History of Astronomy by George Forbes
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
BOOK I. THE GEOMETRICAL PERIOD
1. PRIMITIVE ASTRONOMY AND ASTROLOGY
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
BOOK IV. THE PHYSICAL PERIOD
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 1st, 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.
[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.
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.
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.”
BOOK II. THE DYNAMICAL PERIOD
5. DISCOVERY OF THE TRUE SOLAR SYSTEM—TYCHO BRAHE—KEPLER.
During the period of the intellectual and aesthetic
revival, at the beginning of the sixteenth century,
the “spirit of the age” was fostered by
the invention of printing, by the downfall of the
Byzantine Empire, and the scattering of Greek fugitives,
carrying the treasures of literature through Western
Europe, by the works of Raphael and Michael Angelo,
by the Reformation, and by the extension of the known
world through the voyages of Spaniards and Portuguese.
During that period there came to the front the founder
of accurate observational astronomy. Tycho Brahe,
a Dane, born in 1546 of noble parents, was the most
distinguished, diligent, and accurate observer of
the heavens since the days of Hipparchus, 1,700 years
before.
Tycho was devoted entirely to his science from childhood,
and the opposition of his parents only stimulated
him in his efforts to overcome difficulties.
He soon grasped the hopelessness of the old deductive
methods of reasoning, and decided that no theories
ought to be indulged in until preparations had been
made by the accumulation of accurate observations.
We may claim for him the title of founder of the
inductive method.
For a complete life of this great man the reader is
referred to Dreyer’s Tycho Brahe, Edinburgh,
1890, containing a complete bibliography. The
present notice must be limited to noting the work
done, and the qualities of character which enabled
him to attain his scientific aims, and which have
been conspicuous in many of his successors.
He studied in Germany, but King Frederick of Denmark,
appreciating his great talents, invited him to carry
out his life’s work in that country. He
granted to him the island of Hveen, gave him a pension,
and made him a canon of the Cathedral of Roskilde.
On that island Tycho Brahe built the splendid observatory
which he called Uraniborg, and, later, a second one
for his assistants and students, called Stjerneborg.
These he fitted up with the most perfect instruments,
and never lost a chance of adding to his stock of
careful observations.[1]
The account of all these instruments and observations,
printed at his own press on the island, was published
by Tycho Brahe himself, and the admirable and numerous
engravings bear witness to the excellence of design
and the stability of his instruments.
His mechanical skill was very great, and in his workmanship
he was satisfied with nothing but the best. He
recognised the importance of rigidity in the instruments,
and, whereas these had generally been made of wood,
he designed them in metal. His instruments included
armillae like those which had been used in Alexandria,
and other armillae designed by himself—sextants,
mural quadrants, large celestial globes and various
instruments for special purposes. He lived before
the days of telescopes and accurate clocks. He
invented the method of sub-dividing the degrees on
the arc of an instrument by transversals somewhat
in the way that Pedro Nunez had proposed.
He originated the true system of observation and reduction
of observations, recognising the fact that the best
instrument in the world is not perfect; and with each
of his instruments he set to work to find out the
errors of graduation and the errors of mounting, the
necessary correction being applied to each observation.
When he wanted to point his instrument exactly to
a star he was confronted with precisely the same difficulty
as is met in gunnery and rifle-shooting. The
sights and the object aimed at cannot be in focus
together, and a great deal depends on the form of sight.
Tycho Brahe invented, and applied to the pointers
of his instruments, an aperture-sight of variable
area, like the iris diaphragm used now in photography.
This enabled him to get the best result with stars
of different brightness. The telescope not having
been invented, he could not use a telescopic-sight
as we now do in gunnery. This not only removes
the difficulty of focussing, but makes the minimum
visible angle smaller. Helmholtz has defined the
minimum angle measurable with the naked eye as being
one minute of arc. In view of this it is simply
marvellous that, when the positions of Tycho’s
standard stars are compared with the best modern catalogues,
his probable error in right ascension is only ± 24”,
1, and in declination only ± 25”, 9.
