summaryrefslogtreecommitdiff
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<p align="center"><img src="001.jpg" alt="[Illustration: SIR ISAAC NEWTON (From the bust by Roubiliac In Trinity College, Cambridge.)]" /></p>

<div align="center">
<h1>HISTORY OF ASTRONOMY</h1>

<h2>BY</h2>

<h2>GEORGE FORBES,<br />
M.A., F.R.S., M. INST. C. E.,</h2>

<p><b>(FORMERLY PROFESSOR OF NATURAL PHILOSOPHY, ANDERSON&#8217;S
COLLEGE, GLASGOW)</b></p>

<p>AUTHOR OF &#8220;THE TRANSIT OF VENUS,&#8221; RENDU&#8217;S
&#8220;THEORY OF THE GLACIERS OF SAVOY,&#8221; ETC., ETC.</p>
</div>

<p><br /><br /></p>

<h1>CONTENTS</h1>

<blockquote>
<p><a href="#preface">PREFACE</a></p>
</blockquote>

<h2>BOOK I. THE GEOMETRICAL PERIOD</h2>

<blockquote>
<p><a href="#1">1. PRIMITIVE ASTRONOMY AND ASTROLOGY</a></p>

<p><a href="#2">2. ANCIENT ASTRONOMY&#8212;CHINESE
AND CHALD&#198;ANS</a></p>

<p><a href="#3">3. ANCIENT GREEK ASTRONOMY</a></p>

<p><a href="#4">4. THE REIGN OF EPICYCLES&#8212;FROM PTOLEMY TO COPERNICUS</a></p>
</blockquote>

<h2>BOOK II. THE DYNAMICAL PERIOD</h2>

<blockquote>
<p><a href="#5">5. DISCOVERY OF THE TRUE SOLAR SYSTEM&#8212;TYCHO BRAHE&#8212;KEPLER</a></p>

<p><a href="#6">6. GALILEO AND THE TELESCOPE&#8212;NOTIONS OF GRAVITY BY HORROCKS, ETC.</a></p>

<p><a href="#7">7. SIR ISAAC NEWTON&#8212;LAW OF UNIVERSAL GRAVITATION</a></p>

<p><a href="#8">8. NEWTON&#8217;S SUCCESSORS&#8212;HALLEY, EULER, LAGRANGE, LAPLACE, ETC.</a></p>

<p><a href="#9">9. DISCOVERY OF NEW PLANETS&#8212;HERSCHEL, PIAZZI, ADAMS, AND
LE VERRIER</a></p>
</blockquote>

<h2>BOOK III. OBSERVATION</h2>

<blockquote>

<p><a href="#10">10. INSTRUMENTS OF PRECISION&#8212;SIZE
OF THE SOLAR SYSTEM</a></p>

<p><a href="#11">11. HISTORY OF THE TELESCOPE&#8212;SPECTROSCOPE</a></p>
</blockquote>

<h2>BOOK IV. THE PHYSICAL PERIOD</h2>

<blockquote>
<p><a href="#12">12. THE SUN</a></p>

<p><a href="#13">13. THE MOON AND PLANETS</a></p>

<p><a href="#14">14. COMETS AND METEORS</a></p>

<p><a href="#15">15. THE STARS AND NEBUL&#198;</a></p>

<p><a href="#index">INDEX</a></p>
</blockquote>

<hr width="75%" size="1" align="center" />

<p><br /><br /></p>

<a name="preface"></a>
<h1>PREFACE</h1>

<p>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 &#8220;practical&#8221; or on
&#8220;theoretical astronomy,&#8221; nor a complete
&#8220;descriptive astronomy,&#8221; and still less
a book on &#8220;speculative astronomy.&#8221;
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.</p>

<p>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&#8217;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.</p>

<p>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&#8217;s
analysis to enable people to see that, so far as planetary
orbits are concerned, Kepler&#8217;s three laws (B,
C, D) were identical with Newton&#8217;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.</p>

<p>These reflections, arising from the writing of this
History, go to explain the invariable humility of
the great mathematical astronomers. Newton&#8217;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.</p>

<p>It has been necessary to curtail many parts of the
History in the attempt&#8212;perhaps a hopeless
one&#8212;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.</p>

<p>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&#8212;by observations taken from a
moving platform, the earth, of the directions of a
moving object, Mars&#8212;to deduce the exact
shape of the path of each of these planets, and their
actual positions on these paths at any time.
Kepler&#8217;s masterpiece is one of the most interesting
books that was ever written, combining wit, imagination,
ingenuity, and certainty.</p>

<p>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.</p>

<p>G. F.<br />
<i>August 1st, 1909.</i></p>

<p><br /><br /></p>

<h1>BOOK I.  THE GEOMETRICAL PERIOD</h1>

<p><br /><br /></p>

<a name="1"></a>
<h2>1. PRIMITIVE ASTRONOMY AND ASTROLOGY.</h2>

<p>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 <i>&#224; priori</i> 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.</p>

<p>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.</p>

<p>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.</p>

<p>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 &#8220;working
hypotheses,&#8221; were laying the foundations of observation
and deduction.</p>

<p>If the ancient Chald&#230;ans 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<a href="#fn1_1">[1]</a> 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.</p>

<p>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&#8217;s
<i>Soldier&#8217;s Pocket Book</i>.</p>

<p>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.</p>

<p>So Hipparchus, about 150 B.C., and Ptolemy a little
later, were able to use the observations of Chald&#230;an
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<a href="#fn1_2">[2]</a> has examined the marks made on the baked
bricks used by the Chald&#230;ans 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&#8217;s longitude
and the node of her orbit than any that could be obtained
from modern observations made with instruments of the
highest precision.</p>

<p>So again, Mr. Hind <a href="#fn1_3">[3]</a> was enabled to trace back the
period during which Halley&#8217;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.
<a href="#fn1_4">[4]</a></p>

<p>The theoretical views founded on Newton&#8217;s great
law of universal gravitation led to the conclusion
that the inclination of the earth&#8217;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.</p>

<p>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.</p>

<p>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.</p>

<p>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 <i>if</i> 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 &#8220;flatland&#8221; to a space of three dimensions.</p>

<p>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 <i>heliacal
risings</i>&#8212;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.</p>

<p>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&#8212;by
the Druids, the Mexicans, and the Peruvians, for example.</p>

<p>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.</p>

<p>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&#8217;s day we have had a dynamical astronomy.</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn1_1">[1]</a> Trans. R. S. E., xxiii. 1864, p. 499, <i>On
Sun Spots</i>, <i>etc</i>., by B. Stewart. Also
Trans. R. S. 1860-70. Also Prof. Ernest
Brown, in <i>R. A. S. Monthly Notices</i>, 1900.</p>

<p><a name="fn1_2">[2]</a> <i>R. A. S. Monthly Notices</i>, Sup.; 1905.</p>

<p align="center"><img src="002.jpg" alt="[Illustration: CHALD&#198;AN BAKED BRICK OR TABLET, <i>Obverse and reverse sides</i>,
Containing record of solar eclipse, 1062 B.C., used
lately by Cowell for rendering the lunar theory more
accurate than was possible by finest modern observations.
(British Museum collection, No. 35908.)]" /></p>

<p><a name="fn1_3">[3]</a> <i>R. A. S. Monthly Notices</i>, vol. x.,
p. 65.</p>

<p><a name="fn1_4">[4]</a> R. S. E. Proc., vol. x., 1880.</p>

<p><br /><br /></p>

<a name="2"></a>
<h2>2. ANCIENT ASTRONOMY&#8212;THE CHINESE AND CHALD&#198;ANS.</h2>

<p>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.</p>

<p>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 <i>Observations
Astronomical, Geographical, Chronological, and Physical</i>,
drawn from ancient Chinese books; and later by Father
Moyriac-de-Mailla, who in 1777-1785 published <i>Annals
of the Chinese Empire, translated from Tong-Kien-Kang-Mou</i>.</p>

<p>Bailly, in his <i>Astronomie Ancienne</i> (1781),
drew, from these and other sources, the conclusion
that all we know of the astronomical learning of the
Chinese, Indians, Chald&#230;ans, Assyrians, and Egyptians
is but the remnant of a far more complete astronomy
of which no trace can be found.</p>

<p>Delambre, in his <i>Histoire de l&#8217;Astronomie
Ancienne</i> (1817), ridicules the opinion of Bailly,
and considers that the progress made by all of these
nations is insignificant.</p>

<p>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.</p>

<p><i>China</i>.&#8212;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.).<a href="#fn2_1">[1]</a> 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.</p>

<p>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&#8217;s brightness.</p>

<p>It is also asserted, in the book called <i>Chu-King</i>,
that in the time of Yao the year was known to have
365&#188; 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&#8212;a
characteristic of the Chinese; but many younger nations
got into a terrible mess with their calendar from
ignorance of the year&#8217;s length.</p>

<p>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 <i>Saros</i>. It consists of 235 lunations,
and in that time the pole of the moon&#8217;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.</p>

<p>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&#8212;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&#8212;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 <i>Observations of Comets from 611
B.C. to 1640 A.D., Extracted from the Chinese Annals</i>.</p>

<p>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.</p>

<p><i>Chald&#230;ans</i>.&#8212;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.</p>

<p>The Chald&#230;ans, 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.</p>

<p>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.</p>

<p>We have records of observations carried on under Asshurbanapal,
who sent astronomers to different parts to study celestial
phenomena. Here is one:&#8212;</p>

<p>To the Director of Observations,&#8212;My Lord,
his humble servant Nabushum-iddin, Great Astronomer
of Nineveh, writes thus: &#8220;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.&#8221;</p>

<p>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<a href="#fn2_2">[2]</a> 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 &#8220;little more than a century
after the grandfathers and great-grandfathers of those
whose business is recorded had fled into Egypt with
Jeremiah&#8221; (Sayce); and (2) that the order of
intercalation at that time was not dissimilar to that
in use at the present day.</p>

<p>Then again, Knobel reminds us of &#8220;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.&#8221;
 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.
 Pingr&#233; 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.</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn2_1">[1]</a> These ancient dates are uncertain.</p>

<p><a name="fn2_2">[2]</a> <i>R. A. S. Monthly Notices</i>, vol. lxviii.,
No. 5, March, 1908.</p>

<p><br /><br /></p>

<a name="3"></a>
<h2>3. ANCIENT GREEK ASTRONOMY.</h2>

<p>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&#8217;s light from her. He supposed the
earth to be flat, and to float upon water. He
determined the ratio of the sun&#8217;s diameter to
its orbit, and apparently made out the diameter correctly
as half a degree. He left nothing in writing.</p>

<p>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.</p>

<p>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: &#8220;The circular
motion is the most perfect motion,&#8221; &#8220;Fire
is more worthy than earth,&#8221; &#8220;Ten is the
perfect number.&#8221; 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.</p>

<p>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&#8217;s
shadow&#8212;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.).</p>

<p>Solon dabbled, like many others, in reforms of the
calendar. The common year of the Greeks originally
had 360 days&#8212;twelve months of thirty days.
Solon&#8217;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 <i>Saros</i> 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&#8217;s
cycle being the golden number of our prayer-books.
 Melon&#8217;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.</p>

<p>Callippus (330 B.C.) used a cycle four times as long,
940 lunations, but one day short of Melon&#8217;s
seventy-six years. This was more correct.</p>

<p>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.</p>

<p>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.</p>

<p>Nicetas, Heraclides, and Ecphantes supposed the earth
to revolve on its axis, but to have no orbital motion.</p>

<p>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.</p>

<p>For further references to similar efforts of imagination
the reader is referred to Sir George Cornwall Lewis&#8217;s
<i>Historical Survey of the Astronomy of the Ancients</i>;
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:&#8212;</p>

<p>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 (<i>Xen.
Mem</i>, i. 1, 11-15).</p>

<p>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 <i>the problem
of representing the courses of the planets by circular
and uniform motions</i>.</p>

<p>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&#8217;s diameter,
correctly, to be half a degree.  Eratosthenes
(276-196 B.C.) measured the inclination to the equator
of the sun&#8217;s apparent path in the heavens&#8212;i.e.,
he measured the obliquity of the ecliptic, making
it 23&#176; 51&#8217;, 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.</p>

<p>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&#8212;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 <i>excentric</i>. The line from
the earth to the &#8220;excentric&#8221; was called
the <i>line of apses</i>. A circle having this
centre was called the <i>equant</i>, 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.</p>

<p>He proceeded in the same way to compute Lunar tables.
Making use of Chald&#230;an eclipses, he was able to get
an accurate value of the moon&#8217;s mean motion.
 [Halley, in 1693, compared this value with his own
measurements, and so discovered the acceleration of
the moon&#8217;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&#8217;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&#8217;s excentric
as he had done the sun&#8217;s.  He also discovered
some of the minor irregularities of the moon&#8217;s
motion, due, as Newton&#8217;s theory proves, to the
disturbing action of the sun&#8217;s attraction.</p>

<p>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&#176; from the poles of the earth&#8212;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 <i>precession of the equinoxes</i>, 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&#8217;s
pole round the pole of the ecliptic once in 26,000
years in the opposite direction to the planetary revolutions.</p>

<p>Hipparchus was also the inventor of trigonometry,
both plane and spherical. He explained the method
of using eclipses for determining the longitude.</p>

<p>In connection with Hipparchus&#8217; 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 &#947; 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&#176; and 27&#176; to the horizon and in the plane of the
meridian. It also appears that 4,000 years ago&#8212;i.e.,
about 2100 B.C.&#8212;an observer at the lower
end of the passage would be able to see &#947; Draconis,
the then pole-star, at its lower culmination.<a href="#fn3_1">[1]</a> 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.</p>

<p>(2) The Chald&#230;ans 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.</p>

<p>(3) In the Odyssey, Calypso directs Odysseus, in accordance
with Phoenician rules for navigating the Mediterranean,
to keep the Great Bear &#8220;ever on the left as
he traversed the deep&#8221; 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&#8217;s
inaccuracy.  Likewise Homer, both in the <i>Odyssey</i>
<a href="#fn3_2">[2]</a> (v. 272-5) and in the <i>Iliad</i> (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&#8217;s
character for accuracy. <a href="#fn3_3">[3]</a></p>

<p>(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
<a href="#fn3_4">[4]</a> 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.</p>

<p>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 <i>annual</i> 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 <i>deferent</i>), 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.</p>

<p>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.</p>

<p>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.</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn3_1">[1]</a> <i>Phil. Mag</i>., vol. xxiv., pp. 481-4.</p>

<p><a name="fn3_2">[2]</a></p>

<p>Plaeiadas t&#8217; esoronte kai opse duonta bootaen<br />
&#8216;Arkton th&#8217; aen kai amaxan epiklaesin
kaleousin,<br />
&#8216;Ae t&#8217; autou strephetai kai t&#8217; Oriona
dokeuei,<br />
Oin d&#8217;ammoros esti loetron Okeanoio.</p>

<p>&#8220;The Pleiades and Bo&#246;tes 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.&#8221;</p>

<p><a name="fn3_3">[3]</a> See Pearson in the Camb. Phil. Soc.
Proc., vol. iv., pt. ii., p. 93, on whose authority
the above statements are made.</p>

<p><a name="fn3_4">[4]</a> See p. 6 for definition.</p>

<p><br /><br /></p>

<a name="4"></a>
<h2>4. THE REIGN OF EPICYCLES&#8212;FROM PTOLEMY
TO COPERNICUS.</h2>

<p>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,<a href="#fn4_1">[1]</a> and
its ratio to that of the epicycle,<a href="#fn4_2">[2]</a> the distance
of the excentric<a href="#fn4_3">[3]</a> from the centre of the deferent,
and the position of the line of apses,<a href="#fn4_4">[4]</a> besides the
inclination and position of the plane of the planet&#8217;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.</p>

<p>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&#8217;s orbit, observed the
motion of the moon&#8217;s apse, and thought he detected
a smaller progression of the sun&#8217;s apse.
His tables were much more accurate than Ptolemy&#8217;s.
Abul Wefa, in the tenth century, seems to have discovered
the moon&#8217;s &#8220;variation.&#8221; 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.</p>

<p>At the close of the fifteenth century King Alphonso
of Spain employed computers to produce the Alphonsine
Tables (1488 A.D.), Purbach translated Ptolemy&#8217;s
book, and observations were carried out in Germany
by M&#252;ller, known as Regiomontanus, and Waltherus.</p>

<p>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, <i>De Revolutionibus Orbium
Celestium</i>. 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.</p>

<p>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&#8212;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&#8217;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.</p>

<p>Copernicus could not sever himself from this obnoxious
tradition.<a href="#fn4_5">[5]</a> 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.<a href="#fn4_6">[6]</a> Moreover, observers
had found irregularities in the moon&#8217;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.</p>

<p>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,<a href="#fn4_7">[7]</a> in drawing attention
to the strange conception,</p>

<blockquote>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.</blockquote>

<p>Copernicus made this rotation of the earth&#8217;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).</p>

<p>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.<a href="#fn4_8">[8]</a> He says:&#8212;</p>

<blockquote>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&#8217;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.</blockquote>

<p>According to Copernicus&#8217; 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.</p>

<p>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&#8217;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.</p>

<p>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.<a href="#fn4_9">[9]</a>
He says that whoever is not satisfied with this explanation
must be contented by being told that &#8220;mathematics
are for mathematicians&#8221; (Mathematicis mathematica
scribuntur).</p>

<p>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. &#8220;But&#8221;
(as Dreyer says in his most interesting book, <i>Tycho
Brahe</i>) &#8220;proofs of the physical truth of
his system Copernicus had given none, and could give
none,&#8221; any more than Pythagoras or Aristarchus.</p>

<p>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&#8212;those who have evidently
read his great book&#8212;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&#8217;
system was revived, and when Copernicus supported
his view that the earth moves and is not fixed.</p>

<p>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&#8217;s work,
but by those who desired to put the Church in the
wrong by extolling Copernicus.</p>

<p>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.</p>

<p>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.</p>

<p>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&#8217;s
account of epicycles, in the beautifully clear language
of his <i>Six Lectures on Astronomy</i>, 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.</p>

<p align="center"><img src="003.jpg" alt="[Illustration: &#8220;QUADRANS MURALIS SIVE TICHONICUS.&#8221;
 With portrait of Tycho Brahe, instruments, <i>etc</i>.,
painted on the wall; showing assistants using the
sight, watching the clock, and recording.  (From the
author&#8217;s copy of the <i>Astronomi&#230; Instaurat&#230;
Mechanica.</i>)]" /></p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn4_1">[1]</a> For definition see p. 22.</p>

<p><a name="fn4_2">[2]</a> <i>Ibid</i>.</p>

<p><a name="fn4_3">[3]</a> For definition see p. 18.</p>

<p><a name="fn4_4">[4]</a> For definition see p. 18.</p>

<p><a name="fn4_5">[5]</a> In his great book Copernicus says: &#8220;The
movement of the heavenly bodies is uniform, circular,
perpetual, or else composed of circular movements.&#8221;
In this he proclaimed himself a follower of Pythagoras
(see p. 14), as also when he says: &#8220;The
world is spherical because the sphere is, of all figures,
the most perfect&#8221; (Delambre, <i>Ast. Mod.
Hist</i>., pp. 86, 87).</p>

<p><a name="fn4_6">[6]</a> Kepler tells us that Tycho Brahe was pleased with
this device, and adapted it to his own system.</p>

<p><a name="fn4_7">[7]</a> <i>Hist. Ast.</i>, vol. i., p. 354.</p>

<p><a name="fn4_8">[8]</a> <i>Hist. of Phys. Ast.</i>, p. vii.</p>

<p><a name="fn4_9">[9]</a> &#8220;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.&#8221;</p>

<p><br /><br /></p>

<h1>BOOK II. THE DYNAMICAL PERIOD</h1>

<p><br /><br /></p>

<a name="5"></a>
<h2>5. DISCOVERY OF THE TRUE SOLAR SYSTEM&#8212;TYCHO BRAHE&#8212;KEPLER.</h2>

<p>During the period of the intellectual and aesthetic
revival, at the beginning of the sixteenth century,
the &#8220;spirit of the age&#8221; 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.</p>

<p>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.</p>

<p>For a complete life of this great man the reader is
referred to Dreyer&#8217;s <i>Tycho Brahe</i>, 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.</p>

<p>He studied in Germany, but King Frederick of Denmark,
appreciating his great talents, invited him to carry
out his life&#8217;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.<a href="#fn5_1">[1]</a></p>

<p>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.</p>

<p>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&#8212;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.</p>

<p>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.</p>

<p>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&#8217;s
standard stars are compared with the best modern catalogues,
his probable error in right ascension is only &#177; 24&#8221;,
1, and in declination only &#177; 25&#8221;, 9.</p>

<p>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.</p>

<p>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.</p>

<p>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.</p>

<p>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.</p>

<p>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 &#8220;variation&#8221; by observing
the moon in all phases&#8212;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&#8217;s orbit,
but he feared that these would soon become unmanageable
if further observations showed more new inequalities.</p>

<p>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.</p>

<p>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.</p>

<p>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.</p>

<p>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 (<i>De Mundi</i>, <i>etc</i>.)
that</p>

<blockquote>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.</blockquote>

<p>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&#8217;s
<i>Tischreden</i>, pp.  22, 60) derided him in his
usual pithy manner, that Melancthon (<i>Initia doctrinae
physicae</i>) said that Scripture, and also science,
are against the earth&#8217;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.</p>

<p>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.</p>

<img src="004.jpg" alt="[Illustration: PORTRAIT OF JOHANNES KEPLER.
 By F. Wanderer, from Reitlinger&#8217;s &#8220;Johannes
Kepler&#8221; (original in Strassburg).]" align="right" />

<p>It has seemed to many that Plato&#8217;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 <i>&#224; priori</i> 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.</p>

<p>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&#8217;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: &#8220;Out
of these eight minutes we will construct a new theory
that will explain the motions of all the planets.&#8221;
And he did it, with elliptic orbits having the sun
in a focus of each.<a href="#fn5_2">[2]</a></p>

<p>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.</p>

<p>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&#8217;s great book could hold
such an opinion for a moment. In fact, the excellence
of Copernicus&#8217;s book helped to prolong the life
of the epicyclical theories in opposition to Kepler&#8217;s
teaching.</p>

<p>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&#8217;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.</p>

<p>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.</p>

<p>His first law states that the planets describe ellipses
with the sun at a focus of each ellipse.</p>

<p>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, <i>Astronomia
Nova, sen.  Physica Coelestis tradita commentariis
de Motibus Stelloe; Martis</i>, Prague, 1609.</p>

<p>It took him nine years more<a href="#fn5_3">[3]</a> to discover his third
law, that the squares of the periodic times are proportional
to the cubes of the mean distances from the sun.</p>

<p>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&#8217;s three laws could not be
understood until expounded by the logic of Newton&#8217;s
dynamics.</p>

<p>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 <i>Harmonics</i>, which is not now quoted, only
lest someone might say it was egotistical&#8212;a
term which is simply grotesque when applied to such
a man with such a life&#8217;s work accomplished.</p>

<p>The whole book, <i>Astronomia Nova</i>, 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.</p>

