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[Illustration: SIR ISAAC NEWTON
(From the bust by Roubiliac In Trinity College, Cambridge.)]
HISTORY OF ASTRONOMY
BY
GEORGE FORBES,
M.A., F.R.S., M. INST. C. E.,
(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON’S
COLLEGE, GLASGOW)
AUTHOR OF “THE TRANSIT OF VENUS,” RENDU’S
“THEORY OF THE GLACIERS OF SAVOY,” ETC., ETC.
CONTENTS
PREFACE
BOOK I. THE GEOMETRICAL PERIOD
1. PRIMITIVE ASTRONOMY AND ASTROLOGY
2. ANCIENT ASTRONOMY—CHINESE AND CHALDÆANS
3. ANCIENT GREEK ASTRONOMY
4. THE REIGN OF EPICYCLES—FROM PTOLEMY TO COPERNICUS
BOOK II. THE DYNAMICAL PERIOD
5. DISCOVERY OF THE TRUE SOLAR SYSTEM—TYCHO BRAHE—KEPLER
6. GALILEO AND THE TELESCOPE—NOTIONS OF GRAVITY BY HORROCKS, ETC.
7. SIR ISAAC NEWTON—LAW OF UNIVERSAL GRAVITATION
8. NEWTON’S SUCCESSORS—HALLEY, EULER, LAGRANGE,
LAPLACE, ETC.
9. DISCOVERY OF NEW PLANETS—HERSCHEL, PIAZZI, ADAMS,
AND LE VERRIER
BOOK III. OBSERVATION
10. INSTRUMENTS OF PRECISION—SIZE OF THE SOLAR SYSTEM
11. HISTORY OF THE TELESCOPE—SPECTROSCOPE
BOOK IV. THE PHYSICAL PERIOD
12. THE SUN
13. THE MOON AND PLANETS
14. COMETS AND METEORS
15. THE STARS AND NEBULÆ
ILLUSTRATIONS
INDEX
PREFACE
An attempt has been made in these pages to trace the evolution of
intellectual thought in the progress of astronomical discovery, and, by
recognising the different points of view of the different ages, to give
due credit even to the ancients. No one can expect, in a history of
astronomy of limited size, to find a treatise on “practical” or on
“theoretical astronomy,” nor a complete “descriptive astronomy,” and
still less a book on “speculative astronomy.” Something of each of
these is essential, however, for tracing the progress of thought and
knowledge which it is the object of this History to describe.
The progress of human knowledge is measured by the increased habit of
looking at facts from new points of view, as much as by the
accumulation of facts. The mental capacity of one age does not seem to
differ from that of other ages; but it is the imagination of new points
of view that gives a wider scope to that capacity. And this is
cumulative, and therefore progressive. Aristotle viewed the solar
system as a geometrical problem; Kepler and Newton converted the point
of view into a dynamical one. Aristotle’s mental capacity to understand
the meaning of facts or to criticise a train of reasoning may have been
equal to that of Kepler or Newton, but the point of view was different.
Then, again, new points of view are provided by the invention of new
methods in that system of logic which we call mathematics. All that
mathematics can do is to assure us that a statement A is equivalent to
statements B, C, D, or is one of the facts expressed by the statements
B, C, D; so that we may know, if B, C, and D are true, then A is true.
To many people our inability to understand all that is contained in
statements B, C, and D, without the cumbrous process of a mathematical
demonstration, proves the feebleness of the human mind as a logical
machine. For it required the new point of view imagined by Newton’s
analysis to enable people to see that, so far as planetary orbits are
concerned, Kepler’s three laws (B, C, D) were identical with Newton’s
law of gravitation (A). No one recognises more than the mathematical
astronomer this feebleness of the human intellect, and no one is more
conscious of the limitations of the logical process called mathematics,
which even now has not solved directly the problem of only three
bodies.
These reflections, arising from the writing of this History, go to
explain the invariable humility of the great mathematical astronomers.
Newton’s comparison of himself to the child on the seashore applies to
them all. As each new discovery opens up, it may be, boundless oceans
for investigation, for wonder, and for admiration, the great
astronomers, refusing to accept mere hypotheses as true, have founded
upon these discoveries a science as exact in its observation of facts
as in theories. So it is that these men, who have built up the most
sure and most solid of all the sciences, refuse to invite others to
join them in vain speculation. The writer has, therefore, in this short
History, tried to follow that great master, Airy, whose pupil he was,
and the key to whose character was exactness and accuracy; and he
recognises that Science is impotent except in her own limited sphere.
It has been necessary to curtail many parts of the History in the
attempt—perhaps a hopeless one—to lay before the reader in a limited
space enough about each age to illustrate its tone and spirit, the
ideals of the workers, the gradual addition of new points of view and
of new means of investigation.
It would, indeed, be a pleasure to entertain the hope that these pages
might, among new recruits, arouse an interest in the greatest of all
the sciences, or that those who have handled the theoretical or
practical side might be led by them to read in the original some of the
classics of astronomy. Many students have much compassion for the
schoolboy of to-day, who is not allowed the luxury of learning the art
of reasoning from him who still remains pre-eminently its greatest
exponent, Euclid. These students pity also the man of to-morrow, who is
not to be allowed to read, in the original Latin of the brilliant
Kepler, how he was able—by observations taken from a moving platform,
the earth, of the directions of a moving object, Mars—to deduce the
exact shape of the path of each of these planets, and their actual
positions on these paths at any time. Kepler’s masterpiece is one of
the most interesting books that was ever written, combining wit,
imagination, ingenuity, and certainty.
Lastly, it must be noted that, as a History of England cannot deal with
the present Parliament, so also the unfinished researches and untested
hypotheses of many well-known astronomers of to-day cannot be included
among the records of the History of Astronomy. The writer regrets the
necessity that thus arises of leaving without mention the names of many
who are now making history in astronomical work.
G. F.
_August_ 1_st_, 1909.
BOOK I. THE GEOMETRICAL PERIOD
1. PRIMITIVE ASTRONOMY AND ASTROLOGY.
The growth of intelligence in the human race has its counterpart in
that of the individual, especially in the earliest stages. Intellectual
activity and the development of reasoning powers are in both cases
based upon the accumulation of experiences, and on the comparison,
classification, arrangement, and nomenclature of these experiences.
