
nevertheless, they are too important to
Kepler's reputation to be omitted here,
containing as they do a distinct and
positive enunciation of the law of uni-
versal gravitation. It does not appear,
however, that Kepler estimated rightly
the importance of the theory here traced
out by him, since on every other occa-
sion he advocated principles with which
it is scarcely reconcileable. The dis-
cussion is introduced in the following
terms : —

" The motion of heavy bodies hinders
many from believing that the earth is
moved by- an animal motion, or rather
a magnetic one. Let such consider the
following propositions. A mathematical
point, whether the centre of the universe
or not, has no power, either effectively
or objectively, to move heavy bodies to
approach it. Let physicians prove if
they can, that such power can be pos-
sessed by a point, which neither is a
body, nor is conceived unless by rela-
tion alone. It is impossible that the
form* of a stone should, by moving its
own body, seek a mathematical point,
or in other words, the centre of the uni-
verse, without regard of the body in
which that point exists. Let physicians
prove if they can, that natural things
have any sympathy with that which is
nothing. Neither do heavy bodies tend
to the centre of the universe by reason
that they are avoiding the extremities of
the round universe ; for their distance
from the centre is insensible, in propor-
tion to their distance from the extremi-
ties of the universe. And what reason
could there be for this hatred ? How
strong, how wise must those heavy
bodies be, to be able to escape so care-
fully from an enemy lying on all sides of

* It is not very easy to carry the understanding
aright among these Aristotelian ideas. Many
at the present day might think they understood
better what is meant, if for " form" had been
written " nature."

~K

24

KEPLER.

them : what activity in the extremities
of the world to press their enemy so
closely! Neither are heavy bodies
driven into the centre by the whirling of
the first moveable, as happens in revolv-
ing water. For if we assume such a
motion, either it would not be con-
tinued down to us, or otherwise we
should feel it, and be carried away with
it, and the earth also with us ; nay,
rather, we should be hurried away first,
and the earth would follow ; all which
conclusions are allowed by our oppo-
nents to be absurd. It is therefore plain
that the vulgar theory of gravity is erro-
neous.

The true theory of gravity is founded
on the following axioms : — Every corpo-
real substance, so far forth as it is corpo-
real, has a natural fitness for resting in
every place where it may be situated by
itself beyond the sphere of influence of a
body cognate with it. Gravity is a mu-
tual affection between cognate bodies
towards union or conjunction (similar in
kind to the magnetic virtue), so that the
earth attracts a stone much rather than
the stone seeks the earth. Heavy bodies
(if we begin by assuming the earth to
be in the centre of the world) are not
carried to the centre of the world in its
quality of centre of the world, but as to
the centre of a cognate round body,
namely, the earth ; so that wheresoever
the earth may be placed, or whitherso-
ever it may be carried by its animal
faculty, heavy bodies will always be
carried towards it. If the earth were
not round, heavy bodies would not tend
from every side in a straight line towards
the centre of the earth, but to different
points from different sides. I f two stones
were placed in any part of the world
near each other, and beyond the sphere of
influence of a third cognate body, these
stones, like two magnetic needles, would
come together in the intermediate point,
each approaching the other by a space
proportional to the comparative mass of
the other. If the moon and earth were
not retained in their orbits by their ani-
mal force or some other equivalent, the
earth would mount to the moon by a
lifty-fourth part of their distance, and
the moon fall towards the earth through
the other fifty-three parts and they would
there meet ; assuming however that the
substance of both is of the same density.
If the earth should cease to attract its
waters to itself, all the waters of the sea
would be raised and would flow to 1he
body Of the moon. The sphere of the at-

tractive virtue which is in the moon ex-
tends as far as the earth, and entices up
the waters ; but as the moon flies rapidly ,
across the zenith, and the waters cannot
follow so quickly, a flow of the ocean is
occasioned in the torrid zone towards
the westward. If the attractive virtue
of the moon extends as far as the earth,
it follows with greater reason that the
attractive virtue of the earth extends as
far as the moon, and much farther;
and in short, nothing which consists of
earthly substance any how constituted,
although thrown up to any height, can
ever escape the powerful operation of this
attractive virtue. Nothing which consists
of corporeal matter is absolutely light,
but that is comparatively lighter which
is rarer, either by its own nature, or by
accidental heat. And it is not to be
thought that light bodies are escaping to
the surface of the universe while they are
carried upwards, or that they are not
attracted by the earth. They are at-
tracted, but in a less degree, and so are
driven outwards by the heavy bodies ;
which being done, they stop, and are kept
by the earth in their own place. But
although the attractive virtue of the
earth extends upwards, as has been said,
so very far, yet if any stone should be at
a distance great enough to become sen-
sible, compared with the earth's dia-
meter, it is true that on the motion of
the earth such a stone would not follow
altogether ; its own force of resistance
would be combined with the attractive
force of the earth, and thus it would
extricate itself in some degree from the
motion of the earth/'

Who, after perusing such passages in
the works of an author, whose writings
were in the hands of every student of as-
tronomy, can believe that Newton waited
for the fall of an apple to set him think-
ing for the first time on the theory which
has immortalized his name ? An apple
may have fallen, and Newton may have
seen it; but such speculations as those
which it is asserted to have been the
cause of originating in him had been
long familiar to the thoughts of every
one in Europe pretending to the ritinu
of natural philosopher.

As Kepler always professed to have
derived his notion of a magnetic attrac-
tion among the planetary" bodies from
the writings of Gilbert, it may be worth
while to insert here an extract from the
" New Philosophy " of that author, to
show in what form lie presented a simi-
lar theory of the tides, winch aiibuls the

KEPLER.

25

most striking illustration of that attrac-
tion. This work was not published till
the middle of the seventeenth century,
but a knowledge of its contents may, in
several instances, be traced back to the
period in which it was writlen : —

" There are two primary causes of the
motion of the seas — the moon, and the
diurnal revolution. The moon does
not act on the seas by its rays or its
light. How then ? Certainly by the
common effort of the bodies, and (to ex-
plain it by something similar) by their
magnetic attraction. It should be known,
in the first place, that the whole quan-
tity of water is not contained in the sea
and rivers, but that the mass of earth (I
mean this globe) contains moisture and
spirit much deeper even than the sea.
The moon draws this out by sympathy,
so that they burst forth on the arrival of
the moon, in consequence of the at-
traction of that star ; and for the same
reason, the quicksands which are in the
sea open themselves more, and per-
spire their moisture and spirits during
the flow of the tide, and the whirlpools
in the sea disgorge copious waters ; and
as the star retires, they devour the same
again, and attract the spirits and mois-
ture of the terrestrial globe. Hence the
moon attracts, not so much the sea as
the subterranean spirits and humours ;
and the interposed earth has no more
power of resistance than a table or any
other dense body has to resist the force
of a magnet. The sea rises from the
greatest depths, in consequence of the
ascending humours and spirits ; and
when it is raised up, it necessarily flows
on to the shores, and from the shores it
enters the rivers/'*

This passage, sets in the strongest
light one of the most notorious errors of
the older philosophy, to which Kepler
himself was remarkably addicted. If
Gilbert had asserted, in direct terms,
that the moon attracted the water, it is
certain that the notion would have been
stigmatized (as it was for a long time in
Newton's hands) jas arbitrary, occult,
and unphilosophical : the idea of these
subterranean humours was likely to be
treated with much more indulgence. A
simple statement, that when the moon
was over the water the latter had a ten-
dency to rise towards it, was thought
to convey no instruction ; but the asser-
tion that the moon draws out subterra-
nean spirits by sympathy, carried with it

* De mundo nostro sublunari, Philosophia

Nova, Amsteiodami, JCoi,

a more imposing appearance of theory.
The farther removed these humoms
were from common experience, the
easier it became to discuss them in vague
and general language ; and those who
called themselves philosophers could
endure to hear attributes bestowed on
these fictitious elements which revolted
their imaginations when applied to things
of whose reality at least some evidence
existed.

It is not necessary to dwell upon the
system of Tycho Brahe, which was^ iden-
tical, as we have said, with one rejected
by Copernicus, and consisted in making
the sun revolve about the earth, carrying
with it all the other planets revolving
about him. Tycho went so far as to
deny the rotation of the earth to explain
the vicissitudes of day and night, but
even his favourite assistant Longomon-
tanus differed from him in this part of
his theory. The great merit of Tycho
Brahe, and the service he rendered to
astronomy, was entirely independent of
any theory ; consisting in the vast accu-
mulation of observations made by him
during a residence of fifteen years at
Uraniburg, with the assistance of instru-
ments, and with a degree of care, very far
superior to anything known before his
time in practical astronomy. Kepler is
careful repeatedly to remind us.that with-
out Tycho' s observations he could have
done nothing. The degree of reliance that
might be placed on the results obtained
by observers who acknowledged their in-
feriority to Tycho Brahe', maybe gathered
from an incidental remark of Kepler to
Longomontanus. He had been examin-
ing Tycho' s registers, and had occasion-
ally found a difference amounting some-
times to 4' in the right ascensions of the
same planet, deduced from different stars
on the same night. Longomontanus
could not deny the fact, but declared that
it was impossible to be always correct
within such limits. The reader should
never lose sight of this uncertainty in
the observations, when endeavouring to
estimate the difficulty of finding a theory
that would properly represent them.

When Kepler first joined Tycho Brahe
at Prague, he found him and Longomon-
tanus very busily engaged in correct-
ing the theory of Mars, and accordingly
it was this planet to which he also first
directed his attention. They had formed
a catalogue of the mean oppositions of
Mars during twenty years, and had disco-
vered a position of the equant, which (as
they said) represented them with tolerable

KEPLER.

exactness. On the other hand, they were
much embarrassed by the unexpected
difficulties they met in applying a sys-
tem which seemed on the one hand so
accurate, to the determination of the lati-
tudes, with which it could in no way be
made to agree. Kepler had already sus-
pected the cause of this imperfection, and
was confirmed in the 'view he took of
their theory, when, on a more careful
examination, he found that they over-
rated the accuracy even of their longi-
tudes. The errors in these, instead of
amounting as they said, nearly to 2',
rose sometimes above 21'. In fact they
had reasoned ill on their own principles,
and even if the foundations of their
theory had been correctly laid, could not
have arrived at true results. But Kepkr
had satisfied himself of the contrary,
and the following diagram shews the na-
ture of the first alteration he introduced,
not perhaps so celebrated as some of his
later discoveries, but at least of equal
consequence to astronomy, which could
never have been extricated from the
confusion into which it had fallen, till
this important change had been effected.
The practice of Tycho Brahe, indeed
of all astronomers till the time of Kepler,
had been to fix the position of the pla-
net's orbit and equant from observa-
tions on its mean oppositions, that is to
say, on the times when it was precisely
six signs or half a circle distant from
the mean place of the sun. In the
annexed figure, let S represent the sun,
C the centre of the earth's orbit, T /.

Tycho Brahe's practice amounted to this,
that if Q were supposed the place of the
centre of the planet's equant, the centre
of P p its orbit was taken in Q C, and not
in Q S, as Kepler suggested that it ought
to Le taken. The consequence of this
erroneous practice was, that the observa-

tions were deprived of the character for
which oppositions were selected, of being
entirely tree from the second inequalities.
It followed therefore that as part of
the second inequalities were made con-
ducive towards fixing the relative posi-
tion of the orbit and equant, to which
they did not naturally belong, there was
an additional perplexity in accounting
for the remainder of them by the size
and motion of the epicycle. As the line
of nodes of every planet was also made to
pass through C instead of S, there could
not fail to be corresponding errors in the
latitudes. It would only be in the rare
case of an opposition of the planet, in
the line C S, that the time of .its taking
place would be the same, whether O, the
centre of the orbit, was placed in C Q or
S Q. Every other opposition would in-
volve an error, so much the greater as
it was observed at a greater distance
from the line G S.

It was long however before Tycho
Brahe could be made to acquiesce in the
propriety of the proposed alteration ; and,
in order to remove his doubts as to the
possibility that a method could be erro-
neous which, as he still thought, had
given him such accurate longitudes,
Kepler undertook the ungrateful labour
of the first part of his " Commentaries."
He there shewed, in the three systems of
Copernicus, Tycho Brahe, and Ptolemy,
and in both the concentric and excentric
theories, that though a false position
were given to the orbit, the longitudes
of a planet might be so represented, by
a proper position of the centre of the
equant, as never to err in oppositions
above 5' from those given by observa-
tion ; though the second inequalities and
the latitudes would thereby be very
greatly deranged.

The change Kepler introduced, of ob-
serving apparent instead of mean oppo-
sitions, made it necessary to be very ac-
curate in his reductions of the planet's
place to the ecliptic ; and in order to be
able to do this, a previous knowledge of
the parallax of Mars became indispen-
sable. His next labour was therefore
directed to this point ; and finding that
the assistants to whom Tycho Brahe had
previously committed this labour had
performed it in a negligent and imper-
fect manner, he began afresh with
Tycho's original observations. Having
satisfied himself as to the probable limits
of his errors in the parallax on which
he finally fixed, he proceeded to de-
termine the inclination of the orbit and

KEPLER.

Ihe position of the line of nodes. In
all these operations his talent for as-
tronomical inquiries appeared pre-emi-
nent in a variety of new methods by
which he combined and availed him-
self of the observations ; but it must be
sufficient merely to mention this fact,
without entering into any detail. One
important result may be mentioned, at
which he arrived in the course of them,
the constancy of the inclination of the
planet's orbil, which naturally strength-
ened him in his new theory.

Having gone through these preliminary
inquiries, he came at last to fix the pro-
portions of the orbit ; and, in doing so, he
determined, in the first instance, not to as-
sume, as Ptolemy appeared to have done
arbitrarily, the bisection of the excen-
tricity, but to investigate its proportion
along with the other elements of the orbit,
which resolution involved him in much
more laborious calculations. After he
had gone over all the steps of his theory no
less than seventy times — an appalling la-
bo ur,especially if we remember that loga-
rithms were not then invented — his final
result, was, that in 1587, on the 6th of
March, at 7h 23', the longitude of the
aphelion of Mars was 4s 28° 48' 55" ;
that the planet's mean longitude was
6s 0° 51' 357; that if the semidiameter of
the orbit was taken at 1000UO, the excen-
tricity was 1 1 332 ; and the excentricity of
the equant 18564. He fixed the radius
of the greater epicycle at 14988, and
that of the smaller at 3628.

When he came to compare the longi-
tudes as given by this, which he after-
wards called the vicarious theory, with
the observations at opposition, the result
seemed to promise him the most bril-
liant success. His greatest error did
not exceed 2'; but, notwithstanding
these flattering anticipations, he soon
found by a comparison of longitudes
out of opposition and of latitudes, that
it was yet far from being so com-
plete as he had imagined, and to his in-
finite vexation he soon found that the
labour of four years, which he had ex-
pended on this theory, must be consi-
dered almost entirely fruitless. Even
his favourite principle of dividing the
excentricity in a different ratio from
Ptolemy, was found to lead him ' into
greater error than if he had retained the
old bisection. By restoring that, he made
his latitudes more accurate, but pro-
duced a corresponding change for the
worse in his longitudes ; and although

the errors of 8', to which they now

-

amounted, would probably have been
disregarded by former theorists, Kepler
could not remain satisfied till they were
accounted for. Accordingly he found
himself forced to the conclusion that
one of the two principles on which this
theory rested must be erroneous ; either
the orbit of the planet is not a perfect
circle, or there is no fixed point within
it round which it moves with an uniform
angular motion. He had once before ad-
mitted the possibility of the former of
these facts, conceiving it possible that the
motion of the planets is not at all curvi-
linear, but that they move in polygons
round the sun, a notion to which he pro-
bably inclined in consequence of his fa-
vourite harmonics and geometrical
figures.