Clocks of a sort had been made, but Tycho Brahe found
them so unreliable that he seldom used them, and many
of his position-measurements were made by measuring
the angular distances from known stars.
Taking into consideration the absence of either a
telescope or a clock, and reading his account of the
labour he bestowed upon each observation, we must
all agree that Kepler, who inherited these observations
in MS., was justified, under the conditions then existing,
in declaring that there was no hope of anyone ever
improving upon them.
In the year 1572, on November 11th, Tycho discovered
in Cassiopeia a new star of great brilliance, and
continued to observe it until the end of January,
1573. So incredible to him was such an event that
he refused to believe his own eyes until he got others
to confirm what he saw. He made accurate observations
of its distance from the nine principal stars in Casseiopeia,
and proved that it had no measurable parallax.
Later he employed the same method with the comets of
1577, 1580, 1582, 1585, 1590, 1593, and 1596, and
proved that they too had no measurable parallax and
must be very distant.
The startling discovery that stars are not necessarily
permanent, that new stars may appear, and possibly
that old ones may disappear, had upon him exactly
the same effect that a similar occurrence had upon
Hipparchus 1,700 years before. He felt it his
duty to catalogue all the principal stars, so that
there should be no mistake in the future. During
the construction of his catalogue of 1,000 stars he
prepared and used accurate tables of refraction deduced
from his own observations. Thus he eliminated
(so far as naked eye observations required) the effect
of atmospheric refraction which makes the altitude
of a star seem greater than it really is.
Tycho Brahe was able to correct the lunar theory by
his observations. Copernicus had introduced two
epicycles on the lunar orbit in the hope of obtaining
a better accordance between theory and observation;
and he was not too ambitious, as his desire was to
get the tables accurate to ten minutes. Tycho
Brahe found that the tables of Copernicus were in
error as much as two degrees. He re-discovered
the inequality called “variation” by observing
the moon in all phases—a thing which had
not been attended to. [It is remarkable that in the
nineteenth century Sir George Airy established an
altazimuth at Greenwich Observatory with this special
object, to get observations of the moon in all phases.]
He also discovered other lunar equalities, and wanted
to add another epicycle to the moon’s orbit,
but he feared that these would soon become unmanageable
if further observations showed more new inequalities.
But, as it turned out, the most fruitful work of Tycho
Brahe was on the motions of the planets, and especially
of the planet Mars, for it was by an examination of
these results that Kepler was led to the discovery
of his immortal laws.
After the death of King Frederick the observatories
of Tycho Brahe were not supported. The gigantic
power and industry displayed by this determined man
were accompanied, as often happens, by an overbearing
manner, intolerant of obstacles. This led to friction,
and eventually the observatories were dismantled,
and Tycho Brahe was received by the Emperor Rudolph
II., who placed a house in Prague at his disposal.
Here he worked for a few years, with Kepler as one
of his assistants, and he died in the year 1601.
It is an interesting fact that Tycho Brahe had a firm
conviction that mundane events could be predicted
by astrology, and that this belief was supported by
his own predictions.
It has already been stated that Tycho Brahe maintained
that observation must precede theory. He did
not accept the Copernican theory that the earth moves,
but for a working hypothesis he used a modification
of an old Egyptian theory, mathematically identical
with that of Copernicus, but not involving a stellar
parallax. He says (De Mundi, etc.)
that
the Ptolemean system was too complicated,
and the new one which that great man Copernicus
had proposed, following in the footsteps of Aristarchus
of Samos, though there was nothing in it contrary to
mathematical principles, was in opposition to those
of physics, as the heavy and sluggish earth is unfit
to move, and the system is even opposed to the authority
of Scripture. The absence of annual parallax
further involves an incredible distance between the
outermost planet and the fixed stars.
We are bound to admit that in the circumstances of
the case, so long as there was no question of dynamical
forces connecting the members of the solar system,
his reasoning, as we should expect from such a man,
is practical and sound. It is not surprising,
then, that astronomers generally did not readily accept
the views of Copernicus, that Luther (Luther’s
Tischreden, pp. 22, 60) derided him in his
usual pithy manner, that Melancthon (Initia doctrinae
physicae) said that Scripture, and also science,
are against the earth’s motion; and that the
men of science whose opinion was asked for by the cardinals
(who wished to know whether Galileo was right or wrong)
looked upon Copernicus as a weaver of fanciful theories.
