THE MIDDLE AGES.
“The lamp burns low, and through the casement bars
Grey morning glimmers feebly.”
BROWNING’S _Paracelsus_.
55. About fourteen centuries elapsed between the publication of the
_Almagest_ and the death of Coppernicus (1543), a date which is in
astronomy a convenient landmark on the boundary between the Middle Ages
and the modern world. In this period, nearly twice as long as that
which separated Thales from Ptolemy, almost four times as long as that
which has now elapsed since the death of Coppernicus, no astronomical
discovery of first-rate importance was made. There were some important
advances in mathematics, and the art of observation was improved; but
theoretical astronomy made scarcely any progress, and in some respects
even went backward, the current doctrines, if in some points slightly
more correct than those of Ptolemy, being less intelligently held.
In the Western World we have already seen that there was little to
record for nearly five centuries after Ptolemy. After that time ensued
an almost total blank, and several more centuries elapsed before there
was any appreciable revival of the interest once felt in astronomy.
56. Meanwhile a remarkable development of science had taken place in
the East during the 7th century. The descendants of the wild Arabs
who had carried the banner of Mahomet over so large a part of the
Roman empire, as well as over lands lying farther east, soon began to
feel the influence of the civilisation of the peoples whom they had
subjugated, and Bagdad, which in the 8th century became the capital of
the Caliphs, rapidly developed into a centre of literary and scientific
activity. Al Mansur, who reigned from A.D. 754 to 775, was noted as a
patron of science, and collected round him learned men both from India
and the West. In particular we are told of the arrival at his court
in 772 of a scholar from India bearing with him an Indian treatise on
astronomy,[37] which was translated into Arabic by order of the Caliph,
and remained the standard treatise for nearly half a century. From Al
Mansur’s time onwards a body of scholars, in the first instance chiefly
Syrian Christians, were at work at the court of the Caliphs translating
Greek writings, often through the medium of Syriac, into Arabic. The
first translations made were of the medical treatises of Hippocrates
and Galen; the Aristotelian ideas contained in the latter appear to
have stimulated interest in the writings of Aristotle himself, and thus
to have enlarged the range of subjects regarded as worthy of study.
Astronomy soon followed medicine, and became the favourite science of
the Arabians, partly no doubt out of genuine scientific interest, but
probably still more for the sake of its practical applications. Certain
Mahometan ceremonial observances required a knowledge of the direction
of Mecca, and though many worshippers, living anywhere between the
Indus and the Straits of Gibraltar, must have satisfied themselves
with rough-and-ready solutions of this problem, the assistance which
astronomy could give in fixing the true direction was welcome in
larger centres of population. The Mahometan calendar, a lunar one,
also required some attention in order that fasts and feasts should
be kept at the proper times. Moreover the belief in the possibility
of predicting the future by means of the stars, which had flourished
among the Chaldaeans (chapter I., § 18), but which remained to a great
extent in abeyance among the Greeks, now revived rapidly on a congenial
oriental soil, and the Caliphs were probably quite as much interested
in seeing that the learned men of their courts were proficient in
astrology as in astronomy proper.
The first translation of the _Almagest_ was made by order of Al
Mansur’s successor Harun al Rasid (A.D. 765 or 766-A.D. 809), the
hero of the _Arabian Nights_. It seems, however, to have been found
difficult to translate; fresh attempts were made by _Honein ben
Ishak_ (?-873) and by his son _Ishak ben Honein_ (?-910 or 911), and
a final version by _Tabit ben Korra_ (836-901) appeared towards the
end of the 9th century. Ishak ben Honein translated also a number
of other astronomical and mathematical books, so that by the end of
the 9th century, after which translations almost ceased, most of the
more important Greek books on these subjects, as well as many minor
treatises, had been translated. To this activity we owe our knowledge
of several books of which the Greek originals have perished.