During the infancy of each the succession of events can be watched, but
there can be no _à priori_ anticipations. Experience alone, in both
cases, leads to the idea of cause and effect as a principle that seems
to dominate our present universe, as a rule for predicting the course
of events, and as a guide to the choice of a course of action. This
idea of cause and effect is the most potent factor in developing the
history of the human race, as of the individual.
In no realm of nature is the principle of cause and effect more
conspicuous than in astronomy; and we fall into the habit of thinking
of its laws as not only being unchangeable in our universe, but
necessary to the conception of any universe that might have been
substituted in its place. The first inhabitants of the world were
compelled to accommodate their acts to the daily and annual
alternations of light and darkness and of heat and cold, as much as to
the irregular changes of weather, attacks of disease, and the fortune
of war. They soon came to regard the influence of the sun, in
connection with light and heat, as a cause. This led to a search for
other signs in the heavens. If the appearance of a comet was sometimes
noted simultaneously with the death of a great ruler, or an eclipse
with a scourge of plague, these might well be looked upon as causes in
the same sense that the veering or backing of the wind is regarded as a
cause of fine or foul weather.
For these reasons we find that the earnest men of all ages have
recorded the occurrence of comets, eclipses, new stars, meteor showers,
and remarkable conjunctions of the planets, as well as plagues and
famines, floods and droughts, wars and the deaths of great rulers.
Sometimes they thought they could trace connections which might lead
them to say that a comet presaged famine, or an eclipse war.
Even if these men were sometimes led to evolve laws of cause and effect
which now seem to us absurd, let us be tolerant, and gratefully
acknowledge that these astrologers, when they suggested such “working
hypotheses,” were laying the foundations of observation and deduction.
If the ancient Chaldæans gave to the planetary conjunctions an
influence over terrestrial events, let us remember that in our own time
people have searched for connection between terrestrial conditions and
periods of unusual prevalence of sun spots; while De la Rue, Loewy, and
Balfour Stewart[1] thought they found a connection between sun-spot
displays and the planetary positions. Thus we find scientific men, even
in our own time, responsible for the belief that storms in the Indian
Ocean, the fertility of German vines, famines in India, and high or low
Nile-floods in Egypt follow the planetary positions.
And, again, the desire to foretell the weather is so laudable that we
cannot blame the ancient Greeks for announcing the influence of the
moon with as much confidence as it is affirmed in Lord Wolseley’s
_Soldier’s Pocket Book_.
Even if the scientific spirit of observation and deduction (astronomy)
has sometimes led to erroneous systems for predicting terrestrial
events (astrology), we owe to the old astronomer and astrologer alike
the deepest gratitude for their diligence in recording astronomical
events. For, out of the scanty records which have survived the
destructive acts of fire and flood, of monarchs and mobs, we have found
much that has helped to a fuller knowledge of the heavenly motions than
was possible without these records.
So Hipparchus, about 150 B.C., and Ptolemy a little later, were able to
use the observations of Chaldæan astrologers, as well as those of
Alexandrian astronomers, and to make some discoveries which have helped
the progress of astronomy in all ages. So, also, Mr. Cowell[2] has
examined the marks made on the baked bricks used by the Chaldæans for
recording the eclipses of 1062 B.C. and 762 B.C.; and has thereby been
enabled, in the last few years, to correct the lunar tables of Hansen,
and to find a more accurate value for the secular acceleration of the
moon’s longitude and the node of her orbit than any that could be
obtained from modern observations made with instruments of the highest
precision.
So again, Mr. Hind[3] was enabled to trace back the period during which
Halley’s comet has been a member of the solar system, and to identify
it in the Chinese observations of comets as far back as 12 B.C. Cowell
and Cromellin extended the date to 240 B.C. In the same way the comet
1861.i. has been traced back in the Chinese records to 617 A.D.[4]
The theoretical views founded on Newton’s great law of universal
gravitation led to the conclusion that the inclination of the earth’s
equator to the plane of her orbit (the obliquity of the ecliptic) has
been diminishing slowly since prehistoric times; and this fact has been
confirmed by Egyptian and Chinese observations on the length of the
shadow of a vertical pillar, made thousands of years before the
Christian era, in summer and winter.
There are other reasons why we must be tolerant of the crude notions of
the ancients. The historian, wishing to give credit wherever it may be
due, is met by two difficulties. Firstly, only a few records of very
ancient astronomy are extant, and the authenticity of many of these is
open to doubt. Secondly, it is very difficult to divest ourselves of
present knowledge, and to appreciate the originality of thought
required to make the first beginnings.
With regard to the first point, we are generally dependent upon
histories written long after the events. The astronomy of Egyptians,
Babylonians, and Assyrians is known to us mainly through the Greek
historians, and for information about the Chinese we rely upon the
researches of travellers and missionaries in comparatively recent
times. The testimony of the Greek writers has fortunately been
confirmed, and we now have in addition a mass of facts translated from
the original sculptures, papyri, and inscribed bricks, dating back
thousands of years.
In attempting to appraise the efforts of the beginners we must remember
that it was natural to look upon the earth (as all the first
astronomers did) as a circular plane, surrounded and bounded by the
heaven, which was a solid vault, or hemisphere, with its concavity
turned downwards. The stars seemed to be fixed on this vault; the moon,
and later the planets, were seen to crawl over it. It was a great step
to look on the vault as a hollow sphere carrying the sun too. It must
have been difficult to believe that at midday the stars are shining as
brightly in the blue sky as they do at night. It must have been
difficult to explain how the sun, having set in the west, could get
back to rise in the east without being seen _if_ it was always the same
sun. It was a great step to suppose the earth to be spherical, and to
ascribe the diurnal motions to its rotation. Probably the greatest step
ever made in astronomical theory was the placing of the sun, moon, and
planets at different distances from the earth instead of having them
stuck on the vault of heaven. It was a transition from “flatland” to a
space of three dimensions.
Great progress was made when systematic observations began, such as
following the motion of the moon and planets among the stars, and the
inferred motion of the sun among the stars, by observing their
_heliacal risings_—i.e., the times of year when a star would first be
seen to rise at sunrise, and when it could last be seen to rise at
sunset. The grouping of the stars into constellations and recording
their places was a useful observation. The theoretical prediction of
eclipses of the sun and moon, and of the motions of the planets among
the stars, became later the highest goal in astronomy.