<img src="006.png" alt="" align="right" />

<p>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&#8217;s orbit. Observe the
date at any time when Mars is in opposition. The
earth&#8217;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 E<sub>3</sub> the date of the year
gives the angle E<sub>3</sub>SM. And the observation of
Tycho gives the direction of Mars compared with the
sun, SE<sub>3</sub>M. So all the angles of the triangle SEM
in any of these positions of E are known, and also
the ratios of SE<sub>1</sub>, SE<sub>2</sub>, SE<sub>3</sub>, SE<sub>4</sub> to SM and to each
other.</p>

<p>For the orbit of Mars observations were chosen at
intervals of a year, when the earth was always in
the same place.</p>

<p>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&#8217;s book, <i>De
Mundo Nostro Sublunari, Philosophia Nova</i>, Amstelodami,
1651, containing similar views, was published forty-eight
years after Gilbert&#8217;s death, and forty-two years
after Kepler&#8217;s book and reference.  His
book <i>De Magnete</i> was published in 1600.)</p>

<p>A few of Kepler&#8217;s views on gravitation, extracted
from the Introduction to his <i>Astronomia Nova</i>,
may now be mentioned:&#8212;</p>

<p>1. Every body at rest remains at rest if outside
the attractive power of other bodies.</p>

<p>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.</p>

<p>3. Bodies are attracted to the earth&#8217;s
centre, not because it is the centre of the universe,
but because it is the centre of the attracting particles
of the earth.</p>

<p>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.</p>

<p>5. If the earth and moon were not retained in
their orbits by vital force (<i>aut alia aligua aequipollenti</i>),
the earth and moon would come together.</p>

<p>6. If the earth were to cease to attract its
waters, the oceans would all rise and flow to the
moon.</p>

<p>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 &#8220;research of endowment.&#8221;</p>

<p>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.</p>

<p>From the all too brief epitome here given of Kepler&#8217;s
greatest book, it must be obvious that he had at that
time some inkling of the meaning of his laws&#8212;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?</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn5_1">[1]</a> When the writer visited M. D&#8217;Arrest, the
astronomer, at Copenhagen, in 1872, he was presented
by D&#8217;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.</p>

<img src="005.png" alt="" align="right" />

<p><a name="fn5_2">[2]</a> 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 <i>foci</i>.
Kepler found the sun to be in one focus, say S. AB
is the <i>major axis</i>. DE is the <i>minor
axis</i>. C is the <i>centre</i>. The direction
of AB is the <i>line of apses</i>. The ratio of
CS to CA is the <i>excentricity</i>. The position
of the planet at A is the <i>perihelion</i> (nearest
to the sun). The position of the planet at B is
the <i>aphelion</i> (farthest from the sun).
The angle ASP is the <i>anomaly</i> when the planet
is at P. CA or a line drawn from S to D is the <i>mean
distance</i> of the planet from the sun.</p>

<p><a name="fn5_3">[3]</a> The ruled logarithmic paper we now use was not
then to be had by going into a stationer&#8217;s shop.
Else he would have accomplished this in five minutes.</p>

<p><br /><br /></p>

<a name="6"></a>
<h2>6. GALILEO AND THE TELESCOPE&#8212;NOTIONS OF GRAVITY BY HORROCKS, ETC.</h2>

<p>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&#8217;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.</p>

<p>The laws of motion had not been correctly defined.
 The only man of Galileo&#8217;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.</p>

<p>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.</p>

<p>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.</p>

<p>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 &#8220;instruction&#8221; of a youth
often ruins his &#8220;education.&#8221; Grant,
in his history of Physical Astronomy, has well said
that &#8220;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.&#8221;</p>

<p>But it was work of a different kind that established
Galileo&#8217;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.</p>

<p>His fame flew over Europe like magic, and his discoveries
were much discussed&#8212;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.</p>

<p>He thought that these discoveries proved the truth
of the Copernican theory of the Earth&#8217;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.</p>

<p>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&#8212;a good Catholic&#8212;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&#8217;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.</p>

<p>Galileo died on Christmas Day, 1642&#8212;the
day of Newton&#8217;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.</p>

<p>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.</p>

<p>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.</p>

<p>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 <i>evection</i>
to variations in the value of the eccentricity and
in the direction of the line of apses, at the same
time correctly assigning <i>the disturbing force of
the Sun</i> as the cause. He discovered the errors
in Jupiter&#8217;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&#8217;s mean motion, and indicated
the retardation of Saturn&#8217;s mean motion.</p>

<p>Horrocks&#8217; 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.</p>

<p>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.</p>

<p>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, &#8220;nebular
hypothesis.&#8221; While many were talking and
guessing, a giant mind was needed at this stage to
make things clear.</p>

<p><br /><br /></p>

<a name="7"></a>
<h2>7. SIR ISAAC NEWTON&#8212;LAW OF UNIVERSAL
GRAVITATION.</h2>

<p>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&#8217;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.<a href="#fn7_1">[1]</a></p>

<p>Quite the most important event in the whole history
of physical astronomy was the publication, in 1687,
of Newton&#8217;s <i>Principia (Philosophiae Naturalis
Principia Mathematica)</i>. 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&#8217;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.</p>

<p>Having developed and enunciated the true laws of motion,
he was able to show that Kepler&#8217;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&#8217;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&#8217;s third law is only another
way of saying that the sun&#8217;s force on different
planets (besides depending as above on distance) is
proportional to their masses.</p>

<p>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&#8217;s
laws in propositions which have been summarised as
follows:&#8212;</p>

<p>The law of universal gravitation.&#8212;<i>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</i>.<a href="#fn7_2">[2]</a></p>

<p>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&#8217;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&#8217;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 <i>Principia</i>
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&#8217;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.<a href="#fn7_3">[3]</a></p>

<p>The universality claimed for the law&#8212;if
not by Newton, at least by his commentators&#8212;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.</p>

<p>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&#8217;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.</p>

<p>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&#8217;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.</p>

<p>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.</p>

<p>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&#8212;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.</p>

<p>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&#8212;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&#8217;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
in the plane of the lunar orbit also in about nineteen
years; but the observed period is only ten years.
For a long time this was the one weak point in the
Newtonian theory. It was not till 1747 that Clairaut
reconciled this with the theory, and showed why Newton&#8217;s
calculation was not exact.</p>

<p>Newton proceeded to explain the other inequalities
recognised by Tycho Brahe and older observers, and
to calculate their maximum amounts as indicated by
his theory. He further discovered from his calculations
two new inequalities, one of the apogee, the other
of the nodes, and assigned the maximum value.
Grant has shown the values of some of these as given
by observation in the tables of Meyer and more modern
tables, and has compared them with the values assigned
by Newton from his theory; and the comparison is very
remarkable.</p>

<pre>Newton.      Modern Tables.
&#176; &#8217;  "         &#176; &#8217; "
Mean monthly motion of Apses         1.31.28         3.4.0
Mean annual motion of nodes         19.18.1,23     19.21.22,50
Mean value of &#8220;variation&#8221;              36.10          35.47
Annual equation                        11.51          11.14
Inequality of mean motion of apogee    19.43          22.17
Inequality of mean motion of nodes      9.24           9.0</pre>

<p>The only serious discrepancy is the first, which has
been already mentioned. Considering that some
of these perturbations had never been discovered,
that the cause of none of them had ever been known,
and that he exhibited his results, if he did not also
make the discoveries, by the synthetic methods of
geometry, it is simply marvellous that he reached
to such a degree of accuracy. He invented the
infinitesimal calculus which is more suited for such
calculations, but had he expressed his results in
that language he would have been unintelligible to
many.</p>

<p>Newton&#8217;s method of calculating the precession
of the equinoxes, already referred to, is as beautiful
as anything in the <i>Principia</i>. He had already
proved the regression of the nodes of a satellite
moving in an orbit inclined to the ecliptic. He
now said that the nodes of a ring of satellites revolving
round the earth&#8217;s equator would consequently
all regress. And if joined into a solid ring its
node would regress; and it would do so, only more slowly,
if encumbered by the spherical part of the earth&#8217;s
mass. Therefore the axis of the equatorial belt
of the earth must revolve round the pole of the ecliptic.
Then he set to work and found the amount due to the
moon and that due to the sun, and so he solved the
mystery of 2,000 years.</p>

<p>When Newton applied his law of gravitation to an explanation
of the tides he started a new field for the application
of mathematics to physical problems; and there can
be little doubt that, if he could have been furnished
with complete tidal observations from different parts
of the world, his extraordinary powers of analysis
would have enabled him to reach a satisfactory theory.
 He certainly opened up many mines full of intellectual
gems; and his successors have never ceased in their
explorations. This has led to improved mathematical
methods, which, combined with the greater accuracy
of observation, have rendered physical astronomy of
to-day the most exact of the sciences.</p>

<p>Laplace only expressed the universal opinion of posterity
when he said that to the <i>Principia</i> is assured
&#8220;a pre-eminence above all the other productions
of the human intellect.&#8221;</p>

<p>The name of Flamsteed, First Astronomer Royal, must
here be mentioned as having supplied Newton with the
accurate data required for completing the theory.</p>

<p>The name of Edmund Halley, Second Astronomer Royal,
must ever be held in repute, not only for his own
discoveries, but for the part he played in urging
Newton to commit to writing, and present to the Royal
Society, the results of his investigations. But
for his friendly insistence it is possible that the
<i>Principia</i> would never have been written; and
but for his generosity in supplying the means the
Royal Society could not have published the book.</p>

<p align="center"><img src="007.jpg" alt="[Illustration: DEATH MASK OF SIR ISAAC NEWTON.
Photographed specially for this work from the original,
by kind permission of the Royal Society, London.]" /></p>

<p>Sir Isaac Newton died in 1727, at the age of eighty-five.
 His body lay in state in the Jerusalem Chamber, and
was buried in Westminster Abbey.</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn7_1">[1]</a> The writer inherited from his father (Professor
J. D. Forbes) a small box containing a bit of wood
and a slip of paper, which had been presented to him
by Sir David Brewster. On the paper Sir David
had written these words: &#8220;If there be any
truth in the story that Newton was led to the theory
of gravitation by the fall of an apple, this bit of
wood is probably a piece of the apple tree from which
Newton saw the apple fall. When I was on a pilgrimage
to the house in which Newton was born, I cut it off
an ancient apple tree growing in his garden.&#8221;
When lecturing in Glasgow, about 1875, the writer showed
it to his audience. The next morning, when removing
his property from the lecture table, he found that
his precious relic had been stolen. It would
be interesting to know who has got it now!</p>

<p><a name="fn7_2">[2]</a> It must be noted that these words, in which the
laws of gravitation are always summarised in histories
and text-books, do not appear in the <i>Principia</i>;
but, though they must have been composed by some early
commentator, it does not appear that their origin has
been traced. Nor does it appear that Newton ever
extended the law beyond the Solar System, and probably
his caution would have led him to avoid any statement
of the kind until it should be proved.</p>

<p>With this exception the above statement of the law
of universal gravitation contains nothing that is
not to be found in the <i>Principia</i>; and the nearest
approach to that statement occurs in the Seventh Proposition
of Book III.:&#8212;</p>

<p>Prop.: That gravitation occurs in all bodies,
and that it is proportional to the quantity of matter
in each.</p>

<p>Cor. I.: The total attraction of gravitation
on a planet arises, and is composed, out of the attraction
on the separate parts.</p>

<p>Cor. II.: The attraction on separate equal
particles of a body is reciprocally as the square
of the distance from the particles.</p>

<p><a name="fn7_3">[3]</a> It is said that, when working out this final result,
the probability of its confirming that part of his
theory which he had reluctantly abandoned years before
excited him so keenly that he was forced to hand over
his calculations to a friend, to be completed by him.</p>

<p><br /><br /></p>

<a name="8"></a>
<h2>8. NEWTON&#8217;S SUCCESSORS&#8212;HALLEY,
EULER, LAGRANGE, LAPLACE, ETC.</h2>

<p>Edmund Halley succeeded Flamsteed as Second Astronomer
Royal in 1721. Although he did not contribute
directly to the mathematical proofs of Newton&#8217;s
theory, yet his name is closely associated with some
of its greatest successes.</p>

<p>He was the first to detect the acceleration of the
moon&#8217;s mean motion. Hipparchus, having
compared his own observations with those of more ancient
astronomers, supplied an accurate value of the moon&#8217;s
mean motion in his time. Halley similarly deduced
a value for modern times, and found it sensibly greater.
 He announced this in 1693, but it was not until 1749
that Dunthorne used modern lunar tables to compute
a lunar eclipse observed in Babylon 721 B.C., another
at Alexandria 201 B.C., a solar eclipse observed by
Theon 360 A.D., and two later ones up to the tenth
century.  He found that to explain these eclipses
Halley&#8217;s suggestion must be adopted, the acceleration
being 10&#8221; in one century. In 1757 Lalande
again fixed it at 10.&#8221;</p>

<p>The Paris Academy, in 1770, offered their prize for
an investigation to see if this could be explained
by the theory of gravitation. Euler won the prize,
but failed to explain the effect, and said: &#8220;It
appears to be established by indisputable evidence
that the secular inequality of the moon&#8217;s mean
motion cannot be produced by the forces of gravitation.&#8221;</p>

<p>The same subject was again proposed for a prize which
was shared by Lagrange <a href="#fn8_1">[1]</a> and Euler, neither finding
a solution, while the latter asserted the existence
of a resisting medium in space.</p>

<p>Again, in 1774, the Academy submitted the same subject,
a third time, for the prize; and again Lagrange failed
to detect a cause in gravitation.</p>

<p>Laplace <a href="#fn8_2">[2]</a> now took the matter in hand. He tried
the effect of a non-instantaneous action of gravity,
to no purpose. But in 1787 he gave the true explanation.
 The principal effect of the sun on the moon&#8217;s
orbit is to diminish the earth&#8217;s influence, thus
lengthening the period to a new value generally taken
as constant. But Laplace&#8217;s calculations
showed the new value to depend upon the excentricity
of the earth&#8217;s orbit, which, according; to theory,
has a periodical variation of enormous period, and
has been continually diminishing for thousands of
years. Thus the solar influence has been diminishing,
and the moon&#8217;s mean motion increased. Laplace
computed the amount at 10&#8221; in one century, agreeing
with observation. (Later on Adams showed that Laplace&#8217;s
calculation was wrong, and that the value he found
was too large; so, part of the acceleration is now
attributed by some astronomers to a lengthening of
the day by tidal friction.)</p>

<p>Another contribution by Halley to the verification
of Newton&#8217;s law was made when he went to St.
Helena to catalogue the southern stars. He measured
the change in length of the second&#8217;s pendulum
in different latitudes due to the changes in gravity
foretold by Newton.</p>

<p>Furthermore, he discovered the long inequality of
Jupiter and Saturn, whose period is 929 years.
For an investigation of this also the Academy of Sciences
offered their prize. This led Euler to write a
valuable essay disclosing a new method of computing
perturbations, called the instantaneous ellipse with
variable elements. The method was much developed
by Lagrange.</p>

<p>But again it was Laplace who solved the problem of
the inequalities of Jupiter and Saturn by the theory
of gravitation, reducing the errors of the tables
from 20&#8217; down to 12&#8221;, thus abolishing the
use of empirical corrections to the planetary tables,
and providing another glorious triumph for the law
of gravitation.  As Laplace justly said:
&#8220;These inequalities appeared formerly to be inexplicable
by the law of gravitation&#8212;they now form
one of its most striking proofs.&#8221;</p>

<p>Let us take one more discovery of Halley, furnishing
directly a new triumph for the theory. He noticed
that Newton ascribed parabolic orbits to the comets
which he studied, so that they come from infinity,
sweep round the sun, and go off to infinity for ever,
after having been visible a few weeks or months.
He collected all the reliable observations of comets
he could find, to the number of twenty-four, and computed
their parabolic orbits by the rules laid down by Newton.
His object was to find out if any of them really travelled
in elongated ellipses, practically undistinguishable,
in the visible part of their paths, from parabol&#230;,
in which case they would be seen more than once.
He found two old comets whose orbits, in shape and
position, resembled the orbit of a comet observed by
himself in 1682.  Apian observed one in 1531;
Kepler the other in 1607.  The intervals between
these appearances is seventy-five or seventy-six years.
He then examined and found old records of similar appearance
in 1456, 1380, and 1305. It is true, he noticed,
that the intervals varied by a year and a-half, and
the inclination of the orbit to the ecliptic diminished
with successive apparitions.  But he knew from
previous calculations that this might easily be due
to planetary perturbations. Finally, he arrived
at the conclusion that all of these comets were identical,
travelling in an ellipse so elongated that the part
where the comet was seen seemed to be part of a parabolic
orbit. He then predicted its return at the end
of 1758 or beginning of 1759, when he should be dead;
but, as he said, &#8220;if it should return, according
to our prediction, about the year 1758, impartial posterity
will not refuse to acknowledge that this was first
discovered by an Englishman."<a href="#fn8_3">[3]</a> [<i>Synopsis Astronomiae
Cometicae</i>, 1749.]</p>

<p>Once again Halley&#8217;s suggestion became an inspiration
for the mathematical astronomer. Clairaut, assisted
by Lalande, found that Saturn would retard the comet
100 days, Jupiter 518 days, and predicted its return
to perihelion on April 13th, 1759. In his communication
to the French Academy, he said that a comet travelling
into such distant regions might be exposed to the influence
of forces totally unknown, and &#8220;even of some
planet too far removed from the sun to be ever perceived.&#8221;</p>

<p>The excitement of astronomers towards the end of 1758
became intense; and the honour of first catching sight
of the traveller fell to an amateur in Saxony, George
Palitsch, on Christmas Day, 1758. It reached
perihelion on March 13th, 1759.</p>

<p>This fact was a startling confirmation of the Newtonian
theory, because it was a new kind of calculation of
perturbations, and also it added a new member to the
solar system, and gave a prospect of adding many more.</p>

<p>When Halley&#8217;s comet reappeared in 1835, Pontecoulant&#8217;s
computations for the date of perihelion passage were
very exact, and afterwards he showed that, with more
exact values of the masses of Jupiter and Saturn,
his prediction was correct within two days, after an
invisible voyage of seventy-five years!</p>

<p>Hind afterwards searched out many old appearances
of this comet, going back to 11 B.C., and most of
these have been identified as being really Halley&#8217;s
comet by the calculations of Cowell and Cromellin<a href="#fn8_4">[4]</a>
(of Greenwich Observatory), who have also predicted
its next perihelion passage for April 8th to 16th,
1910, and have traced back its history still farther,
to 240 B.C.</p>

<p>Already, in November, 1907, the Astronomer Royal was
trying to catch it by the aid of photography.</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn8_1">[1]</a> Born 1736; died 1813.</p>

<p><a name="fn8_2">[2]</a> Born 1749; died 1827.</p>

<p><a name="fn8_3">[3]</a> This sentence does not appear in the original
memoir communicated to the Royal Society, but was
first published in a posthumous reprint.</p>

<p><a name="fn8_4">[4]</a> <i>R. A. S. Monthly Notices</i>, 1907-8.</p>

<p><br /><br /></p>

<a name="9"></a>
<h2>9. DISCOVERY OF NEW PLANETS&#8212;HERSCHEL,
PIAZZI, ADAMS, AND LE VERRIER.</h2>

<p>It would be very interesting, but quite impossible
in these pages, to discuss all the exquisite researches
of the mathematical astronomers, and to inspire a
reverence for the names connected with these researches,
which for two hundred years have been establishing
the universality of Newton&#8217;s law. The lunar
and planetary theories, the beautiful theory of Jupiter&#8217;s
satellites, the figure of the earth, and the tides,
were mathematically treated by Maclaurin, D&#8217;Alembert,
Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley,
Bailly, Lalande, Delambre, Mayer, Hansen, Burchardt,
Binet, Damoiseau, Plana, Poisson, Gauss, Bessel, Bouvard,
Airy, Ivory, Delaunay, Le Verrier, Adams, and others
of later date.</p>

<p>By passing over these important developments it is
possible to trace some of the steps in the crowning
triumph of the Newtonian theory, by which the planet
Neptune was added to the known members of the solar
system by the independent researches of Professor J.C.
Adams and of M. Le Verrier, in 1846.</p>

<p>It will be best to introduce this subject by relating
how the eighteenth century increased the number of
known planets, which was then only six, including
the earth.</p>

<p>On March 13th, 1781, Sir William Herschel was, as
usual, engaged on examining some small stars, and,
noticing that one of them appeared to be larger than
the fixed stars, suspected that it might be a comet.
To test this he increased his magnifying power from
227 to 460 and 932, finding that, unlike the fixed
stars near it, its definition was impaired and its
size increased.  This convinced him that the object
was a comet, and he was not surprised to find on succeeding
nights that the position was changed, the motion being
in the ecliptic. He gave the observations of
five weeks to the Royal Society without a suspicion
that the object was a new planet.</p>

<p>For a long time people could not compute a satisfactory
orbit for the supposed comet, because it seemed to
be near the perihelion, and no comet had ever been
observed with a perihelion distance from the sun greater
than four times the earth&#8217;s distance. Lexell
was the first to suspect that this was a new planet
eighteen times as far from the sun as the earth is.
In January, 1783, Laplace published the elliptic elements.
The discoverer of a planet has a right to name it,
so Herschel called it Georgium Sidus, after the king.
 But Lalande urged the adoption of the name Herschel.
 Bode suggested Uranus, and this was adopted.
The new planet was found to rank in size next to Jupiter
and Saturn, being 4.3 times the diameter of the earth.</p>

<p>In 1787 Herschel discovered two satellites, both revolving
in nearly the same plane, inclined 80&#176; to the ecliptic,
and the motion of both was retrograde.</p>

<p>In 1772, before Herschel&#8217;s discovery, Bode<a href="#fn9_1">[1]</a>
had discovered a curious arbitrary law of planetary
distances.  Opposite each planet&#8217;s name
write the figure 4; and, in succession, add the numbers
0, 3, 6, 12, 24, 48, 96, <i>etc</i>., to the 4, always
doubling the last numbers.  You then get the
planetary distances.</p>

<pre>
  Mercury, dist.-- 4  4 +   0 =   4
  Venus      "     7  4 +   3 =   7
  Earth      "    10  4 +   6 =  10
  Mars       "    15  4 +  12 =  16
   --                 4 +  24 =  28
  Jupiter  dist.  52  4 +  48 =  52
  Saturn     "    95  4 +  96 = 100
  (Uranus)   "   192  4 + 192 = 196
   --                 4 + 384 = 388
</pre>

<p>All the five planets, and the earth, fitted this rule,
except that there was a blank between Mars and Jupiter.
When Uranus was discovered, also fitting the rule,
the conclusion was irresistible that there is probably
a planet between Mars and Jupiter. An association
of twenty-four astronomers was now formed in Germany
to search for the planet. Almost immediately
afterwards the planet was discovered, not by any member
of the association, but by Piazzi, when engaged upon
his great catalogue of stars. On January 1st,
1801, he observed a star which had changed its place
the next night. Its motion was retrograde till
January 11th, direct after the 13th.  Piazzi fell
ill before he had enough observations for computing
the orbit with certainty, and the planet disappeared
in the sun&#8217;s rays. Gauss published an approximate
ephemeris of probable positions when the planet should
emerge from the sun&#8217;s light. There was an
exciting hunt, and on December 31st (the day before
its birthday) De Zach captured the truant, and Piazzi
christened it Ceres.</p>