57. During the period in which the Caliphs lived at Damascus an
observatory was erected there, and another on a more magnificent scale
was built at Bagdad in 829 by the Caliph Al Mamun. The instruments
used were superior both in size and in workmanship to those of the
Greeks, though substantially of the same type. The Arab astronomers
introduced moreover the excellent practice of making regular and as
far as possible nearly continuous observations of the chief heavenly
bodies, as well as the custom of noting the positions of known stars
at the beginning and end of an eclipse, so as to have afterwards an
exact record of the times of their occurrence. So much importance was
attached to correct observations that we are told that those of special
interest were recorded in formal documents signed on oath by a mixed
body of astronomers and lawyers.
Al Mamun ordered Ptolemy’s estimate of the size of the earth to be
verified by his astronomers. Two separate measurements of a portion
of a meridian were made, which, however, agreed so closely with one
another and with the erroneous estimate of Ptolemy that they can hardly
have been independent and careful measurements, but rather rough
verifications of Ptolemy’s figures.
58. The careful observations of the Arabs soon shewed the defects in
the Greek astronomical tables, and new tables were from time to time
issued, based on much the same principles as those in the _Almagest_,
but with changes in such numerical data as the relative sizes of the
various circles, the positions of the apogees, and the inclinations of
the planes, etc.
To Tabit ben Korra, mentioned above as the translator of the
_Almagest_, belongs the doubtful honour of the discovery of a supposed
variation in the amount of the precession (chapter II., §§ 42, 50). To
account for this he devised a complicated mechanism which produced a
certain alteration in the position of the ecliptic, thus introducing
a purely imaginary complication, known as the =trepidation=, which
confused and obscured most of the astronomical tables issued during the
next five or six centuries.
59. A far greater astronomer than any of those mentioned in the
preceding articles was the Arab prince called from his birthplace Al
Battani, and better known by the Latinised name _Albategnius_, who
carried on observations from 878 to 918 and died in 929. He tested
many of Ptolemy’s results by fresh observations, and obtained more
accurate values of the obliquity of the ecliptic (chapter I., § 11) and
of precession. He wrote also a treatise on astronomy which contained
improved tables of the sun and moon, and included his most notable
discovery—namely, that the direction of the point in the sun’s orbit
at which it is farthest from the earth (the apogee), or, in other
words, the direction of the centre of the eccentric representing the
sun’s motion (chapter II., § 39), was not the same as that given in
the _Almagest_; from which change, too great to be attributed to mere
errors of observation or calculation, it might fairly be inferred that
the apogee was slowly moving, a result which, however, he did not
explicitly state. Albategnius was also a good mathematician, and the
author of some notable improvements in methods of calculation.[38]
60. The last of the Bagdad astronomers was _Abul Wafa_ (939 or
940-998), the author of a voluminous treatise on astronomy also known
as the _Almagest_, which contained some new ideas and was written on
a different plan from Ptolemy’s book, of which it has sometimes been
supposed to be a translation. In discussing the theory of the moon
Abul Wafa found that, after allowing for the equation of the centre
and for the evection, there remained a further irregularity in the
moon’s motion which was imperceptible at conjunction, opposition, and
quadrature, but appreciable at the intermediate points. It is possible
that Abul Wafa here detected an inequality rediscovered by Tycho Brahe
(chapter _V._, § 111) and known as the =variation=, but it is equally
likely that he was merely restating Ptolemy’s prosneusis (chapter
II., § 48).[39] In either case Abul Wafa’s discovery appears to have
been entirely ignored by his successors and to have borne no fruit.
He also carried further some of the mathematical improvements of his
predecessors.
Another nearly contemporary astronomer, commonly known as _Ibn Yunos_
(?-1008), worked at Cairo under the patronage of the Mahometan rulers
of Egypt. He published a set of astronomical and mathematical tables,
the _Hakemite Tables_, which remained the standard ones for about
two centuries, and he embodied in the same book a number of his
own observations as well as an extensive series by earlier Arabian
astronomers.