In consequence of the failure of a
theory conducted with such care in all
its practical details, Kepler determined
that his next trial' should be of an en-
tirely different complexion. Instead of
first satisfying the first inequalities of
the planet, and then endeavouring to ac-
count for the second inequalities, he re-
solved to reverse the process, or, in
other words, to ascertain as accurately
as possible what part of the planet's
apparent motion should be referred
solely to the optical illusion produced
by the motion of the earth, before pro-
ceeding to any inquiry of the real in-
equality of the planet's proper motion.
It had been hitherto taken for granted,
that the earth moved equably round the
centre of its orbit ; but Kepler, on re-
suming the consideration of it, recurred
to an opinion he had entertained very
early in his astronomical career (rather
from his conviction of the existence of
general laws, than that he had then felt
the want of such a supposition), that it
required an equant distinct from its
orbit no Jess than the other planets.
He now saw, that if this were admitted,
the changes it would everywhere intro-
duce in the optical part of the planet's
irregularities might perhaps relieve him
from the perplexity "in which the vica-
rious theory had involved him. Ac-
cordingly he applied himself with re-
newed assiduity to the examination of
this important question, and the result
of his calculations (founded principally
on observations of Mars' parallax) soon
satisfied him not only that the earth's
orbit does require such an equant, but
that its centre is placed according to the
general law of the bisection of the ex-
centricity which he had previously found

23

KEPLER.

indispensable in the other planets. This
\v as an innovation of the first magni-
tude, and accordingly Kepler did not
venture to proceed farther in his theory,
till by evidence of the most varied and
satisfactory nature, he had established
it beyond the possibility of cavil.

It may be here remarked, that this
principle of the bisection of the eccen-
tricity, so familiar to the Ptolemaic as-
tronomers, is identical with the theory
afterwards known by the name of the
simple elliptic hypothesis, advocated by.
Seth Ward and others. That hypothesis*
consisted in supposing the sun to be
placed in one focus of the elliptic orbit
of the planet, whose angular motion was
uniform round the other focus. In
Ptolemaic phraseology, that other focus
was the centre of the equant, and it is
well known that the centre of the ellipse
lies in the middle point between the two
foci.

It was at this period also, that Kepler
first ventured upon the new method of
representing inequalities which termi-
nated in one of his most celebrated dis-
coveries. We have already seen, in the
account of the " Mysterium Cosmogra-
phicum," that he was speculating, even
at that time, on the effects of a whirling
force exerted by the sun on the planets
with diminished energy at increased dis-
tances, and on the proportion observed
between the distances of the planets from
the sun, and their periods of revolution.
He seems even then to have believed in
the possibility of discovering a relation
between the tinges and distances in dif-
ferent planets. Another analogous con-
sequence of his theory of the radiation of
the whirling force would be, that if the
same planet should recede to a greater
distance from the central body, it would
be acted on by a'diminished energy of
revolution, and consequently, a relation
might be found between the velocity at
any point of its orbit, and its distance
at that point from the sun. Hence he
expected to derive a more direct and
natural method of calculating the in-
equalities, than from th.3 imaginary
equant. But these ingenious ideas had
been checked in the outset by the errone-
ous belief which Kepler, in common with
other astronomers, then entertained of
the coincidence of the earth's equantr
with its orbit ; in other words, by the
belief that the earth's linear motion was
uniform, though it was known not to
remain constantly at the same distance
from the sun, As soon as this prejudice

was removed, his former ideas recurred
to him with increased force, and he set
himself diligently to consider what re-
lation could be found between the ve-
locity and distance of a planet from tli3
sun. The method he adopted in the be-
ginning of this inquiry was to assume
as approximately correct Ptolemy's doc-
trine of the bisection of the excentricity,
and to investigate some simple relation
nearly representing the same effect.

In the annexed figure, S is the place
of the sun, C the centre of the planet's

orbit A B a b, Q the centre of the equant
represented by the equal circle D E d e,
AB, ab, two equal small arcs described
by the planet at the apsides of its orbit :
then, according to Ptolemy's principles,
the arc D E of the equant would be pro-
portional to the time of passing along
A B, on the same scale on which de would
represent the time of passing through
the equal arc a b.

Q D ; Q A : : D E : A B, nearly ; and
because Q S is bisected in C, Q A, CA
or Q D, and S A, are in arithmetical
proportion: and, therefore, since an
arithmetical mean, when the difference
is small, does not differ much from a
geometrical mean, Q D : Q A : : S A :
Q D, nearly. Therefore, D E : A B :.:
S A : Q D, nearly, and in the same man-
ner d e : a b : : S a : Qd nearly ; and
therefore DE: c?e : : S A : S a nearly.
Therefore at the apsides, the times of
passing over equal spaces, on Ptolemy's
theory, are nearly as the distances from
the sun, and Kepler, with his usual
hastiness, immediately concluded that
this was the accurate and general law,
and that the errors of the old theory
arose solely from having departed from ii.

It followed immediately from this
assumption, that after leaving the point
A, the time in which the planet would

KEPLER.

29

arrive at any point P of its orbit
would be proportional to, and might be
represented by, the sums of all the lines
that could be drawn from S to the arc
A P, on the same scale that the whole
period of revolution would be denoted by
the sum of all the lines drawn to every
point of the orbit. Kepler's first at-
tempt to verify this supposition ap-
proximately, was made by dividing the
whole circumference of the orbit into
360 equal parts, and calculating the
distances at every one of the points of
division. Then supposing the planet to
move uniformly, and to remain at the
same distance from the sun during the
time of passing each one of these divisions,
(a supposition which manifestly would not
differ much from the former one, and
would coincide with it more nearly, the
greater was the number of divisions
taken) he proceeded to add together these
calculated distances, and hoped to find
that the time of arriving at any one of the
divisions bore the same ratio to the whole
period, as the sum of the corresponding
set of distances did to the sum of the
whole 360.

This theory was erroneous ; but by al-
most miraculous good fortune, he was
led by it in the following manner to the
true measure. The discovery was aeon-
sequence of the tediousness of his first
method, which required, in order to
know the time of arriving at any point,
that the circle should be subdivided, until
one of the points of division fell exactly
upon the given place. Kepler therefore
endeavoured to discover some shorter
method of representing these sums of
the distances. The idea then occurred
to him of employing for that purpose
the area inclosed between the two dis-
tances, S A, S P, and the arc A P,
in imitation of the manner in which
he remembered that Archimedes had
found the area of the circle, by dividing
it into an infinite number of small tri-
angles by lines drawn from the centre.
He hoped therefore to find, that the
time of passing from A to P bore nearly
the same ratio to the whole period of
revolution that the area ASP bore to
the whole circle.

This last proportion is in fact accu-
rately observed in the revolution of one
body round another, in consequence of
an attractive force in the central body.
Newton afterwards proved this, ground-
ing his demonstration upon laws of
motion altogether irreconcileable with
Kepler's opinions ; and it is impossible

not to admire Kepler's singular good
fortune in arriving at this correct result
in spite, or rather through the means, of
his erroneous principles. It is true that
the labour which he bestowed unspar-
ingly upon every one of his successive
guesses, joined with his admirable can-
dour, generally preserved him from long
retaining a theory altogether at variance
with observations ; and if any relation
subsisted between the times and dis-
tances which could any way be express-
ed by any of the geometrical quantities
under consideration, he could scarcely
have failed — it might be twenty years
earlier or twenty years later, — to light
upon it at last, having once put his in-
defatigable fancy upon this scent. But
in order to prevent an over-estimate of
his merit in detecting this beautiful law
of nature, let us for a moment reflect
what might have been his fate had he
endeavoured in the same manner, and
with the same perseverance, to discover
a relation, where, in reality, none exist-
ed. Let us take for example the incli-
nations or the excentricities of the
planetary orbits, among which no rela-
tion has yet been discovered ; and if any
exists, it is probably of too complicated
a nature to be hit at a venture. If Kep-
ler had exerted his ingenuity in this
direction, he might have wasted his life
in fruitless labour, and whatever repu-
tation he might have left behind him as
an industrious calculator, it would have
been very far inferior to that which has
procured for him the proud title of the
" Legislator of the Heavens."

However this may be, the immediate
consequence of thus lighting upon the
real law observed by the earth in its pas-
sage round the sun was, that he found
himself in possession of a much more ac-
curate method of representing its inequa-
lities than had been reached by any of his
predecessors ; and with renewed hopes
he again attacked the planet Mars,
whose path he was now able to Consider
undistorted by the illusions arising out
of the motion of the earth. Had the
path of Mars been accurately circular,
or even as nearly approaching a circle as
that of the earth, the method he chose
of determining its position and size by
means of three distances carefully
calculated from his observed parallaxes,
would have given a satisfactory result ;
but finding, as he soon did, that almost
every set of three distances led him to a
different result, he began to suspect
another error in the long-received opi-

30

KEPLER.

nion, that the orbits of the planets must
consist of a combination of circles ; he
therefore determined, in the first in-
stance, to fix the distances of the planet
at the apsides without any reference to
the form of the intermediate orbit. Half
the difference between these would, of
course, be the excentricity of the orbit ;
and as this quantity came out very
nearly the same as had been determined
on the vicarious theory, it seemed clear
that the error of that theory, whatever it
might be, did not lie in these elements.

Kepler also found that in the case of
this planet likewise, the times of describ-
ing equal arcs at the apsides were pro-
portional to its distances from the sun,
and he naturally expected that the me-
thod of areas would measure the planet's
motion with as much accuracy as he had
found in the case of the earth. This hope
was disappointed : when he calculated the
motion of the planet by this method, he
obtained places too much advanced when
near the apsides, and too little advanced
at the mean distances. He did not, on
that account, immediately reject the
opinion of circular orbits, but was
rather inclined to suspect the principle
of measurement, at which he felt that
he had arrived in rather a precarious
manner. He was fully sensible that
his areas did not accurately represent
the sums of any distances except those
measured from the centre of the circle ;
and for some time he abandoned the
hope of beino; able to use this substitu-
tion, which he always considered merely
as an approximate representation of the
true measure, the sum of the distances.
But on examination he found that the
errors of this substitution were nearly
insensible, and those it did in fact pro-
duce, were in the contrary direction of
the errors he was at this time combating.
As soon as he had satisfied himself of
this, he ventured once more on the sup-
position, which by this time had, in his
eyes, almost acquired the force of demon-
stration, that the orbits of the planets
are not circular, but of an oval form,
retiring within the circle at the mean
distances, and coinciding with it at the
apsides.

This notion was not altogether new ;
it had been suggested in the case of
Mercury, by Purbach, in his " Theories
of the Planets." In the edition of this
work published by Reinhold, the pupil
of Copernicus, \ve read the following
passage. " Sixthly, it appears from
what lias been said, that the centre of

Mercury's epicycle, by reason of the
motions above-mentioned, does not, as
is the case with the other planets, de-
scribe the circumference of a circular
deferent, but rather the periphery of a
figure resembling a plane oval." To this
is added the following note by Reinhold.
" The centre of the Moon's epicycle de-
scribes a path of a lenticular shape ;
Mercury's on the contrary is egg-shaped,
the big end lying towards his apogee,
and the little end'towards his perigee*."
The excentricity of Mercury's orbit is,
in fact, much greater than "that of any
of the other planets, and the merit of
making this first step cannot reasonably
be withheld from Purbach and his com-
mentator, although they did not pursue
the inquiry so far as Kepler found him-
self in a condition to do.

Before proceeding to the considera-
tion of the particular oval which Kepler
fixed upon in the first instance, it will
be necessary, in order to render intelli-
gible the source of many of his doubts
and difficulties, to make known some-
thing more of his theory of the moving
force by which he supposed the planets
to be carried round in their orbits. In
conformity with the plan hitherto pur-
sued, this shall be done as much as pos-
sible in his own words.

" It is one of the commonest axioms in
natural philosophy, that if two things al-
ways happen together and in the same
manner, and admit the same measure,
either the one is the cause of the other,
or both are the effect of a common cause.
In the present case, the increase or lan-
guor of motion invariably corresponds
with an approach to or departure from
the centre of the universe. Therefore,
either the languor is the cause of the
departure of the star, or the departure
of the languor, or both have a common
cause. But no one can be of opinion
that there is a concurrence of any third
thing to be a common cause of these
two effects, and in the following chap-
ters it will be made clear that there is
no occasion to imagine any such third
thing, since the two are of themselves
sufficient. Now, it is not agreeable to
the nature of things that activity or
languor in linear motion should be the
cause of distance from the centre. For,
distance from the centre is conceived
anteriorly to linear motion. In fact
linear motion cannot exist without dis-

* Theories novre plauetarum. G. Purbachii,
rurisiis, K>'>o.

KEPLER.

31

tance from the centre, since it requires
space for its accomplishment, but dis-
tance from the centre can be conceived
without motion. Therefore distance is
the cause of the activity of motion, and
a greater or less distance of a greater or
less delay. And since distance is of the
kind of relative quantities, whose es-
sence consists in boundaries, (for there
is no efficacy in relation per se without
regard to bounds,) it follows that the
cause of the varying activity of motion
rests in one of the boundaries. But the
body of the planet neither becomes
heavier by receding, nor lighter by ap-
proaching. Besides, it would perhaps
be absurd on the very mention of it,
that an animal force residing in the
moveable body of the planet for the pur-
pose of moving it, should exert and re-
lax itself so often without weariness or
decay. It remains, therefore, that the
cause of this activity and languor re-
sides at the other boundary, that is, in
the very centre of the world, from which
the distances are computed. — Let us
continue our investigation of this mov-
ing virtue which resides in the sun, and
we shall presently recognize its very
close analogy to light. And although
this moving virtue cannot be identical
with the light of the sun, let others look
to it whether the light is employed as
a sort of instrument, or vehicle, to con-
vey the moving virtue. There are these
seeming contradictions: — first, light is
obstructed by opaque bodies, for which
reason if the moving virtue travelled on
the light, darkness would be followed
by a stoppage of the moveable bodies.
Again, light flows out in right lines
spherically, the moving virtue in right
lines also, but cylindrically ; that is, it
turns in one direction only, from west to
east ; not in the opposite direction, not
towards the poles, &c. But perhaps
we shall be able presently to reply to
these objections. In conclusion, since
there is as much virtue in a large and
remote circle as in a narrow and close
one, nothing of the virtue perishes in
the passage from its source, nothing is
scattered between the source and the
moveable. Therefore the efflux, like that
of light, is not material, and is unlike that
of odours, which are accompanied by a
loss of substance, unlike heat from a
raging furnace, unlike eveiy other ema-
nation by which mediums are filled. It
remains, therefore, that as %ht which .
illuminates all earthly things, is the im-
material species of that fire which is in

the body of the sun, so this virtue, em-
bracing and moving all the planetary
bodies, is the immaterial species of that
virtue which resides in the sun itself, of
incalculable energy, and so the primary
act of all mundane motion. — I should
like to know who ever said that there
was anything material in light ! — Guided
by our notion of the efflux of this
species (or archetype), let us con-
template the more intimate nature of
the source itself. For it seems as, if
something divine were latent in the body
of the sun, and comparable to our own
soul, whence that species emanates
which drives round the planets ; just as
from the mind of a slinger the species
of motion sticks to the stones, and car-
ries them forward, even after he who
cast them has drawn back his hand.
But to those who wish to proceed
soberly, reflections differing a little from
these will be offered."