<p>The mean distance from the sun was found to be 2.767,
agreeing with the 2.8 given by Bode&#8217;s law.
Its orbit was found to be inclined over 10&#176; to the
ecliptic, and its diameter was only 161 miles.</p>

<p>On March 28th, 1802, Olbers discovered a new seventh
magnitude star, which turned out to be a planet resembling
Ceres. It was called Pallas. Gauss found
its orbit to be inclined 35&#176; to the ecliptic, and
to cut the orbit of Ceres; whence Olbers considered
that these might be fragments of a broken-up planet.
He then commenced a search for other fragments.
In 1804 Harding discovered Juno, and in 1807 Olbers
found Vesta. The next one was not discovered until
1845, from which date asteroids, or minor planets
(as these small planets are called), have been found
almost every year. They now number about 700.</p>

<p>It is impossible to give any idea of the interest
with which the first additions since prehistoric times
to the planetary system were received. All of
those who showered congratulations upon the discoverers
regarded these discoveries in the light of rewards
for patient and continuous labours, the very highest
rewards that could be desired. And yet there
remained still the most brilliant triumph of all,
the addition of another planet like Uranus, before
it had ever been seen, when the analysis of Adams
and Le Verrier gave a final proof of the powers of
Newton&#8217;s great law to explain any planetary
irregularity.</p>

<p>After Sir William Herschel discovered Uranus, in 1781,
it was found that astronomers had observed it on many
previous occasions, mistaking it for a fixed star
of the sixth or seventh magnitude. Altogether,
nineteen observations of Uranus&#8217;s position, from
the time of Flamsteed, in 1690, had been recorded.</p>

<p>In 1790 Delambre, using all these observations, prepared
tables for computing its position. These worked
well enough for a time, but at last the differences
between the calculated and observed longitudes of
the planet became serious. In 1821 Bouvard undertook
a revision of the tables, but found it impossible
to reconcile all the observations of 130 years (the
period of revolution of Uranus is eighty-four years).
So he deliberately rejected the old ones, expressing
the opinion that the discrepancies might depend upon
&#8220;some foreign and unperceived cause which may
have been acting upon the planet.&#8221; In a
few years the errors even of these tables became intolerable.
In 1835 the error of longitude was 30&#8221;; in 1838,
50&#8221;; in 1841, 70&#8221;; and, by comparing the
errors derived from observations made before and after
opposition, a serious error of the distance (radius
vector) became apparent.</p>

<p>In 1843 John Couch Adams came out Senior Wrangler
at Cambridge, and was free to undertake the research
which as an undergraduate he had set himself&#8212;to
see whether the disturbances of Uranus could be explained
by assuming a certain orbit, and position in that orbit,
of a hypothetical planet even more distant than Uranus.
 Such an explanation had been suggested, but until
1843 no one had the boldness to attack the problem.
 Bessel had intended to try, but a fatal illness overtook
him.</p>

<p>Adams first recalculated all known causes of disturbance,
using the latest determinations of the planetary masses.
Still the errors were nearly as great as ever.
 He could now, however, use these errors as being
actually due to the perturbations produced by the unknown
planet.</p>

<p>In 1844, assuming a circular orbit, and a mean distance
agreeing with Bode&#8217;s law, he obtained a first
approximation to the position of the supposed planet.
 He then asked Professor Challis, of Cambridge, to
procure the latest observations of Uranus from Greenwich,
which Airy immediately supplied. Then the whole
work was recalculated from the beginning, with more
exactness, and assuming a smaller mean distance.</p>

<p>In September, 1845, he handed to Challis the elements
of the hypothetical planet, its mass, and its apparent
position for September 30th, 1845. On September
22nd Challis wrote to Airy explaining the matter,
and declaring his belief in Adams&#8217;s capabilities.
When Adams called on him Airy was away from home,
but at the end of October, 1845, he called again,
and left a paper with full particulars of his results,
which had, for the most part, reduced the discrepancies
to about 1&#8221;. As a matter of fact, it has
since been found that the heliocentric place of the
new planet then given was correct within about 2&#176;.</p>

<p>Airy wrote expressing his interest, and asked for
particulars about the radius vector. Adams did
not then reply, as the answer to this question could
be seen to be satisfactory by looking at the data
already supplied.  He was a most unassuming man,
and would not push himself forward. He may have
felt, after all the work he had done, that Airy&#8217;s
very natural inquiry showed no proportionate desire
to search for the planet.  Anyway, the matter
lay in embryo for nine months.</p>

<p>Meanwhile, one of the ablest French astronomers, Le
Verrier, experienced in computing perturbations, was
independently at work, knowing nothing about Adams.
He applied to his calculations every possible refinement,
and, considering the novelty of the problem, his calculation
was one of the most brilliant in the records of astronomy.
In criticism it has been said that these were exhibitions
of skill rather than helps to a solution of the particular
problem, and that, in claiming to find the elements
of the orbit within certain limits, he was claiming
what was, under the circumstances, impossible, as
the result proved.</p>

<p>In June, 1846, Le Verrier announced, in the <i>Comptes
Rendus de l&#8217;Academie des Sciences</i>, that
the longitude of the disturbing planet, for January
1st, 1847, was 325, and that the probable error did
not exceed 10&#176;.</p>

<p>This result agreed so well with Adams&#8217;s (within
1&#176;) that Airy urged Challis to apply the splendid
Northumberland equatoreal, at Cambridge, to the search.
 Challis, however, had already prepared an exhaustive
plan of attack which must in time settle the point.
 His first work was to observe, and make a catalogue,
or chart, of all stars near Adams&#8217;s position.</p>

<p>On August 31st, 1846, Le Verrier published the concluding
part of his labours.</p>

<p>On September 18th, 1846, Le Verrier communicated his
results to the Astronomers at Berlin, and asked them
to assist in searching for the planet. By good
luck Dr. Bremiker had just completed a star-chart of
the very part of the heavens including Le Verrier&#8217;s
position; thus eliminating all of Challis&#8217;s
preliminary work. The letter was received in
Berlin on September 23rd; and the same evening Galle
found the new planet, of the eighth magnitude, the
size of its disc agreeing with Le Verrier&#8217;s
prediction, and the heliocentric longitude agreeing
within 57&#8217;. By this time Challis had recorded,
without reduction, the observations of 3,150 stars,
as a commencement for his search.  On reducing
these, he found a star, observed on August 12th, which
was not in the same place on July 30th. This
was the planet, and he had also observed it on August
4th.</p>

<p>The feeling of wonder, admiration, and enthusiasm
aroused by this intellectual triumph was overwhelming.
 In the world of astronomy reminders are met every
day of the terrible limitations of human reasoning
powers; and every success that enables the mind&#8217;s
eye to see a little more clearly the meaning of things
has always been heartily welcomed by those who have
themselves been engaged in like researches. But,
since the publication of the <i>Principia</i>, in 1687,
there is probably no analytical success which has raised
among astronomers such a feeling of admiration and
gratitude as when Adams and Le Verrier showed the
inequalities in Uranus&#8217;s motion to mean that
an unknown planet was in a certain place in the heavens,
where it was found.</p>

<p>At the time there was an unpleasant display of international
jealousy. The British people thought that the
earlier date of Adams&#8217;s work, and of the observation
by Challis, entitled him to at least an equal share
of credit with Le Verrier. The French, on the
other hand, who, on the announcement of the discovery
by Galle, glowed with pride in the new proof of the
great powers of their astronomer, Le Verrier, whose
life had a long record of successes in calculation,
were incredulous on being told that it had all been
already done by a young man whom they had never heard
of.</p>

<p>These displays of jealousy have long since passed
away, and there is now universally an <i>entente cordiale</i>
that to each of these great men belongs equally the
merit of having so thoroughly calculated this inverse
problem of perturbations as to lead to the immediate
discovery of the unknown planet, since called Neptune.</p>

<p>It was soon found that the planet had been observed,
and its position recorded as a fixed star by Lalande,
on May 8th and 10th, 1795.</p>

<p>Mr. Lassel, in the same year, 1846, with his two-feet
reflector, discovered a satellite, with retrograde
motion, which gave the mass of the planet about a
twentieth of that of Jupiter.</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn9_1">[1]</a> Bode&#8217;s law, or something like it, had already
been fore-shadowed by Kepler and others, especially
Titius (see <i>Monatliche Correspondenz</i>, vol.
vii., p. 72).</p>

<p><br /><br /></p>

<h1>BOOK III. OBSERVATION</h1>

<p><br /><br /></p>

<a name="10"></a>
<h2>10. INSTRUMENTS OF PRECISION&#8212;STATE
OF THE SOLAR SYSTEM.</h2>

<p>Having now traced the progress of physical astronomy
up to the time when very striking proofs of the universality
of the law of gravitation convinced the most sceptical,
it must still be borne in mind that, while gravitation
is certainly the principal force governing the motions
of the heavenly bodies, there may yet be a resisting
medium in space, and there may be electric and magnetic
forces to deal with. There may, further, be cases
where the effects of luminous radiative repulsion
become apparent, and also Crookes&#8217; vacuum-effects
described as &#8220;radiant matter.&#8221; Nor
is it quite certain that Laplace&#8217;s proofs of
the instantaneous propagation of gravity are final.</p>

<p>And in the future, as in the past, Tycho Brahe&#8217;s
dictum must be maintained, that all theory shall be
preceded by accurate observations. It is the
pride of astronomers that their science stands above
all others in the accuracy of the facts observed, as
well as in the rigid logic of the mathematics used
for interpreting these facts.</p>

<p>It is interesting to trace historically the invention
of those instruments of precision which have led to
this result, and, without entering on the details
required in a practical handbook, to note the guiding
principles of construction in different ages.</p>

<p>It is very probable that the Chaldeans may have made
spheres, like the armillary sphere, for representing
the poles of the heavens; and with rings to show the
ecliptic and zodiac, as well as the equinoctial and
solstitial colures; but we have no record. We
only know that the tower of Belus, on an eminence,
was their observatory.  We have, however, distinct
records of two such spheres used by the Chinese about
2500 B.C.  Gnomons, or some kind of sundial,
were used by the Egyptians and others; and many of
the ancient nations measured the obliquity of the
ecliptic by the shadows of a vertical column in summer
and winter. The natural horizon was the only
instrument of precision used by those who determined
star positions by the directions of their risings and
settings; while in those days the clepsydra, or waterclock,
was the best instrument for comparing their times
of rising and setting.</p>

<p>About 300 B.C. an observatory fitted with circular
instruments for star positions was set up at Alexandria,
the then centre of civilisation. We know almost
nothing about the instruments used by Hipparchus in
preparing his star catalogues and his lunar and solar
tables; but the invention of the astrolabe is attributed
to him.<a href="#fn10_1">[1]</a></p>

<p>In more modern times Nuremberg became a centre of
astronomical culture. Waltherus, of that town,
made really accurate observations of star altitudes,
and of the distances between stars; and in 1484 A.D.
he used a kind of clock. Tycho Brahe tried these,
but discarded them as being inaccurate.</p>

<p>Tycho Brahe (1546-1601 A.D.) made great improvements
in armillary spheres, quadrants, sextants, and large
celestial globes. With these he measured the
positions of stars, or the distance of a comet from
several known stars. He has left us full descriptions
of them, illustrated by excellent engravings.
Previous to his time such instruments were made of
wood.  Tycho always used metal. He paid the
greatest attention to the stability of mounting, to
the orientation of his instruments, to the graduation
of the arcs by the then new method of transversals,
and to the aperture sight used upon his pointer.
There were no telescopes in his day, and no pendulum
clocks. He recognised the fact that there must
be instrumental errors. He made these as small
as was possible, measured their amount, and corrected
his observations.  His table of refractions enabled
him to abolish the error due to our atmosphere so
far as it could affect naked-eye observations.
The azimuth circle of Tycho&#8217;s largest quadrant
had a diameter of nine feet, and the quadrant a radius
of six feet. He introduced the mural quadrant
for meridian observations.<a href="#fn10_2">[2]</a></p>

<p align="center"><img src="008.jpg" alt="[Illustration: ANCIENT CHINESE INSTRUMENTS, Including
quadrant, celestial globe, and two armillae, in the
Observatory at Peking. Photographed in Peking
by the author in 1875, and stolen by the Germans when
the Embassies were relieved by the allies in 1900.]" /></p>

<p>The French Jesuits at Peking, in the seventeenth century,
helped the Chinese in their astronomy. In 1875
the writer saw and photographed, on that part of the
wall of Peking used by the Mandarins as an observatory,
the six instruments handsomely designed by Father
Verbiest, copied from the instruments of Tycho Brahe,
and embellished with Chinese dragons and emblems cast
on the supports. He also saw there two old instruments
(which he was told were Arabic) of date 1279, by Ko
Show-King, astronomer to Koblai Khan, the grandson
of Chenghis Khan. One of these last is nearly
identical with the armillae of Tycho; and the other
with his &#8220;armillae &#230;quatori&#230; maxim&#230;,&#8221; with
which he observed the comet of 1585, besides fixed
stars and planets.<a href="#fn10_3">[3]</a></p>

<p>The discovery by Galileo of the isochronism of the
pendulum, followed by Huyghens&#8217;s adaptation
of that principle to clocks, has been one of the greatest
aids to accurate observation. About the same time
an equally beneficial step was the employment of the
telescope as a pointer; not the Galilean with concave
eye-piece, but with a magnifying glass to examine
the focal image, at which also a fixed mark could
be placed.  Kepler was the first to suggest this.
Gascoigne was the first to use it. Huyghens used
a metal strip of variable width in the focus, as a
micrometer to cover a planetary disc, and so to measure
the width covered by the planet. The Marquis Malvasia,
in 1662, described the network of fine silver threads
at right angles, which he used in the focus, much
as we do now.</p>

<p>In the hands of such a skilful man as Tycho Brahe,
the old open sights, even without clocks, served their
purpose sufficiently well to enable Kepler to discover
the true theory of the solar system. But telescopic
sights and clocks were required for proving some of
Newton&#8217;s theories of planetary perturbations.
Picard&#8217;s observations at Paris from 1667 onwards
seem to embody the first use of the telescope as a
pointer. He was also the first to introduce the
use of Huyghens&#8217;s clocks for observing the right
ascension of stars.  Olaus Romer was born at
Copenhagen in 1644. In 1675, by careful study
of the times of eclipses of Jupiter&#8217;s satellites,
he discovered that light took time to traverse space.
Its velocity is 186,000 miles per second. In 1681
he took up his duties as astronomer at Copenhagen,
and built the first transit circle on a window-sill
of his house. The iron axis was five feet long
and one and a-half inches thick, and the telescope
was fixed near one end with a counterpoise. The
telescope-tube was a double cone, to prevent flexure.
Three horizontal and three vertical wires were used
in the focus. These were illuminated by a speculum,
near the object-glass, reflecting the light from a
lantern placed over the axis, the upper part of the
telescope-tube being partly cut away to admit the
light. A divided circle, with pointer and reading
microscope, was provided for reading the declination.
He realised the superiority of a circle with graduations
over a much larger quadrant. The collimation
error was found by reversing the instrument and using
a terrestrial mark, the azimuth error by star observations.
The time was expressed in fractions of a second.
He also constructed a telescope with equatoreal mounting,
to follow a star by one axial motion. In 1728
his instruments and observation records were destroyed
by fire.</p>

<p>Hevelius had introduced the vernier and tangent screw
in his measurement of arc graduations. His observatory
and records were burnt to the ground in 1679.
Though an old man, he started afresh, and left behind
him a catalogue of 1,500 stars.</p>

<p>Flamsteed began his duties at Greenwich Observatory,
as first Astronomer Royal, in 1676, with very poor
instruments. In 1683 he put up a mural arc of
140&#176;, and in 1689 a better one, seventy-nine inches
radius.  He conducted his measurements with great
skill, and introduced new methods to attain accuracy,
using certain stars for determining the errors of
his instruments; and he always reduced his observations
to a form in which they could be readily used.
He introduced new methods for determining the position
of the equinox and the right ascension of a fundamental
star.  He produced a catalogue of 2,935 stars.
He supplied Sir Isaac Newton with results of observation
required in his theoretical calculations. He died
in 1719.</p>

<p>Halley succeeded Flamsteed to find that the whole
place had been gutted by the latter&#8217;s executors.
In 1721 he got a transit instrument, and in 1726 a
mural quadrant by Graham. His successor in 1742,
Bradley, replaced this by a fine brass quadrant, eight
feet radius, by Bird; and Bradley&#8217;s zenith sector
was purchased for the observatory. An instrument
like this, specially designed for zenith stars, is
capable of greater rigidity than a more universal instrument;
and there is no trouble with refraction in the zenith.
For these reasons Bradley had set up this instrument
at Kew, to attempt the proof of the earth&#8217;s
motion by observing the annual parallax of stars.
He certainly found an annual variation of zenith distance,
but not at the times of year required by the parallax.
This led him to the discovery of the &#8220;aberration&#8221;
of light and of nutation. Bradley has been described
as the founder of the modern system of accurate observation.
He died in 1762, leaving behind him thirteen folio
volumes of valuable but unreduced observations.
Those relating to the stars were reduced by Bessel
and published in 1818, at K&#246;nigsberg, in his well-known
standard work, <i>Fundamenta Astronomiae</i>.
In it are results showing the laws of refraction,
with tables of its amount, the maximum value of aberration,
and other constants.</p>

<p>Bradley was succeeded by Bliss, and he by Maskelyne
(1765), who carried on excellent work, and laid the
foundations of the Nautical Almanac (1767).
Just before his death he induced the Government to
replace Bird&#8217;s quadrant by a fine new mural <i>circle</i>,
six feet in diameter, by Troughton, the divisions
being read off by microscopes fixed on piers opposite
to the divided circle. In this instrument the
micrometer screw, with a divided circle for turning
it, was applied for bringing the micrometer wire actually
in line with a division on the circle&#8212;a
plan which is still always adopted.</p>

<p>Pond succeeded Maskelyne in 1811, and was the first
to use this instrument. From now onwards the
places of stars were referred to the pole, not to
the zenith; the zero being obtained from measures on
circumpolar stars. Standard stars were used for
giving the clock error. In 1816 a new transit
instrument, by Troughton, was added, and from this
date the Greenwich star places have maintained the
very highest accuracy.</p>

<p>George Biddell Airy, Seventh Astronomer Royal,<a href="#fn10_4">[4]</a>
commenced his Greenwich labours in 1835. His
first and greatest reformation in the work of the
observatory was one he had already established at
Cambridge, and is now universally adopted. He
held that an observation is not completed until it
has been reduced to a useful form; and in the case
of the sun, moon, and planets these results were, in
every case, compared with the tables, and the tabular
error printed.</p>

<p>Airy was firmly impressed with the object for which
Charles II. had wisely founded the observatory in
connection with navigation, and for observations of
the moon. Whenever a meridian transit of the moon
could be observed this was done. But, even so,
there are periods in the month when the moon is too
near the sun for a transit to be well observed.
Also weather interferes with many meridian observations.
To render the lunar observations more continuous,
Airy employed Troughton&#8217;s successor, James Simms,
in conjunction with the engineers, Ransome and May,
to construct an altazimuth with three-foot circles,
and a five-foot telescope, in 1847. The result
was that the number of lunar observations was immediately
increased threefold, many of them being in a part
of the moon&#8217;s orbit which had previously been
bare of observations. From that date the Greenwich
lunar observations have been a model and a standard
for the whole world.</p>

<p>Airy also undertook to superintend the reduction of
all Greenwich lunar observations from 1750 to 1830.
 The value of this laborious work, which was completed
in 1848, cannot be over-estimated.</p>

<p>The demands of astronomy, especially in regard to
small minor planets, required a transit instrument
and mural circle with a more powerful telescope.
Airy combined the functions of both, and employed the
same constructors as before to make a <i>transit-circle</i>
with a telescope of eleven and a-half feet focus and
a circle of six-feet diameter, the object-glass being
eight inches in diameter.</p>

<p>Airy, like Bradley, was impressed with the advantage
of employing stars in the zenith for determining the
fundamental constants of astronomy. He devised
a <i>reflex zenith tube</i>, in which the zenith point
was determined by reflection from a surface of mercury.
The design was so simple, and seemed so perfect, that
great expectations were entertained. But unaccountable
variations comparable with those of the transit circle
appeared, and the instrument was put out of use until
1903, when the present Astronomer Royal noticed that
the irregularities could be allowed for, being due
to that remarkable variation in the position of the
earth&#8217;s axis included in circles of about six
yards diameter at the north and south poles, discovered
at the end of the nineteenth century. The instrument
is now being used for investigating these variations;
and in the year 1907 as many as 1,545 observations
of stars were made with the reflex zenith tube.</p>

<p>In connection with zenith telescopes it must be stated
that Respighi, at the Capitol Observatory at Rome,
made use of a deep well with a level mercury surface
at the bottom and a telescope at the top pointing
downwards, which the writer saw in 1871. The reflection
of the micrometer wires and of a star very near the
zenith (but not quite in the zenith) can be observed
together.  His mercury trough was a circular
plane surface with a shallow edge to retain the mercury.
The surface quickly came to rest after disturbance
by street traffic.</p>

<p>Sir W. M. H. Christie, Eighth Astronomer Royal, took
up his duties in that capacity in 1881. Besides
a larger altazimuth that he erected in 1898, he has
widened the field of operations at Greenwich by the
extensive use of photography and the establishment
of large equatoreals.  From the point of view
of instruments of precision, one of the most important
new features is the astrographic equatoreal, set up
in 1892 and used for the Greenwich section of the great
astrographic chart just completed. Photography
has come to be of use, not only for depicting the
sun and moon, comets and nebulae, but also to obtain
accurate relative positions of neighbouring stars;
to pick up objects that are invisible in any telescope;
and, most of all perhaps, in fixing the positions
of faint satellites. Thus Saturn&#8217;s distant
satellite, Phoebe, and the sixth and seventh satellites
of Jupiter, have been followed regularly in their
courses at Greenwich ever since their discovery with
the thirty-inch reflector (erected in 1897); and while
doing so Mr. Melotte made, in 1908, the splendid discovery
on some of the photographic plates of an eighth satellite
of Jupiter, at an enormous distance from the planet.
From observations in the early part of 1908, over
a limited arc of its orbit, before Jupiter approached
the sun, Mr. Cowell computed a retrograde orbit and
calculated the future positions of this satellite,
which enabled Mr. Melotte to find it again in the
autumn&#8212;a great triumph both of calculation
and of photographic observation. This satellite
has never been seen, and has been photographed only
at Greenwich, Heidelberg, and the Lick Observatory.</p>