61. About this time astronomy, in common with other branches of
knowledge, had made some progress in the Mahometan dominions in Spain
and the opposite coast of Africa. A great library and an academy were
founded at Cordova about 970, and centres of education and learning
were established in rapid succession at Cordova, Toledo, Seville, and
Morocco.
The most important work produced by the astronomers of these places
was the volume of astronomical tables published under the direction
of _Arzachel_ in 1080, and known as the _Toletan Tables_, because
calculated for an observer at Toledo, where Arzachel probably lived.
To the same school are due some improvements in instruments and
in methods of calculation, and several writings were published in
criticism of Ptolemy, without, however, suggesting any improvements on
his ideas.
Gradually, however, the Spanish Christians began to drive back their
Mahometan neighbours. Cordova and Seville were captured in 1236 and
1248 respectively, and with their fall Arab astronomy disappeared from
history.
62. Before we pass on to consider the progress of astronomy in Europe,
two more astronomical schools of the East deserve mention, both
of which illustrate an extraordinarily rapid growth of scientific
interests among barbarous peoples. Hulagu Khan, a grandson of the
Mongol conqueror Genghis Khan, captured Bagdad in 1258 and ended the
rule of the Caliphs there. Some years before this he had received
into favour, partly as a political adviser, the astronomer _Nassir
Eddin_ (born in 1201 at Tus in Khorassan), and subsequently provided
funds for the establishment of a magnificent observatory at Meraga,
near the north-west frontier of modern Persia. Here a number of
astronomers worked under the general superintendence of Nassir Eddin.
The instruments they used were remarkable for their size and careful
construction, and were probably better than any used in Europe in the
time of Coppernicus, being surpassed first by those of Tycho Brahe
(chapter V.).
Nassir Eddin and his assistants translated or commented on nearly all
the more important available Greek writings on astronomy and allied
subjects, including Euclid’s _Elements_, several books by Archimedes,
and the _Almagest_. Nassir Eddin also wrote an abstract of astronomy,
marked by some little originality, and a treatise on geometry. He does
not appear to have accepted the authority of Ptolemy without question,
and objected in particular to the use of the equant (chapter II., §
51), which he replaced by a new combination of spheres. Many of these
treatises had for a long time a great reputation in the East, and
became in their turn the subject-matter of commentary.
But the great work of the Meraga astronomers, which occupied them 12
years, was the issue of a revised set of astronomical tables, based
on the Hakemite Tables of Ibn Yunos (§ 60), and called in honour of
their patron the _Ilkhanic Tables_. They contained not only the usual
tables for computing the motions of the planets, etc., but also a star
catalogue, based to some extent on new observations.
An important result of the observations of fixed stars made at Meraga
was that the precession (chapter II., § 42) was fixed at 51″, or
within about 1″ of its true value. Nassir Eddin also discussed the
supposed trepidation (§ 58), but seems to have been a little doubtful
of its reality. He died in 1273, soon after his patron, and with him
the Meraga School came to an end as rapidly as it was formed.
63. Nearly two centuries later _Ulugh Begh_ (born in 1394), a grandson
of the savage Tartar Tamerlane, developed a great personal interest
in astronomy, and built about 1420 an observatory at Samarcand (in
the present Russian Turkestan), where he worked with assistants. He
published fresh tables of the planets, etc., but his most important
work was a star catalogue, embracing nearly the same stars as that of
Ptolemy, but observed afresh. This was probably the first substantially
independent catalogue made since Hipparchus. The places of the stars
were given with unusual precision, the minutes as well as the degrees
of celestial longitude and latitude being recorded; and although a
comparison with modern observation shews that there were usually errors
of several minutes, it is probable that the instruments used were
extremely good. Ulugh Begh was murdered by his son in 1449, and with
him Tartar astronomy ceased.
