THE NINETEENTH CENTURY.
“The greater the sphere of our knowledge, the larger is the surface of
its contact with the infinity of our ignorance.”
272. The last three chapters have contained some account of progress
made in three branches of astronomy which, though they overlap and
exercise an important influence on one another, are to a large extent
studied by different men and by different methods, and have different
aims. The difference is perhaps best realised by thinking of the
work of a great master in each department, Bradley, Laplace, and
Herschel. So great is the difference that Delambre in his standard
history of astronomy all but ignores the work of the great school of
mathematical astronomers who were his contemporaries and immediate
predecessors, not from any want of appreciation of their importance,
but because he regards their work as belonging rather to mathematics
than to astronomy; while Bessel (§ 277), in saying that the function of
astronomy is “to assign the places on the sky where sun, moon, planets,
comets, and stars have been, are, and will be,” excludes from its scope
nearly everything towards which Herschel’s energies were directed.
Current modern practice is, however, more liberal in its use of
language than either Delambre or Bessel, and finds it convenient to
recognise all three of the subjects or groups of subjects referred to
as integral parts of one science.
The mutual relation of gravitational astronomy and what has been for
convenience called observational astronomy has been already referred
to (chapter X., § 196). It should, however, be noticed that the
latter term has in this book hitherto been used chiefly for only one
part of the astronomical work which concerns itself primarily with
observation. Observing played at least as large a part in Herschel’s
work as in Bradley’s, but the aims of the two men were in many ways
different. Bradley was interested chiefly in ascertaining as accurately
as possible the apparent positions of the fixed stars on the celestial
sphere, and the positions and motions of the bodies of the solar
system, the former undertaking being in great part subsidiary to the
latter. Herschel, on the other hand, though certain of his researches,
_e.g._ into the parallax of the fixed stars and into the motions of the
satellites of Uranus, were precisely like some of Bradley’s, was far
more concerned with questions of the appearances, mutual relations, and
structure of the celestial bodies in themselves. This latter branch of
astronomy may conveniently be called =descriptive astronomy=, though
the name is not altogether appropriate to inquiries into the physical
structure and chemical constitution of celestial bodies which are often
put under this head, and which play an important part in the astronomy
of the present day.
273. Gravitational astronomy and exact observational astronomy have
made steady progress during the nineteenth century, but neither has
been revolutionised, and the advances made have been to a great extent
of such a nature as to be barely intelligible, still less interesting,
to those who are not experts. The account of them to be given in this
chapter must therefore necessarily be of the slightest character, and
deal either with general tendencies or with isolated results of a less
technical character than the rest.
Descriptive astronomy, on the other hand, which can be regarded
as being almost as much the creation of Herschel as gravitational
astronomy is of Newton, has not only been greatly developed on the
lines laid down by its founder, but has received—chiefly through the
invention of spectrum analysis (§ 299)—extensions into regions not
only unthought of but barely imaginable a century ago. Most of the
results of descriptive astronomy—unlike those of the older branches
of the subject—are readily intelligible and fairly interesting to
those who have but little knowledge of the subject; in particular they
are as yet to a considerable extent independent of the mathematical
ideas and language which dominate so much of astronomy and render
it unattractive or inaccessible to many. Moreover, not only can
descriptive astronomy be appreciated and studied, but its progress can
materially be assisted, by observers who have neither knowledge of
higher mathematics nor any elaborate instrumental equipment.
Accordingly, while the successors of Laplace and Bradley have been
for the most part astronomers by profession, attached to public
observatories or to universities, an immense mass of valuable
descriptive work has been done by amateurs who, like Herschel in the
earlier part of his career, have had to devote a large part of their
energies to professional work of other kinds, and who, though in some
cases provided with the best of instruments, have in many others been
furnished with only a slender instrumental outfit. For these and
other reasons one of the most notable features of nineteenth century
astronomy has been a great development, particularly in this country
and in the United States, of general interest in the subject, and the
establishment of a large number of private observatories devoted almost
entirely to the study of special branches of descriptive astronomy.
The nineteenth century has accordingly witnessed the acquisition of an
unprecedented amount of detailed astronomical knowledge. But the wealth
of material thus accumulated has outrun our powers of interpretation,
and in a number of cases our knowledge of some particular department
of descriptive astronomy consists, on the one hand of an immense
series of careful observations, and on the other of one or more highly
speculative theories, seldom capable of explaining more than a small
portion of the observed facts.
In dealing with the progress of modern descriptive astronomy the
proverbial difficulty of seeing the wood on account of the trees
is therefore unusually great. To give an account within the limits
of a single chapter of even the most important facts added to our
knowledge would be a hopeless endeavour; fortunately it would also
be superfluous, as they are to be found in many easily accessible
textbooks on astronomy, or in treatises on special parts of the
subject. All that can be attempted is to give some account of the chief
lines on which progress has been made, and to indicate some general
conclusions which seem to be established on a tolerably secure basis.
274. The progress of exact observation has of course been based very
largely on instrumental advances. Not only have great improvements
been made in the extremely delicate work of making large lenses, but
the graduated circles and other parts of the mounting of a telescope
upon which accuracy of measurement depends can also be constructed
with far greater exactitude and certainty than at the beginning of the
century. New methods of mounting telescopes and of making and recording
observations have also been introduced, all contributing to greater
accuracy. For certain special problems photography is found to present
great advantages as compared with eye-observations, though its most
important applications have so far been to descriptive astronomy.
275. The necessity for making allowance for various known sources of
errors in observation, and for diminishing as far as possible the
effect of errors due to unknown causes, had been recognised even by
Tycho Brahe (chapter V., § 110), and had played an important part in
the work of Flamsteed and Bradley (chapter X., §§ 198, 218). Some
further important steps in this direction were taken in the earlier
part of this century. The method of =least squares=, established
independently by two great mathematicians, _Adrien Marie Legendre_
(1752-1833) of Paris and _Carl Friedrich Gauss_ (1777-1855) of
Göttingen,[159] was a systematic method of combining observations,
which gave slightly different results, in such a way as to be as near
the truth as possible. Any ordinary physical measurement, _e.g._ of a
length, however carefully executed, is necessarily imperfect; if the
same measurement is made several times, even under almost identical
conditions, the results will in general differ slightly; and the
question arises of combining these so as to get the most satisfactory
result. The common practice in this simple case has long been to
take the arithmetical mean or average of the different results. But
astronomers have constantly to deal with more complicated cases in
which _two_ or more unknown quantities have to be determined from
observations of different quantities, as, for example, when the
elements of the orbit of a planet (chapter XI., § 236) have to be
found from observations of the planet’s position at different times.