To not one of the above important steps in the progress of astronomy
can we assign the author with certainty. Probably many of them were
independently taken by Chinese, Indian, Persian, Tartar, Egyptian,
Babylonian, Assyrian, Phoenician, and Greek astronomers. And we have
not a particle of information about the discoveries, which may have
been great, by other peoples—by the Druids, the Mexicans, and the
Peruvians, for example.
We do know this, that all nations required to have a calendar. The
solar year, the lunar month, and the day were the units, and it is
owing to their incommensurability that we find so many calendars
proposed and in use at different times. The only object to be attained
by comparing the chronologies of ancient races is to fix the actual
dates of observations recorded, and this is not a part of a history of
astronomy.
In conclusion, let us bear in mind the limited point of view of the
ancients when we try to estimate their merit. Let us remember that the
first astronomy was of two dimensions; the second astronomy was of
three dimensions, but still purely geometrical. Since Kepler’s day we
have had a dynamical astronomy.
FOOTNOTES:
[1] Trans. R. S. E., xxiii. 1864, p. 499, _On Sun Spots_, _etc_., by
B. Stewart. Also Trans. R. S. 1860-70. Also Prof. Ernest Brown, in _R.
A. S. Monthly Notices_, 1900.
[2] _R. A. S. Monthly Notices_, Sup.; 1905.
[Illustration: CHALDÆAN BAKED BRICK OR TABLET,
_Obverse and reverse sides_, Containing record of solar eclipse, 1062
B.C., used lately by Cowell for rendering the lunar theory more
accurate than was possible by finest modern observations. (British
Museum collection, No. 35908.)]
[3] _R. A. S. Monthly Notices_, vol. x., p. 65.
[4] R. S. E. Proc., vol. x., 1880.
2. ANCIENT ASTRONOMY—THE CHINESE AND CHALDÆANS.
The last section must have made clear the difficulties the way of
assigning to the ancient nations their proper place in the development
of primitive notions about astronomy. The fact that some alleged
observations date back to a period before the Chinese had invented the
art of writing leads immediately to the question how far tradition can
be trusted.
Our first detailed knowledge was gathered in the far East by
travellers, and by the Jesuit priests, and was published in the
eighteenth century. The Asiatic Society of Bengal contributed
translations of Brahmin literature. The two principal sources of
knowledge about Chinese astronomy were supplied, first by Father
Souciet, who in 1729 published _Observations Astronomical,
Geographical, Chronological, and Physical_, drawn from ancient Chinese
books; and later by Father Moyriac-de-Mailla, who in 1777-1785
published _Annals of the Chinese Empire, translated from
Tong-Kien-Kang-Mou_.
Bailly, in his _Astronomie Ancienne_ (1781), drew, from these and other
sources, the conclusion that all we know of the astronomical learning
of the Chinese, Indians, Chaldæans, Assyrians, and Egyptians is but the
remnant of a far more complete astronomy of which no trace can be
found.
Delambre, in his _Histoire de l’Astronomie Ancienne_ (1817), ridicules
the opinion of Bailly, and considers that the progress made by all of
these nations is insignificant.
It will be well now to give an idea of some of the astronomy of the
ancients not yet entirely discredited. China and Babylon may be taken
as typical examples.
_China_.—It would appear that Fohi, the first emperor, reigned about
2952 B.C., and shortly afterwards Yu-Chi made a sphere to represent the
motions of the celestial bodies. It is also mentioned, in the book
called Chu-King, supposed to have been written in 2205 B.C., that a
similar sphere was made in the time of Yao (2357 B.C.).[1] It is said
that the Emperor Chueni (2513 B.C.) saw five planets in conjunction the
same day that the sun and moon were in conjunction. This is discussed
by Father Martin (MSS. of De Lisle); also by M. Desvignolles (Mem.
Acad. Berlin, vol. iii., p. 193), and by M. Kirsch (ditto, vol. v., p.
19), who both found that Mars, Jupiter, Saturn, and Mercury were all
between the eleventh and eighteenth degrees of Pisces, all visible
together in the evening on February 28th 2446 B.C., while on the same
day the sun and moon were in conjunction at 9 a.m., and that on March
1st the moon was in conjunction with the other four planets. But this
needs confirmation.
Yao, referred to above, gave instructions to his astronomers to
determine the positions of the solstices and equinoxes, and they
reported the names of the stars in the places occupied by the sun at
these seasons, and in 2285 B.C. he gave them further orders. If this
account be true, it shows a knowledge that the vault of heaven is a
complete sphere, and that stars are shining at mid-day, although
eclipsed by the sun’s brightness.
It is also asserted, in the book called _Chu-King_, that in the time of
Yao the year was known to have 365¼ days, and that he adopted 365 days
and added an intercalary day every four years (as in the Julian
Calendar). This may be true or not, but the ancient Chinese certainly
seem to have divided the circle into 365 degrees. To learn the length
of the year needed only patient observation—a characteristic of the
Chinese; but many younger nations got into a terrible mess with their
calendar from ignorance of the year’s length.
It is stated that in 2159 B.C. the royal astronomers Hi and Ho failed
to predict an eclipse. It probably created great terror, for they were
executed in punishment for their neglect. If this account be true, it
means that in the twenty-second century B.C. some rule for calculating
eclipses was in use. Here, again, patient observation would easily lead
to the detection of the eighteen-year cycle known to the Chaldeans as
the _Saros_. It consists of 235 lunations, and in that time the pole of
the moon’s orbit revolves just once round the pole of the ecliptic, and
for this reason the eclipses in one cycle are repeated with very slight
modification in the next cycle, and so on for many centuries.
It may be that the neglect of their duties by Hi and Ho, and their
punishment, influenced Chinese astronomy; or that the succeeding
records have not been available to later scholars; but the fact remains
that—although at long intervals observations were made of eclipses,
comets, and falling stars, and of the position of the solstices, and of
the obliquity of the ecliptic—records become rare, until 776 B.C., when
eclipses began to be recorded once more with some approach to
continuity. Shortly afterwards notices of comets were added. Biot gave
a list of these, and Mr. John Williams, in 1871, published
_Observations of Comets from 611 B.C. to 1640 A.D., Extracted from the
Chinese Annals_.