Our readers will, perhaps, be satisfied
with the assurance, that these sober
considerations will not enable them to
form a much more accurate notion of
Kepler's meaning than the passages
already cited. We shall therefore pro-
ceed to the various opinions he enter-
tained on the motion of the planets.

He considered it as established by his
theory, that the centre E of the planet's
epicycle (see fig. p. 33.) moved round
the circumference of the deferent ~Dd,
according to the law of the planet's dis-
tances ; the point remaining to be settled
was the motion of the planet in the
epicycle. If it were made to move ac-
cording to the same law, so that when
the centre of the epicycle reached E,the
planet should be at F, taking the angle
BEF equal to BSA, it has been shewn
(p. 19) that the path of F would still be
a circle, excentric from Dd by DA the
radius of the epicycle.

But Kepler fancied that he saw many
sound reasons why this could not be the
true law of motion in the epicycle, on
which reasons he relied much more
firmly than on the indisputable fact,
which he mentions as a collateral proof,
that it was contradicted by the observa-
tions. Some of these reasons are sub-
joined : " In the beginning of the work
it has been declared to be most absurd,
that a planet (even though we suppose
it endowed with mind) should form any
notion of a centre, and a distance from
it, if there be no body in that centre to
serve for a distinguishing mark. And
although you should say, that the planet

32

KEPLER.

has respect to the sun, and knows be-
forehand, and remembers the order in
which the distances from the sun are
comprised, so as to make a perfect ex-
centric ; in the first place, this is rather
far-fetched, and requires, in any mind,
means for connecting the effect of an
accurately circular path with the sign
of an increasing and diminishing dia-
meter of the sun. Butthere are no
such means, except the position of the
centre of the excentric at a given dis-
tance from the sun ; and I have already
said, that this is beyond the power of a
mere mind. I do not deny that a centre
may be imagined, and a circle round it ;
but this I do say, if the circle exists
only in imagination, with no external
sign or division, that it is not possible
that the path of a moveable body should
be really ordered round it in an exact
circle. Besides, if the planet chooses
from memory its just distances from
the sun, so as exactly to form a circle,
it must also take from the same source,
as if out of the Prussian or Alphonsine
tables, equal excentric arcs, to be de-
scribed in unequal times, and to be de-
scribed by a force extraneous from the
sun ; and thus would have, from its
memory, a foreknowledge of what effects
a virtue, senseless and extraneous from
the sun, was about to produce : all these
consequences are absurd."

" It is therefore more agreeable 'to
reason that the planet takes no thought,
either of the excentric or epicycle ; but
that the work which it accomplishes, or
joins in effecting, is a libratory path in
the diameter B b of the epicycle, in the
direction towards the sun. The law is
now to be discovered, according to which
the planet arrives at the proper distances
in anytime. And indeed in this inquiry,
it is easier to say what the law is not
than what it is/' — Here, according to his
custom, Kepler enumerates several laws
of motion by which the planet might
choose to regulate its energies, each of
which is successively condemned. Only
one of them is here mentioned, as a spe-
cimen of the rest. " What then if we
were to say this ? Although the motions
of the planet are not epicyclical, perhaps
the libration is so arranged that the dis-
tances from the sun are equal to what
they would have been in a real epicycli-
cal motion. — This leads to more incredi-
ble consequences than the former suppo-
sitions, and yet in the dearth of better
opinions, let us for the present content
ourselves with this. The greater num-

ber of absurd conclusions it will be found
to involve, the more ready will a physi-
cian be, when we come to the fifty- second
chapter, to admit what the observations
testify, that the path of the planet is not
circular."

The first oval path on which Kepler
was induced to fix, by these and many
other similar considerations, was in the
first instance very different from the
true elliptical form. Most authors would
have thought it unnecessary to detain
their readers with a theory which they
had once entertained and rejected ; but
Kepler's work was written on a different
plan. He thus introduces an explana-
tion of his first oval. " As soon as I
was thus taught by Brahe's very accu-
rate observations that the orbit of a pla-
net is not circular, but more compressed
at the sides, on the instant 1 thought
that I understood the natural cause of
this deflection. But the old proverb was
verified in my case ; — the more haste the
less speed. — For having violently la-
boured in the 39th chapter, in conse-
quence of my inability to find a suffi-
ciently probable cause why the orbit of
the planet should be a perfect circle,
(some absurdities always remaining with
respect to that virtue which resides in
the body of the planet,) and having now
discovered from the observations, that
the orbit is not a perfect circle, I felt fu-
riously inclined to believe that if the
theory which had been recognized as
absurd, when employed in the 39th
chapter for the purpose of fabricating a
circle, were modulated into a more pro-
bable form, it would produce an accurate
orbit agreeing with the observations.
If I had entered on this course a little
more warily, I might have detected the
truth immediately. But, being blinded
by my eagerness, and not sufficiently re-
gardful of every part of the 39th chapter,
and clinging to my first opinion, which
offered itself to me with a wonderful
show of probability, on account of the
equable motion in the epicycle, I got en-
tangled in new perplexities, with which
we shall now have to struggle in this
45th chapter and the following ones as
far as the 50th chapter."

In this theory, Kepler supposed that
whilst the centre of the epicycle was
moving round a circular deferent accord-
ing to the law of the planets' distances
(or areas) the planet itself moved equably
in the epicycle, with the mean angular
velocity of its centre in the deferent.
In consequence of this.supposjtion, since

KEPLER.

33

at D, when the planet is at A. the aphe-
lion, the motion in the deferent is less than
the mean motion, the planet will have ad-
vanced through an angle B E P greater
than B E F or B S A, through which the
centre of the epicycle has moved ; and
consequently, the path will lie every-
where within the circle A a, except at
the apsides. Here was a new train of
laborious calculations to undergo for the
purpose of drawing the curve AP a
according to this law, and of measuring
the area of any part of it. After a
variety of fruitless attempts, for this
curve is one of singular complexity, he
was reduced, as a last resource, to sup-
pose it insensibly different from an
ellipse on the same principal axes, as an
approximate means of estimating its
area. Not content even with the results
so obtained, and not being able to see
very clearly what might be the effect of
his alteration in substituting the ellipse
for the oval, and in other simplifications
introduced by him, he had courage
enough to obtain the sums of the
360 distances by direct calculation, as
he had done in the old circular theory.

In the preface to his book he had spoken
of his labours under the allegory of a
war carried on by him against the planet;
and when exulting in the early prospects
of success this calculation seemed to
offer, he did not omit once more to warn
his readers, in his peculiar strain, that
this exultation was premature.

" Allow me, gentle reader, to enjoy
so splendid a triumph for one little day
(I mean through the five next chapters),
meantime be all rumours suppressed of
new rebellion, that pur preparations
may not perish, yielding us no delight.
Hereafter if anything shall come to pass,
we will go through it in its own time and
season ; now let us be merry, as then
we will be bold and vigorous." At the
time foretold, that is to say, at the end

of the five merry chapters, the bad news
could no longer be kept a secret. It is
announced in the following bulletin : —
" While thus triumphing over Mars,
and preparing for him, as for one
altogether vanquished, tabular prisons,
and equated eccentric fetters, it is
buzzed here and there that the victory
is vain, and that the war is raging
anew as violently as before. For the
enemy, left at home a despised captive,
has burst all the chains of the equations,
and broken forth of the prisons of the
tables. For no method of geometrically
administering the theory of the 45th
chapter was able to come near the accu-
racy of approximation of the vicarious
theory of the 16th chapter, -which gave
me true equations derived from false
principles. Skirmishers, disposed all
round the circuit of the excentric, (I
mean the true distances,) routed my
forces of physical causes levied out of
the '45th chapter, and shaking off the
yoke, regained their liberty. And now
there was little to prevent the fugitive
enemy from effecting a junction with his
rebellious supporters, and reducing me
to despair, had I not suddenly -sent into
the field a reserve of new physical rea-
sonings on the rout and dispersion of the
veterans, and diligently followed, with-
out allowing him the slightest respite, in
the direction in which he had broken
out.'7

In plainer terms, Kepler found, after
this labour was completed, that the
errors in longitude he was still subject
to were precisely of an opposite nature
to those he had found with the circle ;
instead of being too quick at the ap-
sides, the planet was now too slow there,
and too much accelerated in the mean
distances ; and the distances obtained
from direct observation were every-
where greater, except at the apsides,
than those furnished by this oval theory.
It was in the course of these tedious
investigations that he established, still
more satisfactorily than he had before
done, that the inclinations of the planets'
orbits are invariable, and that the lines
of their nodes "pass through the centre
of the Sun, and not, as before his time
had been supposed, through the centre
of the ecliptic.

When Kepler found with certainty
that this oval from which he expected
so much would not satisfy the obser-
vations, his vexation was extreme, not
merely from the mortification of finding
a theory confuted on which he had spent

KEPLER.

such excessive labour, for he was accus-
tomed to disappointments of that kind,
but principally from many anxious and
fruitless speculations as to the real phy-
sical causes why the planet did not move
in the supposed epicycle, that being the
point of view, as has been already shewn,
from which he always preferred to begin
his inquiries. One part of the reason-
ing by which he reconciled himself to
the failure exhibits much too curious a
view of the state of his mind to be
passed over in silence. The argument
is founded on the difficulty which he
met with, as abovementioned, in calcu-
lating the proportions of the oval path
he had imagined. "In order that
you may see the cause of the impracti-
cability of this method which we have
just gone through, consider on what
foundations it rests. The planet is sup-
posed to move equably in the epicycle,
and to be carried by the Sun unequably
in the proportion of the distances. But
by this method it is impossible to be
known how much of the oval path cor-
responds to any given time, although
the distance at that part is known, un-
less we first know the length of the
whole oval. But the length of the oval
cannot be known, except from the law
of the entry of the planet within the
sides of the circle. But neither can the
law of this entry be known before we
know how much of the oval path cor-
responds to any given time. Here you
see that there is a petitio principii ; and
in my operations I was assuming that of
which [ was in search, namely,the length
of the oval. This is at least not the
fault of my understanding, but it is also
most alien to the primary Ordainer of
the planetary courses : I have never yet
found so ungeometrical a contrivance
in his other works. Therefore we must
either hit upon some other method of
reducing the theory of the 45th chapter
to calculation ; or if that cannot be done,
the theory itself, suspected on account of
{\\ispetitioprincipii, will totter." Whilst
his mind was thus occupied, one of those
extraordinary accidents which it has been
said never occur but to those capable
of deriving advantage from them (but
which, in fact, are never noticed when
they occur to any one else), fortunately

Sit him once more upon the right path,
alf the extreme breadth between the
oval and the circle nearly represented the
errors of his distances at the mean point,
and he found that this half was 429 parts
of a radius, consisting of 100000 parts ;

and happening to advert to the greatest
optical inequality of Mars, which amounts
to about 5° 18', it struck him that 429
was precisely the excess of the secant of
5° 18' above the radius taken at 100000.
This was a ray of light, and, to use his
own words, it roused him as out of sleep.
In short, this single observation was
enough to produce conviction in his
singularly constituted mind, that instead
of the distances S F, he should every-
where substitute F V, determined by
drawing S V perpendicular on the line
F C, since the excess of S F above F V
is manifestly that of the secant above
the radius in the optical equation S F C
at that point. It is still more extraor-
dinary that a substitution made for such
a reason should have the luck,"as is
again the case, to be the right one.
This substitution in fact amounted to
supposing that the planet, instead of
being at the distance S P or S F, was
at S n ; or, in other words, that instead of
revolving in the circumference, it librated
in the diameter of the epicycle, which was
to him an additional recommendation.
Upon this new supposition a fresh set of
distances was rapidly calculated, and to
Kepler's inexpressible joy, they were
found to agree with the observations
within the limits of the errors to which
the latter were necessarily subject; Not-
withstanding this success, he had to
undergo, before arriving at the success-
ful termination of his labours, one more
disappointment. Although the distance
corresponding to a time from the aphe-
lion represented approximately by the
area ASF, was thus found to be accu-
rately represented by the line S n, there
was still an error with regard to the di-
rection in which that distance was to be
measured. Kepler's fir.^t idea was to set
it off in the direction S F, but this he
found to lead to inaccurate longitudes ;

KEPLEtt.

35

and it was not until after much per-
plexity, driving him, as he tells us,
"almost to insanity," that he satisfied
himself that the distance S Q tqual to
FV ought to betaken terminating in
F m, the line from F perpendicular to A a,
the line of apsides, and that the curve so
traced out by Q would be an accurate
ellipse.

He then found to his equal gratification
and amazement, a small part of "which he
endeavoured to express by a triumphant'
figure on the side of his diagram, that
the error he had committed in taking the
area A S F to represent the sums of the
distances S F, was exactly counterba-
lanced ; for this area does accurately
represent the sums of the distances F V or
S Q. This compensation, which seemed
to Kepler the greatest confirmation of
his theory, is altogether accidental and
immaterial, resulting from the relation
between the ellipse and circle. If the
laws of planetary attraction had chanced
to have been any other than those which
cause them to describe ellipses, this last
singular confirmation of an erroneous
theory could not have taken place, and
Kepler would have been forced either to
abandon the theory of the areas, which
even then would have continued to mea-
sure and define their motions, or to re-
nounce the physical opinions from which
he professed to have deduced it as an
approximative truth.

These are two of the three celebrated
theorems called Kepler's laws: the first
is, that the planets move in ellipses round
the sun, placed in the focus ; the second,
that the time of describing any arc is
proportional in the same orbit to the
area included between the arc and the
two bounding distances from the sun.
The third will be mentioned on another
occasion, as it was not discovered till
twelve years later. On the establish-
ment of these two theorems, it became
important to discover a method of mea-
suring such elliptic areas, but this is a
problem which cannot be accurately
solved. Kepler, in offering it to the
attention of geometricians, stated his be-
lief that its solution was unattainable by
direct processes, on account of the in-
commensurability of the arc and sine, on
which the measurement of the two parts
AQm, SQm depends. " This," says
he in conclusion, " this is my belief, and
whoever shall shew my mistake, and
point out the true solution,

/* Grit mihi magnus Apollonius"

CHAPTER VI.

Kepler appointed Professor at Linz—
His second marriage — Publishes his
new Method of Gauging — Refuses a
Professorship at Bologna.