Johann Kepler is the name of the man whose place,
as is generally agreed, would have been the most difficult
to fill among all those who have contributed to the
advance of astronomical knowledge. He was born
at Wiel, in the Duchy of Wurtemberg, in 1571.
He held an appointment at Gratz, in Styria, and went
to join Tycho Brahe in Prague, and to assist in reducing
his observations. These came into his possession
when Tycho Brahe died, the Emperor Rudolph entrusting
to him the preparation of new tables (called the Rudolphine
tables) founded on the new and accurate observations.
He had the most profound respect for the knowledge,
skill, determination, and perseverance of the man
who had reaped such a harvest of most accurate data;
and though Tycho hardly recognised the transcendent
genius of the man who was working as his assistant,
and although there were disagreements between them,
Kepler held to his post, sustained by the conviction
that, with these observations to test any theory,
he would be in a position to settle for ever the problem
of the solar system.
It has seemed to many that Plato’s demand for
uniform circular motion (linear or angular) was responsible
for a loss to astronomy of good work during fifteen
hundred years, for a hundred ill-considered speculative
cosmogonies, for dissatisfaction, amounting to disgust,
with these à priori guesses, and for the relegation
of the science to less intellectual races than Greeks
and other Europeans. Nobody seemed to dare to
depart from this fetish of uniform angular motion
and circular orbits until the insight, boldness, and
independence of Johann Kepler opened up a new world
of thought and of intellectual delight.
While at work on the Rudolphine tables he used the
old epicycles and deferents and excentrics, but he
could not make theory agree with observation.
His instincts told him that these apologists for uniform
motion were a fraud; and he proved it to himself by
trying every possible variation of the elements and
finding them fail. The number of hypotheses
which he examined and rejected was almost incredible
(for example, that the planets turn round centres at
a little distance from the sun, that the epicycles
have centres at a little distance from the deferent,
and so on). He says that, after using all these
devices to make theory agree with Tycho’s observations,
he still found errors amounting to eight minutes of
a degree. Then he said boldly that it was impossible
that so good an observer as Tycho could have made
a mistake of eight minutes, and added: “Out
of these eight minutes we will construct a new theory
that will explain the motions of all the planets.”
And he did it, with elliptic orbits having the sun
in a focus of each.[2]
It is often difficult to define the boundaries between
fancies, imagination, hypothesis, and sound theory.
This extraordinary genius was a master in all these
modes of attacking a problem. His analogy between
the spaces occupied by the five regular solids and
the distances of the planets from the sun, which filled
him with so much delight, was a display of pure fancy.
His demonstration of the three fundamental laws of
planetary motion was the most strict and complete
theory that had ever been attempted.
It has been often suggested that the revival by Copernicus
of the notion of a moving earth was a help to Kepler.
No one who reads Kepler’s great book could hold
such an opinion for a moment. In fact, the excellence
of Copernicus’s book helped to prolong the life
of the epicyclical theories in opposition to Kepler’s
teaching.
All of the best theories were compared by him with
observation. These were the Ptolemaic, the Copernican,
and the Tychonic. The two latter placed all of
the planetary orbits concentric with one another, the
sun being placed a little away from their common centre,
and having no apparent relation to them, and being
actually outside the planes in which they move.
Kepler’s first great discovery was that the
planes of all the orbits pass through the sun; his
second was that the line of apses of each planet passes
through the sun; both were contradictory to the Copernican
theory.
He proceeds cautiously with his propositions until
he arrives at his great laws, and he concludes his
book by comparing observations of Mars, of all dates,
with his theory.
His first law states that the planets describe ellipses
with the sun at a focus of each ellipse.
His second law (a far more difficult one to prove)
states that a line drawn from a planet to the sun
sweeps over equal areas in equal times. These
two laws were published in his great work, Astronomia
Nova, sen. Physica Coelestis tradita commentariis
de Motibus Stelloe; Martis, Prague, 1609.