64. No great original idea can be attributed to any of the Arab and
other astronomers whose work we have sketched. They had, however, a
remarkable aptitude for absorbing foreign ideas, and carrying them
slightly further. They were patient and accurate observers, and
skilful calculators. We owe to them a long series of observations,
and the invention or introduction of several important improvements
in mathematical methods.[40] Among the most important of their
services to mathematics, and hence to astronomy, must be counted the
introduction, from India, of our present system of writing numbers,
by which the value of a numeral is altered by its position, and fresh
symbols are not wanted, as in the clumsy Greek and Roman systems,
for higher numbers. An immense simplification was thereby introduced
into arithmetical work.[41] More important than the actual original
contributions of the Arabs to astronomy was the service that they
performed in keeping alive interest in the science and preserving the
discoveries of their Greek predecessors.
Some curious relics of the time when the Arabs were the great masters
in astronomy have been preserved in astronomical language. Thus we have
derived from them, usually in very corrupt forms, the current names
of many individual stars, _e.g._ Aldebaran, Altair, Betelgeux, Rigel,
Vega (the constellations being mostly known by Latin translations of
the Greek names), and some common astronomical terms such as zenith
and =nadir= (the invisible point on the celestial sphere opposite the
zenith); while at least one such word, almanack, has passed into common
language.
65. In Europe the period of confusion following the breakup of the
Roman empire and preceding the definite formation of feudal Europe
is almost a blank as regards astronomy, or indeed any other natural
science. The best intellects that were not absorbed in practical life
were occupied with theology. A few men, such as the Venerable Bede
(672-735), living for the most part in secluded monasteries, were
noted for their learning, which included in general some portions of
mathematics and astronomy; none were noted for their additions to
scientific knowledge. Some advance was made by Charlemagne (742-814),
who, in addition to introducing something like order into his extensive
dominions, made energetic attempts to develop education and learning.
In 782 he summoned to his court our learned countryman _Alcuin_
(735-804) to give instruction in astronomy, arithmetic, and rhetoric,
as well as in other subjects, and invited other scholars to join him,
forming thus a kind of Academy of which Alcuin was the head.
Charlemagne not only founded a higher school at his own court, but was
also successful in urging the ecclesiastical authorities in all parts
of his dominions to do the same. In these schools were taught the seven
liberal arts, divided into the so-called trivium (grammar, rhetoric,
and dialectic) and quadrivium, which included astronomy in addition to
arithmetic, geometry, and music.
66. In the 10th century the fame of the Arab learning began slowly
to spread through Spain into other parts of Europe, and the immense
learning of _Gerbert_, the most famous scholar of the century, who
occupied the papal chair as Sylvester II. from 999 to 1003, was
attributed in large part to the time which he spent in Spain, either in
or near the Moorish dominions. He was an ardent student, indefatigable
in collecting and reading rare books, and was especially interested in
mathematics and astronomy. His skill in making astrolabes (chapter II.,
§ 49) and other instruments was such that he was popularly supposed to
have acquired his powers by selling his soul to the Evil One. Other
scholars shewed a similar interest in Arabic learning, but it was not
till the lapse of another century that the Mahometan influence became
important.
At the beginning of the 12th century began a series of translations
from Arabic into Latin of scientific and philosophic treatises,
partly original works of the Arabs, partly Arabic translations of the
Greek books. One of the most active of the translators was _Plato of
Tivoli_, who studied Arabic in Spain about it 1116, and translated
Albategnius’s _Astronomy_ (§ 59), as well as other astronomical books.
At about the same time Euclid’s _Elements_, among other books, was
translated by _Athelard of Bath_. _Gherardo of Cremona_ (1114-1187) was
even more industrious, and is said to have made translations of about
70 scientific treatises, including the _Almagest_, and the _Toletan
Tables_ of Arzachel (§ 61). The beginning of the 13th century was
marked by the foundation of several Universities, and at that of Naples
(founded in 1224) the Emperor Frederick II., who had come into contact
with the Mahometan learning in Sicily, gathered together a number of
scholars whom he directed to make a fresh series of translations from
the Arabic.