WHEN presenting this celebrated book
to the emperor, Kepler gave notice
that he contemplated a farther attack
upon Mars's relations, father Jupiter,
brother Mercury, and the rest; and
promised that he would be successful,
provided the emperor would not forget
the sinews of war, and order him to be
furnished anew with means for recruit-
ing his army. The death of his unhappy
patron, the Emperor Rodolph, which
happened in 1612, barely in time to save
him from the last disgrace of deposition
from the Imperial throne, seemed to put
additional difficulties in the way of Kep-
ler's receiving the arrears so unjustly
denied to him ; but on the accession of
Rodolph's brother, Matthias, he was
again named to his post of Imperial Ma-
thematician, and had also a permanent
professorship assigned to him in the Uni-
versity of Linz. He quitted Prague with-
out much regret, where he had struggled
against poverty during eleven years.
Whatever disinclination he might feel to
depart, arose from his unwillingness to
loosen still more the hold he yetretained
upon the wreck of Tycho Brahe's instru-
ments and observations. Tengnagel,
son-in-law of Tycho, had abandoned as-
tronomy for a political career, and the
other members of his family, who were
principally females, suffered the costly
instruments to lie neglected and for-
gotten, although they had obstructed
with the utmost jealousy Kepler's at-
tempts to continue their utility. The
only two instruments Kepler possessed
of his own property, were " An iron
sextant of 2£ feet diameter, and a brass
azimuthal quadrant, of 3 4 feet diameter,
both divided into minutes of a degree."
These were the gift, of his friend and
patron, Hoffman, the President of Styria,
and with these he made all the obser-
vations which he added to those of
Tycho Brahe. His constitution was not
favourable to these studies, his health
being always delicate, and suffering
much from exposure to the night air ;
his eyes also were very weak, as he men-
tions himself in several places. In the
summary of his character which he
drew up when proposing to beco.ne
Tycho Brahe's assistant, he describes
himself as follows : — " For observations

36

KEPLER.

my sight is dull ; for mechanical opera-
tions my hand is awkward ; in politics
and domestic matters my nature is
troublesome and choleric ; my constitu-
tion will not allow me, even when in
good health, to remain a long time
sedentary (particularly for an extraor-
dinary time after dinner); 1 must rise
often and walk ahout, and in different
seasons am forced to make correspond-
ing changes in my diet."

The year preceding his departure to
Linz was denounced by him as pregnant
with misfortune and misery. " In the
first place I could get no money from
the court, and my wife, who had for a
long time been suffering under low
spirits and despondency, was taken
violently ill towards the end of 1610, with
the Hungarian fever, epilepsy, and phre-
nitis. She was scarcely convalescent
when all my three children were at once
attacked with small-pox. Leopold with
his army occupied the town beyond the
river, just as I lost the dearest of my
sons, him whose nativity you will find
in my book on the new star. The town
on this side of the river where I lived
was harassed by the Bohemian troops,
whose new levies were insubordinate
and insolent: to complete the whole,
the Austrian army brought the plague
with them into the city. I went into
Austria, and endeavoured to procure the
situation which I now hold. Return-
ing in June, I found my wife in a decline
from her grief at the death of her son,
and on the eVe of an infectious fever ;
and I lost her also, within eleven days
after my return. Then came fresh an-
noyance, of course, and her fortune
was to be divided with my step-sisters.
The Emperor Rodolph would not agree
to my departure; vain hopes were given
me of being paid from Saxony ; my
time and money were wasted together,
till on the death of the emperor, in 1612,
I was named again by his successor,
and suffered to depart to Linz. These,
methinks, were reasons enough why I
should have overlooked not only your
letters, but even astronomy itself."

Kepler's first marriage had not been
a happy one ; but the necessity in which
he felt himself of providing some one to
take charge of histwo surviving children,
of whom the eldest, Susanna, was born
in 1602, and Louis in 1607, determined
him on entering a second time into the
married state. The account he has left
us of the various negotiations which
preceded hi* final choice, does not, in

any point, belie the oddity of his charac •
ter. His friends seem to have received
a general commission to look out for a
suitable match, and in a long and most
amusing letter to the Baron Strahlendorf,
we are made acquainted with the pre-
tensions and qualifications of no less
than eleven ladies among whom his in-
clinations wavered.

The first on the list was a widow, an
intimate friend of his first wife's, and
who, on many accounts, appeared a
most eligible match. "At first she
seemed favourably inclined to the pro-
posal ; it is certain that she took time
to consider it, but at last she very
quietly excused herself." It must have
been from a recollection of this lady's
good qualities that Kepler was induced
to make his offer ; for we learn rather
unexpectedly, after being informed of
her decision,' that when he soon after-
wards paid his respects to her, it was
for the first time that he had seen her
during the last six years ; and he found,
to his great relief," that "there was no
single pleasing point about her." The
truth seems to be that he was nettled
by her answer, and he is at greater
pains than appear necessary, consider-
ing this last discovery, to determine
why she would not accept his offered
hand. Among other reasons he sug-
gested her children, among whom were
two marriageable daughters ; and it is
diverting afterwards to find them also
in the catalogue which Kepler appeared
to be making of all his female acquaint-
ance. He seems to have been much
perplexed in attempting to reconcile his
astrological theory with the fact of his
having taken so much trouble about a
negotiation not destined to succeed.
" Have the stars exercised any influence
here ? For just about this time the
direction of the Mid-Heaven is in hot
opposition to Mars, and the passage of
Saturn, through the ascending point of
the zodiac, in the scheme of my nativity,
will happen again next November and
December. But if these are the causes,
how do they act ? Is that explanation
the true one which I have elsewhere
given ? For I can never think of
handing over to the stars the office of
deities to produce effects. Let us there-
fore suppose it accounted for by the
stars, that at this season I am violent
in my temper and affections, in rashness
of belief, in a shew of pititul tender-
heartedness ; in catching at reputation
by new and paradoxical notions, and the

KEPLER.

37

singularity of my actions ; in busily in-
quiring into, and weighing and dis-
cussing, various reasons ; in the unT
easiness of my mind with respect to my
choice. I thank God that that did not
happen which might have happened ;
that this marriage did not take place :
now for Ihe others." Of these others,
one was too old, another in bad health,
another too proud of her birth and
quarterings; a fourth had learned no-
thing but shewy accomplishments, " not
at all suitable to the sort of life she
would have to lead with me." Another
grew impatient, and married a more
decided admirer, whilst he was hesitat-
ing. "The mischief (says he) in all
these attachments was, that whilst I
was delaying, comparing, and balancing
conflicting reasons, every day saw me
inflamed with anew passion." By the
time he reached the eighth, he found
his match in this respect. " Fortune at
length has avenged herself on my doubt-
ful inclinations. At first she was quite
complying, and her friends also : pre-
sently, whether she did or did not con-
sent, not only I, but she herself did not
know. After the lapse of a few days,
came a renewed promise, which how-
ever had to be confirmed a third time ;
and four clays after that, she again re-
pented her confirmation, and begged to
be excused from it. Upon this I gave
her up, and this time all my counsellors
were of one opinion." This was the
longest courtship in the list, having
lasted three whole months ; and quite
disheartened by its bad success, Kepler's
next attempt was of a more timid com-
plexion. His advances to No. 9, were
made by confiding to her the whole
story of his recent disappointment, pru-
dently determining to be guided in his
behaviour, by observing whether the
treatment he had experienced met with
a proper degree of sympathy. Appa-
rently the experiment did not succeed ;
and almost reduced to despair, Kepler
betook himself to the advice of a friend,
who had for some time past complained
that she was not consulted in this diffi-
cult negotiation. When she produced
No. 10, and the first visit was paid, the
report upon her was as follows : — " She
has, undoubtedly, a good fortune, is of
good family, and of economical habits :
but her physiognomy is most horribly
ugly; she would be stared at in the
streets, not to mention the striking dis-
proportion in our figures. I am lank,
lean, and spare ; she is short and thick :
in a family notorious for fatness she is

considered superfluously fat." The only
objection to No. 1 1 seems to have been
her excessive youth ; and when this
treaty was broken of on that account,
Kepler turned his back upon -all his ad-
visers, and chose for himself one who
had figured as No. 5 in the list, to
whom he professes to have felt attached
throughout, but from whom the repre-
sentations of his friends had hitherto
detained him, probably on account of
her humble station.

The following is Kepler's summary of
her character. "Her name is Susanna, the
daughter of John Reuthinger and Bar-
bara, citizens of the town of Eferdingen ;
the father was by trade a cabinet-maker,
but both her parents are dead. She has
received an education well worth the
largest dowry, by favour of the Lady of
Stahrenberg, the strictness of whose
household is famous throughout the
province. Her person and manners are
suitable to mine ; no pride, no extra-
vagance ; she can bear to work ; she has
a tolerable knowledge how to manage a
family ; middle-aged, and of a disposition
and capability to acquire what she still
wants. Her I shall marry by favour of
the noble baron of Stahrenberg at twelve
o'clock on the 30th of next October, with
all Eferdingen assembled to meet us, and
we shall eat the marriage-dinner at
Maurice's at the Golden Lion."

Hantsch has made an absurd mistake
with regard to this marriage, in stating
that the bride was only twelve years old.
Kastner and other biographers have
been content to repeat the same asser-
tion without any comment, notwith-
standing its evident improbability.
The origin of the blunder is to be found
in Kepler's correspondence with Berneg-
ger, to whom, speaking of his wife, he
says " She has been educated for twelve

¥>ars by the Lady of Stahrenberg."
his is by no means a single instance of
carelessness in Hantsch ; Kastner has
pointed out others of greater consequence.
It was owing to this marriage, that
Kepler took occasion to write his new
method of gauging, for as he tells us in
his own peculiar style " last November
I brought home a new wife, and as the
whole course of Danube was then
covered with the produce of the Aus-
trian vineyards, to be sold at a rea-
sonable rate, I purchased a few casks,
thinking it my duty as a good husband
and a father of a family, to see that my
household was well provided with drink."
When the seller came to ascertain the
quantity, Kepler objected to his method

38

KEPLER.

of gauging, for he allowed no difference,
whatever might be the proportion of the
bulging parts. The reflections to which
this incident gave rise, terminated in the
publication of the above-mentioned
treatise, which claims a place among
the earliest specimens of what is now
called the modern analysis. In it he
extended several properties of plane
figures to segments of cones and cylin-
ders, from the consideration that " these
solids are incorporated circles," and,
therefore, that those properties are true
of the whole which belong to each com-
ponent part. That the book might end
as oddly as it began, Kepler concluded
it with a parody of Catullus :

" Et cum pocula mille mensi erimus
Conturbabimus ilia, ne sciamus. "

His new residence at Linz was not
long undisturbed. He quarrelled there,
as he had done in the early part ef
his life at Gratz, with the Roman Ca-
tholic party, and was excommunicated.
" Judge," says he to Peter Hoffman,
" how far I can assist you, in a place
where the priest and school- inspector
have combined to brand me with the
public stigma of heresy, because in every
question I take that side which seems to
me to be consonant with the word of
God." The particular dogma which oc-
casioned his excommunication, was con-
nected with the doctrine of transubstan-
tiation. He published his creed in a
copy of Latin verses, preserved by his
biographer Hantsch.

Before this occurrence, Kepler had
been called to the diet at Ratisbon to
give his opinion on the propriety of
adopting the Gregorian reformation of
the calendar, and he published a short
essay, pointing out the respective con-
venience of doing so, or of altering
the old Julian Calendar in some other
manner. Notwithstanding the readi-
ness of the diet to avail themselves of
his talents for the. settlement of a dif-
ficult question, the arrears of his salary
were not paid much more regularly than
they had been in Rodolph's time, and he
was driven to provide himself with money
by the publication of his almanac, of
which necessity he heavily and justly
complained. " In order to pay the ex-
pense of the Ephemeris for these two
years, I have also written a vile prophe-
sying almanac, which is scarcely more
respectable than begging; unless it be
because it saves the emperor's credit,
who abandons me entirely ; and with all
his frequent and recent orders in council,

would suffer me to perish with hunger.'"
Kepler published this Ephemeris an-
nually till 1620 ; ten years later he added
those belonging to the years from 1620
to 1628.

In 1617 Kepler was invited into Italy,
to succeed Magini as Professor of Ma-
thematics at Bologna. The offer tempted
him; but, after mature consideration, he
rejected it, on grounds which he thus
explained to Roffini: — "By birth and
spirit I am a German, imbued with Ger-
man principles, and bound by such fa-
mily ties, that even if the emperor should
consent, 1 could not, without the greatest
difficulty, remove my dwelling-place from
Germany into Italy. And although the
glory of holding so distinguished a situa-
tion among the venerable professors of
Bologna stimulates me, and there ap-
pears great likelihood of notably in-
creasing my fortune, as well from the
great concourse to the public lectures, as
from private tuition ; yet, on the other
hand, that period of my life is past which
was once excited by novelty, or which
might promise itself a long enjoyment of
these advantages. Besides, from a boy
up to my present years, living a German
among Germans, I am accustomed to a
degree of freedom in my speech and
manners, which, if persevered in on my
removal to Bologna, seems likely to draw
upon me, if not danger, at least notoriety,
and might expose me to suspicion and
party malice. Notwithstanding this an-
swer, I have yet hopes that your most
honourable invitation will be of service
to me, and may make the imperial trea-
surer more ready than he has hitherto
been to fulfil his master's intentions to-
wards me. In that case I shall the sooner
be able to publish the Rudolphine Tables
and the Ephemerides, of which you had
the scheme so many years back ; and in
this manner you and your advisers may
have no reason to regret this invitation,
though for the present it seems fruit-
less."

In 1619, the Emperor Matthias died,
and was succeeded by Ferdinand III,,
who retained Kepler in the post he had
filled under his two predecessors on the
imperial throne. Kiistner, in his " His-
tory of Mathematics," has corrected a
gross error of Hantsch, in asserting that
Kepler prognosticated Matthias's death.
The letter to which Hantsch refers, in
support of his statement, does indeed
mention the emperor's death, but merely
as a notorious event, for the purpose of
recalling a. date to the memory of his
correspondent.

KEPLER. 39

CHAPTER VII. tion of great importance, for on this

account is it that the heptagon, and other
figures of this kind, have not been em-
ployed by God in the adornment of the
world, as the other intelligible figures
are employed which have been already
explained." Kepler then introduces the
algebraical equation, on the solution of
which this problem depends, and makes
a remark which is curious at this period
of the history of algebra — that the root
of an equation which cannot be accu-
rately found, may yet be found within
any degree of approximation by an ex-
pert calculator. In conclusion he again
remarks that " the side of the heptagon
has no place among scientific existences,
since its formal description is impos-
sible, and therefore it cannot be known
by the human mind, since the possibility
of description precedes the possibility of
knowledge ; nor is it known even by the
simple eternal act of an omniscient
mind, because its nature belongs to
things which cannot be known. "And
yet this scientific nonentity has some
scientific properties, for if a heptagon
were described in a circle, the proportion
of its sides would have analogous pro-
portions."

The third book is a treatise on music, in
the confined and ordinary sense in which
we now use that word, and apparently a
sober and rational one, at least as nearly
so as Kepler could be trusted to write on
a subject so dangerous to his discretion.
All the extravagance of the work seems
reserved for the fourth book, the title of
which already conveys some notion of
the nature of its contents. In this book
he has collected the substance of the
astrological opinions scattered through
his other works. We shall content our-
selves with merely citing his own words,
without any attempt to explain the dif-
ference between the astrology which he
believed, and that which he con-
temptuously rejected. The distinctive
line seems very finely drawn, and as both
one and the other are now discarded by
all who enjoy the full use of their rea-
soning powers, it is not of much conse-
quence that it should be accurately
traced.

It is to be observed, that he does not
in this treatise modify or recant anything
of his earlier opinions, but refers to the
favourable judgment of his contem-
porary philosophers as a reason for
embodying them in a regular form.
" Since many very celebrated professors
of philosophy and medicine are of opinion

Kepler publishes his ' Harmonics —
Account of his Astrological Opinions
and Discovery of the Law of the Pe-
riods of the Planetary Revolutions —
Sketch of Newton" s proof of Kepler's
Laws.