The method of least squares gives a rule for dealing with such cases,
which was a generalisation of the ordinary rule of averages for the
case of a single unknown quantity; and it was elaborated in such a
way as to provide for combining observations of different value, such
as observations taken by observers of unequal skill or with different
instruments, or under more or less favourable conditions as to weather,
etc. It also gives a simple means of testing, by means of their mutual
consistency, the value of a series of observations, and comparing
their probable accuracy with that of some other series executed under
different conditions. The method of least squares and the special case
of the “average” can be deduced from a certain assumption as to the
general character of the causes which produce the error in question;
but the assumption itself cannot be justified _a priori_; on the other
hand, the satisfactory results obtained from the application of the
rule to a great variety of problems in astronomy and in physics has
shewn that in a large number of cases unknown causes of error must be
approximately of the type considered. The method is therefore very
widely used in astronomy and physics wherever it is worth while to take
trouble to secure the utmost attainable accuracy.
276. Legendre’s other contributions to science were almost entirely
to branches of mathematics scarcely affecting astronomy. Gauss, on
the other hand, was for nearly half a century head of the observatory
of Göttingen, and though his most brilliant and important work was in
pure mathematics, while he carried out some researches of first-rate
importance in magnetism and other branches of physics, he also made
some further contributions of importance to astronomy. These were for
the most part processes of calculation of various kinds required for
utilising astronomical observations, the best known being a method of
calculating the orbit of a planet from three complete observations
of its position, which was published in his _Theoria Motus_ (1809).
As we have seen (chapter XI., § 236), the complete determination of
a planet’s orbit depends on six independent elements: any complete
observation of the planet’s position in the sky, at any time, gives
two quantities, _e.g._ the right ascension and declination (chapter
II., § 33); hence three complete observations give six equations and
are theoretically adequate to determine the elements of the orbit; but
it had not hitherto been found necessary to deal with the problem in
this form. The orbits of all the planets but Uranus had been worked
out gradually by the use of a series of observations extending over
centuries; and it was feasible to use observations taken at particular
times so chosen that certain elements could be determined without
any accurate knowledge of the others; even Uranus had been under
observation for a considerable time before its path was determined
with anything like accuracy; and in the case of comets not only was
a considerable series of observations generally available, but the
problem was simplified by the fact that the orbit could be taken to
be nearly or quite a parabola instead of an ellipse (chapter IX., §
190). The discovery of the new planet Ceres on January 1st, 1801 (§
294), and its loss when it had only been observed for a few weeks,
presented virtually a new problem in the calculation of an orbit.
Gauss applied his new methods—including that of least squares—to the
observations available, and with complete success, the planet being
rediscovered at the end of the year nearly in the position indicated by
his calculations.
277. The theory of the “reduction” of observations (chapter X., § 218)
was first systematised and very much improved by _Friedrich Wilhelm
Bessel_ (1784-1846), who was for more than thirty years the director
of the new Prussian observatory at Königsberg. His first great work
was the reduction and publication of Bradley’s Greenwich observations
(chapter X., § 218). This undertaking involved an elaborate study of
such disturbing causes as precession, aberration, and refraction,
as well as of the errors of Bradley’s instruments. Allowance was
made for these on a uniform and systematic plan, and the result was
the publication in 1818, under the title _Fundamenta Astronomiae_,
of a catalogue of the places of 3,222 stars as they were in 1755.
A special problem dealt with in the course of the work was that of
refraction. Although the complete theoretical solution was then as now
unattainable, Bessel succeeded in constructing a table of refractions
which agreed very closely with observation and was presented in such a
form that the necessary correction for a star in almost any position
could be obtained with very little trouble. His general methods of
reduction—published finally in his _Tabulae Regiomontanae_ (1830)—also
had the great advantage of arranging the necessary calculations in
such a way that they could be performed with very little labour and
by an almost mechanical process, such as could easily be carried out
by a moderately skilled assistant. In addition to editing Bradley’s
observations, Bessel undertook a fresh series of observations of his
own, executed between the years 1821 and 1833, upon which were based
two new catalogues, containing about 62,000 stars, which appeared after
his death.
[Illustration: FIG. 85.—_61 Cygni_ and the two neighbouring stars used
by Bessel.]
[Illustration: FIG. 86.—The parallax of _61 Cygni_.]
278. The most memorable of Bessel’s special pieces of work was the
first definite detection of the parallax of a fixed star. He abandoned
the test of brightness as an indication of nearness, and selected a
star (_61 Cygni_) which was barely visible to the naked eye but was
remarkable for its large proper motion (about 5″ per annum); evidently
if a star is moving at an assigned rate (in miles per hour) through
space, the nearer to the observer it is the more rapid does its motion
appear to be, so that apparent rapidity of motion, like brightness,
is a probable but by no means infallible indication of nearness. A
modification of Galilei’s differential method (chapter VI., § 129,
and chapter XII., § 263) being adopted, the angular distance of _61
Cygni_ from two neighbouring stars, the faintness and immovability of
which suggested their great distance in space, was measured at frequent
intervals during a year. From the changes in these distances σ _a_, σ
_b_ (in fig. 85), the size of the small ellipse described by σ could be
calculated. The result, announced at the end of 1838, was that the star
had an annual parallax of about 1∕3″ (chapter VIII., § 161), _i.e._
that the star was at such distance that the greatest angular distance
of the earth from the sun viewed from the star (the angle S σ E in
fig. 86, where S is the sun and E the earth) was this insignificant
angle.[160] The result was confirmed, with slight alterations, by a
fresh investigation of Bessel’s in 1839-40, but later work seems to
shew that the parallax is a little less than 1∕2″.[161] With this
latter estimate, the apparent size of the earth’s path round the sun as
seen from the star is the same as that of a halfpenny at a distance
of rather more than three miles. In other words, the distance of the
star is about 400,000 times the distance of the sun, which is itself
about 93,000,000 miles. A mile is evidently a very small unit by which
to measure such a vast distance; and the practice of expressing such
distances by means of the time required by light to perform the journey
is often convenient. Travelling at the rate of 186,000 miles _per
second_ (§ 283), light takes rather more than six years to reach us
from _61 Cygni_.