<p>Greenwich Observatory has been here selected for tracing
the progress of accurate measurement. But there
is one instrument of great value, the heliometer,
which is not used at Greenwich. This serves the
purpose of a double image micrometer, and is made by
dividing the object-glass of a telescope along a diameter.
Each half is mounted so as to slide a distance of
several inches each way on an arc whose centre is
the focus. The amount of the movement can be accurately
read. Thus two fields of view overlap, and the
adjustment is made to bring an image of one star over
that of another star, and then to do the same by a
displacement in the opposite direction. The total
movement of the half-object glass is double the distance
between the star images in the focal plane. Such
an instrument has long been established at Oxford,
and German astronomers have made great use of it.
But in the hands of Sir David Gill (late His Majesty&#8217;s
Astronomer at the Cape of Good Hope), and especially
in his great researches on Solar and on Stellar parallax,
it has been recognised as an instrument of the very
highest accuracy, measuring the distance between stars
correctly to less than a tenth of a second of arc.</p>

<p>The superiority of the heliometer over all other devices
(except photography) for measuring small angles has
been specially brought into prominence by Sir David
Gill&#8217;s researches on the distance of the sun&#8212;<i>i.e.,</i>
the scale of the solar system. A measurement of
the distance of any planet fixes the scale, and, as
Venus approaches the earth most nearly of all the
planets, it used to be supposed that a Transit of
Venus offered the best opportunity for such measurement,
especially as it was thought that, as Venus entered
on the solar disc, the sweep of light round the dark
disc of Venus would enable a very precise observation
to be made.  The Transit of Venus in 1874, in
which the present writer assisted, overthrew this delusion.</p>

<p>In 1877 Sir David Gill used Lord Crawford&#8217;s
heliometer at the Island of Ascension to measure the
parallax of Mars in opposition, and found the sun&#8217;s
distance 93,080,000 miles. He considered that,
while the superiority of the heliometer had been proved,
the results would be still better with the points
of light shown by minor planets rather than with the
disc of Mars.</p>

<p>In 1888-9, at the Cape, he observed the minor planets
Iris, Victoria, and Sappho, and secured the co-operation
of four other heliometers. His final result was
92,870,000 miles, the parallax being 8",802 (<i>Cape
Obs</i>., Vol. VI.).</p>

<p>So delicate were these measures that Gill detected
a minute periodic error of theory of twenty-seven
days, owing to a periodically erroneous position of
the centre of gravity of the earth and moon to which
the position of the observer was referred. This
led him to correct the mass of the moon, and to fix
its ratio to the earth&#8217;s mass = 0.012240.</p>

<p>Another method of getting the distance from the sun
is to measure the velocity of the earth&#8217;s orbital
motion, giving the circumference traversed in a year,
and so the radius of the orbit. This has been
done by comparing observation and experiment.
The aberration of light is an angle 20&#8221; 48,
giving the ratio of the earth&#8217;s velocity to the
velocity of light. The velocity of light is 186,000
miles a second; whence the distance to the sun is
92,780,000 miles. There seems, however, to be
some uncertainty about the true value of the aberration,
any determination of which is subject to irregularities
due to the &#8220;seasonal errors.&#8221; The
velocity of light was experimentally found, in 1862,
by Fizeau and Foucault, each using an independent
method. These methods have been developed, and
new values found, by Cornu, Michaelson, Newcomb, and
the present writer.</p>

<p>Quite lately Halm, at the Cape of Good Hope, measured
spectroscopically the velocity of the earth to and
from a star by observations taken six months apart.
 Thence he obtained an accurate value of the sun&#8217;s
distance.<a href="#fn10_5">[5]</a></p>

<p>But the remarkably erratic minor planet, Eros, discovered
by Witte in 1898, approaches the earth within 15,000,000
miles at rare intervals, and, with the aid of photography,
will certainly give us the best result. A large
number of observatories combined to observe the opposition
of 1900. Their results are not yet completely
reduced, but the best value deduced so far for the
parallax<a href="#fn10_6">[6]</a> is 8".807 &#177; 0".0028.<a href="#fn10_7">[7]</a></p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn10_1">[1]</a> In 1480 Martin Behaim, of Nuremberg, produced
his <i>astrolabe</i> for measuring the latitude, by
observation of the sun, at sea. It consisted
of a graduated metal circle, suspended by a ring which
was passed over the thumb, and hung vertically.
A pointer was fixed to a pin at the centre. This
arm, called the <i>alhidada</i>, worked round the
graduated circle, and was pointed to the sun.
 The altitude of the sun was thus determined, and,
by help of solar tables, the latitude could be found
from observations made at apparent noon.</p>

<p><a name="fn10_2">[2]</a> See illustration on p. 76.</p>

<p><a name="fn10_3">[3]</a> See Dreyer&#8217;s article on these instruments
in <i>Copernicus</i>, Vol. I. They were stolen
by the Germans after the relief of the Embassies,
in 1900. The best description of these instruments
is probably that contained in an interesting volume,
which may be seen in the library of the R. A. S.,
entitled <i>Chinese Researches</i>, by Alexander Wyllie
(Shanghai, 1897).</p>

<p><a name="fn10_4">[4]</a> Sir George Airy was very jealous of this honourable
title. He rightly held that there is only one
Astronomer Royal at a time, as there is only one Mikado,
one Dalai Lama. He said that His Majesty&#8217;s
Astronomer at the Cape of Good Hope, His Majesty&#8217;s
Astronomer for Scotland, and His Majesty&#8217;s Astronomer
for Ireland are not called Astronomers Royal.</p>

<p><a name="fn10_5">[5]</a> <i>Annals of the Cape Observatory</i>, vol. x.,
part 3.</p>

<p><a name="fn10_6">[6]</a> The parallax of the sun is the angle subtended
by the earth&#8217;s radius at the sun&#8217;s distance.</p>

<p><a name="fn10_7">[7]</a> A. R. Hinks, R.A.S.; <i>Monthly Notices</i>, June,
1909.</p>

<p><br /><br /></p>

<a name="11"></a>
<h2>11. HISTORY OF THE TELESCOPE</h2>

<p>Accounts of wonderful optical experiments by Roger
Bacon (who died in 1292), and in the sixteenth century
by Digges, Baptista Porta, and Antonio de Dominis
(Grant, <i>Hist. Ph. Ast</i>.), have led
some to suppose that they invented the telescope.
The writer considers that it is more likely that these
notes refer to a kind of <i>camera obscura</i>, in
which a lens throws an inverted image of a landscape
on the wall.</p>

<p>The first telescopes were made in Holland, the originator
being either Henry Lipperhey,<a href="#fn11_1">[1]</a> Zacharias Jansen,
or James Metius, and the date 1608 or earlier.</p>

<p>In 1609 Galileo, being in Venice, heard of the invention,
went home and worked out the theory, and made a similar
telescope. These telescopes were all made with
a convex object-glass and a concave eye-lens, and
this type is spoken of as the Galilean telescope.
Its defects are that it has no real focus where cross-wires
can be placed, and that the field of view is very
small.  Kepler suggested the convex eye-lens
in 1611, and Scheiner claimed to have used one in 1617.
But it was Huyghens who really introduced them.
In the seventeenth century telescopes were made of
great length, going up to 300 feet. Huyghens
also invented the compound eye-piece that bears his
name, made of two convex lenses to diminish spherical
aberration.</p>

<p>But the defects of colour remained, although their
cause was unknown until Newton carried out his experiments
on dispersion and the solar spectrum. To overcome
the spherical aberration James Gregory,<a href="#fn11_2">[2]</a> of Aberdeen
and Edinburgh, in 1663, in his <i>Optica Promota</i>,
proposed a reflecting speculum of parabolic form.
But it was Newton, about 1666, who first made a reflecting
telescope; and he did it with the object of avoiding
colour dispersion.</p>

<p>Some time elapsed before reflectors were much used.
 Pound and Bradley used one presented to the Royal
Society by Hadley in 1723. Hawksbee, Bradley,
and Molyneaux made some. But James Short, of Edinburgh,
made many excellent Gregorian reflectors from 1732
till his death in 1768.</p>

<p>Newton&#8217;s trouble with refractors, chromatic
aberration, remained insurmountable until John Dollond
(born 1706, died 1761), after many experiments, found
out how to make an achromatic lens out of two lenses&#8212;one
of crown glass, the other of flint glass&#8212;to
destroy the colour, in a way originally suggested
by Euler. He soon acquired a great reputation
for his telescopes of moderate size; but there was
a difficulty in making flint-glass lenses of large
size. The first actual inventor and constructor
of an achromatic telescope was Chester Moor Hall,
who was not in trade, and did not patent it.
Towards the close of the eighteenth century a Swiss
named Guinand at last succeeded in producing larger
flint-glass discs free from striae. Frauenhofer,
of Munich, took him up in 1805, and soon produced,
among others, Struve&#8217;s Dorpat refractor of 9.9
inches diameter and 13.5 feet focal length, and another,
of 12 inches diameter and 18 feet focal length, for
Lamont, of Munich.</p>

<p>In the nineteenth century gigantic <i>reflectors</i>
have been made. Lassel&#8217;s 2-foot reflector,
made by himself, did much good work, and discovered
four new satellites.  But Lord Rosse&#8217;s 6-foot
reflector, 54 feet focal length, constructed in 1845,
is still the largest ever made.  The imperfections
of our atmosphere are against the use of such large
apertures, unless it be on high mountains. During
the last half century excellent specula have been made
of silvered glass, and Dr.  Common&#8217;s 5-foot
speculum (removed, since his death, to Harvard) has
done excellent work. Then there are the 5-foot
Yerkes reflector at Chicago, and the 4-foot by Grubb
at Melbourne.</p>

<p>Passing now from these large reflectors to refractors,
further improvements have been made in the manufacture
of glass by Chance, of Birmingham, Feil and Mantois,
of Paris, and Schott, of Jena; while specialists in
grinding lenses, like Alvan Clark, of the U.S.A., and
others, have produced many large refractors.</p>

<p>Cooke, of York, made an object-glass, 25-inch diameter,
for Newall, of Gateshead, which has done splendid
work at Cambridge. We have the Washington 26-inch
by Clark, the Vienna 27-inch by Grubb, the Nice 29&#189;-inch
by Gautier, the Pulkowa 30-inch by Clark. Then
there was the sensation of Clark&#8217;s 36-inch for
the Lick Observatory in California, and finally his
<i>tour de force</i>, the Yerkes 40-inch refractor,
for Chicago.</p>

<p>At Greenwich there is the 28-inch photographic refractor,
and the Thompson equatoreal by Grubb, carrying both
the 26-inch photographic refractor and the 30-inch
reflector. At the Cape of Good Hope we find Mr.
Frank McClean&#8217;s 24-inch refractor, with an object-glass
prism for spectroscopic work.</p>

<p>It would be out of place to describe here the practical
adjuncts of a modern equatoreal&#8212;the adjustments
for pointing it, the clock for driving it, the position-micrometer
and various eye-pieces, the photographic and spectroscopic
attachments, the revolving domes, observing seats,
and rising floors and different forms of mounting,
the siderostats and coelostats, and other convenient
adjuncts, besides the registering chronograph and
numerous facilities for aiding observation.
On each of these a chapter might be written; but the
most important part of the whole outfit is the man
behind the telescope, and it is with him that a history
is more especially concerned.</p>

<p><b>SPECTROSCOPE.</b></p>

<p>Since the invention of the telescope no discovery
has given so great an impetus to astronomical physics
as the spectroscope; and in giving us information
about the systems of stars and their proper motions
it rivals the telescope.</p>

<p>Frauenhofer, at the beginning of the nineteenth century,
while applying Dollond&#8217;s discovery to make large
achromatic telescopes, studied the dispersion of light
by a prism. Admitting the light of the sun through
a narrow slit in a window-shutter, an inverted image
of the slit can be thrown, by a lens of suitable focal
length, on the wall opposite. If a wedge or prism
of glass be interposed, the image is deflected to
one side; but, as Newton had shown, the images formed
by the different colours of which white light is composed
are deflected to different extents&#8212;the
violet most, the red least. The number of colours
forming images is so numerous as to form a continuous
spectrum on the wall with all the colours&#8212;red,
orange, yellow, green, blue, indigo, and violet.
But Frauenhofer found with a narrow slit, well focussed
by the lens, that some colours were missing in the
white light of the sun, and these were shown by dark
lines across the spectrum.  These are the Frauenhofer
lines, some of which he named by the letters of the
alphabet. The D line is a very marked one in
the yellow. These dark lines in the solar spectrum
had already been observed by Wollaston. <a href="#fn11_3">[3]</a></p>

<p>On examining artificial lights it was found that incandescent
solids and liquids (including the carbon glowing in
a white gas flame) give continuous spectra; gases,
except under enormous pressure, give bright lines.
If sodium or common salt be thrown on the colourless
flame of a spirit lamp, it gives it a yellow colour,
and its spectrum is a bright yellow line agreeing
in position with line D of the solar spectrum.</p>

<p>In 1832 Sir David Brewster found some of the solar
black lines increased in strength towards sunset,
and attributed them to absorption in the earth&#8217;s
atmosphere.  He suggested that the others were
due to absorption in the sun&#8217;s atmosphere.
Thereupon Professor J. D.  Forbes pointed out that
during a nearly total eclipse the lines ought to be
strengthened in the same way; as that part of the sun&#8217;s
light, coming from its edge, passes through a great
distance in the sun&#8217;s atmosphere.  He tried
this with the annular eclipse of 1836, with a negative
result which has never been accounted for, and which
seemed to condemn Brewster&#8217;s view.</p>

<p>In 1859 Kirchoff, on repeating Frauenhofer&#8217;s
experiment, found that, if a spirit lamp with salt
in the flame were placed in the path of the light,
the black D line is intensified. He also found
that, if he used a limelight instead of the sunlight
and passed it through the flame with salt, the spectrum
showed the D line black; or the vapour of sodium absorbs
the same light that it radiates. This proved to
him the existence of sodium in the sun&#8217;s atmosphere.<a href="#fn11_4">[4]</a>
Iron, calcium, and other elements were soon detected
in the same way.</p>

<p>Extensive laboratory researches (still incomplete)
have been carried out to catalogue (according to their
wave-length on the undulatory theory of light) all
the lines of each chemical element, under all conditions
of temperature and pressure. At the same time,
all the lines have been catalogued in the light of
the sun and the brighter of the stars.</p>

<p>Another method of obtaining spectra had long been
known, by transmission through, or reflection from,
a grating of equidistant lines ruled upon glass or
metal.  H. A. Rowland developed the art of constructing
these gratings, which requires great technical skill,
and for this astronomers owe him a debt of gratitude.</p>

<p>In 1842 Doppler<a href="#fn11_5">[5]</a> proved that the colour of a luminous
body, like the pitch or note of a sounding body, must
be changed by velocity of approach or recession.
Everyone has noticed on a railway that, on meeting
a locomotive whistling, the note is lowered after the
engine has passed. The pitch of a sound or the
colour of a light depends on the number of waves striking
the ear or eye in a second. This number is increased
by approach and lowered by recession.</p>

<p>Thus, by comparing the spectrum of a star alongside
a spectrum of hydrogen, we may see all the lines,
and be sure that there is hydrogen in the star; yet
the lines in the star-spectrum may be all slightly
displaced to one side of the lines of the comparison
spectrum. If towards the violet end, it means
mutual approach of the star and earth; if to the red
end, it means recession. The displacement of
lines does not tell us whether the motion is in the
star, the earth, or both.  The displacement of
the lines being measured, we can calculate the rate
of approach or recession in miles per second.</p>

<p>In 1868 Huggins<a href="#fn11_6">[6]</a> succeeded in thus measuring the
velocities of stars in the direction of the line of
sight.</p>

<p>In 1873 Vogel<a href="#fn11_7">[7]</a> compared the spectra of the sun&#8217;s
East (approaching) limb and West (receding) limb,
and the displacement of lines endorsed the theory.
This last observation was suggested by Z&#246;llner.</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn11_1">[1]</a> In the <i>Encyclopaedia Britannica</i>, article
&#8220;Telescope,&#8221; and in Grant&#8217;s <i>Physical
Astronomy</i>, good reasons are given for awarding
the honour to Lipperhey.</p>

<p><a name="fn11_2">[2]</a> Will the indulgent reader excuse an anecdote which
may encourage some workers who may have found their
mathematics defective through want of use? James
Gregory&#8217;s nephew David had a heap of MS. notes
by Newton. These descended to a Miss Gregory,
of Edinburgh, who handed them to the present writer,
when an undergraduate at Cambridge, to examine.
After perusal, he lent them to his kindest of friends,
J. C. Adams (the discoverer of Neptune), for his opinion.
Adams&#8217;s final verdict was: &#8220;I fear
they are of no value. It is pretty evident that,
when he wrote these notes, <i>Newton&#8217;s mathematics
were a little rusty</i>.&#8221;</p>

<p><a name="fn11_3">[3]</a> <i>R. S. Phil. Trans</i>.</p>

<p><a name="fn11_4">[4]</a> The experiment had been made before by one who
did not understand its meaning;. But Sir George
G. Stokes had already given verbally the true explanation
of Frauenhofer lines.</p>

<p><a name="fn11_5">[5]</a> <i>Abh. d. K&#246;n. B&#246;hm. d. Wiss</i>.,
Bd. ii., 1841-42, p. 467. See also Fizeau in
the <i>Ann. de Chem. et de Phys</i>., 1870, p. 211.</p>

<p><a name="fn11_6">[6]</a> <i>R. S. Phil. Trans</i>., 1868.</p>

<p><a name="fn11_7">[7]</a> <i>Ast. Nach</i>., No. 1, 864.</p>

<p><br /><br /></p>

<h1>BOOK IV. THE PHYSICAL PERIOD</h1>

<p>We have seen how the theory of the solar system was
slowly developed by the constant efforts of the human
mind to find out what are the rules of cause and effect
by which our conception of the present universe and
its development seems to be bound. In the primitive
ages a mere record of events in the heavens and on
the earth gave the only hope of detecting those uniform
sequences from which to derive rules or laws of cause
and effect upon which to rely. Then came the
geometrical age, in which rules were sought by which
to predict the movements of heavenly bodies.
Later, when the relation of the sun to the courses
of the planets was established, the sun came to be
looked upon as a cause; and finally, early in the
seventeenth century, for the first time in history,
it began to be recognised that the laws of dynamics,
exactly as they had been established for our own terrestrial
world, hold good, with the same rigid invariability,
at least as far as the limits of the solar system.</p>

<p>Throughout this evolution of thought and conjecture
there were two types of astronomers&#8212;those
who supplied the facts, and those who supplied the
interpretation through the logic of mathematics.
So Ptolemy was dependent upon Hipparchus, Kepler on
Tycho Brahe, and Newton in much of his work upon Flamsteed.</p>

<p>When Galileo directed his telescope to the heavens,
when Secchi and Huggins studied the chemistry of the
stars by means of the spectroscope, and when Warren
De la Rue set up a photoheliograph at Kew, we see
that a progress in the same direction as before, in
the evolution of our conception of the universe, was
being made. Without definite expression at any
particular date, it came to be an accepted fact that
not only do earthly dynamics apply to the heavenly
bodies, but that the laws we find established here,
in geology, in chemistry, and in the laws of heat,
may be extended with confidence to the heavenly bodies.
Hence arose the branch of astronomy called astronomical
physics, a science which claims a large portion of
the work of the telescope, spectroscope, and photography.
In this new development it is more than ever essential
to follow the dictum of Tycho Brahe&#8212;not
to make theories until all the necessary facts are
obtained. The great astronomers of to-day still
hold to Sir Isaac Newton&#8217;s declaration, &#8220;Hypotheses
non fingo.&#8221; Each one may have his suspicions
of a theory to guide him in a course of observation,
and may call it a working hypothesis.  But the
cautious astronomer does not proclaim these to the
world; and the historian is certainly not justified
in including in his record those vague speculations
founded on incomplete data which may be demolished
to-morrow, and which, however attractive they may
be, often do more harm than good to the progress of
true science.  Meanwhile the accumulation of facts
has been prodigious, and the revelations of the telescope
and spectroscope entrancing.</p>

<p><br /><br /></p>

<a name="12"></a>
<h2>12. THE SUN.</h2>

<p>One of Galileo&#8217;s most striking discoveries,
when he pointed his telescope to the heavenly bodies,
was that of the irregularly shaped spots on the sun,
with the dark central <i>umbra</i> and the less dark,
but more extensive, <i>penumbra</i> surrounding it,
sometimes with several umbrae in one penumbra.
He has left us many drawings of these spots, and he
fixed their period of rotation as a lunar month.</p>

<p align="center"><img src="009.jpg" alt="[Illustration: SOLAR SURFACE, As Photographed
at the Royal Observatory, Greenwich, showing sun-spots
with umbrae, penumbrae, and faculae.]" /></p>

<p>It is not certain whether Galileo, Fabricius, or Schemer
was the first to see the spots. They all did
good work. The spots were found to be ever varying
in size and shape. Sometimes, when a spot disappears
at the western limb of the sun, it is never seen again.
 In other cases, after a fortnight, it reappears at
the eastern limb. The faculae, or bright areas,
which are seen all over the sun&#8217;s surface, but
specially in the neighbourhood of spots, and most
distinctly near the sun&#8217;s edge, were discovered
by Galileo. A high telescopic power resolves
their structure into an appearance like willow-leaves,
or rice-grains, fairly uniform in size, and more marked
than on other parts of the sun&#8217;s surface.</p>

<p>Speculations as to the cause of sun-spots have never
ceased from Galileo&#8217;s time to ours. He
supposed them to be clouds. Scheiner<a href="#fn12_1">[1]</a> said
they were the indications of tumultuous movements occasionally
agitating the ocean of liquid fire of which he supposed
the sun to be composed.</p>

<p>A. Wilson, of Glasgow, in 1769,<a href="#fn12_2">[2]</a> noticed a movement
of the umbra relative to the penumbra in the transit
of the spot over the sun&#8217;s surface; exactly
as if the spot were a hollow, with a black base and
grey shelving sides. This was generally accepted,
but later investigations have contradicted its universality.
Regarding the cause of these hollows, Wilson said:&#8212;</p>

<blockquote>Whether their first production and subsequent
numberless changes depend upon the eructation of
elastic vapours from below, or upon eddies or whirlpools
commencing at the surface, or upon the dissolving
of the luminous matter in the solar atmosphere, as
clouds are melted and again given out by our air;
or, if the reader pleases, upon the annihilation
and reproduction of parts of this resplendent covering,
is left for theory to guess at.<a href="#fn12_3">[3]</a></blockquote>

<p>Ever since that date theory has been guessing at it.
 The solar astronomer is still applying all the instruments
of modern research to find out which of these suppositions,
or what modification of any of them, is nearest the
truth. The obstacle&#8212;one that is perhaps
fatal to a real theory&#8212;lies in the impossibility
of reproducing comparative experiments in our laboratories
or in our atmosphere.</p>

<p>Sir William Herschel propounded an explanation of
Wilson&#8217;s observation which received much notice,
but which, out of respect for his memory, is not now
described, as it violated the elementary laws of heat.</p>