It took him nine years more[3] to discover his third
law, that the squares of the periodic times are proportional
to the cubes of the mean distances from the sun.
These three laws contain implicitly the law of universal
gravitation. They are simply an alternative way
of expressing that law in dealing with planets, not
particles. Only, the power of the greatest human
intellect is so utterly feeble that the meaning of
the words in Kepler’s three laws could not be
understood until expounded by the logic of Newton’s
dynamics.
The joy with which Kepler contemplated the final demonstration
of these laws, the evolution of which had occupied
twenty years, can hardly be imagined by us.
He has given some idea of it in a passage in his work
on Harmonics, which is not now quoted, only
lest someone might say it was egotistical—a
term which is simply grotesque when applied to such
a man with such a life’s work accomplished.
The whole book, Astronomia Nova, is a pleasure
to read; the mass of observations that are used, and
the ingenuity of the propositions, contrast strongly
with the loose and imperfectly supported explanations
of all his predecessors; and the indulgent reader
will excuse the devotion of a few lines to an example
of the ingenuity and beauty of his methods.
It may seem a hopeless task to find out the true paths
of Mars and the earth (at that time when their shape
even was not known) from the observations giving only
the relative direction from night to night. Now,
Kepler had twenty years of observations of Mars to
deal with. This enabled him to use a new method,
to find the earth’s orbit. Observe the
date at any time when Mars is in opposition. The
earth’s position E at that date gives the longitude
of Mars M. His period is 687 days. Now choose
dates before and after the principal date at intervals
of 687 days and its multiples. Mars is in each
case in the same position. Now for any date when
Mars is at M and the earth at E3 the date of the year
gives the angle E3SM. And the observation of
Tycho gives the direction of Mars compared with the
sun, SE3M. So all the angles of the triangle SEM
in any of these positions of E are known, and also
the ratios of SE1, SE2, SE3, SE4 to SM and to each
other.
For the orbit of Mars observations were chosen at
intervals of a year, when the earth was always in
the same place.
But Kepler saw much farther than the geometrical facts.
He realised that the orbits are followed owing to
a force directed to the sun; and he guessed that this
is the same force as the gravity that makes a stone
fall. He saw the difficulty of gravitation acting
through the void space. He compared universal
gravitation to magnetism, and speaks of the work of
Gilbert of Colchester. (Gilbert’s book, De
Mundo Nostro Sublunari, Philosophia Nova, Amstelodami,
1651, containing similar views, was published forty-eight
years after Gilbert’s death, and forty-two years
after Kepler’s book and reference. His
book De Magnete was published in 1600.)
A few of Kepler’s views on gravitation, extracted
from the Introduction to his Astronomia Nova,
may now be mentioned:—
1. Every body at rest remains at rest if outside
the attractive power of other bodies.
2. Gravity is a property of masses mutually attracting
in such manner that the earth attracts a stone much
more than a stone attracts the earth.
3. Bodies are attracted to the earth’s
centre, not because it is the centre of the universe,
but because it is the centre of the attracting particles
of the earth.
4. If the earth be not round (but spheroidal?),
then bodies at different latitudes will not be attracted
to its centre, but to different points in the neighbourhood
of that centre.
5. If the earth and moon were not retained in
their orbits by vital force (aut alia aligua aequipollenti),
the earth and moon would come together.
6. If the earth were to cease to attract its
waters, the oceans would all rise and flow to the
moon.
7. He attributes the tides to lunar attraction.
Kepler had been appointed Imperial Astronomer with
a handsome salary (on paper), a fraction of which
was doled out to him very irregularly. He was
led to miserable makeshifts to earn enough to keep
his family from starvation; and proceeded to Ratisbon
in 1630 to represent his claims to the Diet.
He arrived worn out and debilitated; he failed in his
appeal, and died from fever, contracted under, and
fed upon, disappointment and exhaustion. Those
were not the days when men could adopt as a profession
the “research of endowment.”