279. Bessel’s solution of the great problem which had baffled
astronomers ever since the time of Coppernicus was immediately followed
by two others. Early in 1839 _Thomas Henderson_ (1798-1844) announced
a parallax of nearly 1″ for the bright star α _Centauri_ which he
had observed at the Cape, and in the following year _Friedrich Georg
Wilhelm Struve_ (1793-1864) obtained from observations made at Pulkowa
a parallax of 1∕4″ for _Vega_; later work has reduced these numbers to
3∕4″ and 1∕10″ respectively.
A number of other parallax determinations have subsequently been made.
An interesting variation in method was made by the late Professor
_Charles Pritchard_ (1808-1893) of Oxford by _photographing_ the star
to be examined and its companions, and subsequently measuring the
distances on the photograph, instead of measuring the angular distances
directly with a micrometer.
At the present time some 50 stars have been ascertained with some
reasonable degree of probability to have measurable, if rather
uncertain, parallaxes; α _Centauri_ still holds its own as the nearest
star, the light-journey from it being about four years. A considerable
number of other stars have been examined with negative or highly
uncertain results, indicating that their parallaxes are too small
to be measured with our present means, and that their distances are
correspondingly great.
280. A number of star catalogues and star maps—too numerous to mention
separately—have been constructed during this century, marking steady
progress in our knowledge of the position of the stars, and providing
fresh materials for ascertaining, by comparison of the state of the sky
at different epochs, such quantities as the proper motions of the stars
and the amount of precession. Among the most important is the great
catalogue of 324,198 stars in the northern hemisphere known as the Bonn
_Durchmusterung_, published in 1859-62 by Bessel’s pupil _Friedrich
Wilhelm August Argelander_ (1799-1875); this was extended (1875-85) so
as to include 133,659 stars in a portion of the southern hemisphere
by _Eduard Schönfeld_ (1828-1891); and more recently Dr. _Gill_ has
executed at the Cape photographic observations of the remainder of the
southern hemisphere, the reduction to the form of a catalogue (the
first instalment of which was published in 1896) having been performed
by Professor _Kapteyn_ of Groningen. The star places determined in
these catalogues do not profess to be the most accurate attainable,
and for many purposes it is important to know with the utmost accuracy
the positions of a smaller number of stars. The greatest undertaking
of this kind, set on foot by the German Astronomical Society in
1867, aims at the construction, by the co-operation of a number of
observatories, of catalogues of about 130,000 of the stars contained in
the “approximate” catalogues of Argelander and Schönfeld; nearly half
of the work has now been published.
The greatest scheme for a survey of the sky yet attempted is the
photographic chart, together with a less extensive catalogue to
be based on it, the construction of which was decided on at an
international congress held at Paris in 1887. The whole sky has been
divided between 18 observatories in all parts of the world, from
Helsingfors in the north to Melbourne in the south, and each of these
is now taking photographs with virtually identical instruments. It
is estimated that the complete chart, which is intended to include
stars of the 14th magnitude,[162] will contain about 20,000,000 stars,
2,000,000 of which will be catalogued also.
281. One other great problem—that of the distance of the sun—may
conveniently be discussed under the head of observational astronomy.
The transits of Venus (chapter X., §§ 202, 227) which occurred in
1874 and 1882 were both extensively observed, the old methods of
time-observation being supplemented by photography and by direct
micrometric measurements of the positions of Venus while transiting.
The method of finding the distance of the sun by means of observation
of Mars in opposition (chapter VIII., § 161) has been employed on
several occasions with considerable success, notably by Dr. Gill at
Ascension in 1877. A method originally used by Flamsteed, but revived
in 1857 by _Sir George Biddell Airy_ (1801-1892), the late Astronomer
Royal, was adopted on this occasion. For the determination of the
parallax of a planet observations have to be made from two different
positions at a known distance apart; commonly these are taken to be
at two different observatories, as far as possible removed from one
another in latitude. Airy pointed out that the same object could be
attained if only one observatory were used, but observations taken at
an interval of some hours, as the rotation of the earth on its axis
would in that time produce a known displacement of the observer’s
position and so provide the necessary base line. The apparent shift of
the planet’s position could be most easily ascertained by measuring
(with the micrometer) its distances from neighbouring fixed stars.
This method (known as the =diurnal method=) has the great advantage,
among others, of being simple in application, a single observer and
instrument being all that is needed.
The diurnal method has also been applied with great success to certain
of the minor planets (§ 294). Revolving as they do between Mars and
Jupiter, they are all farther off from us than the former; but there is
the compensating advantage that as a minor planet, unlike Mars, is, as
a rule, too small to shew any appreciable disc, its angular distance
from a neighbouring star is more easily measured. The employment of
the minor planets in this way was first suggested by Professor _Galle_
of Berlin in 1872, and recent observations of the minor planets
_Victoria_, _Sappho_, and _Iris_ in 1888-89, made at a number of
observatories under the general direction of Dr. Gill, have led to some
of the most satisfactory determinations of the sun’s distance.
282. It was known to the mathematical astronomers of the 18th century
that the distance of the sun could be obtained from a knowledge of
various perturbations of members of the solar system; and Laplace had
deduced a value of the solar parallax from lunar theory. Improvements
in gravitational astronomy and in observation of the planets and moon
during the present century have added considerably to the value of
these methods. A certain irregularity in the moon’s motion known as
the =parallactic inequality=, and another in the motion of the sun,
called the =lunar equation=, due to the displacement of the earth by
the attraction of the moon, alike depend on the ratio of the distances
of the sun and moon from the earth; if the amount of either of these
inequalities can be observed, the distance of the sun can therefore
be deduced, that of the moon being known with great accuracy. It was
by a virtual application of the first of these methods that Hansen (§
286) in 1854, in the course of an elaborate investigation of the lunar
theory, ascertained that the current value of the sun’s distance was
decidedly too large, and Leverrier (§ 288) confirmed the correction by
the second method in 1858.