With regard to those centuries concerning which we have no astronomical
Chinese records, it is fair to state that it is recorded that some
centuries before the Christian era, in the reign of Tsin-Chi-Hoang, all
the classical and scientific books that could be found were ordered to
be destroyed. If true, our loss therefrom is as great as from the
burning of the Alexandrian library by the Caliph Omar. He burnt all the
books because he held that they must be either consistent or
inconsistent with the Koran, and in the one case they were superfluous,
in the other case objectionable.
_Chaldæans_.—Until the last half century historians were accustomed to
look back upon the Greeks, who led the world from the fifth to the
third century B.C., as the pioneers of art, literature, and science.
But the excavations and researches of later years make us more ready to
grant that in science as in art the Greeks only developed what they
derived from the Egyptians, Babylonians, and Assyrians. The Greek
historians said as much, in fact; and modern commentators used to
attribute the assertion to undue modesty. Since, however, the records
of the libraries have been unearthed it has been recognised that the
Babylonians were in no way inferior in the matter of original
scientific investigation to other races of the same era.
The Chaldæans, being the most ancient Babylonians, held the same
station and dignity in the State as did the priests in Egypt, and spent
all their time in the study of philosophy and astronomy, and the arts
of divination and astrology. They held that the world of which we have
a conception is an eternal world without any beginning or ending, in
which all things are ordered by rules supported by a divine providence,
and that the heavenly bodies do not move by chance, nor by their own
will, but by the determinate will and appointment of the gods. They
recorded these movements, but mainly in the hope of tracing the will of
the gods in mundane affairs. Ptolemy (about 130 A.D.) made use of
Babylonian eclipses in the eighth century B.C. for improving his solar
and lunar tables.
Fragments of a library at Agade have been preserved at Nineveh, from
which we learn that the star-charts were even then divided into
constellations, which were known by the names which they bear to this
day, and that the signs of the zodiac were used for determining the
courses of the sun, moon, and of the five planets Mercury, Venus, Mars,
Jupiter, and Saturn.
We have records of observations carried on under Asshurbanapal, who
sent astronomers to different parts to study celestial phenomena. Here
is one:—
To the Director of Observations,—My Lord, his humble servant
Nabushum-iddin, Great Astronomer of Nineveh, writes thus: “May Nabu and
Marduk be propitious to the Director of these Observations, my Lord.
The fifteenth day we observed the Node of the moon, and the moon was
eclipsed.”
The Phoenicians are supposed to have used the stars for navigation, but
there are no records. The Egyptian priests tried to keep such
astronomical knowledge as they possessed to themselves. It is probable
that they had arbitrary rules for predicting eclipses. All that was
known to the Greeks about Egyptian science is to be found in the
writings of Diodorus Siculus. But confirmatory and more authentic facts
have been derived from late explorations. Thus we learn from E. B.
Knobel[2] about the Jewish calendar dates, on records of land sales in
Aramaic papyri at Assuan, translated by Professor A. H. Sayce and A. E.
Cowley, (1) that the lunar cycle of nineteen years was used by the Jews
in the fifth century B.C. [the present reformed Jewish calendar dating
from the fourth century A.D.], a date a “little more than a century
after the grandfathers and great-grandfathers of those whose business
is recorded had fled into Egypt with Jeremiah” (Sayce); and (2) that
the order of intercalation at that time was not dissimilar to that in
use at the present day.
Then again, Knobel reminds us of “the most interesting discovery a few
years ago by Father Strassmeier of a Babylonian tablet recording a
partial lunar eclipse at Babylon in the seventh year of Cambyses, on
the fourteenth day of the Jewish month Tammuz.” Ptolemy, in the
Almagest (Suntaxis), says it occurred in the seventh year of Cambyses,
on the night of the seventeenth and eighteenth of the Egyptian month
Phamenoth. Pingré and Oppolzer fix the date July 16th, 533 B.C. Thus
are the relations of the chronologies of Jews and Egyptians established
by these explorations.
FOOTNOTES:
[1] These ancient dates are uncertain.
[2] _R. A. S. Monthly Notices_, vol. lxviii., No. 5, March, 1908.
3. ANCIENT GREEK ASTRONOMY.
We have our information about the earliest Greek astronomy from
Herodotus (born 480 B.C.). He put the traditions into writing. Thales
(639-546 B.C.) is said to have predicted an eclipse, which caused much
alarm, and ended the battle between the Medes and Lydians. Airy fixed
the date May 28th, 585 B.C. But other modern astronomers give different
dates. Thales went to Egypt to study science, and learnt from its
priests the length of the year (which was kept a profound secret!), and
the signs of the zodiac, and the positions of the solstices. He held
that the sun, moon, and stars are not mere spots on the heavenly vault,
but solids; that the moon derives her light from the sun, and that this
fact explains her phases; that an eclipse of the moon happens when the
earth cuts off the sun’s light from her. He supposed the earth to be
flat, and to float upon water. He determined the ratio of the sun’s
diameter to its orbit, and apparently made out the diameter correctly
as half a degree. He left nothing in writing.
His successors, Anaximander (610-547 B.C.) and Anaximenes (550-475
B.C.), held absurd notions about the sun, moon, and stars, while
Heraclitus (540-500 B.C.) supposed that the stars were lighted each
night like lamps, and the sun each morning. Parmenides supposed the
earth to be a sphere.
Pythagoras (569-470 B.C.) visited Egypt to study science. He deduced
his system, in which the earth revolves in an orbit, from fantastic
first principles, of which the following are examples: “The circular
motion is the most perfect motion,” “Fire is more worthy than earth,”
“Ten is the perfect number.” He wrote nothing, but is supposed to have
said that the earth, moon, five planets, and fixed stars all revolve
round the sun, which itself revolves round an imaginary central fire
called the Antichthon. Copernicus in the sixteenth century claimed
Pythagoras as the founder of the system which he, Copernicus, revived.
Anaxagoras (born 499 B.C.) studied astronomy in Egypt. He explained the
return of the sun to the east each morning by its going under the flat
earth in the night. He held that in a solar eclipse the moon hides the
sun, and in a lunar eclipse the moon enters the earth’s shadow—both
excellent opinions. But he entertained absurd ideas of the vortical
motion of the heavens whisking stones into the sky, there to be ignited
by the fiery firmament to form stars. He was prosecuted for this
unsettling opinion, and for maintaining that the moon is an inhabited
earth. He was defended by Pericles (432 B.C.).
