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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- 

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 

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. 



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 

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. 


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."* 


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 


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 

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 


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 



-\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. 


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 

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. 


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. 


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 


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 w r hether 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 



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 



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, 


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- 




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 


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- 

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 

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 tw r enty-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?. 



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. 


\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- 

" 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 



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. 



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. 

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. 


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

GALILEO'S reputation was now rapidly 
increasing: his lectures were attended 
by many persons of the highest rank ; 
among whom w r eie 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. 


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 

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 



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, 

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 



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 

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 


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 



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.* 


Invention of the telesccpeFracastoro 
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. 



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 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?. 


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- 


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 ear r 
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, 



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, 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 




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- 

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- 

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, . 



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

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.* 


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 

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 



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 

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 



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. 



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 

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- 

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 



(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. 



&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 

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 


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 

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. 




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- 



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- 

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 

" 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 

" 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 



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 

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 



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." 

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. 565590, 722733 ; iv, 589 ; v. 
2b'l, 414; vii. 577; via. 1178. 

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. 



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. 



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. 



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." * 


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

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. 



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- 



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 

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. 


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 

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, 



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 

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



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- 


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- 

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 ; 



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." 


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

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 

" 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- 



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 

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. 


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 



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 

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- 



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 



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. 


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. 



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 Grassi 1 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 

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, 



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 



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 

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 



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. 


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

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. 



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, 



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 



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. 



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 


" 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- 

" 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. 



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 

" 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 



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, 

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- 

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. 


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 


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." 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 

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- 



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. 




Extracts from the Dialogues on the 

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 

" 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 

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. 



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- 

" 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 
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- 



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 r forgery.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 

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

Reflexiones Fhysico-Mathematicse, Pansiis,167 
If Yeutuvi. 


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 




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 ISimp. 
I do not ask you the name but the na- No, he does not say any thing more. 


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 

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 



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?. 



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. Colcmiae t 



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- 

" 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. W r e 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. 


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." 


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- 

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 
In a letter written in. April to Boe- 


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- 



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- 


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 


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. 


State of the Science of Motion before 

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 


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 

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.^ 



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 

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. 

Ev $i iv tifitvi 

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



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 

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 



d s 


*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 


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- 


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 


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 
,3que ponderibus non sequis concita ferri." 

De Rerura Natura, lib, U, v. 184239. 



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, 



" 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 

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 

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. 

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 



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." 



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. 


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 

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 

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 

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. 


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 

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 



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- 

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- 


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, 

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. 


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 



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. 


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 

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



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, 

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.' 



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. 


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, 



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." 



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- 

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 

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, 



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?. 



" 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 



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- 

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, 

f StoriadellaLett. Ital. 

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



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 Huyghens 1 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 

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. 




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 



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 

* Natural and Political Observations. London, 

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 

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. 



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- 



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; 



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. 



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. 



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 

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 
Galileo 1 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. 



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. 






4 to. 


















4 to. 






4 to. 















much that was 


Opere di Gal. Galilei 

Milano, 1811. 13 vols. 8vo. 

2 vols. 

3 vols. 

4 vols. 


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. 



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 


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

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 


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 


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- 


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 
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 



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. 

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


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 
of the 


be taken at 
1000, then 

the outer 

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

1 According to 
they are 

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

orbit of 


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. 







D. Scr. 




























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 

9.27 ^ be successively 
,- 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 


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 136 2 3 : 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 


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 


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 


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. 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. 



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 

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- 

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, 



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 

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 



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 

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- 



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." 


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 



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 w r as 
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- 


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- 

" 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 the 1 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 



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 



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 now n 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 mode 1 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 



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. 

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 



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 

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- 

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, 


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 

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- 



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 

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 


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 

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- 

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. 



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 

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." 




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- 

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 



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 

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 


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 


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 7 h 23', the longitude of the 
aphelion of Mars was 4 s 28 48' 55" ; 
that the planet's mean longitude was 
6 s 51' 35 7 ; 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 

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 



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 

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 



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- 



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 

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. 



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 



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 

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 



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 


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 ; 



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 

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" 


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 
Tycho Brahe's assistant, he describes 
himself as follows : " For observations 



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 



singularity of my actions ; in busily in- 
quiring into, and weighing and dis- 
cussing, various reasons ; in the un T 
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 



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- 

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 


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- 

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 

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 

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 

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- 


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- 

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. 


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, 



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. 



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 



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, or r 
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 


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 


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- 



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- 

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 

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- 


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 


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 

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 



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 C 2 x DA 9 , 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. 


The Epitome prohibited at Rome Lo- 
garithmic Tables Trial of Catha- 
rine Kepler Kepler invited to Eng- 
land Rudolphine Tables Death 

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 



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." 

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 

" 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- 

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- 



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- 

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 

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 



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 

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- 

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. 



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 

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 



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 

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 


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 

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 16171620 

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 . . 


Tabulae liudolphinae . . . 

Resp. ad epist. J. Bartschii 

De anni 1631 phaenomenis 

Terrentii epistolium cum conimentatiuncu]& 

Ephemerides .... 





. Pragce, 












. Lincii, 


Aug. Vindelic. 

. UlmcK, 










, Sagani, 



1596, 4 to. 
1602, 4to. 
1604, 4to. 
1606, 4 to. 

1608, 4to. 

1609, 4to. 

1609, fol. 

1610, 4to. 

1610, 4to. 

1611, 4to. 
1611, 4to. 

1613, 4to. 

1614, 4 to. 
1616, 4to. 

1618, 8vo. 

1619, fol. 

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. 
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