Again, certain changes in the orbits of our two neighbours, Venus and
Mars, are known to depend upon the ratio of the masses of the sun and
earth, and can hence be connected, by gravitational principles, with
the quantity sought. Leverrier pointed out in 1861 that the motions of
Venus and of Mars, like that of the moon, were inconsistent with the
received estimate of the sun’s distance, and he subsequently worked out
the method more completely and deduced (1872) values of the parallax.
The displacements to be observed are very minute, and their accurate
determination is by no means easy, but they are both secular (chapter
XI., § 242), so that in the course of time they will be capable of very
exact measurement. Leverrier’s method, which is even now a valuable
one, must therefore almost inevitably outstrip all the others which
are at present known; it is difficult to imagine, for example, that
the transits of Venus due in 2004 and 2012 will have any value for the
purpose of the determination of the sun’s distance.
283. One other method, in two slightly different forms, has become
available during this century. The displacement of a star by aberration
(chapter X., § 210) depends upon the ratio of the velocity of light
to that of the earth in its orbit round the sun; and observations of
Jupiter’s satellites after the manner of Roemer (chapter VIII., § 162)
give the =light-equation=, or time occupied by light in travelling from
the sun to the earth. Either of these astronomical quantities—of which
aberration is the more accurately known—can be used to determine the
velocity of light when the dimensions of the solar system are known,
or _vice versa_. No independent method of determining the velocity
of light was known until 1849, when _Hippolyte Fizeau_ (1819-1896)
invented and successfully carried out a laboratory method.
New methods have been devised since, and three comparatively recent
series of experiments, by M. _Cornu_ in France (1874 and 1876) and by
Dr. _Michelson_ (1879) and Professor _Newcomb_ (1880-82) in the United
States, agreeing closely with one another, combine to fix the velocity
of light at very nearly 186,300 miles (299,800 kilometres) per second;
the solar parallax resulting from this by means of aberration is very
nearly 8″·8.[163]
284. Encke’s value of the sun’s parallax, 8″·571, deduced from
the transits of Venus (chapter X., § 227) in 1761 and 1769, and
published in 1835, corresponding to a distance of about 95,000,000
miles, was generally accepted till past the middle of the century.
Then the gravitational methods of Hansen and Leverrier, the earlier
determinations of the velocity of light, and the observations made
at the opposition of Mars in 1862, all pointed to a considerably
larger value of the parallax; a fresh examination of the 18th century
observations shewed that larger values than Encke’s could easily be
deduced from them; and for some time—from about 1860 onwards—a parallax
of nearly 8″·95, corresponding to a distance of rather more than
91,000,000 miles, was in common use. Various small errors in the new
methods were, however, detected, and the most probable value of the
parallax has again increased. Three of the most reliable methods, the
diurnal method as applied to Mars in 1877, the same applied to the
minor planets in 1888-89, and aberration, unite in giving values
not differing from 8″·80 by more than two or three hundredths of a
second. The results of the last transits of Venus, the publication and
discussion of which have been spread over a good many years, point to a
somewhat larger value of the parallax. Most astronomers appear to agree
that a parallax of 8″·8, corresponding to a distance of rather less
than 93,000,000 miles, represents fairly the available data.
285. The minute accuracy of modern observations is well illustrated
by the recent discovery of a variation in the latitude of several
observatories. Observations taken at Berlin in 1884-85 indicated a
minute variation in the latitude; special series of observations to
verify this were set on foot in several European observatories, and
subsequently at Honolulu and at Cordoba. A periodic alteration in
latitude amounting to about 1∕2″ emerged as the result. Latitude being
defined (chapter X., § 221) as the angle which the vertical at any
place makes with the equator, which is the same as the elevation of the
pole above the horizon, is consequently altered by any change in the
equator, and therefore by an alteration in the position of the earth’s
poles or the ends of the axis about which it rotates.
Dr. _S. C. Chandler_ succeeded (1891 and subsequently) in shewing
that the observations in question could be in great part explained by
supposing the earth’s axis to undergo a minute change of position in
such a way that either pole of the earth describes a circuit round its
mean position in about 427 days, never deviating more than some 30 feet
from it. It is well known from dynamical theory that a rotating body
such as the earth can be displaced in this manner, but that if the
earth were perfectly rigid the period should be 306 days instead of
427. The discrepancy between the two numbers has been ingeniously used
as a test of the extent to which the earth is capable of yielding—like
an elastic solid—to the various forces which tend to strain it.
286. All the great problems of gravitational astronomy have been
rediscussed since Laplace’s time, and further steps taken towards their
solution.
Laplace’s treatment of the lunar theory was first developed by _Marie
Charles Theodore Damoiseau_ (1768-1846), whose _Tables de la Lune_
(1824 and 1828) were for some time in general use.
Some special problems of both lunar and planetary theory were dealt
with by _Siméon Denis Poisson_ (1781-1840), who is, however, better
known as a writer on other branches of mathematical physics than as
an astronomer. A very elaborate and detailed theory of the moon,
investigated by the general methods of Laplace, was published by
_Giovanni Antonio Amadeo Plana_ (1781-1869) in 1832, but unaccompanied
by tables. A general treatment of both lunar and planetary theories,
the most complete that had appeared up to that time, by _Philippe
Gustave Doulcet de Pontécoulant_ (1795-1874), appeared in 1846, with
the title _Théorie Analytique du Système du Monde_; and an incomplete
lunar theory similar to his was published by _John William Lubbock_
(1803-1865) in 1830-34.
A great advance in lunar theory was made by _Peter Andreas Hansen_
(1795-1874) of Gotha, who published in 1838 and 1862-64 the treatises
commonly known respectively as the _Fundamenta_[164] and the
_Darlegung_,[165] and produced in 1857 tables of the moon’s motion
of such accuracy that the discrepancies between the tables and
observations in the century 1750-1850 were never greater than 1″
or 2″. These tables were at once used for the calculation of the
_Nautical Almanac_ and other periodicals of the same kind, and with
some modifications have remained in use up to the present day.