Solon dabbled, like many others, in reforms of the calendar. The common
year of the Greeks originally had 360 days—twelve months of thirty
days. Solon’s year was 354 days. It is obvious that these erroneous
years would, before long, remove the summer to January and the winter
to July. To prevent this it was customary at regular intervals to
intercalate days or months. Meton (432 B.C.) introduced a reform based
on the nineteen-year cycle. This is not the same as the Egyptian and
Chaldean eclipse cycle called _Saros_ of 223 lunations, or a little
over eighteen years. The Metonic cycle is 235 lunations or nineteen
years, after which period the sun and moon occupy the same position
relative to the stars. It is still used for fixing the date of Easter,
the number of the year in Melon’s cycle being the golden number of our
prayer-books. Melon’s system divided the 235 lunations into months of
thirty days and omitted every sixty-third day. Of the nineteen years,
twelve had twelve months and seven had thirteen months.
Callippus (330 B.C.) used a cycle four times as long, 940 lunations,
but one day short of Melon’s seventy-six years. This was more correct.
Eudoxus (406-350 B.C.) is said to have travelled with Plato in Egypt.
He made astronomical observations in Asia Minor, Sicily, and Italy, and
described the starry heavens divided into constellations. His name is
connected with a planetary theory which as generally stated sounds most
fanciful. He imagined the fixed stars to be on a vault of heaven; and
the sun, moon, and planets to be upon similar vaults or spheres,
twenty-six revolving spheres in all, the motion of each planet being
resolved into its components, and a separate sphere being assigned for
each component motion. Callippus (330 B.C.) increased the number to
thirty-three. It is now generally accepted that the real existence of
these spheres was not suggested, but the idea was only a mathematical
conception to facilitate the construction of tables for predicting the
places of the heavenly bodies.
Aristotle (384-322 B.C.) summed up the state of astronomical knowledge
in his time, and held the earth to be fixed in the centre of the world.
Nicetas, Heraclides, and Ecphantes supposed the earth to revolve on its
axis, but to have no orbital motion.
The short epitome so far given illustrates the extraordinary deductive
methods adopted by the ancient Greeks. But they went much farther in
the same direction. They seem to have been in great difficulty to
explain how the earth is supported, just as were those who invented the
myth of Atlas, or the Indians with the tortoise. Thales thought that
the flat earth floated on water. Anaxagoras thought that, being flat,
it would be buoyed up and supported on the air like a kite. Democritus
thought it remained fixed, like the donkey between two bundles of hay,
because it was equidistant from all parts of the containing sphere, and
there was no reason why it should incline one way rather than another.
Empedocles attributed its state of rest to centrifugal force by the
rapid circular movement of the heavens, as water is stationary in a
pail when whirled round by a string. Democritus further supposed that
the inclination of the flat earth to the ecliptic was due to the
greater weight of the southern parts owing to the exuberant vegetation.
For further references to similar efforts of imagination the reader is
referred to Sir George Cornwall Lewis’s _Historical Survey of the
Astronomy of the Ancients_; London, 1862. His list of authorities is
very complete, but some of his conclusions are doubtful. At p. 113 of
that work he records the real opinions of Socrates as set forth by
Xenophon; and the reader will, perhaps, sympathise with Socrates in his
views on contemporary astronomy:—
With regard to astronomy he [Socrates] considered a knowledge of it
desirable to the extent of determining the day of the year or month,
and the hour of the night, ... but as to learning the courses of the
stars, to be occupied with the planets, and to inquire about their
distances from the earth, and their orbits, and the causes of their
motions, he strongly objected to such a waste of valuable time. He
dwelt on the contradictions and conflicting opinions of the physical
philosophers, ... and, in fine, he held that the speculators on the
universe and on the laws of the heavenly bodies were no better than
madmen (_Xen. Mem_, i. 1, 11-15).
Plato (born 429 B.C.), the pupil of Socrates, the fellow-student of
Euclid, and a follower of Pythagoras, studied science in his travels in
Egypt and elsewhere. He was held in so great reverence by all learned
men that a problem which he set to the astronomers was the keynote to
all astronomical investigation from this date till the time of Kepler
in the sixteenth century. He proposed to astronomers _the problem of
representing the courses of the planets by circular and uniform
motions_.
Systematic observation among the Greeks began with the rise of the
Alexandrian school. Aristillus and Timocharis set up instruments and
fixed the positions of the zodiacal stars, near to which all the
planets in their orbits pass, thus facilitating the determination of
planetary motions. Aristarchus (320-250 B.C.) showed that the sun must
be at least nineteen times as far off as the moon, which is far short
of the mark. He also found the sun’s diameter, correctly, to be half a
degree. Eratosthenes (276-196 B.C.) measured the inclination to the
equator of the sun’s apparent path in the heavens—i.e., he measured the
obliquity of the ecliptic, making it 23° 51’, confirming our knowledge
of its continuous diminution during historical times. He measured an
arc of meridian, from Alexandria to Syene (Assuan), and found the
difference of latitude by the length of a shadow at noon, summer
solstice. He deduced the diameter of the earth, 250,000 stadia.
Unfortunately, we do not know the length of the stadium he used.
Hipparchus (190-120 B.C.) may be regarded as the founder of
observational astronomy. He measured the obliquity of the ecliptic, and
agreed with Eratosthenes. He altered the length of the tropical year
from 365 days, 6 hours to 365 days, 5 hours, 53 minutes—still four
minutes too much. He measured the equation of time and the irregular
motion of the sun; and allowed for this in his calculations by
supposing that the centre, about which the sun moves uniformly, is
situated a little distance from the fixed earth. He called this point
the _excentric_. The line from the earth to the “excentric” was called
the _line of apses_. A circle having this centre was called the
_equant_, and he supposed that a radius drawn to the sun from the
excentric passes over equal arcs on the equant in equal times. He then
computed tables for predicting the place of the sun.