THE " Cosmographical Mystery" was
written, as has been already mentioned,
when Kepler was only twenty-six, and
the wildness of its theories might be con-
sidered as due merely to the vivacity of
a young man ; but as if purposely to
shew that his maturer age did not re-
nounce the creations of his youthful
fancy, he reprinted the " Mystery" in
1619, nearly at the same time when he
published his celebrated work on Har-
monics ; and the extravagance of the
latter publication does not at all lose in
comparison with its predecessor. It is
dedicated to James I. of England, and
divided into five books : " The first, Geo-
metrical, on the origin and demonstration
of the laws of t'ne figures which produce
harmonious proportions ; — the second,
Architectonical, on figurate geometry,
and the congruence of plane and solid
regular figures; — the third, properly
Harmonic, on the derivation of musical
proportions from figures, and on the na-
ture and distinction of things relating to
song, in opposition to the old theories ; —
the fourth, Metaphysical, Psychological,
and Astrological, on the mental essence
of harmonies, and of their kinds in the
world, especially on the harmony of rays
emanating on the earth from the hea-
venly bodies, and on their effect in na-
ture, and on the sublunary and human
soul ;— the fifth, Astronomical and Me-
taphysical, on the very exquisite harmo-
nies of the celestial motions, and the
origin of the excentricities in harmonious
proportions."

The two first books are almost strictly,
as Kepler styles them, geometrical,
relating in great measure to the inscrip-
tion of regular polygons in a circle.
The following passage is curious, pre-
senting an analogous idea to that con-
tained in one of the extracts already
given fropi the Commentaries on Mars.
" The heptagon, and all other polygons
and stars beyond it, which have a prime
number of sides, and all other figures
derived from them, cannot be inscribed
geometrically in a circle; although their
sides have a necessary magnitude, it is
equally a matter of necessity that we
remain ignorant of it. This is a ques-

KEPLER.

that I have created a new and most true
philosophy, this tender plant, like all
novelties, ought to be carefully nursed
and cherished, so that it may strike root
in the minds of philosophers, and not be
choked by the excessive humours of vain
sophistications, or washed away by the
torrents of vulgar prejudices, or frozen
by the chill of public neglect ; and if I
succeed in guarding it from these
dangers, I have no fear that it will be
crushed by the storms of calumny, or
parched by the sun of sterling criticism."
One thing is very remarkable in Kep-
ler's creed, that he whose candour is so
indisputable in every other part of his
conduct, professed to have been forced
to adopt his astrological opinions from
direct and positive observation. — " It is
now more than twenty years since I
began to maintain opinions like these on
the predominant nature of the elements,
which, adopting the common name, I
call sublunary. I have been driven to
this not by studying or admiring Plato,
but singly and solely by observing
seasons, and noting the aspects by which
they are produced. I have seen the
state of the atmosphere almost uniformly
disturbed as often as the planets are in
conjunction, or in the other configura-
tions so celebrated among astrologers.
I have noticed its tranquil state, either
when there are none or few such aspects,
or when they are transitory and of short
duration. I "have not formed an opinion
on this matter without good grounds,
like the common herd of prophesiers,
who describe the operations of the stars
as if they were a sort of deities, the lords
of heaven and earth, and producing
everything at their pleasure. They never
trouble themselves to consider what
means the stars have of working any
effects among us on the earth, whilst
they remain in the sky, and send down
nothing to us which is obvious to the
senses except rays of light. This is the
principal source of the filthy astrolo-
gical superstitions of that vulgar and
childish race of dreamers, the prognos-
ticators."

The real manner in which the con-
figurations of the stars operate, accord-
ing to Kepler, is as follows : — " Like one
who listens to a sweet melodious song,
and by the gladness of his countenance,
by his voice, and by the beating of his
hand or foot attunted to the music, gives
token that he perceives and approves
the harmony: just so does sublunary
nature, with the notable and evident

emotion of the bowels of the earth, bear
like witness to the same feelings, espe-
cially at those times when the rays of
the planets form harmonious configura-
tions on the earth." — " I have been con-
firmed in this theory by that which
might have deterred others ; I mean, by
observing that the emotions do not agree
nicely with the instants of the configu-
Yations ; but the earth sometimes ap-
pears lazy and obstinate, and at another
time (after important and long-continued
configurations) she becomes exas-
perated, and gives way to her passion,
even without the continuation of aspects.
For in fact the earth is not an animal
like a dog, ready at every nod ; but more
like a bull, or an elephant, slow to be-
come angry, and so much the more
furious when incensed."

This singular doctrine must not be
mistaken for one of Kepler's favourite
allegories ; he actually and literally
professed to believe that the earth
was an enormous living animal; and
he has enumerated, with a particula-
rity of details into which we forbear
to follow him, the analogies he re-
cognized between its habits and those
of men and other animals. A few
samples of these may speak for the
rest. " If any one who has climbed the
peaks of the highest, mountains throw a
stone down their very deep clefts, a
sound is heard from them ; or if he
throw it into one of the mountain lakes,
which beyond doubt are bottomless, a
storm will immediately arise, just as
when you thrust a straw into the ear or
nose of a ticklish animal, it shakes its
head, or runs shuddering away. What
so like breathing, especially of those fish
who draw water into their mouths and
spout it out again through their gills, as
that wonderful tide! For although it
is so regulated according to the course
of the moon, that, in the preface to my
* Commentaries on Mars,' I have men-
tioned it as probable that the waters are
attracted by the moon as iron is by the
loadstone ; yet, if any one uphold that
the earth regulates its breathing accord-
ing to the motion of the sun and moon,
as animals have daily and nightly alter-
nations of sleep and waking, I shall not
think his philqsophy unworthy of being
listened to; especially if any flexible
parts should be discovered in the depths
of the earth to supply the functions of
lungs or gills."

From the next extract, we must leave
the reader to learn as well as he may.

KEPLER.

how much Kepler did, and how much he
didnotbelieveonthe subject of genethliac
astrology. — " Hence it is that human
spirits, at the time of celestial aspects,
are particularly urged to complete the
matters which they have in hand. What
the goad is to the ox, what the spur or
the rowel is to the horse, to the soldier
the bell and trumpet, an animated
speech to an audience, to a crowd of
rustics a performance on the fife and
bagpipes, that to all, and especially in
the aggregate, is a heavenly configu-
ration of suitable planets ; so that every
single one is excited in his thoughts and
actions, and all become more ready to
unite and associate their efforts. For
instance, in war you may see that
tumults, battles, fights, invasions, as-
saults, attacks, and panic fears, gene-
rally happen at the time of ihe aspects
of Mars and Mercury, Mars and Ju-
piter, Mars and the Sun, Mars and
Saturn, &c. In epidemic diseases, a
greater number of persons are attacked
at the times of the powerful aspects,
they suffer more severely, or even die,
owing to the failure of nature in her
strife with the disease, which strife (and
not the death) is occasioned by the
aspect. It is not the sky which does all
these things immediately, but the faculty
of the vital soul, associating its operation
with the celestial harmonies, is the prin-
cipal agent in this so-called influence of
the heavens. Indeed this word influ-
ence has so fascinated some philosophers
that they prefer raving with the sense-
less vulgar, to learning the truth with
me. This essential property is the prin-
cipal foundation of that admirable ge-
nethliac art. For when anything begins
to have its being when that is working
harmonies, the sensible harmony of the
rays of the planets has peculiar influence
on it. This then is the cause why those
who are born under a season of many
aspects among the planets, generally
turn out busy and industrious, whether
they accustom themselves from child-
hood to amass wealth, or are born or
chosen to direct public affairs, or finally,
have given their attention to study. If
any one think that I might be taken as
an instance of this last class, I do not
grudge him the knowledge of my na-
tivity. I am not checked by the re-
proach of boastfulness, notwithstanding
those who, by speech or conduct, con-
demn as folly all kinds of writing on
this subject; the idiots, the half-learned,
the inventors of titles and trappings, to

throw dust in the eyes of the people,
and those whom Picus calls the ple-
beian theologians : among the true
lovers of wisdom, I easily clear myself
of this imputation, by the advantage of
my reader ; for there is no one whose
nativity or whose internal disposition
and temper I can learn so well as I
know my own. Well then, Jupiter
nearest the nonagesimal had passed by
four degrees the trine of Saturn ; the
Sun and Venus, in conjunction, were
moving from the latter towards the
former, nearly in sextiles with both:
they were also removing from quadra-
tures with Mars, to which Mercury was
closely approaching : the moon drew near
the trine of the same planet, close to the
Bull's Eye, even in latitude. The 25th
degree of Gemini was rising, and the
22d of Aquarius culminating. That
there was this triple configuration on
that day — namely, the sextile of Saturn
and the Sun, the sextile of Mars and
Jupiter, the quadrature of Mercury and
Mars, is proved by the change of wea-
ther; for, after a frost of some days,
that very day became warmer, there
was a thaw and a fall of rain.*"

" I do not wish this single instance to
be taken as a defence and proof of all
the aphorisms of astrologers, nor do I
attribute to the heavens the government
of human affairs : what a vast interval
still separates these philosophical obser-
vations from that folly or madness as it
should rather be called. For, following
up this example, I knew a ladyt, born
under nearly the same aspects, whose
disposition, indeed, was exceedingly
restless, but who not only makes no
progress in literature (that is not strange
in a woman), but troubles her whole fa-
mily,, and is the cause to herself of de-
plorable misery. What, in my case,
assisted the aspects was — firstly, the
fancy of my mother when pregnant
with me, a great admirer of her mother-
in-law, my grandmother, who had some
knowledge of medicine, my grandfather's
profession; a second cause is, that I

* Tliis mode of verifying configurations, though
something of the boldest, was by no means un-
usual. ,Ona former occasion Kepler, wishing to
cast the nativity of his friend Zehentmaier, and
being unable to procure more accurate informa-
tion than that he was born about three o'clock in
the afternoon of the 21st of October, 1751, sup-
plied the deficiency by a record of fevers and acci-
dents at known periods of his life, from which he
deduced a more exact horoscope.

f Kepler probably meant his own mother, whose
horoscope he in many places declared to be nearly
the same as his own,

L2

KEPLER.

was born a male, and not a female, for
astrologers have sought in vain to dis-
tinguish sexes in the sky ; thirdly, I de-
rive from my mother a habit of body,
more fit for study than other kinds of
life : fourthly, my parents' fortune was
not large, and there was no landed pro-
perty to which I might succeed and be-
come attached ; fifthly, there were the
schools, and the liberality of the magis-
tracy towards such boys as were apt
for learning. But now if I am to
speak of the result of my studies, what
I pray can I find in the sky, even re-
motely alluding to it. The learned con-
fess that several not despicable branches
of philosophy have been newly extri-
cated or amended or brought to per-
fection by me : but here my constella-
tions were, not Mercury from the east,
in the angle of the seventh, and in
quadratures with Mars, but Copernicus,
but Tycho Brahe, without whose books
of observations everything now set by
me in the clearest light must have re-
mained buried in darkness ; not Saturn
predominating Mercury, but my Lords
the Emperors Rodolph and Matthias ;
not Capricorn, the house of Saturn, but
Upper Austria, the home of the Em-
peror, and the ready and unexampled
bounty of his nobles to my petition.
Here is that corner, not the western one
of the horoscope, but on the Earth,
whither, by permission of my imperial
master, I have betaken myself from a
too uneasy court ; and whence, during
these years of my life, which now tends
towards its setting, emanate these Har-
monies, and the other matters on which
I am engaged."

" However, it may be owing to Ju-
piter's ascendancy that I take greater
delight in the application of geometry
to physics, than in that abstract pursuit
which partakes of the dryness of Saturn ;
and it is perhaps the gibbous moon, in
the bright constellation of the Bull's
forehead, which fills my mind with fan-
tastic images."

The most remarkable thing contained
in the 5th Book, is the announcement
of the celebrated law connecting the
mean distances of the planets with the
periods of their revolution about the
Sun. This law is expressed in mathe-
matical language, by saying that the
squares of the times vary as the cubes
of the distances*. Kepler's rapture on
detecting it was unbounded, as may be

* See Preliminary Treatise, p. 13.

seen from the exulting rhapsody with
which he announced it. "What Ipro-
phecied two-and-twenty years ago, as
soon as I discovered the five solids
among the heavenly orbits — what I
firmly believed long before I had seen
Ptolemy's * Harmonics ' — what I had
promised my friends in the title of this
book, which I named before I was sure of
my discovery — what, sixteen years ago, I
urged as a thing to be sought — that for
which I joined Tycho Brahe, for which
I settled in Prague, for which I have
devoted the best part of my life to astro
nomical contemplations, at 'length I
have brought to light, and have recog-
nized its truth beyond my most san-
guine expectations. Great as is the
absolute nature of Harmonics with all
its details, as set forth in my third book,
it is all found among the celestial mo-
tions, not indeed in the manner which
I imagined, (that is not the least part of
my delight,) but in another very differ-
ent, and yet most perfect and excellent.
It is now eighteen months since I got
the first glimpse of light, three months
since the dawn, very few days since the
unveiled sun, most admirable to gaze
on, burst out upon me. Nothing holds
me ; I will indulge in my sacred fury ;
I will triumph over mankind by the
honest confession, that I have stolen
the golden vases of the Egyptians*, to
build up a tabernacle for my God far
away from the confines of Egypt. If
you forgive me, I rejoice; if you are
angry, I can bear it : the die is cast,
the book is written ; to be read either
now or by posterity, I care not which :
it may well wait a century for a reader,
as God has waited six -thousand years
for an observer."

He has told, with his usual particu-
larity, the manner and precise moment
of the discovery. " Another part of my
1 Cosmographical Mystery,' suspended
twenty-two years ago, because it was
then undetermined, is completed and in-
troduced here, after I had discovered
the true intervals of the orbits, by means
of Brahe's observations, and had spent
the continuous toil of a long time in in-
vestigating the true proportion of the
periodic times to the orbits,

Sera quidem respexit inertcm,

Respexit tamen, et longo post tempore venit.

If you would know the precise moment,
the first idea came across me on Hie 8th
March of this year, 1G18 ; but chancing

* Jn allusion to the Harmonics of Ptolemy.

KEPLER.

43

to make a mistake in the calculation, I
rejected it as false. I returned again to
it with new force on the 1 5th May, and
it has dissipated the darkness of my
mind by such an agreement between
this idea and my seventeen years' labour
on Brahe's observations, that at first I
thought I must be dreaming, and had
taken my result for granted in my first
assumptions. But the fact is perfect,
the fact is certain, that the proportion
existing between the periodic times of
any two planets is exactly the sesquipli-
cate proportion of the mean distances of
the orbits."

There is high authority for not attempt-
ing over anxiously to understand the
rest of the work. Delambre sums it up
as follows: — "In the music of the ce-
lestial bodies it appears that Saturn and
Jupiter take the bass, Mars the tenor,
the Earth and Venus the counter-tenor,
and Mercury the treble." If the patience
of this indefatigable historian gave way,
as he confesses, in the perusal, any
further notice of it here may be well
excused. Kepler became engaged, in
consequence of this publication, in an
angry controversy with the eccentric
Robert Fludd, who was at least Kepler's
match in wild extravagance and mysti-
cism, if far inferior to him in genius. It
is diverting to hear each reproaching the
other with obscurity.