Aristotle’s writings on logic had been preserved in Latin translations
from classical times, and were already much esteemed by the scholars of
the 11th and 12th centuries. His other writings were first met with in
Arabic versions, and were translated into Latin during the end of the
12th and during the 13th centuries; in one or two cases translations
were also made from the original Greek. The influence of Aristotle over
mediæval thought, already considerable, soon became almost supreme, and
his works were by many scholars regarded with a reverence equal to or
greater than that felt for the Christian Fathers.
Western knowledge of Arab astronomy was very much increased by the
activity of _Alfonso X._ of Leon and Castile (1223-1284), who collected
at Toledo, a recent conquest from the Arabs, a body of scholars, Jews
and Christians, who calculated under his general superintendence a set
of new astronomical tables to supersede the _Toletan Tables_. These
_Alfonsine Tables_ were published in 1252, on the day of Alfonso’s
accession, and spread rapidly through Europe. They embodied no new
ideas, but several numerical data, notably the length of the year, were
given with greater accuracy than before. To Alfonso is due also the
publication of the _Libros del Saber_, a voluminous encyclopædia of the
astronomical knowledge of the time, which, though compiled largely from
Arab sources, was not, as has sometimes been thought, a mere collection
of translations. One of the curiosities in this book is a diagram
representing Mercury’s orbit as an ellipse, the earth being in the
_centre_ (cf. chapter VII., § 140), this being probably the first trace
of the idea of representing the celestial motions by means of curves
other than circles.
67. To the 13th century belong also several of the great scholars, such
as _Albertus Magnus_, _Roger Bacon_, and _Cecco d’ Ascoli_ (from whom
Dante learnt), who took all knowledge for their province. Roger Bacon,
who was born in Somersetshire about 1214 and died about 1294, wrote
three principal books, called respectively the _Opus Majus_, _Opus
Minus_, and _Opus Tertium_, which contained not only treatises on most
existing branches of knowledge, but also some extremely interesting
discussions of their relative importance and of the right method for
the advancement of learning. He inveighs warmly against excessive
adherence to authority, especially to that of Aristotle, whose books
he wishes burnt, and speaks strongly of the importance of experiment
and of mathematical reasoning in scientific inquiries. He evidently
had a good knowledge of optics and has been supposed to have been
acquainted with the telescope, a supposition which we can hardly regard
as confirmed by his story that the invention was known to Caesar, who
when about to invade Britain surveyed the new country from the opposite
shores of Gaul with a telescope!
Another famous book of this period was written by the Yorkshireman John
Halifax or Holywood, better known by his Latinised name _Sacrobosco_,
who was for some time a well-known teacher of mathematics at Paris,
where he died about 1256. His _Sphaera Mundi_ as an elementary treatise
on the easier parts of current astronomy, dealing in fact with little
but the more obvious results of the daily motion of the celestial
sphere. It enjoyed immense popularity for three or four centuries, and
was frequently re-edited, translated, and commented on: it was one of
the very first astronomical books ever printed; 25 editions appeared
between 1472 and the end of the century, and 40 more by the middle of
the 17th century.