He proceeded in the same way to compute Lunar tables. Making use of
Chaldæan eclipses, he was able to get an accurate value of the moon’s
mean motion. [Halley, in 1693, compared this value with his own
measurements, and so discovered the acceleration of the moon’s mean
motion. This was conclusively established, but could not be explained
by the Newtonian theory for quite a long time.] He determined the plane
of the moon’s orbit and its inclination to the ecliptic. The motion of
this plane round the pole of the ecliptic once in eighteen years
complicated the problem. He located the moon’s excentric as he had done
the sun’s. He also discovered some of the minor irregularities of the
moon’s motion, due, as Newton’s theory proves, to the disturbing action
of the sun’s attraction.
In the year 134 B.C. Hipparchus observed a new star. This upset every
notion about the permanence of the fixed stars. He then set to work to
catalogue all the principal stars so as to know if any others appeared
or disappeared. Here his experiences resembled those of several later
astronomers, who, when in search of some special object, have been
rewarded by a discovery in a totally different direction. On comparing
his star positions with those of Timocharis and Aristillus he found no
stars that had appeared or disappeared in the interval of 150 years;
but he found that all the stars seemed to have changed their places
with reference to that point in the heavens where the ecliptic is 90°
from the poles of the earth—i.e., the equinox. He found that this could
be explained by a motion of the equinox in the direction of the
apparent diurnal motion of the stars. This discovery of _precession of
the equinoxes_, which takes place at the rate of 52".1 every year, was
necessary for the progress of accurate astronomical observations. It is
due to a steady revolution of the earth’s pole round the pole of the
ecliptic once in 26,000 years in the opposite direction to the
planetary revolutions.
Hipparchus was also the inventor of trigonometry, both plane and
spherical. He explained the method of using eclipses for determining
the longitude.
In connection with Hipparchus’ great discovery it may be mentioned that
modern astronomers have often attempted to fix dates in history by the
effects of precession of the equinoxes. (1) At about the date when the
Great Pyramid may have been built γ Draconis was near to the pole, and
must have been used as the pole-star. In the north face of the Great
Pyramid is the entrance to an inclined passage, and six of the nine
pyramids at Gizeh possess the same feature; all the passages being
inclined at an angle between 26° and 27° to the horizon and in the
plane of the meridian. It also appears that 4,000 years ago—i.e., about
2100 B.C.—an observer at the lower end of the passage would be able to
see γ Draconis, the then pole-star, at its lower culmination.[1] It has
been suggested that the passage was made for this purpose. On other
grounds the date assigned to the Great Pyramid is 2123 B.C.
(2) The Chaldæans gave names to constellations now invisible from
Babylon which would have been visible in 2000 B.C., at which date it is
claimed that these people were studying astronomy.
(3) In the Odyssey, Calypso directs Odysseus, in accordance with
Phoenician rules for navigating the Mediterranean, to keep the Great
Bear “ever on the left as he traversed the deep” when sailing from the
pillars of Hercules (Gibraltar) to Corfu. Yet such a course taken now
would land the traveller in Africa. Odysseus is said in his voyage in
springtime to have seen the Pleiades and Arcturus setting late, which
seemed to early commentators a proof of Homer’s inaccuracy. Likewise
Homer, both in the _Odyssey_[2] (v. 272-5) and in the _Iliad_ (xviii.
489), asserts that the Great Bear never set in those latitudes. Now it
has been found that the precession of the equinoxes explains all these
puzzles; shows that in springtime on the Mediterranean the Bear was
just above the horizon, near the sea but not touching it, between 750
B.C. and 1000 B.C.; and fixes the date of the poems, thus confirming
other evidence, and establishing Homer’s character for accuracy.[3]
(4) The orientation of Egyptian temples and Druidical stones is such
that possibly they were so placed as to assist in the observation of
the heliacal risings[4] of certain stars. If the star were known, this
would give an approximate date. Up to the present the results of these
investigations are far from being conclusive.
Ptolemy (130 A.D.) wrote the Suntaxis, or Almagest, which includes a
cyclopedia of astronomy, containing a summary of knowledge at that
date. We have no evidence beyond his own statement that he was a
practical observer. He theorised on the planetary motions, and held
that the earth is fixed in the centre of the universe. He adopted the
excentric and equant of Hipparchus to explain the unequal motions of
the sun and moon. He adopted the epicycles and deferents which had been
used by Apollonius and others to explain the retrograde motions of the
planets. We, who know that the earth revolves round the sun once in a
year, can understand that the apparent motion of a planet is only its
motion relative to the earth. If, then, we suppose the earth fixed and
the sun to revolve round it once a year, and the planets each in its
own period, it is only necessary to impose upon each of these an
additional _annual_ motion to enable us to represent truly the apparent
motions. This way of looking at the apparent motions shows why each
planet, when nearest to the earth, seems to move for a time in a
retrograde direction. The attempts of Ptolemy and others of his time to
explain the retrograde motion in this way were only approximate. Let us
suppose each planet to have a bar with one end centred at the earth. If
at the other end of the bar one end of a shorter bar is pivotted,
having the planet at its other end, then the planet is given an annual
motion in the secondary circle (the epicycle), whose centre revolves
round the earth on the primary circle (the _deferent_), at a uniform
rate round the excentric. Ptolemy supposed the centres of the epicycles
of Mercury and Venus to be on a bar passing through the sun, and to be
between the earth and the sun. The centres of the epicycles of Mars,
Jupiter, and Saturn were supposed to be further away than the sun.
Mercury and Venus were supposed to revolve in their epicycles in their
own periodic times and in the deferent round the earth in a year. The
major planets were supposed to revolve in the deferent round the earth
in their own periodic times, and in their epicycles once in a year.
It did not occur to Ptolemy to place the centres of the epicycles of
Mercury and Venus at the sun, and to extend the same system to the
major planets. Something of this sort had been proposed by the
Egyptians (we are told by Cicero and others), and was accepted by Tycho
Brahe; and was as true a representation of the relative motions in the
solar system as when we suppose the sun to be fixed and the earth to
revolve.
The cumbrous system advocated by Ptolemy answered its purpose, enabling
him to predict astronomical events approximately. He improved the lunar
theory considerably, and discovered minor inequalities which could be
allowed for by the addition of new epicycles. We may look upon these
epicycles of Apollonius, and the excentric of Hipparchus, as the
responses of these astronomers to the demand of Plato for uniform
circular motions. Their use became more and more confirmed, until the
seventeenth century, when the accurate observations of Tycho Brahe
enabled Kepler to abolish these purely geometrical makeshifts, and to
substitute a system in which the sun became physically its controller.