In the " Epitome of the Copernican
Astronomy," which Kepler published
about the same time, we find the manner
in which he endeavoured to deduce the
beautiful law of periodic times, from
his principles of motion and radiation
of whirling forces. This work is in
fact a summary of all his astronomi-
cal opinions, drawn up in a popular
style in the form of question and an-
swer. We find there a singular argu-
ment against believing, as some did,
that each planet is carried round by an
angel, for in that case, says Kepler,
" the orbits would be perfectly circular ;
but the elliptic form, which we find in
them, rather smacks of the nature of
the lever and material necessity."

The investigation of the relation be-
tween the periodic times and distances
of the planets is introduced by a query
whether or not they are to be considered
heavy. The answer is given in the fol-
lowing terms : — " Although none of the
celestial globes are heavy, in the sense
in which we say on earth that a stone is
heavy, nor light as fire is light with us,
yet have they, by reason of their mate*

riality, a naturaHnability to move from
place to place : they have a natural in-
ertness or quietude, in consequence of
which they remain still in every situation
where they are placed alone."

" P. Is it then the sun, which by its
turning carries round the planets ? How
can the sun do this, having no hands to
seize the planet at so great a distance,
and force it round along with itself? —
Its bodily virtue, sent forth in straight
lines into the whole space of the world,
serves instead of hands ; and this virtue,
being a corporeal species, turns with the
body of the sun like a very rapid vortex,
and travels over the whole of that space
which it fills as quickly as the sun re-
volves in its very confined space round
the centre.

" P. Explain what this virtue is, and
belonging to what class of things ? —
As there are two bodies, the mover and
the moved, so are there two powers by
which the motion is obtained. The one
is passive, and rather belonging to
matter, namely, the resemblance of the
body of the planet to the body of the
sun in its corporeal form, and so that
part of the planetary body is friendly, the
opposite part hostile to the sun. The
other power is active, and bearing more
relation to form, namely, the body of
the sun has a power of attracting the
planet by its friendly part, of repelling
it by the hostile part, and finally, of re-
taining it if it be placed so that neither
the one nor the other be turned directly
towards the sun.

" P. How can it be that the whole body
of the planet should be like or cognate to
the body of the sun, and yet part of the
planet friendly, part hostile to the sun ?
— Just as when one magnet attracts
another, the bodies are cognate ; but at-
traction takes place only on one side, re-
pulsion on the other.

" P. Whence, then, arises that differ-
ence of opposite parts in the same body ?
— In magnets the diversity arises from
the situation of the parts with respect to
the whole. In the heavens the matter is
a little differently arranged, for the sun
does not, like the magnet, possess only
on one side, but in all the parts of its
substance, this active and energetic fa-
culty of attracting, repelling, or retain-
ing the planet. So that it is probable
that the centre of the solar body corre-
sponds to one extremity or pole of the
magnet, and its whole surface to the
other pole,
" P. If this were so, all the planets

44

KEPLER.

would be restored* in the same time with
the sun ? — True, if this were all : but it
has been said already that, besides this
carrying power of the sun, there is also in
the planets a natural inertness to motion,
which causes that, by reason of their
material substance, they are inclined to
remain each in its place. The carrying
power of the sun, and the impotence or
material inertness of the planet, are thus
in opposition. Each shares the victory ;
the sun moves the planet from its place,
although in some degree it escapes from
the chains with which it was held by the
sun, and so is taken hold of successively
by every part of this circular virtue, orr
as it may be called, solar circumference,
namely, by the parts which follow those
from which it has just extricated itself.

" P. But how does one planet extricate
itself more than another from this vio-
lence— First, because the virtue emana-
ting from the sun has the same degree of
weakness at different distances, as the
distances or the width of the circles de-
scribed on these distancest. This is the
principal reason. Secondly, the cause
is partly in the greater or less inertness
or resistance of the planetary globes,
which reduces the proportions to one-
half; but of this more hereafter.

" P. How can it be that the virtue ema-
nating from the sun becomes weaker at
a greater distance ? What is there to
hurt or weaken it ? — Because that
virtue is corporeal, and partaking of
quantity, which can be spread out and
rarefied. Then, since there is as much
virtue diffused in the vast orb of Sa-
turn as is collected in the very narrow
one of Mercury, it is very rare and there-
fore weak in Saturn's orbit, very dense
and therefore powerful at Mercury.

" P. You said, in the beginning of this
inquiry into motion, that the periodic
times of the planets are exactly in the
sesquiplicate proportion of their orbits or
circles : pray what is the cause of this ?
— Four causes concur for lengthening
the periodic time. First, the length of
the path; secondly, the weight or quan-
tity of matter to be carried ; thirdly, the
degree of strength of the moving virtue ;
fourthly, the bulk or space into which
is spread out the matter to be moved.

* This is a word borrowed from the Ptolemaic
astronomy, according to which the sun and
planets are hurried from their places by the daily
motion of the primum mobile, and by their own
peculiar motion seek to regain or be restored to
their former places.

>„ f In other parts of -his works,.Kepler assumes
The diminution to be proportional to the circles
themselves, not to the diameters.

The circular paths of the planets are in
the simple ratio of the distances ; the
weights or quantities of matter in diffe-
rent planets are in the subduplicate ratio
of the same distances, as has been
already proved; so that with every in-
crease of distance, a planet, has more
matter, and therefore is moved more
slowly, and accumulates more time in its
revolution, requiring already as it did
more time by reason of the length of the
way. The third and fourth causes com-
pensate each other in a comparison of
different planets: the simple and sub-
duplicate proportion compound the ses-
quiplicate proportion, which therefore is
the ratio of the periodic times."

Three of the four suppositions here
made by Kepler to explain the beautiful
law he had detected, are now indisputa-
bly known to be false. Neither the
weights nor the sizes of the different
planets observe the proportions assigned
by him, nor is the force by which they
are retained in their orbits in any respect
similar in its effects to those attributed
by him to it. The wonder which might
naturally be felt that he should never-
theless reach the desired conclusion, will
be considerably abated on examining the
mode in which he arrived at and satisfied
himself of the truth of these three sup-
positions. It has been already mentioned
that his notions on the existence of a
whirling force emanating from the sun,
and decreasing in energy at increased
distances, are altogether inconsistent
with all the experiments and observa-
tions we are able to collect. His reason
for asserting that the sizes of the dif-
ferent planets are proportional to their
distances from the sun, was simply be-
cause he chose to take for granted that
either their solidities, surfaces, or dia-
meters, must necessarily be in that
proportion, and of the three, the solidities
appeared to him least liable, to objection.
The last element of his precarious rea-
soning rested upon equally groundless
assumptions. Taking as a principle, that
where there is a number of different
things they must be different in every
respect, he declared that it was quite
unreasonable to suppose all the planets
of the same density. He thought it in-
disputable that they must be rarer as they
were farther from the sun, " and yet not
in the proportion of their^distances, for
thus we should sin against the law of
variety in another way, and make the
quantity of matter (according to what he
had just said of their bulk) the same in

KEPLER,

all. But if 'we assume the ratio of the
quantities of matter to be half that of the
distances, we shall observe the best mean
of all ; for thus Saturn will be half as
heavy again as Jupiter, and Jupiter half
again as dense as Saturn. And the
strongest argument of all is, that unless
we assume this proportion of the densi-
ties, the law of the periodic times will
not answer." This is the proof alluded
to, and it is clear that by such reasoning
any required result might be deduced
from any given principles.

It may not be uninstructive to subjoin
a sketch of the manner in which Newton
established the same celebrated results,
starting from principles of motion dia-
metrically opposed to Kepler's, and it
need scarcely be added, reasoning upon
them in a manner not less different.
For this purpose, a very few prefatory
remarks will be found sufficient.

The different motions seen in nature
are best analysed and classified by sup-
posing that every body in motion, if left
to itself, will continue to move forward
at the same rate in a straight line, and
by considering all the observed devia-
tions from this manner of moving, as
exceptions and disturbances occasioned
by some external cause. To this sup-
posed cause is generally given the name
pf Force, and it is said to be the first
law of motion, that, unless acted on by
some force, every body at rest remains
at rest, and every body in motion pro-
ceeds uniformly in a straight line. Many
employ this language, without perceiving
that it involves a definition of force, on
the admission of which, it is reduced to
a truism. We see common instances of
force in a blow, or a pull from the end of
a string fastened to the body : we shall
also have occasion presently to mention
some forces where no visible connexion
exists between the moving body and
that towards which the motion takes
place, and from which the force is said
to proceed.

A second law of motion, founded upon
experiment, is this : if a body have mo-
tion communicated to it in two directions,
by one of which motions alone it would
have passed through a given space in a
given time, as for instance, through B C'
in one second, and by the other alone
through any other space Be in the same-
time, it will, when both are
given to it at the same in
stant, pass in the same
time (in the present in-
stance in one second) through B C the

diagonal of the parallelogram of which
B C' and B c are sides.

Let a body, acted upon by no force,
be moving along the line AE ; that

15

means, according to what has been said,
let it pass over the equal straight lines
A B, B C, C D, D E, Sec., in equal times.
If we take any point S not in the line
A E, and join A S, B S, &c., the triangles
A S B, B S C, &c. are also equal, having
a common altitude and standing on
equal bases, so that if a string were con-
ceived reaching from S to the moving
body (being lengthened or shortened in
each posit ion to suit its distance from
S), this string, as the body moved along
A E, would sweep over equal trian-
gular areas in equal times.

Let us now examine how far these

conclusions will be altered if the body
from time to time is forced towards S.
We will suppose it moving uniformly
from A to B as before, no matter for the
present how it got to A, or into the
direction A B. If left to itself it would,
in an equal time (say 1") go through
B C' in the same straight line with and
equal to AB. But just as it reaches
B, and is beginning to move along B C',
let it be suddenly pulled towards S with
a motion which, had it been at rest,
would have carried it in the same time,
1", through any other space B c. Ac-
cording to the second law of motion, its
direction during this I", in consequence
of the two motions combined, will be
along B C, the diagonal of the parallelo-
gram of which B C', B c, are sides. In-

46

KEPLER.

this case, as this figure is drawn, B C,
though passed in the same time, is longer
than A B ; that is to say, the body is
moving quicker than at first. How is it
with the triangular areas, supposed as
before to be swept by a string constantly
stretched between S and the body ? It
will soon be seen that these still remain
equal, notwithstanding the change of
direction, and increased swiftness. For
since C C' is parallel to B c, the tri-
angles SCB, SC'B are equal, being
on the same base S B, arid between
the same parallels S B, C C', and S C'B
is equal to S B A as before, therefore
S C B, S B A are equal. The body is
now moving uniformly (though quicker
than along A B) along B C. As before,
it would in a time equal to the time of
passing along B C, go through an equal
space C D' in the same straight line.
But if at C it has a second pull towards
S, strong enough to carry it to d in the
same time, its direction will change a
second time to C D, the diagonal of the
parallelogram, whose sides are C D', C d\
and the circumstances being exactly
similar to those at the first pull, it is
shewn in the same manner that the
triangular area SDC = SCB = SBA.

Thus it appears, that in consequence
of these intermitting pulls towards S,
the body may be moving round, some-
times faster, sometimes slower, but that
the triangles formed by any of the
straight portions of its path (which are
all described in equal times), and the
lines joining S to the ends of that por-
tion, are all equal. The path it will take
depends of course, in other respects,
upon the frequency and strength of the
different pulls, and it might happen, if
they were duly proportionate, that when
at H, and moving off in the direction
H A', the pull H a might be such as just
to carry the body back to A, the point
from which it started, and with such a
motion, that after one pull more, A b, at
A, it might move along A B as it did at
first. If this were so, the body would
continue to move round in the same
polygonal path, alternately approaching
and receding from S, as long as the
same pulls were repeated in the same
order, and at the same intervals.

It seems almost unnecessary to re-
mark, that the same equality which sub-
sists between any two of these triangular
areas subsists also between an equal
number of them, from whatever part of
the path taken ; so that, for instance, the
four paths AB, B C, CD, D E, cor-

responding to the four areas A S B,
B S C, C S D, D S E, that is, to the area
ABODES, are passed in the same
time as the four E F, F G, GH, H A, cor-
responding to the equal area E F G H A S.
Hence it may be seen, if the whole
time of revolution from A round to A
again be called a year, that in half a
year the body will have got to E, which
in the present figure is more than half
way round, and so of any other pe-
riods.

The more frequently the pulls are
supposed to recur, the more frequently
will the body change its direction ; and if
the pull were supposed constantly ex-
erted in the direction towards S, the body
would move in a curve round S, for no
three successive positions of it could be
in a straight line. Those who are not
familiar with the methods of measuring
curvilinear spaces must here be con-
tented to observe, that the law holds,
however close the pulls are brought to-
gether, and however closely the polygon
is consequently made to resemble a
curve : they may, if they please, consider
the minute portions into which the curve
is so divided, as differing insensibly
from little rectilinear triangles, any equal
number of which, according to what has
been said above, wherever taken in the
curve, would be swept in equal times.
The theorem admits, in this case also,
a rigorous proof; but it is not easy to
make it entirely satisfactory, without
entering into explanations which would
detain us too long from our principal
subject.

The proportion in which the pull
is strong or weak at different dis-
tances from the central spot, is called
" the law of the central or centripetal
force," and it may be observed, that
after assuming the laws of motion, our
investigations cease to have anything
hypothetical or experimental in them ;
and that if we wish, according to these
principles of motion, to determine the
law of force necessary to make a body
move in a curve of any required form,
or conversely to discover the form of
the curve described, in consequence of
any assumed law of force, the inquiry
is purely geometrical, depending upon
the nature and properties of geometrical
quantities only. This distinction be-
tween what is hypothetical, and what
necessary truth, ought never to be lost
sight of.

As the object of the present treatise
is not to teach geometry, we shall de-

KEPLER.

scribe, in very general terms, the manner
in which Newton, who was the first who
systematically extended the laws of mo-
tion to the heavenly bodies, identified
their results with the two remaining
laws of Kepler. His " Principles of
Natural Philosophy" contain general
propositions with regard to any law of
centripetal force, but that which he sup-
posed to be the true one in our system, is
expressed in mathematical language, by
saying that the centripetal force varies
inversely as the square of the distance,
which means, that if the force at any
distance be taken for the unit of force,
at half that distance, it is two times
twice, or four times as strong ; at one-
third the distance, three times thrice, or
nine times as strong, and so for other
distances. He shewed the probability
of this law in the first instance by com-
paring the motion of the moon with that
of heavy bodies at the surface of the
earth. Taking L P*
to represent part of
the moon's orbit de-
scribed in one minute,
the line P M between
the orbit and the
tangent at L would
shew the space through which the central
force at the earth (assuming the above
principles of motion to be correct) would
draw the moon. From the known dis-
tance and motion of the moon, this line
P M is found to be about sixteen feet.
The distance of the moon is about sixty
times the radius of the earth, and there-
fore if the law of the central force in this
instance were such as has been supposed,
the force at the earth's surface would
be 60 times 60, or 3600 times stronger,
and at the earth's surface, the central
force would make a body fall through
3600 times 16 feet in one minute. Ga-
lileo had already taught that the spaces
through which a body would be made
to fall, by the constant action of the
same unvarying force, would be pro-
portional to the squares of the times du-
ring which the force was exerted, and
therefore according to these laws, a
body at the earth's surface ought (since
there are sixty seconds in a minute) to
fall through 1 6 feet in one second, which
was precisely the space previously esta-
blished by numerous experiments.