<p>Sir John Herschel noticed that the spots are mostly
confined to two zones extending to about 35&#176; on each
side of the equator, and that a zone of equatoreal
calms is free from spots. But it was R. C. Carrington<a href="#fn12_4">[4]</a>
who, by his continuous observations at Redhill, in
Surrey, established the remarkable fact that, while
the rotation period in the highest latitudes, 50&#176;,
where spots are seen, is twenty-seven-and-a-half days,
near the equator the period is only twenty-five days.
His splendid volume of observations of the sun led
to much new information about the average distribution
of spots at different epochs.</p>

<p>Schwabe, of Dessau, began in 1826 to study the solar
surface, and, after many years of work, arrived at
a law of frequency which has been more fruitful of
results than any discovery in solar physics.<a href="#fn12_5">[5]</a> In
1843 he announced a decennial period of maxima and
minima of sun-spot displays. In 1851 it was generally
accepted, and, although a period of eleven years has
been found to be more exact, all later observations,
besides the earlier ones which have been hunted up
for the purpose, go to establish a true periodicity
in the number of sun-spots. But quite lately
Schuster<a href="#fn12_6">[6]</a> has given reasons for admitting a number
of co-existent periods, of which the eleven-year period
was predominant in the nineteenth century.</p>

<p>In 1851 Lament, a Scotchman at Munich, found a decennial
period in the daily range of magnetic declination.
 In 1852 Sir Edward Sabine announced a similar period
in the number of &#8220;magnetic storms&#8221; affecting
all of the three magnetic elements&#8212;declination,
dip, and intensity. Australian and Canadian observations
both showed the decennial period in all three elements.
Wolf, of Zurich, and Gauthier, of Geneva, each independently
arrived at the same conclusion.</p>

<p>It took many years before this coincidence was accepted
as certainly more than an accident by the old-fashioned
astronomers, who want rigid proof for every new theory.
But the last doubts have long vanished, and a connection
has been further traced between violent outbursts of
solar activity and simultaneous magnetic storms.</p>

<p>The frequency of the Aurora Borealis was found by
Wolf to follow the same period. In fact, it is
closely allied in its cause to terrestrial magnetism.
Wolf also collected old observations tracing the periodicity
of sun-spots back to about 1700 A.D.</p>

<p>Spoerer deduced a law of dependence of the average
latitude of sun-spots on the phase of the sun-spot
period.</p>

<p>All modern total solar eclipse observations seem to
show that the shape of the luminous corona surrounding
the moon at the moment of totality has a special distinct
character during the time of a sun-spot maximum, and
another, totally different, during a sun-spot minimum.</p>

<p>A suspicion is entertained that the total quantity
of heat received by the earth from the sun is subject
to the same period. This would have far-reaching
effects on storms, harvests, vintages, floods, and
droughts; but it is not safe to draw conclusions of
this kind except from a very long period of observations.</p>

<p>Solar photography has deprived astronomers of the
type of Carrington of the delight in devoting a life&#8217;s
work to collecting data. It has now become part
of the routine work of an observatory.</p>

<p>In 1845 Foucault and Fizeau took a daguerreotype photograph
of the sun. In 1850 Bond produced one of the
moon of great beauty, Draper having made some attempts
at an even earlier date. But astronomical photography
really owes its beginning to De la Rue, who used the
collodion process for the moon in 1853, and constructed
the Kew photoheliograph in 1857, from which date these
instruments have been multiplied, and have given us
an accurate record of the sun&#8217;s surface.
Gelatine dry plates were first used by Huggins in 1876.</p>

<p>It is noteworthy that from the outset De la Rue recognised
the value of stereoscopic vision, which is now known
to be of supreme accuracy. In 1853 he combined
pairs of photographs of the moon in the same phase,
but under different conditions regarding libration,
showing the moon from slightly different points of
view.  These in the stereoscope exhibited all
the relief resulting from binocular vision, and looked
like a solid globe.  In 1860 he used successive
photographs of the total solar eclipse stereoscopically,
to prove that the red prominences belong to the sun,
and not to the moon.  In 1861 he similarly combined
two photographs of a sun-spot, the perspective effect
showing the umbra like a floor at the bottom of a hollow
penumbra; and in one case the facul&#230; were discovered
to be sailing over a spot apparently at some considerable
height.  These appearances may be partly due
to a proper motion; but, so far as it went, this was
a beautiful confirmation of Wilson&#8217;s discovery.
Hewlett, however, in 1894, after thirty years of work,
showed that the spots are not always depressions,
being very subject to disturbance.</p>

<p>The Kew photographs <a href="#fn12_7">[7]</a> contributed a vast amount
of information about sun-spots, and they showed that
the facul&#230; generally follow the spots in their rotation
round the sun.</p>

<p>The constitution of the sun&#8217;s photosphere, the
layer which is the principal light-source on the sun,
has always been a subject of great interest; and much
was done by men with exceptionally keen eyesight,
like Mr. Dawes. But it was a difficult subject,
owing to the rapidity of the changes in appearance
of the so-called rice-grains, about 1&#8221; in diameter.
The rapid transformations and circulations of these
rice-grains, if thoroughly studied, might lead to a
much better knowledge of solar physics. This
seemed almost hopeless, as it was found impossible
to identify any &#8220;rice-grain&#8221; in the turmoil
after a few minutes. But M.  Hansky, of Pulkowa
(whose recent death is deplored), introduced successfully
a scheme of photography, which might almost be called
a solar cinematograph. He took photographs of
the sun at intervals of fifteen or thirty seconds,
and then enlarged selected portions of these two hundred
times, giving a picture corresponding to a solar disc
of six metres diameter. In these enlarged pictures
he was able to trace the movements, and changes of
shape and brightness, of individual rice-grains.
Some granules become larger or smaller. Some
seem to rise out of a mist, as it were, and to become
clearer.  Others grow feebler. Some are split
in two. Some are rotated through a right angle
in a minute or less, although each of the grains may
be the size of Great Britain. Generally they move
together in groups of very various velocities, up to
forty kilometres a second.  These movements seem
to have definite relation to any sun-spots in the
neighbourhood. From the results already obtained
it seems certain that, if this method of observation
be continued, it cannot fail to supply facts of the
greatest importance.</p>

<p>It is quite impossible to do justice here to the work
of all those who are engaged on astronomical physics.
 The utmost that can be attempted is to give a fair
idea of the directions of human thought and endeavour.
 During the last half-century America has made splendid
progress, and an entirely new process of studying the
photosphere has been independently perfected by Professor
Hale at Chicago, and Deslandres at Paris.<a href="#fn12_8">[8]</a> They
have succeeded in photographing the sun&#8217;s surface
in monochromatic light, such as the light given off
as one of the bright lines of hydrogen or of calcium,
by means of the &#8220;Spectroheliograph.&#8221;
The spectroscope is placed with its slit in the focus
of an equatoreal telescope, pointed to the sun, so
that the circular image of the sun falls on the slit.
At the other end of the spectroscope is the photographic
plate. Just in front of this plate there is another
slit parallel to the first, in the position where the
image of the first slit formed by the K line of calcium
falls. Thus is obtained a photograph of the section
of the sun, made by the first slit, only in K light.
As the image of the sun passes over the first slit
the photographic plate is moved at the same rate and
in the same direction behind the second slit; and
as successive sections of the sun&#8217;s image in
the equatoreal enter the apparatus, so are these sections
successively thrown in their proper place on the photographic
plate, always in K light. By using a high dispersion
the facul&#230; which give off K light can be correctly
photographed, not only at the sun&#8217;s edge, but
all over his surface. The actual mechanical method
of carrying out the observation is not quite so simple
as what is here described.</p>

<p>By choosing another line of the spectrum instead of
calcium K&#8212;for example, the hydrogen line
H<sub>(3)</sub>&#8212;we obtain two photographs, one showing
the appearance of the calcium floculi, and the other
of the hydrogen floculi, on the same part of the solar
surface; and nothing is more astonishing than to note
the total want of resemblance in the forms shown on
the two. This mode of research promises to afford
many new and useful data.</p>

<p>The spectroscope has revealed the fact that, broadly
speaking, the sun is composed of the same materials
as the earth. &#197;ngstrom was the first to map out all
of the lines to be found in the solar spectrum.
But Rowland, of Baltimore, after having perfected
the art of making true gratings with equidistant lines
ruled on metal for producing spectra, then proceeded
to make a map of the solar spectrum on a large scale.</p>

<p>In 1866 Lockyer<a href="#fn12_9">[9]</a> threw an image of the sun upon
the slit of a spectroscope, and was thus enabled to
compare the spectrum of a spot with that of the general
solar surface. The observation proved the darkness
of a spot to be caused by increased absorption of light,
not only in the dark lines, which are widened, but
over the entire spectrum. In 1883 Young resolved
this continuous obscurity into an infinite number
of fine lines, which have all been traced in a shadowy
way on to the general solar surface. Lockyer also
detected displacements of the spectrum lines in the
spots, such as would be produced by a rapid motion
in the line of sight. It has been found that
both uprushes and downrushes occur, but there is no
marked predominance of either in a sun-spot.
The velocity of motion thus indicated in the line
of sight sometimes appears to amount to 320 miles
a second. But it must be remembered that pressure
of a gas has some effect in displacing the spectral
lines.  So we must go on, collecting data, until
a time comes when the meaning of all the facts can
be made clear.</p>

<p><i>Total Solar Eclipses</i>.&#8212;During total
solar eclipses the time is so short, and the circumstances
so impressive, that drawings of the appearance could
not always be trusted. The red prominences of
jagged form that are seen round the moon&#8217;s edge,
and the corona with its streamers radiating or interlacing,
have much detail that can hardly be recorded in a
sketch. By the aid of photography a number of
records can be taken during the progress of totality.
From a study of these the extent of the corona is
demonstrated in one case to extend to at least six
diameters of the moon, though the eye has traced it
farther. This corona is still one of the wonders
of astronomy, and leads to many questions. What
is its consistency, if it extends many million miles
from the sun&#8217;s surface? How is it that it
opposed no resistance to the motion of comets which
have almost grazed the sun&#8217;s surface? Is
this the origin of the zodiacal light?  The character
of the corona in photographic records has been shown
to depend upon the phase of the sun-spot period.
During the sun-spot maximum the corona seems most
developed over the spot-zones&#8212;i.e., neither
at the equator nor the poles. The four great
sheaves of light give it a square appearance, and
are made up of rays or plumes, delicate like the petals
of a flower.  During a minimum the nebulous ring
seems to be made of tufts of fine hairs with aigrettes
or radiations from both poles, and streamers from
the equator.</p>

<p align="center"><img src="010.jpg" alt="[Illustration: SOLAR ECLIPSE, 1882.  From
drawing by W. H. Wesley, Secretary R.A.S.; showing
the prominences, the corona, and an unknown comet.]" /></p>

<p>On September 19th, 1868, eclipse spectroscopy began
with the Indian eclipse, in which all observers found
that the red prominences showed a bright line spectrum,
indicating the presence of hydrogen and other gases.
 So bright was it that Jansen exclaimed: &#8220;<i>Je
verrai ces lignes-l&#224; en dehors des &#233;clipses</i>.&#8221;
And the next day he observed the lines at the edge
of the uneclipsed sun.  Huggins had suggested
this observation in February, 1868, his idea being
to use prisms of such great dispersive power that
the continuous spectrum reflected by our atmosphere
should be greatly weakened, while a bright line would
suffer no diminution by the high dispersion.
On October 20th Lockyer,<a href="#fn12_10">[10]</a> having news of the eclipse,
but not of Jansen&#8217;s observations the day after,
was able to see these lines. This was a splendid
performance, for it enabled the prominences to be observed,
not only during eclipses, but every day. Moreover,
the next year Huggins was able, by using a wide slit,
to see the whole of a prominence and note its shape.
 Prominences are classified, according to their form,
into &#8220;flame&#8221; and &#8220;cloud&#8221; prominences,
the spectrum of the latter showing calcium, hydrogen,
and helium; that of the former including a number
of metals.</p>

<p>The D line of sodium is a double line, and in the
same eclipse (1868) an orange line was noticed which
was afterwards found to lie close to the two components
of the D line. It did not correspond with any
known terrestrial element, and the unknown element
was called &#8220;helium.&#8221; It was not until
1895 that Sir William Ramsay found this element as
a gas in the mineral cleavite.</p>

<p>The spectrum of the corona is partly continuous, indicating
light reflected from the sun&#8217;s body. But
it also shows a green line corresponding with no known
terrestrial element, and the name &#8220;coronium&#8221;
has been given to the substance causing it.</p>

<p>A vast number of facts have been added to our knowledge
about the sun by photography and the spectroscope.
Speculations and hypotheses in plenty have been offered,
but it may be long before we have a complete theory
evolved to explain all the phenomena of the storm-swept
metallic atmosphere of the sun.</p>

<p>The proceedings of scientific societies teem with
such facts and &#8220;working hypotheses,&#8221; and
the best of them have been collected by Miss Clerke
in her <i>History of Astronomy during the Nineteenth
Century</i>. As to established facts, we learn
from the spectroscopic researches (1) that the continuous
spectrum is derived from the <i>photosphere</i> or
solar gaseous material compressed almost to liquid
consistency; (2) that the <i>reversing layer</i> surrounds
it and gives rise to black lines in the spectrum;
that the <i>chromosphere</i> surrounds this, is composed
mainly of hydrogen, and is the cause of the red prominences
in eclipses; and that the gaseous <i>corona</i> surrounds
all of these, and extends to vast distances outside
the sun&#8217;s visible surface.</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn12_1">[1]</a> <i>Rosa Ursina</i>, by C. Scheiner, <i>fol</i>.;
Bracciani, 1630.</p>

<p><a name="fn12_2">[2]</a> <i>R. S. Phil. Trans</i>., 1774.</p>

<p><a name="fn12_3">[3]</a> <i>Ibid</i>, 1783.</p>

<p><a name="fn12_4">[4]</a> <i>Observations on the Spots on the Sun, etc.,</i>
4&#176;; London and Edinburgh, 1863.</p>

<p><a name="fn12_5">[5]</a> <i>Periodicit&#228;t der Sonnenflecken. Astron.
Nach. XXI.</i>, 1844, P. 234.</p>

<p><a name="fn12_6">[6]</a> <i>R.S. Phil. Trans.</i> (ser.
A), 1906, p. 69-100.</p>

<p><a name="fn12_7">[7]</a> &#8220;Researches on Solar Physics,&#8221; by
De la Rue, Stewart and Loewy; <i>R. S. Phil.
Trans</i>., 1869, 1870.</p>

<p><a name="fn12_8">[8]</a> &#8220;The Sun as Photographed on the K line&#8221;;
<i>Knowledge</i>, London, 1903, p. 229.</p>

<p><a name="fn12_9">[9]</a> <i>R. S. Proc.</i>, xv., 1867, p. 256.</p>

<p><a name="fn12_10">[10]</a> <i>Acad. des Sc.</i>, Paris; <i>C. R.</i>,
lxvii., 1868, p. 121.</p>

<p><br /><br /></p>

<a name="13"></a>
<h2>13. THE MOON AND PLANETS.</h2>

<p><i>The Moon</i>.&#8212;Telescopic discoveries
about the moon commence with Galileo&#8217;s discovery
that her surface has mountains and valleys, like the
earth. He also found that, while she always turns
the same face to us, there is periodically a slight
twist to let us see a little round the eastern or
western edge. This was called <i>libration</i>,
and the explanation was clear when it was understood
that in showing always the same face to us she makes
one revolution a month on her axis <i>uniformly</i>,
and that her revolution round the earth is not uniform.</p>

<p>Galileo said that the mountains on the moon showed
greater differences of level than those on the earth.
 Shr&#246;ter supported this opinion. W. Herschel
opposed it. But Beer and M&#228;dler measured the
heights of lunar mountains by their shadows, and found
four of them over 20,000 feet above the surrounding
plains.</p>

<p>Langrenus <a href="#fn13_1">[1]</a> was the first to do serious work on
selenography, and named the lunar features after eminent
men. Riccioli also made lunar charts. In
1692 Cassini made a chart of the full moon. Since
then we have the charts of Schr&#246;ter, Beer and M&#228;dler
(1837), and of Schmidt, of Athens (1878); and, above
all, the photographic atlas by Loewy and Puiseux.</p>

<p>The details of the moon&#8217;s surface require for
their discussion a whole book, like that of Neison
or the one by Nasmyth and Carpenter. Here a few
words must suffice. Mountain ranges like our Andes
or Himalayas are rare. Instead of that, we see
an immense number of circular cavities, with rugged
edges and flat interior, often with a cone in the
centre, reminding one of instantaneous photographs
of the splash of a drop of water falling into a pool.
Many of these are fifty or sixty miles across, some
more. They are generally spoken of as resembling
craters of volcanoes, active or extinct, on the earth.
But some of those who have most fully studied the
shapes of craters deny altogether their resemblance
to the circular objects on the moon. These so-called
craters, in many parts, are seen to be closely grouped,
especially in the snow-white parts of the moon.
But there are great smooth dark spaces, like the clear
black ice on a pond, more free from craters, to which
the equally inappropriate name of seas has been given.
The most conspicuous crater, <i>Tycho</i>, is near
the south pole. At full moon there are seen to
radiate from Tycho numerous streaks of light, or &#8220;rays,&#8221;
cutting through all the mountain formations, and extending
over fully half the lunar disc, like the star-shaped
cracks made on a sheet of ice by a blow.  Similar
cracks radiate from other large craters. It must
be mentioned that these white rays are well seen only
in full light of the sun at full moon, just as the
white snow in the crevasses of a glacier is seen bright
from a distance only when the sun is high, and disappears
at sunset. Then there are deep, narrow, crooked
&#8220;rills&#8221; which may have been water-courses;
also &#8220;clefts&#8221; about half a mile wide, and
often hundreds of miles long, like deep cracks in
the surface going straight through mountain and valley.</p>

<p>The moon shares with the sun the advantage of being
a good subject for photography, though the planets
are not. This is owing to her larger apparent
size, and the abundance of illumination. The consequence
is that the finest details of the moon, as seen in
the largest telescope in the world, may be reproduced
at a cost within the reach of all.</p>

<p>No certain changes have ever been observed; but several
suspicions have been expressed, especially as to the
small crater <i>Linn&#233;</i>, in the <i>Mare Serenitatis</i>.
It is now generally agreed that no certainty can be
expected from drawings, and that for real evidence
we must await the verdict of photography.</p>

<p>No trace of water or of an atmosphere has been found
on the moon. It is possible that the temperature
is too low. In any case, no displacement of a
star by atmospheric refraction at occultation has
been surely recorded. The moon seems to be dead.</p>

<p>The distance of the moon from the earth is just now
the subject of re-measurement. The base line
is from Greenwich to Cape of Good Hope, and the new
feature introduced is the selection of a definite point
on a crater (M&#246;sting A), instead of the moon&#8217;s
edge, as the point whose distance is to be measured.</p>

<p><i>The Inferior Planets</i>.&#8212;When the telescope
was invented, the phases of Venus attracted much attention;
but the brightness of this planet, and her proximity
to the sun, as with Mercury also, seemed to be a bar
to the discovery of markings by which the axis and
period of rotation could be fixed. Cassini gave
the rotation as twenty-three hours, by observing a
bright spot on her surface. Shr&#246;ter made it 23h.
21m. 19s. This value was supported by others.
In 1890 Schiaparelli<a href="#fn13_2">[2]</a> announced that Venus rotates,
like our moon, once in one of her revolutions, and
always directs the same face to the sun. This
property has also been ascribed to Mercury; but in
neither case has the evidence been generally accepted.
Twenty-four hours is probably about the period of
rotation for each of these planets.</p>

<p>Several observers have claimed to have seen a planet
within the orbit of Mercury, either in transit over
the sun&#8217;s surface or during an eclipse.
It has even been named <i>Vulcan</i>. These announcements
would have received little attention but for the fact
that the motion of Mercury has irregularities which
have not been accounted for by known planets; and
Le Verrier<a href="#fn13_3">[3]</a> has stated that an intra-Mercurial planet
or ring of asteroids would account for the unexplained
part of the motion of the line of apses of Mercury&#8217;s
orbit amounting to 38&#8221; per century.</p>

<p><i>Mars</i>.&#8212;The first study of the appearance
of Mars by Miraldi led him to believe that there were
changes proceeding in the two white caps which are
seen at the planet&#8217;s poles. W. Herschel
attributed these caps to ice and snow, and the dates
of his observations indicated a melting of these ice-caps
in the Martian summer.</p>

<p>Schroter attributed the other markings on Mars to drifting
clouds. But Beer and M&#228;dler, in 1830-39, identified
the same dark spots as being always in the same place,
though sometimes blurred by mist in the local winter.
A spot sketched by Huyghens in 1672, one frequently
seen by W. Herschel in 1783, another by Arago in 1813,
and nearly all the markings recorded by Beer and M&#228;dler
in 1830, were seen and drawn by F. Kaiser in Leyden
during seventeen nights of the opposition of 1862
(<i>Ast. Nacht.</i>, No. 1,468), whence he deduced
the period of rotation to be 24h. 37m. 22s.,62&#8212;or
one-tenth of a second less than the period deduced
by R. A. Proctor from a drawing by Hooke in 1666.</p>

<p>It must be noted that, if the periods of rotation
both of Mercury and Venus be about twenty-four hours,
as seems probable, all the four planets nearest to
the sun rotate in the same period, while the great
planets rotate in about ten hours (Uranus and Neptune
being still indeterminate).</p>

<p>The general surface of Mars is a deep yellow; but
there are dark grey or greenish patches. Sir
John Herschel was the first to attribute the ruddy
colour of Mars to its soil rather than to its atmosphere.</p>

<p>The observations of that keen-sighted observer Dawes
led to the first good map of Mars, in 1869. In
the 1877 opposition Schiaparelli revived interest
in the planet by the discovery of canals, uniformly
about sixty miles wide, running generally on great
circles, some of them being three or four thousand
miles long. During the opposition of 1881-2 the
same observer re-observed the canals, and in twenty
of them he found the canals duplicated,<a href="#fn13_4">[4]</a> the second
canal being always 200 to 400 miles distant from its
fellow.</p>

<p>The existence of these canals has been doubted.
 Mr. Lowell has now devoted years to the subject,
has drawn them over and over again, and has photographed
them; and accepts the explanation that they are artificial,
and that vegetation grows on their banks.  Thus
is revived the old controversy between Whewell and
Brewster as to the habitability of the planets.
The new arguments are not yet generally accepted.
Lowell believes he has, with the spectroscope, proved
the existence of water on Mars.</p>

<p>One of the most unexpected and interesting of all
telescopic discoveries took place in the opposition
of 1877, when Mars was unusually near to the earth.
The Washington Observatory had acquired the fine 26-inch
refractor, and Asaph Hall searched for satellites,
concealing the planet&#8217;s disc to avoid the glare.
On August 11th he had a suspicion of a satellite.
This was confirmed on the 16th, and on the following
night a second one was added. They are exceedingly
faint, and can be seen only by the most powerful telescopes,
and only at the times of opposition. Their diameters
are estimated at six or seven miles. It was soon
found that the first, Deimos, completes its orbit
in 30h. 18m.  But the other, Phobos, at first
was a puzzle, owing to its incredible velocity being
unsuspected. Later it was found that the period
of revolution was only 7h. 39m. 22s. Since the
Martian day is twenty-four and a half hours, this
leads to remarkable results. Obviously the easterly
motion of the satellite overwhelms the diurnal rotation
of the planet, and Phobos must appear to the inhabitants,
if they exist, to rise in the west and set in the
east, showing two or even three full moons in a day,
so that, sufficiently well for the ordinary purposes
of life, the hour of the day can be told by its phases.</p>