Before taking leave of Kepler, who was by no means
a man of one idea, it ought to be here recorded that
he was the first to suggest that a telescope made
with both lenses convex (not a Galilean telescope)
can have cross wires in the focus, for use as a pointer
to fix accurately the positions of stars. An
Englishman, Gascoigne, was the first to use this in
practice.
From the all too brief epitome here given of Kepler’s
greatest book, it must be obvious that he had at that
time some inkling of the meaning of his laws—universal
gravitation. From that moment the idea of universal
gravitation was in the air, and hints and guesses were
thrown out by many; and in time the law of gravitation
would doubtless have been discovered, though probably
not by the work of one man, even if Newton had not
lived. But, if Kepler had not lived, who else
could have discovered his laws?
FOOTNOTES:
[1] When the writer visited M. D’Arrest, the
astronomer, at Copenhagen, in 1872, he was presented
by D’Arrest with one of several bricks collected
from the ruins of Uraniborg. This was one of his
most cherished possessions until, on returning home
after a prolonged absence on astronomical work, he
found that his treasure had been tidied away from
his study.
[2] An ellipse is one of the plane, sections of a
cone. It is an oval curve, which may be drawn
by fixing two pins in a sheet of paper at S and H,
fastening a string, SPH, to the two pins, and stretching
it with a pencil point at P, and moving the pencil
point, while the string is kept taut, to trace the
oval ellipse, APB. S and H are the foci.
Kepler found the sun to be in one focus, say S. AB
is the major axis. DE is the minor
axis. C is the centre. The direction
of AB is the line of apses. The ratio of
CS to CA is the excentricity. The position
of the planet at A is the perihelion (nearest
to the sun). The position of the planet at B is
the aphelion (farthest from the sun).
The angle ASP is the anomaly when the planet
is at P. CA or a line drawn from S to D is the mean
distance of the planet from the sun.
[3] The ruled logarithmic paper we now use was not
then to be had by going into a stationer’s shop.
Else he would have accomplished this in five minutes.
6. GALILEO AND THE TELESCOPE—NOTIONS OF GRAVITY BY HORROCKS, ETC.
It is now necessary to leave the subject of dynamical
astronomy for a short time in order to give some account
of work in a different direction originated by a contemporary
of Kepler’s, his senior in fact by seven years.
Galileo Galilei was born at Pisa in 1564. The
most scientific part of his work dealt with terrestrial
dynamics; but one of those fortunate chances which
happen only to really great men put him in the way
of originating a new branch of astronomy.
The laws of motion had not been correctly defined.
The only man of Galileo’s time who seems to
have worked successfully in the same direction as
himself was that Admirable Crichton of the Italians,
Leonardo da Vinci. Galileo cleared the ground.
It had always been noticed that things tend to come
to rest; a ball rolled on the ground, a boat moved
on the water, a shot fired in the air. Galileo
realised that in all of these cases a resisting force
acts to stop the motion, and he was the first to arrive
at the not very obvious law that the motion of a body
will never stop, nor vary its speed, nor change its
direction, except by the action of some force.
It is not very obvious that a light body and a heavy
one fall at the same speed (except for the resistance
of the air). Galileo proved this on paper, but
to convince the world he had to experiment from the
leaning tower of Pisa.
At an early age he discovered the principle of isochronism
of the pendulum, which, in the hands of Huyghens in
the middle of the seventeenth century, led to the
invention of the pendulum clock, perhaps the most
valuable astronomical instrument ever produced.
These and other discoveries in dynamics may seem very
obvious now; but it is often the most every-day matters
which have been found to elude the inquiries of ordinary
minds, and it required a high order of intellect to
unravel the truth and discard the stupid maxims scattered
through the works of Aristotle and accepted on his
authority. A blind worship of scientific authorities
has often delayed the progress of human knowledge,
just as too much “instruction” of a youth
often ruins his “education.” Grant,
in his history of Physical Astronomy, has well said
that “the sagacity and skill which Galileo displays
in resolving the phenomena of motion into their constituent
elements, and hence deriving the original principles
involved in them, will ever assure to him a distinguished
place among those who have extended the domains of
science.”