With this confirmation of the suppo-
sition, Newton proceeded to the purely
geometrical calculation of the law of
centripetal* force necessary to make a
* In many curves, as in the circle and ellipse,

moving body describe an ellipse round
its foci>s, which Kepler's observations
had established to be the form of the or-
bits of the planets round the sun. The
result of the inquiry shewed that this
curve required the same law of the force,
varying inversely as the square of the
distance, which therefore of course re-
ceived additional confirmation. His me-
thod of doing this may, perhaps, be un-
derstood by referring to the last figure
but one, in which C d, for instance,
representing the space fallen from
any point C towards S, in a given
time, and the area C S D being pro
portional to the corresponding time,
the space through which the body would
have fallen at C in any other time (which
would be greater, by Galileo's law, in
proportion to the squares of the times),
might be represented by a quantity va-
rying directly as C d, and inversely in the
duplicate proportion of the triangular
area C S D, that is to say, proportional to

perpendicular on S C. If this polygon
represent an ellipse, so that C D repre-
sents a small arc of the curve, of which
S is the focus, it is found by the nature

of that curve, that _ , , is the same at

(D liy

all points of the curve, so that the law of
variation of the force in the same ellipse

is represented solely by p 2. If C d,

Sec. are drawn so that

Cd

is not the

same at every point, the curve ceases to
be an ellipse whose focus is at S, as
Newton has shewn in the same work.

The line to which

is found to be

equal, is one drawn through the focus at
right angles to the longest axis of the
ellipse till it meets the curve; — this line
is called the latus rectum, and is a
third proportional to the two principal
axes.

Kepler's third law follows as an im-
mediate consequence of this determina-
tion ; for, according to what has been
already shown, the time of revolution
round the whole ellipse, or, as it is corn-

there is a point to which the name of centre is
given, on uccount of peculiar properties belonging
to it : but the term " centripetal force" always re-
fers to the place towards which the force is di-
rected, whether or not situated in the centre of the
curve.

48

KEPLER.

monly called, the periodic time, bears the
same ratio to the unit of time as the
whole area of the ellipse does to the area
described in that unit. The area of the
whole ellipse is proportional in different
ellipses to the rectangle contained by the
two principal axes, and the area de-
scribed in an unit of time is proportional
to S C x DA, that is to say, is in the sub-

D A-

duplicate ratio of S C2 x DA9, or 77-71

L> a

when the force varies inversely as the
square of the distance S C ; and in the
ellipse, as we have said already, this is
equal to a third proportional to the
principal axes; consequently the pe-
riodic times in different ellipses, which
are proportional to the whole areas of
the ellipses directly, and the areas de-
scribed in the 'unit of time inversely,
are in the compound ratio of the rec-
tangle of the axes directly, and subdu-
plicatly as a third proportional to the
axes inversely ; that is to say, the squares
of these times are proportional to the
cubes t of the longest axes, which is
Kepler's law.

CHAPTER VIII.

The Epitome prohibited at Rome — Lo-
garithmic Tables — Trial of Catha-
rine Kepler— Kepler invited to Eng-
land— Rudolphine Tables — Death —
Conclusion.

KEPLER'S " Epitome," almost immedi-
ately on its appearance, enjoyed the ho-
nour of being placed by the side of the
work of Copernicus, on the list of books
prohibited by the congregation of the
Index at Rome. He was considerably
alarmed on receiving this intelligence,
anticipating that it might occasion diffi-
culties in publishing his future writings.
His words to Remus, who had communi-
cated the news to him, are as follows : —
" I learn from your letter, for the first
time, that my book is prohibited at Rome
and Florence. I particularly beg of you,
to send me the exact words of the cen-
sure, and that you will inform me whe-
ther that censure would be a snare for
the author, if he were caught in Italy, or
whether, if taken, he would be enjoined
a recantation. It is also of consequence
for rne to know whether there is any
chance of the same censure being ex-
tended into Austria. For if this be so,
not only shall I never again find a printer
there, but also the copies which the
bookseller, has left in Austria at my de-
sire will be endangered, and the ultimate

loss will fall upon me. It will amount
to giving me to understand, that I must
cease to profess Astronomy, after I have
grown old in the belief of these opinions,
having been hitherto gainsay ed by no
one, — and, in short, I must give up Aus-
tria itself, if room is no longer to be left
in it for philosophical liberty." He was,
however, tranquillized, in a great degree,
by the reply of his friend, who told him
that " the book is only prohibited as
contrary to the decree pronounced by the
holy office two years ago. This has been
partly occasioned by a Neapolitan monk
(Foscarini), who was spreading these
notions by publishing them in Italian,
whence were arising dangerous conse-
quences and opinions : and besides, Ga-
lileo was at the same time pleading his
cause at Rome with too much violence.
Copernicus has been corrected in the
same manner for some lines, at least in
the beginning of his first book. But by
Obtaining a permission, they may be
read (and, as I suppose, this " Epitome"
also) by the learned and skilful in this
science, both at Rome and throughout
all Italy. There is therefore no ground
for your alarm, either in Italy or Austria;
only keep yourself within bounds, and
put a guard upon your own passions.11

We shall not dwell upon Kepler's dif-
ferent works on comets, beyond men-
tioning that they were divided, on the
plan of many of his other publications,
into three parts, Astronomical, Physical,
and Astrological. He maintained that
comets move in straight lines, with a
varying degree of velocity. Later theo-
ries have shewn that they obey the same
laws of motion as the planets, differing
from them only in the extreme excen-
tricity of their orbits. In the second
book, which contains the Physiology of
Comets, there is a passing remark that
comets come out from the remotest
parts of ether, as whales and monsters
ifrom the depth of the sea; and the sug-
gestion is thrown out that perhaps
comets are something of the nature of
silkworms, and are wasted and con-
sumed in spinning their own tails.

Among his other laborious employ-
ments, Kepler yet found time to cal-
culate tables of logarithms, he having
been one of the first in Germany to appre-
ciate the full importance of the facilities
they afford to the numerical calculator.
In 1618 he wrote to his friend Schick-
hard : " There is a Scottish Baron (whose
name has escaped my memory), who has
made a famous contrivance, by which

KEPLER.

49

all need of multiplication and division is
supplied by mere addition and subtrac-
tion ; and he does it without sines. But
even he wants a table of tangents *, and
the variety, frequency, and difficulty of
the additions and subtractions, in some
cases, is greater than the labour of mul-

tiplying and dividing."
K(

lepler dedicated his " Ephemeris" for
1620 to the author of this celebrated in-
vention, Baron Napier, of Merchistoun ;
and in 1624, published what he called
*' Chilias Logarithmorum," containing
the Napierian logarithms of the quotients
of 100,000 divided by the first ten num-
bers, then proceeding by the quotients of
every ten to 100, and by hundreds to
1 00,000. In the supplement published the
following year, is a curious notice of the
manner in which this subtle contrivance
was at first received : " In the year 1621,
when I had gone into Upper Austria, and
had conferred everywhere with those
skilled in mathematics, on the subject of
Napier's logarithms, I found that those
whose prudence had increased, and
whose readiness had diminished, through
age, were hesitating whether to adopt
this new sort of numbers, instead of
a table of sines ; because they said
it was disgraceful to a professor of
mathematics to exult like a child at
some compendious method of working,
and meanwhile to admit a form of cal-
culation, resting on no legitimate proof,
and which at some time might entangle
us in error, when we least feared it.
They complained that Napier's demon-
stration rested on a fiction of geometri-
cal motion, too loose and slippery for a
sound method of reasonable demonstra-
tion to be founded on itt. " This led

* The meaning of this passage is not very clear:
Kepler evidently had seen and used logarithms at
the time of writing this letter; yet there is nothing
in the method to justify this expression, — " At
tamen opus est ipsi Tangentium canone."

f This was the objection originally made to
Newton's " Fluxions," and in fact, Napier's idea of
logarithms is identical with that method of con-
ceiving quantities. This may be seen at once from
a few of his definitions,

1 Def. A line is said to increase uniformly, when

the point by which it is described passes
through equal intervals, in equal times.

2 Def. A line is said to diminish to a shorter one

proportionally, when the point passing along
it cuts off in equal times segments propor-
tional to the remainder.

6 Def. The logarithm of any sine is the number
most nearly denoting the line, which has
increased uniformly, whilst the radius has
diminished to that sine proportionally, the
initial velocity being the same in both mo-
tions. (Mirifici logarithmorum cauonis
descriptio, Edinburgi 1614.)

- This last definition contains what we should now

call the differential equation between a number

and the logarithm of its reciprocal,

me forthwith to conceive the germ of a
legitimate demonstration, which during
that same winter I attempted, without
reference to lines or motion, or flow, or
any other which I may call sensible
quality."

" Now to answer the question ; what is
the use of logarithms ? Exactly what ten
years ago was announced by their author,
Napier, and which may be told in these
words. — Wheresoever in common arith-
metic, and in the Rule of Three, come two
numbers to be multiplied together, there
the sum of the logarithms is to be taken ;
where one number is to be divided by
another, the difference ; and the num-
ber corresponding to this sum or differ-
ence, as the case may be, will be the
required product or quotient. This,
1 say, is the use of logarithms. But
in the same work in which I gave
the demonstration of the principles, I
could not satisfy the unfledged arith-
metical chickens, greedy of facilities,
and gaping with their beaks wide
open, at the mention of this use, as
if to bolt down every particular gobbet,
till they are crammed with my precepti-
cles."

The year 1622 was marked by the ca-
tastrophe of a singular adventure which
befell Kepler's mother, Catharine, then
nearly seventy years old, and by which
he had been greatly harassed and an-
noyed during several years. From her
youth she had been noted for a rude and
passionate temper, which on the present
occasion involved her in serious diffi-
culties. One of her female acquaint-
ance, whose manner of life had been by
no means unblemished, was attacked
after a miscarriage by violent head-
aches, and Catharine, who had often
taken occasion to sneer at her noto-
rious reputation, was accused with hav-
ing produced these consequences, by
the administration of poisonous potions.
She repelled the charge with violence,
and instituted an action of scandal against
this person, but was unlucky (according
to Kepler's statement) in the choice of a
young doctor, whom she employed as
her advocate. Considering the suit to be
very instructive, he delayed its termina-
tion during five years, until the judge
before whom it was tried was displaced.
He was succeeded by another, already in-
disposed against Catharine Kepler, who
on some occasion had taunted him with
his sudden accession to wealth from a
very inferior situation. Her opponent,
aware of this advantage, turned the ta-

50

KEPLER.

hies on her, and in her turn became the
accuser. The end of the matter was,
that in July, 1620, Catharine was im-
prisoned, and condemned to the torture.
Kepler was then at Linz, but as soon
as he learned his mother's danger, hur-
ried to the scene of trial. He found the
charges against her supported only by"
evidence which never could have been
listened to, if her own intemperate con-
duct had not given advantage to her
adversaries. He arrived in time to save
her from the question, but she was not
finally acquitted and released, from pri-
son till November in the following year.
Kepler then returned to Linz, leaving
behind him his mother, whose spirit
seemed in no degree broken by the un-
expected turn in the course of her liti-
gation. She immediately commenced
a new action for costs and damages
against the same antagonist, but this
was stopped by her death, in April 1622,
in her seventy-fifth year.

In 1620 Kepler was visited by Sir
Henry Wotton, the English ambassador
at Venice, who finding him, as indeed
he might have been found at every period
of his life, oppressed by pecuniary diffi-
culties, urged him to go over to England,
where he assured him of a welcome
and honourable reception; but Kepler
could not resolve upon the proposed
journey, although in his letters he often
returned to the consideration of it. In
one of them, dated a year later, he says,
"The fires of civil war are raging in
Germany — they who are opposed to the
honour of the empire are getting the
upper hand— everything in my neigh-
bourhood seems abandoned to flame and
destruction. Shall I then cross the sea,
whither Wotton invites me ? I, a Ger-
man ? a lover of firm land ? who dread
the confinement of an island ? who pre-
sage its dangers, and must drag along
with me my little wife and flock of chil-
dren? Besides my son Louis, now
thirteen years old, 1 have a marriage-
able daughter, a two-year old son by my
second marriage, an infant daughter, and
its mother but just recovering from
her confinement." Six years later, he
says again, — "As soon as the Rudol-
phine Tables are published, my desire will
be to find a place where I can lecture
on them to a considerable assembly ; if
possible,- in Germany ; if not, why then
in Italy, France, the Netherlands, or
England, provided the salary is ade-
quate for a traveller."
In the same year in which he received

this invitation an affront was put upon
Kepler by his early patrons, the States
of Styria, who ordered all the" copies of
his " Calendar," for 1624, to be publicly
burnt. Kepler declares that the reason
of this was, that he had given prece-
dence in the title-page to the States of
Upper Ens, in whose service he then
was, above Styria. As this happened
during his absence in Wirlembenr, it was
immediately coupled by rumour with
his hasty .departure from Linz : it was
said that he had incurred the Emperor's
displeasure, and that a large sum was
set upon his head. At this period Mat-
thias had been succeeded by Ferdi-
nand III., who still continued to Kepler
his barren title of imperial mathema-
tician.

In 1624 Kepler went to Vienna, in
the hopes of getting money to complete
theRudolphineTables,but was obliged to
be satisfied with the sum of 6000 florins
and with recommendatory letters to the
States of Suabia, from whom he also
collected some money due to the em-
peror. On his return he revisited the
University of Tubingen, where he found
his old preceptor, Mastlin, still alive,
but almost worn out with old age.
Mastlin had well deserved the' regard
Kepler always appears to have enter-
tained for him ; he had treated him with
great liberality whilst at the University,
where he refused to receive any remune-
ration for his instruction. Kepler took
every opportunity of shewing his grati-
tude ; even whilst he was struggling with
poverty he contrived to send his old
master a handsome silver cup, in ac-
knowledging the receipt of which Mast-
lin says, — " Your mother had taken it
into her head that you owed me two
hundred florins, and had brought fifteen
florins and a chandelier towards reducing
the debt, which I advised her to send to
you. I asked her to stay to dinner, which
she refused : however, we handselled
your cup, as you know she is of a thirsty
temperament."

The publication of the Rudolphine
Tables, which Kepler always had so
much at heart, was again delayed, not-
withstanding the recent grant, by the
disturbances arising out of the two par-
ties into which the Reformation had
divided the whole of Germany. Kepler's
library was sealed up by desire of the
Jesuits, and nothing but his connexion
with the Imperial Court secured to him
his own personal indemnity. Then fol-
lowed a popular insurrection, and the

KEPLER.

51

peasantry blockaded Linz, so that it was
not until 1627 that these celebrated tables
finally made their appearance, the ear-
liest calculated on the supposition that
the planets move in elliptic orbits.
Ptolemy's tables had been succeeded by
the " Alphonsine," so called from Al-
phonso, King of Castile, who, in the
thirteenth century, was an enlightened
patron of astronomy. After the disco-
veries of Copernicus, these again made
way for the Prussian, or Prutenic tables,"
calculated by his pupils Reinhold and
Rheticus. These remained in use till
the observations of TychoBrahe showed
their insufficiency, and Kepler's new
theories enabled him to improve upon
them. The necessary types for these
tables were cast at Kepler's own expense.
They are divided into four parts, the
first and third containing a variety of
logarithmic and other tables, for the
purpose of facilitating astronomical cal-
culations. In the second are tables of
the elements of the sun, moon, and
planets. The fourth gives the places of
1000 stars as determined byTycho, and
also at the end his table of refractions,
which appears to have been different for
the sun, moon, and stars. Tycho Brahe
assumed the horizontal refraction of the
sun to be 7' 30", of the moon 8', and of
the other stars 3'. He considered all
refraction of the atmosphere to be in-
sensible above 45° of altitude, and
even at half that altitude in the case of
the fixed stars. A more detailed ac-
count of these tables is here obviously
unsuitable: it will be sufficient to say
merely, that if Kepler had done' nothing
in the course of his whole life but con-
struct these, he would have well earned
the title of a most useful and indefati-
gable calculator.