A completely new lunar theory—of great mathematical interest and of
equal complexity—was published by _Charles Delaunay_ (1816-1872) in
1860 and 1867. Unfortunately the author died before he was able to work
out the corresponding tables.
Professor Newcomb of Washington (§ 283) has rendered valuable
services to lunar theory—as to other branches of astronomy—by a
number of delicate and intricate calculations, the best known being
his comparison of Hansen’s tables with observation and consequent
corrections of the tables.
New methods of dealing with lunar theory were devised by the late
Professor _John Couch Adams_ of Cambridge (1819-1892), and similar
methods have been developed by Dr. _G. W. Hill_ of Washington; so
far they have not been worked out in detail in such a way as to be
available for the calculation of tables, and their interest seems to
be at present mathematical rather than practical; but the necessary
detailed work is now in progress, and these and allied methods may be
expected to lead to a considerable diminution of the present excessive
intricacy of lunar theory.
287. One special point in lunar theory may be worth mentioning. The
secular acceleration of the moon’s mean motion which had perplexed
astronomers since its first discovery by Halley (chapter X., § 201)
had, as we have seen (chapter XI., § 240), received an explanation in
1787 at the hands of Laplace. Adams, on going through the calculation,
found that some quantities omitted by Laplace as unimportant had
in reality a very sensible effect on the result, so that a certain
quantity expressing the rate of increase of the moon’s motion came out
to be between 5″ and 6″, instead of being about 10″, as Laplace had
found and as observation required. The correction was disputed at first
by several of the leading experts, but was confirmed independently
by Delaunay and is now accepted. The moon appears in consequence to
have a certain very minute increase in speed for which the theory of
gravitation affords no explanation. An ingenious though by no means
certain explanation was suggested by Delaunay in 1865. It had been
noticed by Kant that =tidal friction=—that is, the friction set up
between the solid earth and the ocean as the result of the tidal
motion of the latter—would have the effect of checking to some extent
the rotation of the earth; but as the effect seemed to be excessively
minute and incapable of precise calculation it was generally ignored.
An attempt to calculate its amount was, however, made in 1853 by
_William Ferrel_, who also pointed out that, as the period of the
earth’s rotation—the day—is our fundamental unit of time, a reduction
of the earth’s rate of rotation involves the lengthening of our unit
of time, and consequently produces an apparent increase of speed in
all other motions measured in terms of this unit. Delaunay, working
independently, arrived at like conclusions, and shewed that tidal
friction might thus be capable of producing just such an alteration
in the moon’s motion as had to be explained; if this explanation were
accepted the observed motion of the moon would give a measure of the
effect of tidal friction. The minuteness of the quantities involved
is shewn by the fact that an alteration in the earth’s rotation
equivalent to the lengthening of the day by 1∕10 second in 10,000 years
is sufficient to explain the acceleration in question. Moreover it
is by no means certain that the usual estimate of the amount of this
acceleration—based as it is in part on ancient eclipse observations—is
correct, and even then a part of it may conceivably be due to some
indirect effect of gravitation even more obscure than that detected by
Laplace, or to some other cause hitherto unsuspected.
288. Most of the writers on lunar theory already mentioned have also
made contributions to various parts of planetary theory, but some of
the most important advances in planetary theory made since the death of
Laplace have been due to the French mathematician _Urbain Jean Joseph
Leverrier_ (1811-1877), whose methods of determining the distance of
the sun have been already referred to (§ 282). His first important
astronomical paper (1839) was a discussion of the stability (chapter
XI., § 245) of the system formed by the sun and the three largest
and most distant planets then known, Jupiter, Saturn, and Uranus.
Subsequently he worked out afresh the theory of the motion of the sun
and of each of the principal planets, and constructed tables of them,
which at once superseded earlier ones, and are now used as the basis
of the chief planetary calculations in the _Nautical Almanac_ and most
other astronomical almanacs. Leverrier failed to obtain a satisfactory
agreement between observation and theory in the case of Mercury, a
planet which has always given great trouble to astronomers, and was
inclined to explain the discrepancies as due to the influence either
of a planet revolving between Mercury and the sun or of a number of
smaller bodies analogous to the minor planets (§ 294).
Researches of a more abstract character, connecting planetary theory
with some of the most recent advances in pure mathematics, have
been carried out by _Hugo Gyldén_ (1841-1896), while one of the most
eminent pure mathematicians of the day, M. _Henri Poincaré_ of Paris,
has recently turned his attention to astronomy, and is engaged in
investigations which, though they have at present but little bearing on
practical astronomy, seem likely to throw important light on some of
the general problems of celestial mechanics.
289. One memorable triumph of gravitational astronomy, the discovery of
Neptune, has been described so often and so fully elsewhere[166] that
a very brief account will suffice here. Soon after the discovery of
Uranus (chapter XII., § 253) it was found that the planet had evidently
been observed, though not recognised as a planet, as early as 1690, and
on several occasions afterwards.
When the first attempts were made to compute its orbit carefully, it
was found impossible satisfactorily to reconcile the earlier with the
later observations, and in Bouvard’s tables (chapter XI., § 247, note)
published in 1821 the earlier observations were rejected. But even
this drastic measure did not cure the evil; discrepancies between the
observed and calculated places soon appeared and increased year by
year. Several explanations were proposed, and more than one astronomer
threw out the suggestion that the irregularities might be due to the
attraction of a hitherto unknown planet. The first serious attempt to
deduce from the irregularities in the motion of Uranus the position
of this hypothetical body was made by Adams immediately after taking
his degree (1843). By October 1845 he had succeeded in constructing an
orbit for the new planet, and in assigning for it a position differing
(as we now know) by less than 2° (four times the diameter of the full
moon) from its actual position. No telescopic search for it was,
however, undertaken. Meanwhile, Leverrier had independently taken up
the inquiry, and by August 31st, 1846, he, like Adams, had succeeded
in determining the orbit and the position of the disturbing body. On
the 23rd of the following month Dr. Galle of the Berlin Observatory
received from Leverrier a request to search for it, and on the same
evening found close to the position given by Leverrier a strange body
shewing a small planetary disc, which was soon recognised as a new
planet, known now as Neptune.