<p>The discovery of these two satellites is, perhaps,
the most interesting telescopic visual discovery made
with the large telescopes of the last half century;
photography having been the means of discovering all
the other new satellites except Jupiter&#8217;s fifth
(in order of discovery).</p>

<p align="center"><img src="011.jpg" alt="[Illustration: JUPITER.  From a drawing
by E. M. Antoniadi, showing transit of a satellite&#8217;s
shadow, the belts, and the &#8220;great red spot&#8221;
(<i>Monthly Notices</i>, R. A. S., vol. lix., pl. x.).]" /></p>

<p><i>Jupiter.</i>&#8212;Galileo&#8217;s discovery
of Jupiter&#8217;s satellites was followed by the
discovery of his belts. Zucchi and Torricelli
seem to have seen them. Fontana, in 1633, reported
three belts. In 1648 Grimaldi saw but two, and
noticed that they lay parallel to the ecliptic.
Dusky spots were also noticed as transient. Hooke<a href="#fn13_5">[5]</a>
measured the motion of one in 1664. In 1665 Cassini,
with a fine telescope, 35-feet focal length, observed
many spots moving from east to west, whence he concluded
that Jupiter rotates on an axis like the earth.
He watched an unusually permanent spot during twenty-nine
rotations, and fixed the period at 9h. 56m. Later
he inferred that spots near the equator rotate quicker
than those in higher latitudes (the same as Carrington
found for the sun); and W. Herschel confirmed this
in 1778-9.</p>

<p>Jupiter&#8217;s rapid rotation ought, according to
Newton&#8217;s theory, to be accompanied by a great
flattening at the poles. Cassini had noted an
oval form in 1691. This was confirmed by La Hire,
R&#246;mer, and Picard. Pound measured the ellipticity
= 1/(13.25).</p>

<p>W. Herschel supposed the spots to be masses of cloud
in the atmosphere&#8212;an opinion still accepted.
 Many of them were very permanent. Cassini&#8217;s
great spot vanished and reappeared nine times between
1665 and 1713. It was close to the northern margin
of the southern belt. Herschel supposed the belts
to be the body of the planet, and the lighter parts
to be clouds confined to certain latitudes.</p>

<p>In 1665 Cassini observed transits of the four satellites,
and also saw their shadows on the planet, and worked
out a lunar theory for Jupiter. Mathematical
astronomers have taken great interest in the perturbations
of the satellites, because their relative periods
introduce peculiar effects. Airy, in his delightful
book, <i>Gravitation</i>, has reduced these investigations
to simple geometrical explanations.</p>

<p>In 1707 and 1713 Miraldi noticed that the fourth satellite
varies much in brightness. W. Herschel found
this variation to depend upon its position in its
orbit, and concluded that in the positions of feebleness
it is always presenting to us a portion of its surface,
which does not well reflect the sun&#8217;s light;
proving that it always turns the same face to Jupiter,
as is the case with our moon. This fact had also
been established for Saturn&#8217;s fifth satellite,
and may be true for all satellites.</p>

<p>In 1826 Struve measured the diameters of the four
satellites, and found them to be 2,429, 2,180, 3,561,
and 3,046 miles.</p>

<p>In modern times much interest has been taken in watching
a rival to Cassini&#8217;s famous spot. The &#8220;great
red spot&#8221; was first observed by Niesten, Pritchett,
and Tempel, in 1878, as a rosy cloud attached to a
whitish zone beneath the dark southern equatorial band,
shaped like the new war balloons, 30,000 miles long
and 7,000 miles across. The next year it was
brick-red. A white spot beside it completed a
rotation in less time by 5&#189; minutes than the red spot&#8212;a
difference of 260 miles an hour. Thus they came
together again every six weeks, but the motions did
not continue uniform.  The spot was feeble in
1882-4, brightened in 1886, and, after many changes,
is still visible.</p>

<p>Galileo&#8217;s great discovery of Jupiter&#8217;s
four moons was the last word in this connection until
September 9th, 1892, when Barnard, using the 36-inch
refractor of the Lick Observatory, detected a tiny
spot of light closely following the planet. This
proved to be a new satellite (fifth), nearer to the
planet than any other, and revolving round it in 11h.
57m. 23s. Between its rising and setting there
must be an interval of 2&#189; Jovian days, and two or
three full moons. The sixth and seventh satellites
were found by the examination of photographic plates
at the Lick Observatory in 1905, since which time they
have been continuously photographed, and their orbits
traced, at Greenwich. On examining these plates
in 1908 Mr. Melotte detected the eighth satellite,
which seems to be revolving in a retrograde orbit three
times as far from its planet as the next one (seventh),
in these two points agreeing with the outermost of
Saturn&#8217;s satellites (Phoebe).</p>

<p><i>Saturn.</i>&#8212;This planet, with its marvellous
ring, was perhaps the most wonderful object of those
first examined by Galileo&#8217;s telescope. He
was followed by Dominique Cassini, who detected bands
like Jupiter&#8217;s belts. Herschel established
the rotation of the planet in 1775-94. From observations
during one hundred rotations he found the period to
be 10h. 16m. 0s., 44. Herschel also measured the
ratio of the polar to the equatoreal diameter as 10:11.</p>

<p>The ring was a complete puzzle to Galileo, most of
all when the planet reached a position where the plane
of the ring was in line with the earth, and the ring
disappeared (December 4th, 1612). It was not until
1656 that Huyghens, in his small pamphlet <i>De Saturni
Luna Observatio Nova</i>, was able to suggest in a
cypher the ring form; and in 1659, in his Systema
Saturnium, he gave his reasons and translated the cypher:
&#8220;The planet is surrounded by a slender flat ring,
everywhere distinct from its surface, and inclined
to the ecliptic.&#8221; This theory explained
all the phases of the ring which had puzzled others.
This ring was then, and has remained ever since, a
unique structure.  We in this age have got accustomed
to it. But Huyghens&#8217;s discovery was received
with amazement.</p>

<p>In 1675 Cassini found the ring to be double, the concentric
rings being separated by a black band&#8212;a
fact which was placed beyond dispute by Herschel,
who also found that the thickness of the ring subtends
an angle less than 0".3. Shr&#246;ter estimated its
thickness at 500 miles.</p>

<p>Many speculations have been advanced to explain the
origin and constitution of the ring. De Sejour
said <a href="#fn13_6">[6]</a> that it was thrown off from Saturn&#8217;s
equator as a liquid ring, and afterwards solidified.
He noticed that the outside would have a greater velocity,
and be less attracted to the planet, than the inner
parts, and that equilibrium would be impossible; so
he supposed it to have solidified into a number of
concentric rings, the exterior ones having the least
velocity.</p>

<p>Clerk Maxwell, in the Adams prize essay, gave a physico-mathematical
demonstration that the rings must be composed of meteoritic
matter like gravel. Even so, there must be collisions
absorbing the energy of rotation, and tending to make
the rings eventually fall into the planet. The
slower motion of the external parts has been proved
by the spectroscope in Keeler&#8217;s hands, 1895.</p>

<p>Saturn has perhaps received more than its share of
attention owing to these rings. This led to other
discoveries. Huyghens in 1655, and J. D. Cassini
in 1671, discovered the sixth and eighth satellites
(Titan and Japetus). Cassini lost his satellite,
and in searching for it found Rhea (the fifth) in
1672, besides his old friend, whom he lost again.
He added the third and fourth in 1684 (Tethys and
Dione). The first and second (Mimas and Encelades)
were added by Herschel in 1789, and the seventh (Hyperion)
simultaneously by Lassel and Bond in 1848. The
ninth (Phoebe) was found on photographs, by Pickering
in 1898, with retrograde motion; and he has lately
added a tenth.</p>

<p>The occasional disappearance of Cassini&#8217;s Japetus
was found on investigation to be due to the same causes
as that of Jupiter&#8217;s fourth satellite, and proves
that it always turns the same face to the planet.</p>

<p><i>Uranus and Neptune</i>.&#8212;The splendid
discoveries of Uranus and two satellites by Sir William
Herschel in 1787, and of Neptune by Adams and Le Verrier
in 1846, have been already described. Lassel added
two more satellites to Uranus in 1851, and found Neptune&#8217;s
satellite in 1846. All of the satellites of Uranus
have retrograde motion, and their orbits are inclined
about 80&#176; to the ecliptic.</p>

<p>The spectroscope has shown the existence of an absorbing
atmosphere on Jupiter and Saturn, and there are suspicions
that they partake something of the character of the
sun, and emit some light besides reflecting solar
light. On both planets some absorption lines seem
to agree with the aqueous vapour lines of our own
atmosphere; while one, which is a strong band in the
red common to both planets, seems to agree with a
line in the spectrum of some reddish stars.</p>

<p>Uranus and Neptune are difficult to observe spectroscopically,
but appear to have peculiar spectra agreeing together.
Sometimes Uranus shows Frauenhofer lines, indicating
reflected solar light. But generally these are
not seen, and six broad bands of absorption appear.
 One is the F. of hydrogen; another is the red-star
line of Jupiter and Saturn. Neptune is a very
difficult object for the spectroscope.</p>

<p>Quite lately <a href="#fn13_7">[7]</a> P. Lowell has announced that V. M.
 Slipher, at Flagstaff Observatory, succeeded in 1907
in rendering some plates sensitive far into the red.
A reproduction is given of photographed spectra of
the four outermost planets, showing (1) a great number
of new lines and bands; (2) intensification of hydrogen
F.  and C. lines; (3) a steady increase of effects
(1) and (2) as we pass from Jupiter and Saturn to
Uranus, and a still greater increase in Neptune.</p>

<p><i>Asteroids</i>.&#8212;The discovery of these
new planets has been described. At the beginning
of the last century it was an immense triumph to catch
a new one. Since photography was called into the
service by Wolf, they have been caught every year in
shoals. It is like the difference between sea
fishing with the line and using a steam trawler.
In the 1908 almanacs nearly seven hundred asteroids
are included. The computation of their perturbations
and ephemerides by Euler&#8217;s and Lagrange&#8217;s
method of variable elements became so laborious that
Encke devised a special process for these, which can
be applied to many other disturbed orbits. <a href="#fn13_8">[8]</a></p>

<p>When a photograph is taken of a region of the heavens
including an asteroid, the stars are photographed
as points because the telescope is made to follow
their motion; but the asteroids, by their proper motion,
appear as short lines.</p>

<p>The discovery of Eros and the photographic attack
upon its path have been described in their relation
to finding the sun&#8217;s distance.</p>

<p>A group of four asteroids has lately been found, with
a mean distance and period equal to that of Jupiter.
To three of these masculine names have been given&#8212;Hector,
Patroclus, Achilles; the other has not yet been named.</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn13_1">[1]</a> Langrenus (van Langren), F. Selenographia sive
lumina austriae philippica; Bruxelles, 1645.</p>

<p><a name="fn13_2">[2]</a> <i>Astr. Nach.</i>, 2,944.</p>

<p><a name="fn13_3">[3]</a> <i>Acad. des Sc.</i>, Paris; <i>C.R.</i>, lxxxiii.,
1876.</p>

<p><a name="fn13_4">[4]</a> <i>Mem. Spettr. Ital.</i>, xi., p. 28.</p>

<p><a name="fn13_5">[5]</a> <i>R. S. Phil. Trans</i>., No. 1.</p>

<p><a name="fn13_6">[6]</a> Grant&#8217;s <i>Hist. Ph. Ast</i>.,
p. 267.</p>

<p><a name="fn13_7">[7]</a> <i>Nature</i>, November 12th, 1908.</p>

<p><a name="fn13_8">[8]</a> <i>Ast. Nach</i>., Nos. 791, 792, 814, translated
by G. B. Airy. <i>Naut. Alm</i>., Appendix, 1856.</p>

<p><br /><br /></p>

<a name="14"></a>
<h2>14. COMETS AND METEORS.</h2>

<p>Ever since Halley discovered that the comet of 1682
was a member of the solar system, these wonderful
objects have had a new interest for astronomers; and
a comparison of orbits has often identified the return
of a comet, and led to the detection of an elliptic
orbit where the difference from a parabola was imperceptible
in the small portion of the orbit visible to us.
A remarkable case in point was the comet of 1556,
of whose identity with the comet of 1264 there could
be little doubt.  Hind wanted to compute the
orbit more exactly than Halley had done. He knew
that observations had been made, but they were lost.
Having expressed his desire for a search, all the
observations of Fabricius and of Heller, and also a
map of the comet&#8217;s path among the stars, were
eventually unearthed in the most unlikely manner,
after being lost nearly three hundred years.
Hind and others were certain that this comet would
return between 1844 and 1848, but it never appeared.</p>

<p>When the spectroscope was first applied to finding
the composition of the heavenly bodies, there was
a great desire to find out what comets are made of.
The first opportunity came in 1864, when Donati observed
the spectrum of a comet, and saw three bright bands,
thus proving that it was a gas and at least partly
self-luminous.  In 1868 Huggins compared the spectrum
of Winnecke&#8217;s comet with that of a Geissler tube
containing olefiant gas, and found exact agreement.
Nearly all comets have shown the same spectrum.<a href="#fn14_1">[1]</a>
A very few comets have given bright band spectra differing
from the normal type. Also a certain kind of
continuous spectrum, as well as reflected solar light
showing Frauenhofer lines, have been seen.</p>

<p align="center"><img src="012.jpg" alt="[Illustration: COPY OF THE DRAWING MADE BY PAUL
FABRICIUS.  To define the path of comet 1556.
After being lost for 300 years, this drawing was recovered
by the prolonged efforts of Mr. Hind and Professor
Littrow in 1856.]" /></p>

<p>When Wells&#8217;s comet, in 1882, approached very
close indeed to the sun, the spectrum changed to a
mono-chromatic yellow colour, due to sodium.</p>

<p>For a full account of the wonders of the cometary
world the reader is referred to books on descriptive
astronomy, or to monographs on comets.<a href="#fn14_2">[2]</a> Nor can
the very uncertain speculations about the structure
of comets&#8217; tails be given here. A new explanation
has been proposed almost every time that a great discovery
has been made in the theory of light, heat, chemistry,
or electricity.</p>

<p>Halley&#8217;s comet remained the only one of which
a prediction of the return had been confirmed, until
the orbit of the small, ill-defined comet found by
Pons in 1819 was computed by Encke, and found to have
a period of 3 1/3 years. It was predicted to
return in 1822, and was recognised by him as identical
with many previous comets. This comet, called
after Encke, has showed in each of its returns an inexplicable
reduction of mean distance, which led to the assertion
of a resisting medium in space until a better explanation
could be found.<a href="#fn14_3">[3]</a></p>

<p>Since that date fourteen comets have been found with
elliptic orbits, whose aphelion distances are all
about the same as Jupiter&#8217;s mean distance; and
six have an aphelion distance about ten per cent,
greater than Neptune&#8217;s mean distance. Other
comets are similarly associated with the planets Saturn
and Uranus.</p>

<p>The physical transformations of comets are among the
most wonderful of unexplained phenomena in the heavens.
But, for physical astronomers, the greatest interest
attaches to the reduction of radius vector of Encke&#8217;s
comet, the splitting of Biela&#8217;s comet into two
comets in 1846, and the somewhat similar behaviour
of other comets. It must be noted, however, that
comets have a sensible size, that all their parts cannot
travel in exactly the same orbit under the sun&#8217;s
gravitation, and that their mass is not sufficient
to retain the parts together very forcibly; also that
the inevitable collision of particles, or else fluid
friction, is absorbing energy, and so reducing the
comet&#8217;s velocity.</p>

<p>In 1770 Lexell discovered a comet which, as was afterwards
proved by investigations of Lexell, Burchardt, and
Laplace, had in 1767 been deflected by Jupiter out
of an orbit in which it was invisible from the earth
into an orbit with a period of 5&#189; years, enabling it
to be seen. In 1779 it again approached Jupiter
closer than some of his satellites, and was sent off
in another orbit, never to be again recognised.</p>

<p>But our interest in cometary orbits has been added
to by the discovery that, owing to the causes just
cited, a comet, if it does not separate into discrete
parts like Biela&#8217;s, must in time have its parts
spread out so as to cover a sensible part of the orbit,
and that, when the earth passes through such part
of a comet&#8217;s orbit, a meteor shower is the result.</p>

<p>A magnificent meteor shower was seen in America on
November 12th-13th, 1833, when the paths of the meteors
all seemed to radiate from a point in the constellation
Leo. A similar display had been witnessed in
Mexico by Humboldt and Bonpland on November 12th, 1799.
H. A. Newton traced such records back to October 13th,
A.D. 902. The orbital motion of a cloud or stream
of small particles was indicated. The period
favoured by H. A. Newton was 354&#189; days; another suggestion
was 375&#189; days, and another 33&#188; years.  He noticed
that the advance of the date of the shower between
902 and 1833, at the rate of one day in seventy years,
meant a progression of the node of the orbit.
 Adams undertook to calculate what the amount would
be on all the five suppositions that had been made
about the period. After a laborious work, he found
that none gave one day in seventy years except the
33&#188;-year period, which did so exactly. H. A.
Newton predicted a return of the shower on the night
of November 13th-14th, 1866. He is now dead; but
many of us are alive to recall the wonder and enthusiasm
with which we saw this prediction being fulfilled
by the grandest display of meteors ever seen by anyone
now alive.</p>

<p>The <i>progression</i> of the nodes proved the path
of the meteor stream to be retrograde. The <i>radiant</i>
had almost the exact longitude of the point towards
which the earth was moving. This proved that
the meteor cluster was at perihelion. The period
being known, the eccentricity of the orbit was obtainable,
also the orbital velocity of the meteors in perihelion;
and, by comparing this with the earth&#8217;s velocity,
the latitude of the radiant enabled the inclination
to be determined, while the longitude of the earth
that night was the longitude of the node. In
such a way Schiaparelli was able to find first the
elements of the orbit of the August meteor shower
(Perseids), and to show its identity with the orbit
of Tuttle&#8217;s comet 1862.iii. Then, in January
1867, Le Verrier gave the elements of the November
meteor shower (Leonids); and Peters, of Altona, identified
these with Oppolzer&#8217;s elements for Tempel&#8217;s
comet 1866&#8212;Schiaparelli having independently
attained both of these results. Subsequently
Weiss, of Vienna, identified the meteor shower of April
20th (Lyrids) with comet 1861. Finally, that
indefatigable worker on meteors, A. S. Herschel, added
to the number, and in 1878 gave a list of seventy-six
coincidences between cometary and meteoric orbits.</p>

<p>Cometary astronomy is now largely indebted to photography,
not merely for accurate delineations of shape, but
actually for the discovery of most of them.
The art has also been applied to the observation of
comets at distances from their perihelia so great as
to prevent their visual observation. Thus has
Wolf, of Heidelburg, found upon old plates the position
of comet 1905.v., as a star of the 15.5 magnitude,
783 days before the date of its discovery. From
the point of view of the importance of finding out
the divergence of a cometary orbit from a parabola,
its period, and its aphelion distance, this increase
of range attains the very highest value.</p>

<p>The present Astronomer Royal, appreciating this possibility,
has been searching by photography for Halley&#8217;s
comet since November, 1907, although its perihelion
passage will not take place until April, 1910.</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn14_1">[1]</a> In 1874, when the writer was crossing the Pacific
Ocean in H.M.S. &#8220;Scout,&#8221; Coggia&#8217;s
comet unexpectedly appeared, and (while Colonel Tupman
got its positions with the sextant) he tried to use
the prism out of a portable direct-vision spectroscope,
without success until it was put in front of the object-glass
of a binocular, when, to his great joy, the three
band images were clearly seen.</p>

<p><a name="fn14_2">[2]</a> Such as <i>The World of Comets</i>, by A. Guillemin;
<i>History of Comets</i>, by G. R. Hind, London, 1859;
<i>Theatrum Cometicum</i>, by S. de Lubienietz, 1667;
<i>Cometographie</i>, by Pingr&#233;, Paris, 1783; <i>Donati&#8217;s
Comet</i>, by Bond.</p>

<p><a name="fn14_3">[3]</a> The investigations by Von Asten (of St. Petersburg)
seem to support, and later ones, especially those
by Backlund (also of St. Petersburg), seem to discredit,
the idea of a resisting medium.</p>

<p><br /><br /></p>

<a name="15"></a>
<h2>15. THE FIXED STARS AND NEBUL&#198;.</h2>

<p>Passing now from our solar system, which appears to
be subject to the action of the same forces as those
we experience on our globe, there remains an innumerable
host of fixed stars, nebulas, and nebulous clusters
of stars. To these the attention of astronomers
has been more earnestly directed since telescopes
have been so much enlarged. Photography also
has enabled a vast amount of work to be covered in
a comparatively short period, and the spectroscope
has given them the means, not only of studying the
chemistry of the heavens, but also of detecting any
motion in the line of sight from less than a mile a
second and upwards in any star, however distant, provided
it be bright enough.</p>

<img src="013.jpg" alt="[Illustration: SIR WILLIAM HERSCHEL, F.R.S.&#8212;1738-1822.
 Painted by Lemuel F. Abbott; National Portrait Gallery,
Room XX.]" align="right" />

<p>In the field of telescopic discovery beyond our solar
system there is no one who has enlarged our knowledge
so much as Sir William Herschel, to whom we owe the
greatest discovery in dynamical astronomy among the
stars&#8212;viz., that the law of gravitation
extends to the most distant stars, and that many of
them describe elliptic orbits about each other.
W. Herschel was born at Hanover in 1738, came to England
in 1758 as a trained musician, and died in 1822.
He studied science when he could, and hired a telescope,
until he learnt to make his own specula and telescopes.
He made 430 parabolic specula in twenty-one years.
He discovered 2,500 nebul&#230; and 806 double stars, counted
the stars in 3,400 guage-fields, and compared the
principal stars photometrically.</p>

<p>Some of the things for which he is best known were
results of those accidents that happen only to the
indefatigable enthusiast. Such was the discovery
of Uranus, which led to funds being provided for constructing
his 40-feet telescope, after which, in 1786, he settled
at Slough. In the same way, while trying to detect
the annual parallax of the stars, he failed in that
quest, but discovered binary systems of stars revolving
in ellipses round each other; just as Bradley&#8217;s
attack on stellar parallax failed, but led to the discovery
of aberration, nutation, and the true velocity of
light.</p>