Some copies of these tables have pre-
fixed to them a very remarkable map,
divided by hour lines, the object of
which is thus explained : —

" The use of this nautical map is, that
if at a given hour the place of the moon
is known by its edge being observed to
touch any known star, or the edges of
the sun, or the shadow of the earth ;
and if that place shall (if necessary) be
reduced from apparent to real by clear-
ing it of parallax ; and if the hour at
Uraniburg be computed by the Rudol-
phine tables, when the moon occupied
that true place, the difference will show
the observer's meridian, whether the
picture of the shores be accurate or net,

for by this means it may come to be
corrected."

This is probably one pf the earliest
announcements of the method of deter-
mining longitudes by occultations ; the
imperfect theory of the moon long re-
mained a principal obstacle to its intro-
duction in practice. Another interesting
passage connected with the same object
may be introduced here. In a letter to
his friend Cruger, 'dated in 1616, Kep-
ler says : " You propose a method of
observing the distances of places by sun-
dials and automata. It is good, but needs
a very accurate practice, and confidence
in those who have the care of the clocks.
Let there be only one clock, and let it
be transported ; and in both places let
meridian lines be drawn with which the
clock may be compared when brought.
The only doubt remaining is, whether a
greater error is likely from the unequal
tension in the automaton, and from its
motion, which varies with the state of
the air, or from actually measuring the
distances. For if we trust the latter,
we can easily determine the longitudes by
observing the -differences of the height
of the pole."

In an Appendix to the Rudolphine
Tables, or, as Kepler calls it, " an
alms doled out to the nativity casters,"
he has shown how they may use his
tables fbr their astrological predictions.
Everything in his hands became an
allegory ; and on this occasion he says,
—"Astronomy is the daughter of As-
trology, and this modern Astrology,
again, is the daughter of Astronomy,
bearing something of the lineaments of
her grandmother; and, as 1 have al-
ready said, this foolish daughter, Astro-
logy, supports her wise but needy mother,
Astronomy, from the profits of a profes-
sion not generally considered credit-
able."

Soon after the publication of these
tables, the Grand Duke of Tuscany sent
him a golden chain ; and if we remem-
ber the high credit in which Galileo
stood at this time in Florence, it does
not seem too much to attribute this
honourable mark of approbation to his
representation of the value of Kepler's
services to astronomy. This was soon
followed by a new and final change in his
fortunes. He received permission from
the emperor to attach himself to the
celebrated Duke of Friedland, Albert
Wallenstein, one of the most remark-
able men in the history of that time.

52

KEPLER.

Wallenstein was a firm believer in as-
trology, and the reception Kepler ex-
perienced by him was probably due, in
great measure, to his reputation in that
art. However that may be, Kepler
found in him a more munificent pa-
tron than any one of his three em-
perors ; but he was not destined long to
enjoy the appearance of better fortune.
Almost the last work which he published
was a commentary on the letter address-
ed, by the missionary Terrentio, from
China, to the Jesuits at Ingolstadt. The
object of this communication was to ob-
tain from Europe means for carrying
into effect a projected scheme for im-
proving the Chinese calendar. In this
essay Kepler maintains the opinion,
which has been discussed with soiimich
warmth in more modern times, that the
pretended ancient observations of the
Chinese were obtained by computing
them backwards from a much more re-
cent date. Wallenstein furnished him
with an assistant for his calculations, and
with a printing press ; and through his
influence nominated him to the profes-
sorship in the University of Rostoch, in
the Duchy of Mecklenburg. His
claims on the imperial treasury, which
amounted at this time to 8000 crowns,
and vvhich Ferdinand would gladly have
transferred to the charge of "Wallenstein,
still remained unsatisfied. Kepler made
a last attempt to obtain them at Ratis-
bon, where the imperial meeting was
held, but without success. The fatigue
and vexation occasioned by his fruitless
journey brought on a fever, which un-
expectedly put an end to his life, in the
early part of November, 1630, in his
fifty-ninth year. His old master, Mast-
lin, survived him for* about a year, dy-
ing at the age of eighty-one.

Kepler left behind him two children
by his first wife, Susanna and Louis ; and
three sons and two daughters, Sebald,
Cordelia, Friedman, Hildebert, and Anna
Maria, by his widow. Susanna mar-
ried, a few months before her father's
death, a physician named Jacob Bartsch,
the same who latterly assisted Kepler
in preparing his "Ephemeris." He died
very shortly after Kepler himself. Louis
studied medicine, and died in 1663,
whilst practising as a physician at
Konigsberg. The other children died
young.

Upon Kepler's death the Duke of Fried-
land caused an inventory to be taken of
his effects, when it appeared that near

24,000 florins were due to him, chiefly
on account of his salary from the em-
peror. His daughter Susanna, Bartsch's
widow, managed to obtain a part of these
arrears by refusing to give up Tycho
Brahe's observations till her claims were
satisfied. The widow and younger chil-
dren were left in very straightened cir-
cumstances, which induced Louis, Kep-
ler's eldest son, to print, for their relief,
one of his father's works, which had
been left by him unpublished. It was
not without much reluctance, in conse-
quence of a superstitious feeling which
he did not attempt to conceal or deny.
Kepler himself, and his son-in-law,
Bartsch, had been employed in prepar-
ing it for publication at the time of
their respective deaths ; and Louis con-
fessed that he did not approach the task
without apprehension that he was in-
curring some risk of a similar fate.
This little rhapsody is entitled a " Dream
on Lunar Astronomy;" and was in-
intended to illustrate the appearances
which would present themselves to an
astronomer living upon the moon.

The narrative in the dream is put into
the .mouth of a personage, named Du-
racoto, the son of an Icelandic enchan-
tress, of the name of Fiolxhildis. Kep-
ler tells us that he chose the last name
from an old map of Europe in his house,
in which Iceland was called Fiolx : Du-
racoto seemed to him analogous to the
names he found in the history of Scot-
land, the neighbouring country. Fiolx-
hildis was in the habit of selling winds
to mariners, and used to collect herbs
to use in her incantations on the sides
of Mount Hecla, on the Eve of St.
John. Duracotb cut open one of his
mother's bags, in punishment of which
she sold him to some traders, who
brought him to Denmark, where he be-
came acquainted with Tycho Brahe.
On his return to Iceland, Fiolxhildis
received him kindly, and was delighted
with the progress he had made in astro-
nomy. She then informed him of the
existence of certain spirits, or demons,
from whom, although no traveller her-
self, she acquired a knowledge of other
countries, and especially of a very re-
markable country, called Livania. Du-
racoto requesting further information,
the necessary ceremonies were performed
for invoking the demon ; Duracoto and
his mother enveloped their heads in their
clothing, and presently " the screaking of
a harsh dissonant voice began to speak

KEPLER.

53

in'the Icelandic tongue." The island of
Livania is situated in the depths of
ether, at the distance of about 250000
miles ; the road thence or thither is very
seldom open, and even when it is
passable, mankind find the journey a
most difficult and dangerous one. The
demon describes the method employed
by his fellow spirits to convey such
travellers as are thought fit for the
undertaking : " We bring no sedentary
people into our company, no corpulent
or delicate persons ; but we pick out
those who waste their life in the con-
tinual use of post-horses, or who sail
frequently to the Indies ; who are ac-
customed to live upon biscuit, garlic,
dried fish, and such abominable feeding.
Those withered old hags are exactly fit
for us, of whom the story is familiar
that they travel immense distances by
night on goats, and forks, and old petti-
coats. The Germans do not suit us
at all; but we do not reject the dry
Spaniards." This extract will probably
be sufficient to show the style of the
work. The inhabitants of Livania are
represented to be divided into two
classes, the Privolvans and Subvolvans,
by whom are meant those supposed to
live in the hemisphere facing the earth,
which is called the Volva, and those on
the opposite half of the moon : but
there is nothing very striking in the ac-
count given of the various pheno-
mena as respects these two classes. In
some notes which were added some time
after the book was first written, are
some odd insights into Kepler's method,.
of composing. Fiolxhildis had been made
to invoke the daemon with twenty-one
characters ; Kepler declares, in a note,
that he cannot remember why he fixed
on this number, "except because that is
the number of letters in A&tronomia
Copernicana, or because there are
twenty-one combinations of the planets,
two together, or because there are
twenty-one different throws upon two
dice." The dream is abruptly termi-
nated by a storm, in which, says Kep-
ler, " I suddenly waked ; the Demon,
Duracoto, and Fiolxhildis were gone,
and instead of their covered heads, I
found myself rolled up among the
blankets."

Besides this trifle, Kepler left behind
him a vast mass of unpublished writings,
which came at last, into the hands of his
biographer, Hantsch. In 17 14, Hantsch
issued a prospectus for publishing them
by subscription, in twenty -two folio

volumes. The plan met no encourage-
ment, and nothing was published but a
single folio volume of letters to and from
Kepler, which seem to have furnished
the principal materials for the memoir
prefixed to them. After various un-
availing attempts to interest different
learned bodies in their appearance, the
manuscripts were purchased for the
library at St. Petersburg, where Euler,
Lexell, and Kraft, undertook to examine
them, and select the most interesting
parts for publication. The result of this
examination does not appear.

Kepler's body was buried in St. Pe-
ter's churchyard at Ratisbon, and a
simple inscription was placed on his
tombstone. This appears to have
been destroyed not long after, in the
course of the wars which still deso-
lated the country. In 1786, a proposal
was made to erect a marble monument
to his memory, but nothing was done.
Kastner, on whose authority it is men-
tioned, says upon this, rather bitterly,
that it matters little whether or not Ger-
many, having almost refused him bread
during his life, should, a, century and a
half after his death, offer him a stone.

Delambre mentions, in his History of
Astronomy, that this design was resumed
in 1803 by the Prince Bishop of Con-
stance, and that a monument has been
erected in the Botanical Garden at Ra-
tisbon, near the place of his interment.
It is built in, the form of a temple, sur-
mounted by a sphere ; in the centre is
placed a bust of Kepler, in Carrara
marble. Delambre does not mention the
original of the bust ; but says it is not
unlike the figure engraved in the frontis-
piece of the Rudolphine Tables. That
frontispiece consists of a portico of ten
pillars, supporting a cupola covered with
astronomical emblems. Copernicus,
Tycho Brahe, Ptolemy, Hipparchus, and
other astronomers, are seen among them.
In one of the compartments of the com-
mon pedestal is apian of the observatory
at Uraniburg ; in another, a printing
press ; in a third is the figure of a man,
meant for Kepler, sealed at a table. He
is identified by the titles of his works,
which are round him ; but the whole is
so small as to convey very little idea of
his figure or countenance. The only
portrait known of Kepler was given by
him to his assistant Gringallet, who pre-
sented it'toBernegger; and it was placed
by the latter in the library at Strasburg.
Hantsch -had a copy taken for the purpose
of engraving it, but died before it was

KEPLER.

completed. A portrait of Kepler is en-
graved in the seventh part of Boissard's
Bibliotheca Chalcographica. It is not
known whence this was taken, but it
may, perhaps, be a copy of that which
was engraved by desire of Bernegger in
1620. The likeness is said not to have
been well preserved. " His heart and
genius," says Kiistner, " are faithfully
depicted in his writings ; and that may
console us, if we cannot entirely trust
his portrait." In the preceding pages, it
has been endeavoured to select such
passages from his writings as might
throw the greatest light on his character,
•with a subordinate reference only to the
importance of the subjects treated. In
conclusion, it maybe well to support the
opinion which has been ventured on the
real nature of his triumphs, and on the
danger of attempting to follow his me-
thod in the pursuit of truth, by the judg-
ment pronounced by Delambre, as well

sidering these matters in another point of
view, it is not impossible to convince
ourselves that Kepler may have been
always the same. Ardent, restless,
burning to distinguish himself by his
discoveries, he attempted everything ;
and having once obtained a glimpse of
one, no labour was too hard for him in
following or verifying it. All his at-
tempts had not the same success, and,
in fact, that was impossible. Those
which have failed seem to us only
fanciful ; those which have been more
fortunate appear sublime. When in
search of that which really existed, he
has sometimes found it ; when he devoted
himself to the pursuit of a chimera,' he
could not but fail; but even there he
unfolded the same qualities, and that ob-
stinate perseverance that must triumph
over all difficulties but those which are
insurmountable*."

On his failures as On his SUCCeSS. "Con- * HUtoiredel'AstronomieModerne, Paris, 1821.

List of Kepler's published Works.

Ein Calender

Prodromus Dissertat. Cosmograph.

De fundamentis Astrologiae

Paralipomena ad Vitellionem . ,

Epistola de Solis deliquio

De Stella nova .

Vom Kometen . . .

Antwort an Rb'slin .

Astronomia Nova

Tertius interveniens ...

Dissertatio cum Nuncio Sidereo

Strena, seu De nive sexangula .

Dioptrica ....

Vom Geburts Jahre des Heylandes

Respons. ad e'pist S. Calvisiii

Eclogae Chronicae . . .

Nova Stereometria . . .

Ephemerides 1617—1620

Epitomes Astron. Copern. Libri i. ii. iii.

De Cometis ....

Harm on ice Mundi . ,

Kanones Pueriles . . .

Epitomes Astron. Copern. Liber iv.

Epitomes Astron. Copern. Libri v. vi. vii.

Discurs von der grossen Conjunction

Chilias Logarithmorum .

Supplementum . .

Hyperaspistes

Tabulae liudolphinae . . .

Resp. ad epist. J. Bartschii

De anni 1631 phaenomenis

Terrentii epistolium cum conimentatiuncu]&

Ephemerides ....

Gratz,

Tubingce,

Pragce,

Francofurli,

. Pragce,

Halle,

Pragce,

Pragce.

Frankfurt',

Francofurti,

Frankfurt,

Francofurti,

Strasburg,

Francofurti,

Frankfurt,

Lincii,

. Lincii,

Lentiis,

Aug. Vindelic.
Lincii.

. UlmcK,

Lentiis,

Francofurti,

iMZ.

Marpurgi,

Lentiis,

Francofurti,

U/mce,

Sagani,

Lipsa,

, Sagani,

Sagani,

1594

1596, 4 to.
1602, 4to.
1604, 4to.
1605
1606, 4 to.

1608, 4to.

1609, 4to.

1609, fol.

1610, 4to.

1610, 4to.

1611, 4to.
1611, 4to.

1613, 4to.

1614, 4 to.
1615,4(o.
1615,4to.
1616, 4to.

1618, 8vo.
1619,4lo.

1619, fol.
1620

1622, 8vo.
1622, 8vo.
Ifi23, 4to.

1624, fol.

1625, 4to.
1625, 8vo.
1627, fol.
1629, 4to.

1629, 4to.

1630, 4to.
1630, 4to.

Somnium .
Tabulae mannales

Francofurti, 1634, 4 to.
Arycnlorati, 1700, 12mo.

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