68. The European writers of the Middle Ages whom we have hitherto
mentioned, with the exception of Alfonso and his assistants, had
contented themselves with collecting and rearranging such portions
of the astronomical knowledge of the Greeks and Arabs as they could
master; there were no serious attempts at making progress, and no
observations of importance were made. A new school, however, grew up
in Germany during the 15th century which succeeded in making some
additions to knowledge, not in themselves of first-rate importance,
but significant of the greater independence that was beginning to
inspire scientific work. _George Purbach_, born in 1423, became in
1450 professor of astronomy and mathematics at the University of
Vienna, which had soon after its foundation (1365) become a centre for
these subjects. He there began an _Epitome of Astronomy_ based on the
_Almagest_, and also a Latin version of Ptolemy’s planetary theory,
intended partly as a supplement to Sacrobosco’s textbook, from which
this part of the subject had been omitted, but in part also as a
treatise of a higher order; but he was hindered in both undertakings
by the badness of the only available versions of the _Almagest_—Latin
translations which had been made not directly from the Greek, but
through the medium at any rate of Arabic and very possibly of Syriac
as well (cf. § 56), and which consequently swarmed with mistakes. He
was assisted in this work by his more famous pupil John Müller of
Königsberg (in Franconia), hence known as _Regiomontanus_, who was
attracted to Vienna at the age of 16 (1452) by Purbach’s reputation.
The two astronomers made some observations, and were strengthened
in their conviction of the necessity of astronomical reforms by the
serious inaccuracies which they discovered in the _Alfonsine Tables_,
now two centuries old; an eclipse of the moon, for example, occurring
an hour late and Mars being seen 2° from its calculated place. Purbach
and Regiomontanus were invited to Rome by one of the Cardinals, largely
with a view to studying a copy of the _Almagest_ contained among the
Greek manuscripts which since the fall of Constantinople (1453) had
come into Italy in considerable numbers, and they were on the point of
starting when the elder man suddenly died (1461).
Regiomontanus, who decided on going notwithstanding Purbach’s death,
was altogether seven years in Italy; he there acquired a good knowledge
of Greek, which he had already begun to study in Vienna, and was thus
able to read the _Almagest_ and other treatises in the original; he
completed Purbach’s _Epitome of Astronomy_, made some observations,
lectured, wrote a mathematical treatise[42] of considerable merit,
and finally returned to Vienna in 1468 with originals or copies of
several important Greek manuscripts. He was for a short time professor
there, but then accepted an invitation from the King of Hungary to
arrange a valuable collection of Greek manuscripts. The king, however,
soon turned his attention from Greek to fighting, and Regiomontanus
moved once more, settling this time in Nürnberg, then one of the most
flourishing cities in Germany, a special attraction of which was that
one of the early printing presses was established there. The Nürnberg
citizens received Regiomontanus with great honour, and one rich man
in particular, _Bernard Walther_ (1430-1504), not only supplied him
with funds, but, though an older man, became his pupil and worked with
him. The skilled artisans of Nürnberg were employed in constructing
astronomical instruments of an accuracy hitherto unknown in Europe,
though probably still inferior to those of Nassir Eddin and Ulugh
Begh (§§ 62, 63). A number of observations were made, among the most
interesting being those of the comet of 1472, the first comet which
appears to have been regarded as a subject for scientific study rather
than for superstitious terror. Regiomontanus recognised at once the
importance for his work of the new invention of printing, and, finding
probably that the existing presses were unable to meet the special
requirements of astronomy, started a printing press of his own. Here he
brought out in 1472 or 1473 an edition of Purbach’s book on planetary
theory, which soon became popular and was frequently reprinted. This
book indicates clearly the discrepancy already being felt between the
views of Aristotle and those of Ptolemy. Aristotle’s original view was
that sun, moon, the five planets, and the fixed stars were attached
respectively to eight spheres, one inside the other; and that the outer
one, which contained the fixed stars, by its revolution was the primary
cause of the apparent daily motion of all the celestial bodies. The
discovery of precession required on the part of those who carried on
the Aristotelian tradition the addition of another sphere. According
to this scheme, which was probably due to some of the translators
or commentators at Bagdad (§ 56), the fixed stars were on a sphere,
often called the =firmament=, and outside this was a ninth sphere,
known as the =primum mobile=, which moved all the others; another
sphere was added by Tabit ben Korra to account for trepidation (§
58), and accepted by Alfonso and his school; an eleventh sphere was
added towards the end of the Middle Ages to account for the supposed
changes in the obliquity of the ecliptic. A few writers invented a
larger number. Outside these spheres mediaeval thought usually placed
the Empyrean or Heaven. The accompanying diagram illustrates the whole
arrangement.