But it was work of a different kind that established
Galileo’s popular reputation. In 1609 Galileo
heard that a Dutch spectacle-maker had combined a
pair of lenses so as to magnify distant objects.
Working on this hint, he solved the same problem,
first on paper and then in practice. So he came
to make one of the first telescopes ever used in astronomy.
No sooner had he turned it on the heavenly bodies than
he was rewarded by such a shower of startling discoveries
as forthwith made his name the best known in Europe.
He found curious irregular black spots on the sun,
revolving round it in twenty-seven days; hills and
valleys on the moon; the planets showing discs of sensible
size, not points like the fixed stars; Venus showing
phases according to her position in relation to the
sun; Jupiter accompanied by four moons; Saturn with
appendages that he could not explain, but unlike the
other planets; the Milky Way composed of a multitude
of separate stars.
His fame flew over Europe like magic, and his discoveries
were much discussed—and there were many
who refused to believe. Cosmo de Medici induced
him to migrate to Florence to carry on his observations.
He was received by Paul V., the Pope, at Rome, to
whom he explained his discoveries.
He thought that these discoveries proved the truth
of the Copernican theory of the Earth’s motion;
and he urged this view on friends and foes alike.
Although in frequent correspondence with Kepler, he
never alluded to the New Astronomy, and wrote to him
extolling the virtue of epicycles. He loved to
argue, never shirked an encounter with any number
of disputants, and laughed as he broke down their arguments.
Through some strange course of events, not easy to
follow, the Copernican theory, whose birth was welcomed
by the Church, had now been taken up by certain anti-clerical
agitators, and was opposed by the cardinals as well
as by the dignitaries of the Reformed Church.
Galileo—a good Catholic—got mixed
up in these discussions, although on excellent terms
with the Pope and his entourage. At last it came
about that Galileo was summoned to appear at Rome,
where he was charged with holding and teaching heretical
opinions about the movement of the earth; and he then
solemnly abjured these opinions. There has been
much exaggeration and misstatement about his trial
and punishment, and for a long time there was a great
deal of bitterness shown on both sides. But the
general verdict of the present day seems to be that,
although Galileo himself was treated with consideration,
the hostility of the Church to the views of Copernicus
placed it in opposition also to the true Keplerian
system, and this led to unprofitable controversies.
From the time of Galileo onwards, for some time,
opponents of religion included the theory of the Earth’s
motion in their disputations, not so much for the love,
or knowledge, of astronomy, as for the pleasure of
putting the Church in the wrong. This created
a great deal of bitterness and intolerance on both
sides. Among the sufferers was Giordano Bruno,
a learned speculative philosopher, who was condemned
to be burnt at the stake.
Galileo died on Christmas Day, 1642—the
day of Newton’s birth. The further consideration
of the grand field of discovery opened out by Galileo
with his telescopes must be now postponed, to avoid
discontinuity in the history of the intellectual development
of this period, which lay in the direction of dynamical,
or physical, astronomy.
Until the time of Kepler no one seems to have conceived
the idea of universal physical forces controlling
terrestrial phenomena, and equally applicable to the
heavenly bodies. The grand discovery by Kepler
of the true relationship of the Sun to the Planets,
and the telescopic discoveries of Galileo and of those
who followed him, spread a spirit of inquiry and philosophic
thought throughout Europe, and once more did astronomy
rise in estimation; and the irresistible logic of
its mathematical process of reasoning soon placed it
in the position it has ever since occupied as the
foremost of the exact sciences.
The practical application of this process of reasoning
was enormously facilitated by the invention of logarithms
by Napier. He was born at Merchistoun, near Edinburgh,
in 1550, and died in 1617. By this system the
tedious arithmetical operations necessary in astronomical
calculations, especially those dealing with the trigonometrical
functions of angles, were so much simplified that Laplace
declared that by this invention the life-work of an
astronomer was doubled.
Jeremiah Horrocks (born 1619, died 1641) was an ardent
admirer of Tycho Brahe and Kepler, and was able to
improve the Rudolphine tables so much that he foretold
a transit of Venus, in 1639, which these tables failed
to indicate, and was the only observer of it.