It may be worth while noticing that the error in the motion of Uranus
which led to this remarkable discovery never exceeded 2′, a quantity
imperceptible to the ordinary eye; so that if two stars were side
by side in the sky, one in the true position of Uranus and one in
the calculated position as given by Bouvard’s tables, an observer of
ordinary eyesight would see one star only.
290. The lunar tables of Hansen and Professor Newcomb, and the
planetary and solar tables of Leverrier, Professor Newcomb, and
Dr. Hill, represent the motions of the bodies dealt with much more
accurately than the corresponding tables based on Laplace’s work, just
as these were in turn much more accurate than those of Euler, Clairaut,
and Halley. But the agreement between theory and observation is by no
means perfect, and the discrepancies are in many cases greater than
can be explained as being due to the necessary imperfections in our
observations.
The two most striking cases are perhaps those of Mercury and the moon.
Leverrier’s explanation of the irregularities of the former (§ 288) has
never been fully justified or generally accepted; and the position of
the moon as given in the _Nautical Almanac_ and in similar publications
is calculated by means of certain corrections to Hansen’s tables
which were deduced by Professor Newcomb from observation and have no
justification in the theory of gravitation.
291. The calculation of the paths of comets has become of some
importance during this century owing to the discovery of a number of
comets revolving round the sun in comparatively short periods. Halley’s
comet (chapter XI., § 231) reappeared duly in 1835, passing through
its perihelion within a few days of the times predicted by three
independent calculators; and it may be confidently expected again about
1910. Four other comets are now known which, like Halley’s, revolve
in elongated elliptic orbits, completing a revolution in between 70
and 80 years; two of these have been seen at two returns, that known
as Olbers’s comet in 1815 and 1887, and the Pons-Brooks comet in 1812
and 1884. Fourteen other comets with periods varying between 3-1∕3
years (Encke’s) and 14 years (Tuttle’s), have been seen at more than
one return; about a dozen more have periods estimated at less than
a century; and 20 or 30 others move in orbits that are decidedly
elliptic, though their periods are longer and consequently not known
with much certainty. Altogether the paths of about 230 or 240 comets
have been computed, though many are highly uncertain.
[Illustration: FIG. 87.—The path of Halley’s comet.]
292. In the theory of the tides the first important advance made after
the publication of the _Mécanique Céleste_ was the collection of actual
tidal observations on a large scale, their interpretation, and their
comparison with the results of theory. The pioneers in this direction
were Lubbock (§ 286), who presented a series of papers on the subject
to the Royal Society in 1830-37, and _William Whewell_ (1794-1866),
whose papers on the subject appeared between 1833 and 1851. Airy (§
281), then Astronomer Royal, also published in 1845 an important
treatise dealing with the whole subject, and discussing in detail the
theory of tides in bodies of water of limited extent and special form.
The analysis of tidal observations, a large number of which taken from
all parts of the world are now available, has subsequently been carried
much further by new methods due to Lord _Kelvin_ and Professor _G. H.
Darwin_. A large quantity of information is thus available as to the
way in which tides actually vary in different places and according to
different positions of the sun and moon.
Of late years a good deal of attention has been paid to the effect of
the attraction of the sun and moon in producing alterations—analogous
to oceanic tides—in the earth itself. No body is perfectly rigid, and
the forces in question must therefore produce some tidal effect. The
problem was first investigated by Lord Kelvin in 1863, subsequently
by Professor Darwin and others. Although definite numerical results
are hardly attainable as yet, the work so far carried out points to
the comparative smallness of these bodily tides and the consequent
great rigidity of the earth, a result of interest in connection with
geological inquiries into the nature of the interior of the earth.
Some speculations connected with tidal friction are referred to
elsewhere (§ 320).
293. The series of propositions as to the stability of the solar
system established by Lagrange and Laplace (chapter XI., §§ 244,
245), regarded as abstract propositions mathematically deducible from
certain definite assumptions, have been confirmed and extended by
later mathematicians such as Poisson and Leverrier; but their claim to
give information as to the condition of the actual solar system at an
indefinitely distant future time receives much less assent now than
formerly. The general trend of scientific thought has been towards the
fuller recognition of the merely approximate and probable character of
even the best ascertained portions of our knowledge; “exact,” “always,”
and “certain” are words which are disappearing from the scientific
vocabulary, except as convenient abbreviations. Propositions which
profess to be—or are commonly interpreted as being—“exact” and valid
throughout all future time are consequently regarded with considerable
distrust, unless they are clearly mere abstractions.
In the case of the particular propositions in question the progress of
astronomy and physics has thrown a good deal of emphasis on some of the
points in which the assumptions required by Lagrange and Laplace are
not satisfied by the actual solar system.
It was assumed for the purposes of the stability theorems that the
bodies of the solar system are perfectly rigid; in other words, the
motions relative to one another of the parts of any one body were
ignored. Both the ordinary tides of the ocean and the bodily tides to
which modern research has called attention were therefore left out of
account. Tidal friction, though at present very minute in amount (§
287), differs essentially from the perturbations which form the main
subject-matter of gravitational astronomy, inasmuch as its action is
irreversible. The stability theorems shewed in effect that the ordinary
perturbations produced effects which sooner or later compensated one
another, so that if a particular motion was accelerated at one time
it would be retarded at another; but this is not the case with tidal
friction. Tidal action between the earth and the moon, for example,
gradually lengthens both the day and the month, and increases the
distance between the earth and the moon. Solar tidal action has a
similar though smaller effect on the sun and earth. The effect in each
case—as far as we can measure it at all—seems to be minute almost
beyond imagination, but there is no compensating action tending at
any time to reverse the process. And on the whole the energy of the
bodies concerned is thereby lessened. Again, modern theories of light
and electricity require space to be filled with an “ether” capable of
transmitting certain waves; and although there is no direct evidence
that it in any way affects the motions of earth or planets, it is
difficult to imagine a medium so different from all known forms
of ordinary matter as to offer _no_ resistance to a body moving
through it. Such resistance would have the effect of slowly bringing
the members of the solar system nearer to the sun, and gradually
diminishing their times of revolution round it. This is again an
irreversible tendency for which we know of no compensation.