<p><i>Parallax</i>.&#8212;The absence of stellar
parallax was the great objection to any theory of
the earth&#8217;s motion prior to Kepler&#8217;s time.
It is true that Kepler&#8217;s theory itself could
have been geometrically expressed equally well with
the earth or any other point fixed. But in Kepler&#8217;s
case the obviously implied physical theory of the
planetary motions, even before Newton explained the
simplicity of conception involved, made astronomers
quite ready to waive the claim for a rigid proof of
the earth&#8217;s motion by measurement of an annual
parallax of stars, which they had insisted on in respect
of Copernicus&#8217;s revival of the idea of the earth&#8217;s
orbital motion.</p>

<p>Still, the desire to measure this parallax was only
intensified by the practical certainty of its existence,
and by repeated failures. The attempts of Bradley
failed. The attempts of Piazzi and Brinkley,<a href="#fn15_1">[1]</a>
early in the nineteenth century, also failed.
The first successes, afterwards confirmed, were by
Bessel and Henderson.  Both used stars whose
proper motion had been found to be large, as this argued
proximity. Henderson, at the Cape of Good Hope,
observed &#945; Centauri, whose annual proper motion
he found to amount to 3".6, in 1832-3; and a few years
later deduced its parallax 1".16.  His successor
at the Cape, Maclear, reduced this to 0".92.</p>

<p>In 1835 Struve assigned a doubtful parallax of 0".261
to Vega (&#945; Lyr&#230;). But Bessel&#8217;s observations,
between 1837 and 1840, of 61 Cygni, a star with the
large proper motion of over 5&#8221;, established its
annual parallax to be 0".3483; and this was confirmed
by Peters, who found the value 0".349.</p>

<p>Later determinations for &#945;<sub>2</sub> Centauri, by Gill,<a href="#fn15_2">[2]</a>
make its parallax 0".75&#8212;This is the nearest
known fixed star; and its light takes 4 1/3 years
to reach us. The lightyear is taken as the unit
of measurement in the starry heavens, as the earth&#8217;s
mean distance is &#8220;the astronomical unit&#8221;
for the solar system.<a href="#fn15_3">[3]</a> The proper motions and parallaxes
combined tell us the velocity of the motion of these
stars across the line of sight: &#945; Centauri
14.4 miles a second=4.2 astronomical units a year;
61 Cygni 37.9 miles a second=11.2 astronomical units
a year. These successes led to renewed zeal, and
now the distances of many stars are known more or less
accurately.</p>

<p>Several of the brightest stars, which might be expected
to be the nearest, have not shown a parallax amounting
to a twentieth of a second of arc. Among these
are Canopus, &#945; Orionis, &#945; Cygni, &#946; Centauri,
and &#947; Cassiopeia. Oudemans has published a
list of parallaxes observed.<a href="#fn15_4">[4]</a></p>

<p><i>Proper Motion.</i>&#8212;In 1718 Halley<a href="#fn15_5">[5]</a>
detected the proper motions of Arcturus and Sirius.
In 1738 J. Cassinis<a href="#fn15_6">[6]</a> showed that the former had
moved five minutes of arc since Tycho Brahe fixed its
position. In 1792 Piazzi noted the motion of
61 Cygni as given above. For a long time the
greatest observed proper motion was that of a small
star 1830 Groombridge, nearly 7&#8221; a year; but
others have since been found reaching as much as 10&#8221;.</p>

<p>Now the spectroscope enables the motion of stars to
be detected at a single observation, but only that
part of the motion that is in the line of sight.
For a complete knowledge of a star&#8217;s motion the
proper motion and parallax must also be known.</p>

<p>When Huggins first applied the Doppler principle to
measure velocities in the line of sight,<a href="#fn15_7">[7]</a> the faintness
of star spectra diminished the accuracy; but V&#246;gel,
in 1888, overcame this to a great extent by long exposures
of photographic plates.</p>

<p>It has often been noticed that stars which seem to
belong to a group of nearly uniform magnitude have
the same proper motion. The spectroscope has
shown that these have also often the same velocity
in the line of sight. Thus in the Great Bear,
&#946;, &#947;, &#948;, &#949;, &#950;, all agree as to
angular proper motion. &#948; was too faint for a spectroscopic
measurement, but all the others have been shown to
be approaching us at a rate of twelve to twenty miles
a second. The same has been proved for proper
motion, and line of sight motion, in the case of Pleiades
and other groups.</p>

<p>Maskelyne measured many proper motions of stars, from
which W. Herschel<a href="#fn15_8">[8]</a> came to the conclusion that these
apparent motions are for the most part due to a motion
of the solar system in space towards a point in the
constellation Hercules, R.A. 257&#176;; N. Decl. 25&#176;.
 This grand discovery has been amply confirmed, and,
though opinions differ as to the exact direction,
it happens that the point first indicated by Herschel,
from totally insufficient data, agrees well with modern
estimates.</p>

<p>Comparing the proper motions and parallaxes to get
the actual velocity of each star relative to our system,
C.L. Struve found the probable velocity of the
solar system in space to be fifteen miles a second,
or five astronomical units a year.</p>

<p>The work of Herschel in this matter has been checked
by comparing spectroscopic velocities in the line
of sight which, so far as the sun&#8217;s motion is
concerned, would give a maximum rate of approach for
stars near Hercules, a maximum rate of recession for
stars in the opposite part of the heavens, and no
effect for stars half-way between. In this way
the spectroscope has confirmed generally Herschel&#8217;s
view of the direction, and makes the velocity eleven
miles a second, or nearly four astronomical units
a year.</p>

<p>The average proper motion of a first magnitude star
has been found to be 0".25 annually, and of a sixth
magnitude star 0".04. But that all bright stars
are nearer than all small stars, or that they show
greater proper motion for that reason, is found to
be far from the truth. Many statistical studies
have been made in this connection, and interesting
results may be expected from this treatment in the
hands of Kapteyn of Groningen, and others.<a href="#fn15_9">[9]</a></p>

<p>On analysis of the directions of proper motions of
stars in all parts of the heavens, Kapteyn has shown<a href="#fn15_10">[10]</a>
that these indicate, besides the solar motion towards
Hercules, two general drifts of stars in nearly opposite
directions, which can be detected in any part of the
heavens. This result has been confirmed from independent
data by Eddington (<i>R.A.S., M.N.</i>) and Dyson
(<i>R.S.E. Proc.</i>).</p>

<p>Photography promises to assist in the measurement
of parallax and proper motions. Herr Pulfrich,
of the firm of Carl Zeiss, has vastly extended the
applications of stereoscopic vision to astronomy&#8212;a
subject which De la Rue took up in the early days of
photography.  He has made a stereo-comparator
of great beauty and convenience for comparing stereoscopically
two star photographs taken at different dates.
Wolf of Heidelberg has used this for many purposes.
His investigations depending on the solar motion in
space are remarkable. He photographs stars in
a direction at right angles to the line of the sun&#8217;s
motion. He has taken photographs of the same region
fourteen years apart, the two positions of his camera
being at the two ends of a base-line over 5,000,000,000
miles apart, or fifty-six astronomical units.
On examining these stereoscopically, some of the stars
rise out of the general plane of the stars, and seem
to be much nearer. Many of the stars are thus
seen to be suspended in space at different distances
corresponding exactly to their real distances from
our solar system, except when their proper motion
interferes. The effect is most striking; the
accuracy of measurement exceeds that of any other method
of measuring such displacements, and it seems that
with a long interval of time the advantage of the
method increases.</p>

<p><i>Double Stars.</i>&#8212;The large class of
double stars has always been much studied by amateurs,
partly for their beauty and colour, and partly as
a test for telescopic definition. Among the many
unexplained stellar problems there is one noticed
in double stars that is thought by some to be likely
to throw light on stellar evolution. It is this:
There are many instances where one star of the pair
is comparatively faint, and the two stars are contrasted
in colour; and in every single case the general colour
of the faint companion is invariably to be classed
with colours more near to the blue end of the spectrum
than that of the principal star.</p>

<p><i>Binary Stars.</i>&#8212;Sir William Herschel
began his observations of double stars in the hope
of discovering an annual parallax of the stars.
In this he was following a suggestion of Galileo&#8217;s.
The presumption is that, if there be no physical connection
between the stars of a pair, the largest is the nearest,
and has the greatest parallax. So, by noting
the distance between the pair at different times of
the year, a delicate test of parallax is provided,
unaffected by major instrumental errors.</p>

<p>Herschel did, indeed, discover changes of distance,
but not of the character to indicate parallax.
Following this by further observation, he found that
the motions were not uniform nor rectilinear, and by
a clear analysis of the movements he established the
remarkable and wholly unexpected fact that in all
these cases the motion is due to a revolution about
their common centre of gravity.<a href="#fn15_11">[11]</a> He gave the approximate
period of revolution of some of these: Castor,
342 years; &#948; Serpentis, 375 years; &#947; Leonis, 1,200
years; &#949; Bootis, 1,681 years.</p>

<p>Twenty years later Sir John Herschel and Sir James
South, after re-examination of these stars, confirmed<a href="#fn15_12">[12]</a>
and extended the results, one pair of Coron&#230; having
in the interval completed more than a whole revolution.</p>

<p>It is, then, to Sir William Herschel that we owe the
extension of the law of gravitation, beyond the limits
of the solar system, to the whole universe. His
observations were confirmed by F.G.W. Struve (born
1793, died 1864), who carried on the work at Dorpat.
But it was first to Savary,<a href="#fn15_13">[13]</a> and later to Encke
and Sir John Herschel, that we owe the computation
of the elliptic elements of these stars; also the
resulting identification of their law of force with
Newton&#8217;s force of gravitation applied to the
solar system, and the force that makes an apple fall
to the ground. As Grant well says in his <i>History</i>:
&#8220;This may be justly asserted to be one of the
most sublime truths which astronomical science has
hitherto disclosed to the researches of the human
mind.&#8221;</p>

<p>Latterly the best work on double stars has been done
by S. W. Burnham,<a href="#fn15_14">[14]</a> at the Lick Observatory.
The shortest period he found was eleven years (&#954;
Pegasi).  In the case of some of these binaries
the parallax has been measured, from which it appears
that in four of the surest cases the orbits are about
the size of the orbit of Uranus, these being probably
among the smallest stellar orbits.</p>

<p>The law of gravitation having been proved to extend
to the stars, a discovery (like that of Neptune in
its origin, though unlike it in the labour and originality
involved in the calculation) that entrances the imagination
became possible, and was realised by Bessel&#8212;the
discovery of an unknown body by its gravitational
disturbance on one that was visible. In 1834
and 1840 he began to suspect a want of uniformity in
the proper motion of Sirius and Procyon respectively.
In 1844, in a letter to Sir John Herschel,<a href="#fn15_15">[15]</a> he
attributed these irregularities in each case to the
attraction of an invisible companion, the period of
revolution of Sirius being about half a century.
Later he said: &#8220;I adhere to the conviction
that Procyon and Sirius form real binary systems,
consisting of a visible and an invisible star.
 There is no reason to suppose luminosity an essential
quality of cosmical bodies. The visibility of
countless stars is no argument against the invisibility
of countless others.&#8221; This grand conception
led Peters to compute more accurately the orbit, and
to assign the place of the invisible companion of
Sirius. In 1862 Alvan G. Clark was testing a
new 18-inch object-glass (now at Chicago) upon Sirius,
and, knowing nothing of these predictions, actually
found the companion in the very place assigned to
it. In 1896 the companion of Procyon was discovered
by Professor Schaeberle at the Lick Observatory.</p>

<p>Now, by the refined parallax determinations of Gill
at the Cape, we know that of Sirius to be 0".38.
From this it has been calculated that the mass of
Sirius equals two of our suns, and its intrinsic brightness
equals twenty suns; but the companion, having a mass
equal to our sun, has only a five-hundredth part of
the sun&#8217;s brightness.</p>

<p><i>Spectroscopic Binaries</i>.&#8212;On measuring
the velocity of a star in the line of sight at frequent
intervals, periodic variations have been found, leading
to a belief in motion round an invisible companion.
Vogel, in 1889, discovered this in the case of Spica
(&#945; Virginis), whose period is 4d. 0h. 19m., and
the diameter of whose orbit is six million miles.
Great numbers of binaries of this type have since
then been discovered, all of short period.</p>

<p>Also, in 1889, Pickering found that at regular intervals
of fifty-two days the lines in the spectrum of &#950;
of the Great Bear are duplicated, indicating a relative
velocity, equal to one hundred miles a second, of
two components revolving round each other, of which
that apparently single star must be composed.</p>

<p>It would be interesting, no doubt, to follow in detail
the accumulating knowledge about the distances, proper
motions, and orbits of the stars; but this must be
done elsewhere. Enough has been said to show
how results are accumulating which must in time unfold
to us the various stellar systems and their mutual
relationships.</p>

<p><i>Variable Stars.</i>&#8212;It has often happened
in the history of different branches of physical science
that observation and experiment were so far ahead
of theory that hopeless confusion appeared to reign;
and then one chance result has given a clue, and from
that time all differences and difficulties in the
previous researches have stood forth as natural consequences,
explaining one another in a rational sequence.
So we find parallax, proper motion, double stars, binary
systems, variable stars, and new stars all bound together.</p>

<p>The logical and necessary explanation given of the
cause of ordinary spectroscopic binaries, and of irregular
proper motions of Sirius and Procyon, leads to the
inference that if ever the plane of such a binary
orbit were edge-on to us there ought to be an eclipse
of the luminous partner whenever the non-luminous
one is interposed between us. This should give
rise either to intermittence in the star&#8217;s light
or else to variability.  It was by supposing the
existence of a dark companion to Algol that its discoverer,
Goodricke of York,<a href="#fn15_16">[16]</a> in 1783, explained variable
stars of this type. Algol (&#946; Persei) completes
the period of variable brightness in 68.8 hours.
It loses three-fifths of its light, and regains it
in twelve hours. In 1889 Vogel,<a href="#fn15_17">[17]</a> with the
Potsdam spectrograph, actually found that the luminous
star is receding before each eclipse, and approaching
us after each eclipse; thus entirely supporting Goodricke&#8217;s
opinion. There are many variables of the Algol
type, and information is steadily accumulating.
But all variable stars do not suffer the sudden variations
of Algol. There are many types, and the explanations
of others have not proved so easy.</p>

<p>The Harvard College photographs have disclosed the
very great prevalence of variability, and this is
certainly one of the lines in which modern discovery
must progress.</p>

<p>Roberts, in South Africa, has done splendid work on
the periods of variables of the Algol type.</p>

<p><i>New Stars</i>.&#8212;Extreme instances of
variable stars are the new stars such as those detected
by Hipparchus, Tycho Brahe, and Kepler, of which many
have been found in the last half-century. One
of the latest great &#8220;Nov&#230;&#8221; was discovered
in Auriga by a Scotsman, Dr. Anderson, on February
1st, 1892, and, with the modesty of his race, he communicated
the fact to His Majesty&#8217;s Astronomer for Scotland
on an unsigned post-card.<a href="#fn15_18">[18]</a> Its spectrum was observed
and photographed by Huggins and many others.
It was full of bright lines of hydrogen, calcium,
helium, and others not identified. The astounding
fact was that lines were shown in pairs, bright and
dark, on a faint continuous spectrum, indicating apparently
that a dark body approaching us at the rate of 550
miles a second<a href="#fn15_19">[19]</a> was traversing a cold nebulous atmosphere,
and was heated to incandescence by friction, like
a meteor in our atmosphere, leaving a luminous train
behind it. It almost disappeared, and on April
26th it was of the sixteenth magnitude; but on August
17th it brightened to the tenth, showing the principal
nebular band in its spectrum, and no sign of approach
or recession.  It was as if it emerged from one
part of the nebula, cooled down, and rushed through
another part of the nebula, rendering the nebular gas
more luminous than itself.<a href="#fn15_20">[20]</a></p>

<p>Since 1892 one Nova after another has shown a spectrum
as described above, like a meteor rushing towards
us and leaving a train behind, for this seems to be
the obvious meaning of the spectra.</p>

<p>The same may be said of the brilliant Nova Persei,
brighter at its best than Capella, and discovered
also by Dr. Anderson on February 22nd, 1901.
It increased in brightness as it reached the densest
part of the nebula, then it varied for some weeks
by a couple of magnitudes, up and down, as if passing
through separate nebular condensations. In February,
1902, it could still be seen with an opera-glass.
As with the other Nov&#230;, when it first dashed into the
nebula it was vaporised and gave a continuous spectrum
with dark lines of hydrogen and helium. It showed
no bright lines paired with the dark ones to indicate
a train left behind; but in the end its own luminosity
died out, and the nebular spectrum predominated.</p>

<p>The nebular illumination as seen in photographs, taken
from August to November, seemed to spread out slowly
in a gradually increasing circle at the rate of 90&#8221;
in forty-eight days. Kapteyn put this down to
the velocity of light, the original outburst sending
its illumination to the nebulous gas and illuminating
a spherical shell whose radius increased at the velocity
of light. This supposition seems correct, in
which case it can easily be shown from the above figures
that the distance of this Nova was 300 light years.</p>

<p><i>Star Catalogues.</i>&#8212;Since the days
of very accurate observations numerous star-catalogues
have been produced by individuals or by observatories.
Bradley&#8217;s monumental work may be said to head
the list. Lacaille&#8217;s, in the Southern hemisphere,
was complementary.  Then Piazzi, Lalande, Groombridge,
and Bessel were followed by Argelander with his 324,000
stars, Rumker&#8217;s Paramatta catalogue of the southern
hemisphere, and the frequent catalogues of national
observatories. Later the Astronomische Gesellschaft
started their great catalogue, the combined work of
many observatories. Other southern ones were
Gould&#8217;s at Cordova and Stone&#8217;s at the Cape.</p>

<p>After this we have a new departure. Gill at the
Cape, having the comet 1882.ii. all to himself in
those latitudes, wished his friends in Europe to see
it, and employed a local photographer to strap his
camera to the observatory equatoreal, driven by clockwork,
and adjusted on the comet by the eye. The result
with half-an-hour&#8217;s exposure was good, so he
tried three hours. The result was such a display
of sharp star images that he resolved on the Cape Photographic
Durchmusterung, which after fourteen years, with Kapteyn&#8217;s
aid in reducing, was completed. Meanwhile the
brothers Henry, of Paris, were engaged in going over
Chacornac&#8217;s zodiacal stars, and were about to
catalogue the Milky Way portion, a serious labour,
when they saw Gill&#8217;s Comet photograph and conceived
the idea of doing the rest of their work by photography.
 Gill had previously written to Admiral Mouchez, of
the Paris Observatory, and explained to him his project
for charting the heavens photographically, by combining
the work of many observatories. This led Admiral
Mouchez to support the brothers Henry in their scheme.<a href="#fn15_21">[21]</a>
Gill, having got his own photographic work underway,
suggested an international astrographic chart, the
materials for different zones to be supplied by observatories
of all nations, each equipped with similar photographic
telescopes. At a conference in Paris, 1887, this
was decided on, the stars on the charts going down
to the fourteenth magnitude, and the catalogues to
the eleventh.</p>

<p align="center"><img src="014.jpg" alt="[Illustration: GREAT COMET, Nov. 14TH, 1882.
(Exposure 2hrs. 20m.)  By kind permission of Sir David
Gill. From this photograph originated all stellar
chart-photography.]" /></p>

<p>This monumental work is nearing completion. The
labour involved was immense, and the highest skill
was required for devising instruments and methods
to read off the star positions from the plates.</p>

<p>Then we have the Harvard College collection of photographic
plates, always being automatically added to; and their
annex at Arequipa in Peru.</p>

<p>Such catalogues vary in their degree of accuracy;
and fundamental catalogues of standard stars have
been compiled. These require extension, because
the differential methods of the heliometer and the
camera cannot otherwise be made absolute.</p>

<p>The number of stars down to the fourteenth magnitude
may be taken at about 30,000,000; and that of all
the stars visible in the greatest modern telescopes
is probably about 100,000,000.</p>

<p><i>Nebul&#230; and Star-clusters.</i>&#8212;Our knowledge
of nebul&#230; really dates from the time of W. Herschel.
In his great sweeps of the heavens with his giant
telescopes he opened in this direction a new branch
of astronomy.  At one time he held that all nebul&#230;
might be clusters of innumerable minute stars at a
great distance. Then he recognised the different
classes of nebul&#230;, and became convinced that there
is a widely-diffused &#8220;shining fluid&#8221; in
space, though many so-called nebul&#230; could be resolved
by large telescopes into stars.  He considered
that the Milky Way is a great star cluster, whose
form may be conjectured from numerous star-gaugings.
He supposed that the compact &#8220;planetary nebul&#230;&#8221;
might show a stage of evolution from the diffuse nebul&#230;,
and that his classifications actually indicate various
stages of development. Such speculations, like
those of the ancients about the solar system, are
apt to be harmful to true progress of knowledge unless
in the hands of the ablest mathematical physicists;
and Herschel violated their principles in other directions.
But here his speculations have attracted a great deal
of attention, and, with modifications, are accepted,
at least as a working hypothesis, by a fair number
of people.</p>

<p>When Sir John Herschel had extended his father&#8217;s
researches into the Southern Hemisphere he was also
led to the belief that some nebulae were a phosphorescent
material spread through space like fog or mist.</p>

<p>Then his views were changed by the revelations due
to the great discoveries of Lord Rosse with his gigantic
refractor,<a href="#fn15_22">[22]</a> when one nebula after another was resolved
into a cluster of minute stars. At that time
the opinion gained ground that with increase of telescopic
power this would prove to be the case with all nebul&#230;.</p>

<p>In 1864 all doubt was dispelled by Huggins<a href="#fn15_23">[23]</a> in
his first examination of the spectrum of a nebula,
and the subsequent extension of this observation to
other nebul&#230;; thus providing a certain test which
increase in the size of telescopes could never have
given. In 1864 Huggins found that all true nebulae
give a spectrum of bright lines. Three are due
to hydrogen; two (discovered by Copeland) are helium
lines; others are unknown. Fifty-five lines have
been photographed in the spectrum of the Orion nebula.
It seems to be pretty certain that all true nebulae
are gaseous, and show almost exactly the same spectrum.</p>

<p>Other nebul&#230;, and especially the white ones like that
in Andromeda, which have not yet been resolved into
stars, show a continuous spectrum; others are greenish
and give no lines.</p>

<p>A great deal has to be done by the chemist before
the astronomer can be on sure ground in drawing conclusions
from certain portions of his spectroscopic evidence.</p>

<p>The light of the nebulas is remarkably actinic, so
that photography has a specially fine field in revealing
details imperceptible in the telescope. In 1885
the brothers Henry photographed, round the star Maia
in the Pleiades, a spiral nebula 3&#8217; long, as
bright on the plate as that star itself, but quite
invisible in the telescope; and an exposure of four
hours revealed other new nebula in the same district.
That painstaking and most careful observer, Barnard,
with 10&#188; hours&#8217; exposure, extended this nebulosity
for several degrees, and discovered to the north of
the Pleiades a huge diffuse nebulosity, in a region
almost destitute of stars. By establishing a 10-inch
instrument at an altitude of 6,000 feet, Barnard has
revealed the wide distribution of nebular matter in
the constellation Scorpio over a space of 4&#176; or 5&#176;
square.  Barnard asserts that the &#8220;nebular
hypothesis&#8221; would have been killed at its birth
by a knowledge of these photographs. Later he
has used still more powerful instruments, and extended
his discoveries.</p>