His life was short, but he accomplished a great deal,
and rightly ascribed the lunar inequality called evection
to variations in the value of the eccentricity and
in the direction of the line of apses, at the same
time correctly assigning the disturbing force of
the Sun as the cause. He discovered the errors
in Jupiter’s calculated place, due to what we
now know as the long inequality of Jupiter and Saturn,
and measured with considerable accuracy the acceleration
at that date of Jupiter’s mean motion, and indicated
the retardation of Saturn’s mean motion.
Horrocks’ investigations, so far as they could
be collected, were published posthumously in 1672,
and seldom, if ever, has a man who lived only twenty-two
years originated so much scientific knowledge.
At this period British science received a lasting
impetus by the wise initiation of a much-abused man,
Charles II., who founded the Royal Society of London,
and also the Royal Observatory of Greeenwich, where
he established Flamsteed as first Astronomer Royal,
especially for lunar and stellar observations likely
to be useful for navigation. At the same time
the French Academy and the Paris Observatory were
founded. All this within fourteen years, 1662-1675.
Meanwhile gravitation in general terms was being discussed
by Hooke, Wren, Halley, and many others. All
of these men felt a repugnance to accept the idea
of a force acting across the empty void of space.
Descartes (1596-1650) proposed an ethereal medium whirling
round the sun with the planets, and having local whirls
revolving with the satellites. As Delambre and
Grant have said, this fiction only retarded the progress
of pure science. It had no sort of relation to
the more modern, but equally misleading, “nebular
hypothesis.” While many were talking and
guessing, a giant mind was needed at this stage to
make things clear.
7. SIR ISAAC NEWTON—LAW OF UNIVERSAL
GRAVITATION.
We now reach the period which is the culminating point
of interest in the history of dynamical astronomy.
Isaac Newton was born in 1642. Pemberton states
that Newton, having quitted Cambridge to avoid the
plague, was residing at Wolsthorpe, in Lincolnshire,
where he had been born; that he was sitting one day
in the garden, reflecting upon the force which prevents
a planet from flying off at a tangent and which draws
it to the sun, and upon the force which draws the moon
to the earth; and that he saw in the case of the planets
that the sun’s force must clearly be unequal
at different distances, for the pull out of the tangential
line in a minute is less for Jupiter than for Mars.
He then saw that the pull of the earth on the moon
would be less than for a nearer object. It is
said that while thus meditating he saw an apple fall
from a tree to the ground, and that this fact suggested
the questions: Is the force that pulled that apple
from the tree the same as the force which draws the
moon to the earth? Does the attraction for both
of them follow the same law as to distance as is given
by the planetary motions round the sun? It has
been stated that in this way the first conception
of universal gravitation arose.[1]
Quite the most important event in the whole history
of physical astronomy was the publication, in 1687,
of Newton’s Principia (Philosophiae Naturalis
Principia Mathematica). In this great work
Newton started from the beginning of things, the laws
of motion, and carried his argument, step by step,
into every branch of physical astronomy; giving the
physical meaning of Kepler’s three laws, and
explaining, or indicating the explanation of, all the
known heavenly motions and their irregularities; showing
that all of these were included in his simple statement
about the law of universal gravitation; and proceeding
to deduce from that law new irregularities in the
motions of the moon which had never been noticed, and
to discover the oblate figure of the earth and the
cause of the tides. These investigations occupied
the best part of his life; but he wrote the whole
of his great book in fifteen months.
Having developed and enunciated the true laws of motion,
he was able to show that Kepler’s second law
(that equal areas are described by the line from the
planet to the sun in equal times) was only another
way of saying that the centripetal force on a planet
is always directed to the sun. Also that Kepler’s
first law (elliptic orbits with the sun in one focus)
was only another way of saying that the force urging
a planet to the sun varies inversely as the square
of the distance. Also (if these two be granted)
it follows that Kepler’s third law is only another
way of saying that the sun’s force on different
planets (besides depending as above on distance) is
proportional to their masses.