In fact, from the point of view which Lagrange and Laplace occupied,
the solar system appeared like a clock which, though not going
quite regularly, but occasionally gaining and occasionally losing,
nevertheless required no winding up; whereas modern research emphasises
the analogy to a clock which after all is running down, though at an
excessively slow rate. Modern study of the sun’s heat (§ 319) also
indicates an irreversible tendency towards the “running down” of the
solar system in another way.
294. Our account of modern descriptive astronomy may conveniently begin
with planetary discoveries.
The first day of the 19th century was marked by the discovery of a new
planet, known as Ceres. It was seen by _Giuseppe Piazzi_ (1746-1826)
as a strange star in a region of the sky which he was engaged in
mapping, and soon recognised by its motion as a planet. Its orbit—first
calculated by Gauss (§ 276)—shewed it to belong to the space between
Mars and Jupiter, which had been noted since the time of Kepler as
abnormally large. That a planet should be found in this region was
therefore no great surprise; but the discovery by _Heinrich Olbers_
(1758-1840), scarcely a year later (March 1802), of a second body
(_Pallas_), revolving at nearly the same distance from the sun, was
wholly unexpected, and revealed an entirely new planetary arrangement.
It was an obvious conjecture that if there was room for two planets
there was room for more, and two fresh discoveries (_Juno_ in 1804,
_Vesta_ in 1807) soon followed.
[Illustration: FIG. 88.—Photographic trail of a minor planet.]
The new bodies were very much smaller than any of the other planets,
and, so far from readily shewing a planetary disc like their neighbours
Mars and Jupiter, were barely distinguishable in appearance from fixed
stars, except in the most powerful telescopes of the time; hence the
name =asteroid= (suggested by William Herschel) or =minor planet= has
been generally employed to distinguish them from the other planets.
Herschel attempted to measure their size, and estimated the diameter
of the largest at under 200 miles (that of Mercury, the smallest of
the ordinary planets, being 3000), but the problem was in reality
too difficult even for his unrivalled powers of observation. The minor
planets were also found to be remarkable for the great inclination
and eccentricity of some of the orbits; the path of Pallas, for
example, makes an angle of 35° with the ecliptic, and its eccentricity
is 1∕4, so that its least distance from the sun is not much more
than half its greatest distance. These characteristics suggested to
Olbers that the minor planets were in reality fragments of a primeval
planet of moderate dimensions which had been blown to pieces, and the
theory, which fitted most of the facts then known, was received with
great favour in an age when “catastrophes” were still in fashion as
scientific explanations.
The four minor planets named were for nearly 40 years the only ones
known; then a fifth was discovered in 1845 by _Karl Ludwig Hencke_
(1793-1866) after 15 years, of search. Two more were found in 1847,
another in 1848, and the number has gone on steadily increasing
ever since. The process of discovery has been very much facilitated
by improvements in star maps, and latterly by the introduction of
photography. In this last method, first used by Dr. _Max Wolf_ of
Heidelberg in 1891, a photographic plate is exposed for some hours;
any planet present in the region of the sky photographed, having moved
sensibly relatively to the stars in this period, is thus detected by
the trail which its image leaves on the plate. The annexed figure shews
(near the centre) the trail of the minor planet _Svea_, discovered by
Dr. Wolf on March 21st, 1892.
At the end of 1897 no less than 432 minor planets were known, of which
92 had been discovered by a single observer, M. _Charlois_ of Nice, and
only nine less by Professor _Palisa_ of Vienna.
The paths of the minor planets practically occupy the whole region
between the paths of Mars and Jupiter, though few are near the
boundaries; no orbit is more inclined to the ecliptic than that of
Pallas, and the eccentricities range from almost zero up to about 1∕3.
Fig. 89 shews the orbits of the first two minor planets discovered, as
well as of No. 323 (_Brucia_), which comes nearest to the sun, and of
No. 361 (not yet named), which goes farthest from it. All the orbits
are described in the standard, or west to east, direction. The most
interesting characteristic in the distribution of the minor planets,
first noted in 1866 by _Daniel Kirkwood_ (1815-1895) is the existence
of comparatively clear spaces in the regions where the disturbing
action of Jupiter would by Lagrange’s principle (chapter XI., § 243)
be most effective: for instance, at a distance from the sun about
five-eighths that of Jupiter, a planet would by Kepler’s law revolve
exactly _twice_ as fast as Jupiter; and accordingly there is a gap
among the minor planets at about this distance.
[Illustration: FIG. 89.—Paths of minor planets.]
Estimates of the sizes and masses of the minor planets are still very
uncertain. The first direct measurement of any of the discs which
seem reliable are those of Professor _E. E. Barnard_, made at the Lick
Observatory in 1894 and 1895; according to these the three largest
minor planets, Ceres, Pallas, and Vesta, have diameters of nearly 500
miles, about 300 and about 250 miles respectively. Their sizes compared
with the moon are shewn on the diagram (fig. 90). An alternative
method—the only one available except for a few of the very largest of
the minor planets—is to measure the amount of light received, and hence
to deduce the size, on the assumption that the reflective power is the
same as that of some known planet. This method gives diameters of about
300 miles for the brightest and of about a dozen miles for the faintest
known.
[Illustration: FIG. 90.—Comparative sizes of three minor planets and
the moon.]
Leverrier calculated from the perturbations of Mars that the total
mass of all known or unknown bodies between Mars and Jupiter could not
exceed a fourth that of the earth; but such knowledge of the sizes as
we can derive from light-observations seems to indicate that the total
mass of those at present known is many hundred times less than this
limit.
295. Neptune and the minor planets are the only planets which have been
discovered during this century, but several satellites have been added
to our system.
[Illustration: FIG. 91.—Saturn and its system.]
Barely a fortnight after the discovery of Neptune (1846) a satellite
was detected by _William Lassell_ (1799-1880) at Liverpool. Like the
satellites of Uranus, this revolves round its primary from east to
west—that is, in the direction contrary to that of all the other known
motions of the solar system (certain long-period comets not being
counted).
[Illustration: FIG. 92.—Mars and its satellites.]