FOOTNOTES:
[1] _Phil. Mag_., vol. xxiv., pp. 481-4.
[2]
Plaeiadas t’ esoronte kai opse duonta bootaen
‘Arkton th’ aen kai amaxan epiklaesin kaleousin,
‘Ae t’ autou strephetai kai t’ Oriona dokeuei,
Oin d’ammoros esti loetron Okeanoio.
“The Pleiades and Boötes that setteth late, and the Bear, which they
likewise call the Wain, which turneth ever in one place, and keepeth
watch upon Orion, and alone hath no part in the baths of the ocean.”
[3] See Pearson in the Camb. Phil. Soc. Proc., vol. iv., pt. ii., p.
93, on whose authority the above statements are made.
[4] See p. 6 for definition.
4. THE REIGN OF EPICYCLES—FROM PTOLEMY TO COPERNICUS.
After Ptolemy had published his book there seemed to be nothing more to
do for the solar system except to go on observing and finding more and
more accurate values for the constants involved--viz., the periods of
revolution, the diameter of the deferent,[1] and its ratio to that of
the epicycle,[2] the distance of the excentric[3] from the centre of
the deferent, and the position of the line of apses,[4] besides the
inclination and position of the plane of the planet’s orbit. The only
object ever aimed at in those days was to prepare tables for predicting
the places of the planets. It was not a mechanical problem; there was
no notion of a governing law of forces.
From this time onwards all interest in astronomy seemed, in Europe at
least, to sink to a low ebb. When the Caliph Omar, in the middle of the
seventh century, burnt the library of Alexandria, which had been the
centre of intellectual progress, that centre migrated to Baghdad, and
the Arabs became the leaders of science and philosophy. In astronomy
they made careful observations. In the middle of the ninth century
Albategnius, a Syrian prince, improved the value of excentricity of the
sun’s orbit, observed the motion of the moon’s apse, and thought he
detected a smaller progression of the sun’s apse. His tables were much
more accurate than Ptolemy’s. Abul Wefa, in the tenth century, seems to
have discovered the moon’s “variation.” Meanwhile the Moors were
leaders of science in the west, and Arzachel of Toledo improved the
solar tables very much. Ulugh Begh, grandson of the great Tamerlane the
Tartar, built a fine observatory at Samarcand in the fifteenth century,
and made a great catalogue of stars, the first since the time of
Hipparchus.
At the close of the fifteenth century King Alphonso of Spain employed
computers to produce the Alphonsine Tables (1488 A.D.), Purbach
translated Ptolemy’s book, and observations were carried out in Germany
by Müller, known as Regiomontanus, and Waltherus.
Nicolai Copernicus, a Sclav, was born in 1473 at Thorn, in Polish
Prussia. He studied at Cracow and in Italy. He was a priest, and
settled at Frauenberg. He did not undertake continuous observations,
but devoted himself to simplifying the planetary systems and devising
means for more accurately predicting the positions of the sun, moon,
and planets. He had no idea of framing a solar system on a dynamical
basis. His great object was to increase the accuracy of the
calculations and the tables. The results of his cogitations were
printed just before his death in an interesting book, _De
Revolutionibus Orbium Celestium_. It is only by careful reading of this
book that the true position of Copernicus can be realised. He noticed
that Nicetas and others had ascribed the apparent diurnal rotation of
the heavens to a real daily rotation of the earth about its axis, in
the opposite direction to the apparent motion of the stars. Also in the
writings of Martianus Capella he learnt that the Egyptians had supposed
Mercury and Venus to revolve round the sun, and to be carried with him
in his annual motion round the earth. He noticed that the same
supposition, if extended to Mars, Jupiter, and Saturn, would explain
easily why they, and especially Mars, seem so much brighter in
opposition. For Mars would then be a great deal nearer to the earth
than at other times. It would also explain the retrograde motion of
planets when in opposition.
We must here notice that at this stage Copernicus was actually
confronted with the system accepted later by Tycho Brahe, with the
earth fixed. But he now recalled and accepted the views of Pythagoras
and others, according to which the sun is fixed and the earth revolves;
and it must be noted that, geometrically, there is no difference of any
sort between the Egyptian or Tychonic system and that of Pythagoras as
revived by Copernicus, except that on the latter theory the stars ought
to seem to move when the earth changes its position—a test which failed
completely with the rough means of observation then available. The
radical defect of all solar systems previous to the time of Kepler
(1609 A.D.) was the slavish yielding to Plato’s dictum demanding
uniform circular motion for the planets, and the consequent evolution
of the epicycle, which was fatal to any conception of a dynamical
theory.
Copernicus could not sever himself from this obnoxious tradition.[5] It
is true that neither the Pythagorean nor the Egypto-Tychonic system
required epicycles for explaining retrograde motion, as the Ptolemaic
theory did. Furthermore, either system could use the excentric of
Hipparchus to explain the irregular motion known as the equation of the
centre. But Copernicus remarked that he could also use an epicycle for
this purpose, or that he could use both an excentric and an epicycle
for each planet, and so bring theory still closer into accord with
observation. And this he proceeded to do.[6] Moreover, observers had
found irregularities in the moon’s motion, due, as we now know, to the
disturbing attraction of the sun. To correct for these irregularities
Copernicus introduced epicycle on epicycle in the lunar orbit.
This is in its main features the system propounded by Copernicus. But
attention must, to state the case fully, be drawn to two points to be
found in his first and sixth books respectively. The first point
relates to the seasons, and it shows a strange ignorance of the laws of
rotating bodies. To use the words of Delambre,[7] in drawing attention
to the strange conception,
he imagined that the earth, revolving round the sun, ought always to
show to it the same face; the contrary phenomena surprised him: to
explain them he invented a third motion, and added it to the two real
motions (rotation and orbital revolution). By this third motion the
earth, he held, made a revolution on itself and on the poles of the
ecliptic once a year ... Copernicus did not know that motion in a
straight line is the natural motion, and that motion in a curve is the
resultant of several movements. He believed, with Aristotle, that
circular motion was the natural one.