Having further proved the, for that day, wonderful
proposition that, with the law of inverse squares,
the attraction by the separate particles of a sphere
of uniform density (or one composed of concentric
spherical shells, each of uniform density) acts as
if the whole mass were collected at the centre, he
was able to express the meaning of Kepler’s
laws in propositions which have been summarised as
follows:—
The law of universal gravitation.—Every
particle of matter in the universe attracts every
other particle with a force varying inversely as the
square of the distance between them, and directly as
the product of the masses of the two particles.[2]
But Newton did not commit himself to the law until
he had answered that question about the apple; and
the above proposition now enabled him to deal with
the Moon and the apple. Gravity makes a stone
fall 16.1 feet in a second. The moon is 60 times
farther from the earth’s centre than the stone,
so it ought to be drawn out of a straight course through
16.1 feet in a minute. Newton found the distance
through which she is actually drawn as a fraction of
the earth’s diameter. But when he first
examined this matter he proceeded to use a wrong diameter
for the earth, and he found a serious discrepancy.
This, for a time, seemed to condemn his theory, and
regretfully he laid that part of his work aside.
Fortunately, before Newton wrote the Principia
the French astronomer Picard made a new and correct
measure of an arc of the meridian, from which he obtained
an accurate value of the earth’s diameter.
Newton applied this value, and found, to his great
joy, that when the distance of the moon is 60 times
the radius of the earth she is attracted out of the
straight course 16.1 feet per minute, and that the
force acting on a stone or an apple follows the same
law as the force acting upon the heavenly bodies.[3]
The universality claimed for the law—if
not by Newton, at least by his commentators—was
bold, and warranted only by the large number of cases
in which Newton had found it to apply. Its universality
has been under test ever since, and so far it has
stood the test. There has often been a suspicion
of a doubt, when some inequality of motion in the
heavenly bodies has, for a time, foiled the astronomers
in their attempts to explain it. But improved
mathematical methods have always succeeded in the
end, and so the seeming doubt has been converted into
a surer conviction of the universality of the law.
Having once established the law, Newton proceeded
to trace some of its consequences. He saw that
the figure of the earth depends partly on the mutual
gravitation of its parts, and partly on the centrifugal
tendency due to the earth’s rotation, and that
these should cause a flattening of the poles.
He invented a mathematical method which he used for
computing the ratio of the polar to the equatorial
diameter.
He then noticed that the consequent bulging of matter
at the equator would be attracted by the moon unequally,
the nearest parts being most attracted; and so the
moon would tend to tilt the earth when in some parts
of her orbit; and the sun would do this to a less extent,
because of its great distance. Then he proved
that the effect ought to be a rotation of the earth’s
axis over a conical surface in space, exactly as the
axis of a top describes a cone, if the top has a sharp
point, and is set spinning and displaced from the vertical.
He actually calculated the amount; and so he explained
the cause of the precession of the equinoxes discovered
by Hipparchus about 150 B.C.
One of his grandest discoveries was a method of weighing
the heavenly bodies by their action on each other.
By means of this principle he was able to compare
the mass of the sun with the masses of those planets
that have moons, and also to compare the mass of our
moon with the mass of the earth.
Thus Newton, after having established his great principle,
devoted his splendid intellect to the calculation
of its consequences. He proved that if a body
be projected with any velocity in free space, subject
only to a central force, varying inversely as the square
of the distance, the body must revolve in a curve
which may be any one of the sections of a cone—a
circle, ellipse, parabola, or hyperbola; and he found
that those comets of which he had observations move
in parabolae round the Sun, and are thus subject to
the universal law.
Newton realised that, while planets and satellites
are chiefly controlled by the central body about which
they revolve, the new law must involve irregularities,
due to their mutual action—such, in fact,
as Horrocks had indicated. He determined to put
this to a test in the case of the moon, and to calculate
the sun’s effect, from its mass compared with
that of the earth, and from its distance. He proved
that the average effect upon the plane of the orbit
would be to cause the line in which it cuts the plane
of the ecliptic (i.e., the line of nodes) to revolve
in the ecliptic once in about nineteen years.
This had been a known fact from the earliest ages.
He also concluded that the line of apses would revolve