[Illustration: FIG. 36.—The celestial spheres. From Apian’s
_Cosmographia_.]
These spheres, which were almost entirely fanciful and in no serious
way even professed to account for the details of the celestial motions,
are of course quite different from the circles known as deferents
and epicycles, which Hipparchus and Ptolemy used. These were mere
geometrical abstractions, which enabled the planetary motions to
be represented with tolerable accuracy. Each planet moved freely in
space, its motion being represented or described (not _controlled_) by
a particular geometrical arrangement of circles. Purbach suggested a
compromise by hollowing out Aristotle’s crystal spheres till there was
room for Ptolemy’s epicycles inside!
From the new Nürnberg press were issued also a succession of almanacks
which, like those of to-day, gave the public useful information about
moveable feasts, the phases of the moon, eclipses, etc.; and, in
addition, a volume of less popular _Ephemerides_, with astronomical
information of a fuller and more exact character for a period of about
30 years. This contained, among other things, astronomical data for
finding latitude and longitude at sea, for which Regiomontanus had
invented a new method.[43]
The superiority of these tables over any others available was such that
they were used on several of the great voyages of discovery of this
period, probably by Columbus himself on his first voyage to America.
In 1475 Regiomontanus was invited to Rome by the Pope to assist in a
reform of the calendar, but died there the next year at the early age
of forty.
Walther carried on his friend’s work and took a number of good
observations; he was the first to make any successful attempt to allow
for the atmospheric refraction of which Ptolemy had probably had some
knowledge (chapter II., § 46); to him is due also the practice of
obtaining the position of the sun by comparison with Venus instead of
with the moon (chapter II., § 39), the much slower motion of the planet
rendering greater accuracy possible.
After Walther’s death other observers of less merit carried on the
work, and a Nürnberg astronomical school of some kind lasted into the
17th century.
69. A few minor discoveries in astronomy belong to this or to a
slightly later period and may conveniently be dealt with here.
_Leonardo da Vinci_ (1452-1519), who was not only a great painter and
sculptor, but also an anatomist, engineer, mechanician, physicist, and
mathematician, was the first to explain correctly the dim illumination
seen over the rest of the surface of the moon when the bright part is
only a thin crescent. He pointed out that when the moon was nearly new
the half of the earth which was then illuminated by the sun was turned
nearly directly towards the moon, and that the moon was in consequence
illuminated slightly by this =earthshine=, just as we are by moonshine.
The explanation is interesting in itself, and was also of some value
as shewing an analogy between the earth and moon which tended to break
down the supposed barrier between terrestrial and celestial bodies
(chapter VI., § 119).
_Jerome Fracastor_ (1483-1543) and _Peter Apian_ (1495-1552), two
voluminous writers on astronomy, made observations of comets of some
interest, both noticing that a comet’s tail continually points away
from the sun, as the comet changes its position, a fact which has been
used in modern times to throw some light on the structure of comets
(chapter XIII., § 304).
_Peter Nonius_ (1492-1577) deserves mention on account of the knowledge
of twilight which he possessed; several problems as to the duration of
twilight, its variation in different latitudes, etc., were correctly
solved by him; but otherwise his numerous books are of no great
interest.[44]
A new determination of the size of the earth, the first since the time
of the Caliph Al Mamun (§ 57), was made about 1528 by the French doctor
_John Fernel_ (1497-1558), who arrived at a result the error in which
(less than 1 per cent.) was far less than could reasonably have been
expected from the rough methods employed.
The life of Regiomontanus overlapped that of Coppernicus by three
years; the four writers last named were nearly his contemporaries; and
we may therefore be said to have come to the end of the comparatively
stationary period dealt with in this chapter.