Copernicus made this rotation of the earth’s axis about the pole of the
ecliptic retrograde (i.e., opposite to the orbital revolution), and by
making it perform more than one complete revolution in a year, the
added part being 1/26000 of the whole, he was able to include the
precession of the equinoxes in his explanation of the seasons. His
explanation of the seasons is given on leaf 10 of his book (the pages
of this book are not all numbered, only alternate pages, or leaves).
In his sixth book he discusses the inclination of the planetary orbits
to the ecliptic. In regard to this the theory of Copernicus is unique;
and it will be best to explain this in the words of Grant in his great
work.[8] He says:—
Copernicus, as we have already remarked, did not attack the principle
of the epicyclical theory: he merely sought to make it more simple by
placing the centre of the earth’s orbit in the centre of the universe.
This was the point to which the motions of the planets were referred,
for the planes of their orbits were made to pass through it, and their
points of least and greatest velocities were also determined with
reference to it. By this arrangement the sun was situate
mathematically near the centre of the planetary system, but he did not
appear to have any physical connexion with the planets as the centre
of their motions.
According to Copernicus’ sixth book, the planes of the planetary orbits
do not pass through the sun, and the lines of apses do not pass through
to the sun.
Such was the theory advanced by Copernicus: The earth moves in an
epicycle, on a deferent whose centre is a little distance from the sun.
The planets move in a similar way on epicycles, but their deferents
have no geometrical or physical relation to the sun. The moon moves on
an epicycle centred on a second epicycle, itself centred on a deferent,
excentric to the earth. The earth’s axis rotates about the pole of the
ecliptic, making one revolution and a twenty-six thousandth part of a
revolution in the sidereal year, in the opposite direction to its
orbital motion.
In view of this fanciful structure it must be noted, in fairness to
Copernicus, that he repeatedly states that the reader is not obliged to
accept his system as showing the real motions; that it does not matter
whether they be true, even approximately, or not, so long as they
enable us to compute tables from which the places of the planets among
the stars can be predicted.[9] He says that whoever is not satisfied
with this explanation must be contented by being told that “mathematics
are for mathematicians” (Mathematicis mathematica scribuntur).
At the same time he expresses his conviction over and over again that
the earth is in motion. It is with him a pious belief, just as it was
with Pythagoras and his school and with Aristarchus. “But” (as Dreyer
says in his most interesting book, _Tycho Brahe_) “proofs of the
physical truth of his system Copernicus had given none, and could give
none,” any more than Pythagoras or Aristarchus.
There was nothing so startlingly simple in his system as to lead the
cautious astronomer to accept it, as there was in the later Keplerian
system; and the absence of parallax in the stars seemed to condemn his
system, which had no physical basis to recommend it, and no
simplification at all over the Egypto-Tychonic system, to which
Copernicus himself drew attention. It has been necessary to devote
perhaps undue space to the interesting work of Copernicus, because by a
curious chance his name has become so widely known. He has been spoken
of very generally as the founder of the solar system that is now
accepted. This seems unfair, and on reading over what has been written
about him at different times it will be noticed that the
astronomers—those who have evidently read his great book—are very
cautious in the words with which they eulogise him, and refrain from
attributing to him the foundation of our solar system, which is
entirely due to Kepler. It is only the more popular writers who give
the idea that a revolution had been effected when Pythagoras’ system
was revived, and when Copernicus supported his view that the earth
moves and is not fixed.
It may be easy to explain the association of the name of Copernicus
with the Keplerian system. But the time has long passed when the
historian can support in any way this popular error, which was started
not by astronomers acquainted with Kepler’s work, but by those who
desired to put the Church in the wrong by extolling Copernicus.
Copernicus dreaded much the abuse he expected to receive from
philosophers for opposing the authority of Aristotle, who had declared
that the earth was fixed. So he sought and obtained the support of the
Church, dedicating his great work to Pope Paul III. in a lengthy
explanatory epistle. The Bishop of Cracow set up a memorial tablet in
his honour.
Copernicus was the most refined exponent, and almost the last
representative, of the Epicyclical School. As has been already stated,
his successor, Tycho Brahe, supported the same use of epicycles and
excentrics as Copernicus, though he held the earth to be fixed. But
Tycho Brahe was eminently a practical observer, and took little part in
theory; and his observations formed so essential a portion of the
system of Kepler that it is only fair to include his name among these
who laid the foundations of the solar system which we accept to-day.
In now taking leave of the system of epicycles let it be remarked that
it has been held up to ridicule more than it deserves. On reading
Airy’s account of epicycles, in the beautifully clear language of his
_Six Lectures on Astronomy_, the impression is made that the jointed
bars there spoken of for describing the circles were supposed to be
real. This is no more the case than that the spheres of Eudoxus and
Callippus were supposed to be real. Both were introduced only to
illustrate the mathematical conception upon which the solar, planetary,
and lunar tables were constructed. The epicycles represented nothing
more nor less than the first terms in the Fourier series, which in the
last century has become a basis of such calculations, both in astronomy
and physics generally.
[Illustration: “QUADRANS MURALIS SIVE TICHONICUS.”
With portrait of Tycho Brahe, instruments, etc., painted on the wall;
showing assistants using the sight, watching the clock, and recording.
(From the author’s copy of the _Astronomiæ Instauratæ Mechanica_.)]
FOOTNOTES:
[1] For definition see p. 22.
[2] _Ibid_.
[3] For definition see p. 18.
[4] For definition see p. 18.
[5] In his great book Copernicus says: “The movement of the heavenly
bodies is uniform, circular, perpetual, or else composed of circular
movements.” In this he proclaimed himself a follower of Pythagoras
(see p. 14), as also when he says: “The world is spherical because the
sphere is, of all figures, the most perfect” (Delambre, _Ast. Mod.
Hist_., pp. 86, 87).
[6] Kepler tells us that Tycho Brahe was pleased with this device, and
adapted it to his own system.
[7] _Hist. Ast._, vol. i., p. 354.
[8] _Hist. of Phys. Ast._, p. vii.
[9] “Est enim Astronomi proprium, historiam motuum coelestium
diligenti et artificiosa observatione colligere. Deinde causas
earundem, seu hypotheses, cum veras assequi nulla ratione possit ...
Neque enim necesse est, eas hypotheses esse veras, imo ne verisimiles
quidem, sed sufficit hoc usum, si calculum observationibus congruentem
exhibeant.”