<p>The association of stars with planetary nebul&#230;, and
the distribution of nebul&#230; in the heavens, especially
in relation to the Milky Way, are striking facts,
which will certainly bear fruit when the time arrives
for discarding vague speculations, and learning to
read the true physical structure and history of the
starry universe.</p>

<p><i>Stellar Spectra.</i>&#8212;When the spectroscope
was first available for stellar research, the leaders
in this branch of astronomy were Huggins and Father
Secchi,<a href="#fn15_24">[24]</a> of Rome. The former began by devoting
years of work principally to the most accurate study
of a few stars.  The latter devoted the years
from 1863 to 1867 to a general survey of the whole
heavens, including 4,000 stars. He divided these
into four principal classes, which have been of the
greatest service. Half of his stars belonged
to the first class, including Sirius, Vega, Regulus,
Altair. The characteristic feature of their spectra
is the strength and breadth of the hydrogen lines
and the extreme faintness of the metallic lines.
This class of star is white to the eye, and rich in
ultra violet light.</p>

<p>The second class includes about three-eighths of his
stars, including Capella, Pollux, and Arcturus.
These stars give a spectrum like that of our sun,
and appear yellowish to the eye.</p>

<p>The third class includes &#945; Herculis, &#945; Orionis
(Betelgeux), Mira Ceti, and about 500 red and variable
stars.  The spectrum has fluted bands shaded
from blue to red, and sharply defined at the more
refrangible edge.</p>

<p>The fourth class is a small one, containing no stars
over fifth magnitude, of which 152 Schjellerup, in
Canes Venatici, is a good example. This spectrum
also has bands, but these are shaded on the violet
side and sharp on the red side. They are due to
carbon in some form.  These stars are ruby red
in the telescope.</p>

<p>It would appear, then, that all stars are suns with
continuous spectra, and the classes are differentiated
by the character of the absorbent vapours of their
atmospheres.</p>

<p>It is very likely that, after the chemists have taught
us how to interpret all the varieties of spectrum,
it will be possible to ascribe the different spectrum-classes
to different stages in the life-history of every star.
 Already there are plenty of people ready to lay down
arbitrary assumptions about the lessons to be drawn
from stellar spectra. Some say that they know
with certainty that each star begins by being a nebula,
and is condensed and heated by condensation until
it begins to shine as a star; that it attains a climax
of temperature, then cools down, and eventually becomes
extinct.  They go so far as to declare that they
know what class of spectrum belongs to each stage
of a star&#8217;s life, and how to distinguish between
one that is increasing and another that is decreasing
in temperature.</p>

<p>The more cautious astronomers believe that chemistry
is not sufficiently advanced to justify all of these
deductions; that, until chemists have settled the
lately raised question of the transmutation of elements,
no theory can be sure. It is also held that until
they have explained, without room for doubt, the reasons
for the presence of some lines, and the absence of
others, of any element in a stellar spectrum; why
the arc-spectrum of each element differs from its spark
spectrum; what are all the various changes produced
in the spectrum of a gas by all possible concomitant
variations of pressure and temperature; also the meanings
of all the flutings in the spectra of metalloids and
compounds; and other equally pertinent matters&#8212;until
that time arrives the part to be played by the astronomer
is one of observation. By all means, they say,
make use of &#8220;working hypotheses&#8221; to add
an interest to years of laborious research, and to
serve as a guide to the direction of further labours;
but be sure not to fall into the error of calling
any mere hypothesis a theory.</p>

<p><i>Nebular Hypothesis.</i>&#8212;The Nebular
Hypothesis, which was first, as it were, tentatively
put forward by Laplace as a note in his <i>Syst&#232;me
du Monde</i>, supposes the solar system to have been
a flat, disk-shaped nebula at a high temperature in
rapid rotation. In cooling it condensed, leaving
revolving rings at different distances from the centre.
These themselves were supposed to condense into the
nucleus for a rotating planet, which might, in contracting,
again throw off rings to form satellites.  The
speculation can be put in a really attractive form,
but is in direct opposition to many of the actual
facts; and so long as it is not favoured by those who
wish to maintain the position of astronomy as the
most exact of the sciences&#8212;exact in its
facts, exact in its logic&#8212;this speculation
must be recorded by the historian, only as he records
the guesses of the ancient Greeks--as an interesting
phase in the history of human thought.</p>

<p>Other hypotheses, having the same end in view, are
the meteoritic hypothesis of Lockyer and the planetesimal
hypothesis that has been largely developed in the
United States. These can best be read in the
original papers to various journals, references to
which may be found in the footnotes of Miss Clerke&#8217;s
<i>History of Astronomy during the Nineteenth Century</i>.
The same can be said of Bredichin&#8217;s hypothesis
of comets&#8217; tails, Arrhenius&#8217;s book on
the applications of the theory of light repulsion,
the speculations on radium, the origin of the sun&#8217;s
heat and the age of the earth, the electron hypothesis
of terrestrial magnetism, and a host of similar speculations,
all combining to throw an interesting light on the
evolution of a modern train of thought that seems
to delight in conjecture, while rebelling against that
strict mathematical logic which has crowned astronomy
as the queen of the sciences.</p>

<p><br /><br /></p>

<p><b>FOOTNOTES:</b></p>

<p><a name="fn15_1">[1]</a> <i>R. S. Phil Trans</i>., 1810 and 1817-24.</p>

<p><a name="fn15_2">[2]</a> One of the most valuable contributions to our
knowledge of stellar parallaxes is the result of Gill&#8217;s
work (<i>Cape Results</i>, vol. iii., part ii., 1900).</p>

<p><a name="fn15_3">[3]</a> Taking the velocity of light at 186,000 miles
a second, and the earth&#8217;s mean distance at 93,000,000
miles, 1 light-year=5,865,696,000,000 miles or 63,072
astronomical units; 1 astronomical unit a year=2.94
miles a second; and the earth&#8217;s orbital velocity=18.5
miles a second.</p>

<p><a name="fn15_4">[4]</a> Ast. Nacht., 1889.</p>

<p><a name="fn15_5">[5]</a> R. S. Phil. Trans., 1718.</p>

<p><a name="fn15_6">[6]</a> Mem. Acad. des Sciences, 1738, p. 337.</p>

<p><a name="fn15_7">[7]</a> R. S Phil. Trans., 1868.</p>

<p><a name="fn15_8">[8]</a> <i>R.S. Phil Trans.</i>, 1783.</p>

<p><a name="fn15_9">[9]</a> See Kapteyn&#8217;s address to the Royal Institution,
1908. Also Gill&#8217;s presidential address
to the British Association, 1907.</p>

<p><a name="fn15_10">[10]</a> <i>Brit. Assoc. Rep.</i>, 1905.</p>

<p><a name="fn15_11">[11]</a> R. S. Phil. Trans., 1803, 1804.</p>

<p><a name="fn15_12">[12]</a> Ibid, 1824.</p>

<p><a name="fn15_13">[13]</a> Connaisance des Temps, 1830.</p>

<p><a name="fn15_14">[14]</a> <i>R. A. S. Mem.</i>, vol. xlvii., p. 178;
<i>Ast. Nach.</i>, No. 3,142; Catalogue published
by Lick Observatory, 1901.</p>

<p><a name="fn15_15">[15]</a> <i>R. A. S., M. N.</i>, vol. vi.</p>

<p><a name="fn15_16">[16]</a> <i>R. S. Phil. Trans.</i>, vol. lxxiii.,
p. 484.</p>

<p><a name="fn15_17">[17]</a> <i>Astr. Nach.</i>, No. 2,947.</p>

<p><a name="fn15_18">[18]</a> <i>R. S. E. Trans</i>., vol. xxvii.
In 1901 Dr. Anderson discovered Nova Persei.</p>

<p><a name="fn15_19">[19]</a> <i>Astr. Nach</i>., No. 3,079.</p>

<p><a name="fn15_20">[20]</a> For a different explanation see Sir W. Huggins&#8217;s
lecture, Royal Institution, May 13th, 1892.</p>

<p><a name="fn15_21">[21]</a> For the early history of the proposals for photographic
cataloguing of stars, see the <i>Cape Photographic
Durchmusterung</i>, 3 vols. (<i>Ann. of the Cape Observatory</i>,
vols. in., iv., and v., Introduction.)</p>

<p><a name="fn15_22">[22]</a> <i>R. S. Phil. Trans.</i>, 1850, p.
499 <i>et seq.</i></p>

<p><a name="fn15_23">[23]</a> <i>Ibid</i>, vol. cliv., p. 437.</p>

<p><a name="fn15_24">[24]</a> <i>Brit. Assoc. Rep.</i>, 1868, p.
165.</p>

<p><br /><br /></p>

<h1>INDEX</h1>

<p>Abul Wefa, 24<br />
Acceleration of moon&#8217;s mean motion, 60<br />
Achromatic lens invented, 88<br />
Adams, J. C., 61, 65, 68, 69, 70, 87, 118, 124<br />
Airy, G. B., 13, 30, 37, 65, 69, 70, 80, 81, 114,
119<br />
Albetegnius, 24<br />
Alphonso, 24<br />
Altazimuth, 81<br />
Anaxagoras, 14, 16<br />
Anaximander, 14<br />
Anaximenes, 14<br />
Anderson, T. D., 137, 138<br />
&#197;ngstrom, A. J., 102<br />
Antoniadi, 113<br />
Apian, P., 63<br />
Apollonius, 22, 23<br />
Arago, 111<br />
Argelander, F. W. A., 139<br />
Aristarchus, 18, 29<br />
Aristillus, 17, 19<br />
Aristotle, 16, 30, 47<br />
Arrhenius, 146<br />
Arzachel, 24<br />
Asshurbanapal, 12<br />
Asteroids, discovery of, 67, 119<br />
Astrology, ancient and modern, 1-7, 38</p>

<p>Backlund, 122<br />
Bacon, R., 86<br />
Bailly, 8, 65<br />
Barnard, E. E., 115, 143<br />
Beer and M&#228;dler, 107, 110, 111<br />
Behaim, 74<br />
Bessel, F.W., 65, 79, 128, 134, 139<br />
Biela, 123<br />
Binet, 65<br />
Biot, 10<br />
Bird, 79, 80<br />
Bliss, 80<br />
Bode, 66, 69<br />
Bond, G. P., 99, 117, 122<br />
Bouvard, A., 65, 68<br />
Bradley, J., 79, 80, 81, 87, 127, 128, 139<br />
Bredechin, 146<br />
Bremiker, 71<br />
Brewster, D., 52, 91, 112<br />
Brinkley, 128<br />
Bruno, G., 49<br />
Burchardt, 65, 123<br />
Burnham, S. W., 134</p>

<p>Callippus, 15, 16, 31<br />
Carrington, R. C., 97, 99, 114<br />
Cassini, G. D., 107, 114, 115, 116, 117, 118<br />
Cassini, J., 109, 129<br />
Chacornac, 139<br />
Chald&#230;an astronomy, 11-13<br />
Challis, J., 69, 70, 71, 72<br />
Chance, 88<br />
Charles, II., 50, 81<br />
Chinese astronomy, 8-11<br />
Christie, W. M. H. (Ast. Roy.), 64, 82, 125<br />
Chueni, 9<br />
Clairaut, A. C., 56, 63, 65<br />
Clark, A. G., 89, 135<br />
Clerke, Miss, 106, 146<br />
Comets, 120<br />
Common, A. A., 88<br />
Cooke, 89<br />
Copeland, R., 142<br />
Copernicus, N., 14, 24-31, 37, 38, 41, 42, 49, 128<br />
Cornu, 85<br />
Cowell, P. H., 3, 5, 64, 83<br />
Crawford, Earl of, 84<br />
Cromellin, A. C., 5, 64</p>

<p>D&#8217;Alembert, 65<br />
Damoiseau, 65<br />
D&#8217;Arrest, H. L., 34<br />
Dawes, W. R., 100, 111<br />
Delambre, J. B. J., 8, 27, 51, 65, 68<br />
De la Rue, W., 2, 94, 99, 100, 131<br />
Delaunay, 65<br />
Democritus, 16<br />
Descartes, 51<br />
De Sejour, 117<br />
Deslandres, II., 101<br />
Desvignolles, 9<br />
De Zach, 67<br />
Digges, L., 86<br />
Dollond, J., 87, 90<br />
Dominis, A. di., 86<br />
Donati, 120<br />
Doppler, 92, 129<br />
Draper, 99<br />
Dreyer, J. L. E., 29,77<br />
Dunthorne, 60<br />
Dyson, 131</p>

<p>Eclipses, total solar, 103<br />
Ecphantes, 16<br />
Eddington, 131<br />
Ellipse, 41<br />
Empedocles, 16<br />
Encke, J. F., 119, 122, 123, 133<br />
Epicycles, 22<br />
Eratosthenes, 18<br />
Euclid, 17<br />
Eudoxus, 15, 31<br />
Euler, L., 60, 61, 62, 65, 88, 119</p>

<p>Fabricius, D.,95, 120, 121<br />
Feil and Mantois, 88<br />
Fizeau, H. L., 85, 92, 99<br />
Flamsteed, J., 50, 58, 68, 78, 79, 93<br />
Fohi, 8<br />
Forbes, J. D., 52, 91<br />
Foucault, L., 85, 99<br />
Frauenhofer, J., 88, 90, 91</p>

<p>Galilei, G., 38, 46-49, 77, 93, 94, 95, 96, 107, 113,
115, 116, 133<br />
Galle, 71, 72<br />
Gascoigne, W., 45, 77<br />
Gauss, C. F., 65, 67<br />
Gauthier, 98<br />
Gautier, 89<br />
Gilbert, 44<br />
Gill, D., 84, 85, 128, 135, 139, 140<br />
Goodricke, J., 136<br />
Gould, B. A., 139<br />
Grant, R., 27, 47, 51, 86, 134<br />
Graham, 79<br />
Greek astronomy, 8-11<br />
Gregory, J. and D., 87<br />
Grimaldi, 113<br />
Groombridge, S., 139<br />
Grubb, 88, 89<br />
Guillemin, 122<br />
Guinand, 88</p>

<p>Hale, G. E., 101<br />
Hall, A., 112<br />
Hall, C. M., 88<br />
Halley, E., 19, 51, 58, 60, 61, 62, 63, 64, 79, 120,
122, 125, 129<br />
Halley&#8217;s comet, 62-64<br />
Halm, 85<br />
Hansen, P. A., 3, 65<br />
Hansky, A. P., 100<br />
Harding, C. L., 67<br />
Heliometer, 83<br />
Heller, 120<br />
Helmholtz, H. L. F., 35<br />
Henderson, T., 128<br />
Henry, P. and P., 139, 140, 143<br />
Heraclides, 16<br />
Heraclitus, 14<br />
Herodotus, 13<br />
Herschel, W., 65, 68, 97, 107, 110, 114, 115, 116,
117, 118, 126, 127,<br />
130, 131, 132, 141, 142<br />
Herschel, J., 97, 111, 133, 134, 142<br />
Herschel, A. S., 125<br />
Hevelius, J., 178<br />
Hind, J. R., 5, 64, 120, 121, 122<br />
Hipparchus, 3, 18, 19, 20, 22, 23, 24, 26, 36, 55,
60, 74, 93, 137<br />
Hooke, R., 51, 111, 114<br />
Horrocks, J., 50, 56<br />
Howlett, 100<br />
Huggins, W., 92, 93, 99, 106, 120, 129, 137, 138,
142, 144<br />
Humboldt and Bonpland, 124<br />
Huyghens, C., 47, 77, 87, 110, 116, 117</p>

<p>Ivory, 65</p>

<p>Jansen, P. J. C., 105, 106<br />
Jansen, Z., 86</p>

<p>Kaiser, F., 111<br />
Kapteyn, J. C., 131, 138, 139<br />
Keeler, 117<br />
Kepler, J., 17, 23, 26, 29, 30, 36, 37, 38-46, 48,
49, 50, 52, 53, 63,<br />
66, 77, 87, 93, 127, 137<br />
Kepler&#8217;s laws, 42<br />
Kirchoff, G.R., 91<br />
Kirsch, 9<br />
Knobel, E.B., 12, 13<br />
Ko-Show-King, 76</p>

<p>Lacaile, N.L., 139<br />
Lagrange, J.L., 61, 62, 65, 119<br />
La Hire, 114<br />
Lalande, J.J.L., 60, 63, 65, 66, 72, 139<br />
Lamont, J., 98<br />
Langrenus, 107<br />
Laplace, P.S. de, 50, 58, 61, 62, 65,66, 123, 146<br />
Lassel, 72, 88, 117, 118<br />
Law of universal gravitation, 53<br />
Legendre, 65<br />
Leonardo da Vinci, 46<br />
Lewis, G.C., 17<br />
Le Verrier, U.J.J., 65, 68, 70, 71,72, 110, 118, 125<br />
Lexell, 66, 123<br />
Light year, 128<br />
Lipperhey, H., 86<br />
Littrow, 121<br />
Lockyer, J.N., 103, 105, 146<br />
Logarithms invented, 50<br />
Loewy, 2, 100<br />
Long inequality of Jupiter and Saturn, 50, 62<br />
Lowell, P., 111, 112, 118<br />
Lubienietz, S. de, 122<br />
Luther, M., 38<br />
Lunar theory, 37, 50, 56, 64</p>

<p>Maclaurin, 65<br />
Maclear, T., 128<br />
Malvasia, 77<br />
Martin, 9<br />
Maxwell, J. Clerk, 117<br />
Maskelyne, N., 80, 130<br />
McLean, F., 89<br />
Medici, Cosmo di, 48<br />
Melancthon, 38<br />
Melotte, 83, 116<br />
Meteors, 123<br />
Meton, 15<br />
Meyer, 57, 65<br />
Michaelson, 85<br />
Miraldi, 110, 114<br />
Molyneux, 87<br />
Moon, physical observations, 107<br />
Mouchez, 139<br />
Moyriac de Mailla, 8</p>

<p>Napier, Lord, 50<br />
Nasmyth and Carpenter, 108<br />
Nebulae, 141, 146<br />
Neison, E., 108<br />
Neptune, discovery of, 68-72<br />
Newall, 89<br />
Newcomb, 85<br />
Newton, H.A., 124<br />
Newton, I., 5, 19, 43, 49, 51-60, 62, 64, 68, 77,
79, 87, 90, 93, 94,<br />
114, 127, 133<br />
Nicetas, 16, 25<br />
Niesten, 115<br />
Nunez, P., 35</p>

<p>Olbers, H.W.M., 67<br />
Omar, 11, 24<br />
Oppolzer, 13, 125<br />
Oudemans, 129</p>

<p>Palitsch, G., 64<br />
Parallax, solar, 85, 86<br />
Parmenides, 14<br />
Paul III., 30<br />
Paul V., 48<br />
Pemberton, 51<br />
Peters, C.A.F., 125, 128, 135<br />
Photography, 99<br />
Piazzi, G., 67, 128, 129, 139<br />
Picard, 54, 77, 114<br />
Pickering, E.C., 118, 135<br />
Pingr&#233;, 13, 122<br />
Plana, 65<br />
Planets and satellites, physical observations, 109-119<br />
Plato, 17, 23, 26, 40<br />
Poisson, 65<br />
Pond, J., 80<br />
Pons, 122<br />
Porta, B., 86<br />
Pound, 87, 114<br />
Pontecoulant, 64<br />
Precession of the equinoxes, 19-21, 55, 57<br />
Proctor, R.A., 111<br />
Pritchett, 115<br />
Ptolemy, 11, 13, 21, 22, 23, 24, 93<br />
Puiseux and Loewy, 108<br />
Pulfrich, 131<br />
Purbach, G., 24<br />
Pythagoras, 14, 17, 25, 29</p>

<p>Ramsay, W., 106<br />
Ransome and May, 81<br />
Reflecting telescopes invented, 87<br />
Regiomontanus (M&#252;ller), 24<br />
Respighi, 82<br />
Retrograde motion of planets, 22<br />
Riccioli, 107<br />
Roberts, 137<br />
R&#246;mer, O.,78, 114<br />
Rosse, Earl of, 88, 142<br />
Rowland, H. A., 92, 102<br />
Rudolph H.,37, 39<br />
Rumker, C., 139</p>

<p>Sabine, E., 98<br />
Savary, 133<br />
Schaeberle, J. M., 135<br />
Schiaparelli, G. V., 110, 111, 124, 125<br />
Scheiner, C., 87, 95, 96<br />
Schmidt, 108<br />
Schott, 88<br />
Schr&#246;ter, J. H., 107, 110, 111, 124, 125<br />
Schuster, 98<br />
Schwabe, G. H., 97<br />
Secchi, A., 93, 144<br />
Short, 87<br />
Simms, J., 81<br />
Slipher, V. M., 119<br />
Socrates, 17<br />
Solon, 15<br />
Souciet, 8<br />
South, J., 133<br />
Spectroscope, 89-92<br />
Spectroheliograph, 101<br />
Spoerer, G. F. W., 98<br />
Spots on the sun, 84;<br />
periodicity of, 97<br />
Stars, Parallax, 127;<br />
proper motion, 129;<br />
double, 132;<br />
binaries, 132, 135;<br />
new, 19, 36, 137;<br />
catalogues of, 19, 36, 139;<br />
spectra of, 143<br />
Stewart, B., 2, 100<br />
Stokes, G. G., 91<br />
Stone, E. J., 139<br />
Struve, C. L., 130<br />
Struve, F. G. W,, 88, 115, 128, 133</p>

<p>Telescopes invented, 47, 86;<br />
large, 88<br />
Temple, 115, 125<br />
Thales, 13, 16<br />
Theon, 60<br />
Transit circle of R&#246;mer, 78<br />
Timocharis, 17, 19<br />
Titius, 66<br />
Torricelli, 113<br />
Troughton, E., 80<br />
Tupman, G. L., 120<br />
Tuttle, 125<br />
Tycho Brahe, 23, 25, 30, 33-38, 39, 40, 44, 50, 75,
77, 93, 94, 129, 137</p>

<p>Ulugh Begh, 24<br />
Uranus, discovery of, 65</p>

<p>Velocity of light, 86, 128;<br />
of earth in orbit, 128<br />
Verbiest, 75<br />
Vogel, H. C., 92, 129, 135, 136<br />
Von Asten, 122</p>

<p>Walmsley, 65<br />
Walterus, B., 24, 74<br />
Weiss, E., 125<br />
Wells, 122<br />
Wesley, 104<br />
Whewell, 112<br />
Williams, 10<br />
Wilson, A., 96, 100<br />
Winnecke, 120<br />
Witte, 86<br />
Wollaston, 90<br />
Wolf, M., 119, 125, 132<br />
Wolf, R., 98<br />
Wren, C., 51<br />
Wyllie, A., 77</p>

<p>Yao, 9<br />
Young, C. A., 103<br />
Yu-Chi, 8</p>

<p>Zenith telescopes, 79, 82<br />
Z&#246;llner, 92<br />
Zucchi, 113 </p>








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