Two years later (September 16th, 1848) _William Cranch Bond_
(1789-1859) discovered, at the Harvard College Observatory, an,
eighth satellite of Saturn, called _Hyperion_, which was detected
independently by Lassell two days afterwards. In the following year
Bond discovered that Saturn was accompanied by a third comparatively
dark ring-now commonly known as the =crape ring=—lying immediately
inside the bright rings (see fig. 95); and the discovery was made
independently a fortnight later by _William Rutter Dawes_ (1799-1868)
in England. Lassell discovered in 1851 two new satellites of Uranus,
making a total of four belonging to that planet. The next discoveries
were those of two satellites of Mars, known as _Deimos_ and _Phobos_,
by Professor _Asaph Hall_ of Washington on August 11th and 17th, 1877.
These are remarkable chiefly for their close proximity to Mars and
their extremely rapid motion, the nearer one revolving more rapidly
than Mars rotates, so that to the Martians it must rise in the west
and set in the east. Lastly, Jupiter’s system received an addition
after nearly three centuries by Professor Barnard’s discovery at the
Lick Observatory (September 9th, 1892) of an extremely faint fifth
satellite, a good deal nearer to Jupiter than the nearest of Galilei’s
satellites (chapter VI., § 121).
[Illustration: FIG. 93.—Jupiter and its satellites.]
296. The surfaces of the various planets and satellites have been
watched with the utmost care by an army of observers, but the
observations have to a large extent remained without satisfactory
interpretation, and little is known of the structure or physical
condition of the bodies concerned.
[Illustration: FIG. 94.—The Apennines and adjoining regions of the
moon. From a photograph taken at the Paris Observatory.]
Astronomers are naturally most familiar with the surface of our
nearest neighbour, the moon. The visible half has been elaborately
mapped, and the heights of the chief mountain ranges measured by means
of their shadows. Modern knowledge has done much to dispel the view,
held by the earlier telescopists and shared to some extent even by
Herschel, that the moon closely resembles the earth and is suitable for
inhabitants like ourselves. The dark spaces which were once taken to
be seas and still bear that name are evidently covered with dry rock;
and the craters with which the moon is covered are all—with one or
two doubtful exceptions—extinct; the long dark lines known as =rills=
and formerly taken for river-beds have clearly no water in them. The
question of a lunar atmosphere is more difficult: if there is air its
density must be very small, some hundredfold less than that of our
atmosphere at the surface of the earth; but with this restriction
there seems to be no bar to the existence of a lunar atmosphere
of considerable extent, and it is difficult to explain certain
observations without assuming the existence of some atmosphere.
297. Mars, being the nearest of the superior planets, is the most
favourably situated for observation. The chief markings on its
surface—provisionally interpreted as being land and water—are fairly
permanent and therefore recognisable; several tolerably consistent maps
of the surface have been constructed; and by observation of certain
striking features the rotation period has been determined to a fraction
of a second. Signor _Schiaparelli_ of Milan detected at the opposition
of 1877 a number of intersecting dark lines generally known as
=canals=, and as the result of observations made during the opposition
of 1881-82 announced that certain of them appeared doubled, two nearly
parallel lines being then seen instead of one. These remarkable
observations have been to a great extent confirmed by other observers,
but remain unexplained.
The visible surfaces of Jupiter and Saturn appear to be layers of
clouds; the low density of each planet (1·3 and ·7 respectively, that
of water being 1 and of the earth 5·5), the rapid changes on the
surface, and other facts indicate that these planets are to a great
extent in a fluid condition, and have a high temperature at a very
moderate distance below the visible surface. The surface markings are
in each case definite enough for the rotation periods to be fixed with
some accuracy; though it is clear in the case of Jupiter, and probably
also in that of Saturn, that—as with the sun (§ 298)—different parts of
the surface move at different rates.
Laplace had shewn that Saturn’s ring (or rings) could not be, as it
appeared, a uniform solid body; he rashly inferred—without any complete
investigation—that it might be an irregularly weighted solid body. The
first important advance was made by _James Clerk Maxwell_ (1831-1879),
best known as a writer on electricity and other branches of physics.
Maxwell shewed (1857) that the rings could neither be continuous solid
bodies nor liquid, but that all the important dynamical conditions
would be satisfied if they were made up of a very large number of
small solid bodies revolving independently round the sun.[167] The
theory thus suggested on mathematical grounds has received a good deal
of support from telescopic evidence. The rings thus bear to Saturn
a relation having some analogy to that which the minor planets bear
to the sun; and Kirkwood pointed out in 1867 that Cassini’s division
between the two main rings can be explained by the perturbations due to
certain of the satellites, just as the corresponding gaps in the minor
planets can be explained by the action of Jupiter (§ 294).
The great distance of Uranus and Neptune naturally makes the study
of them difficult, and next to nothing is known of the appearance or
constitution of either; their rotation periods are wholly uncertain.
[Illustration: FIG. 95.—Saturn and its rings. From a drawing by
Professor Barnard.]
Mercury and Venus, being inferior planets, are never very far from
the sun in the sky, and therefore also extremely difficult to observe
satisfactorily. Various bright and dark markings on their surfaces have
been recorded, but different observers give very different accounts of
them. The rotation periods are also very uncertain, though a good many
astronomers support the view put forward by Sig. Schiaparelli, in 1882
and 1890 for Mercury and Venus respectively, that each rotates in a
time equal to its period of revolution round the sun, and thus always
turns the same face towards the sun. Such a motion—which is analogous
to that of the moon round the earth and of Japetus round Saturn
(chapter XII., § 267)—could be easily explained as the result of tidal
action at some past time when the planets were to a great extent fluid.
[Illustration: FIG. 96.—A group of sun-spots. From a photograph taken
by M. Janssen at Meudon on April 1st, 1894.]
298. Telescopic study of the surface of the sun during the century
has resulted in an immense accumulation of detailed knowledge of
peculiarities of the various markings on the surface. The most
interesting results of a general nature are connected with the
distribution and periodicity of sun-spots. The earliest telescopists
had noticed that the number of spots visible on the sun varied from
time to time, but no law of variation was established till 1851, when
_Heinrich Schwabe_ of Dessau (1789-1875) published in Humboldt’s
_Cosmos_ the results of observations of sun-spots carried out during
the preceding quarter of a century, shewing that the number of spots
visible increased and decreased in a tolerably regular way in a period
of about ten years.
Earlier records and later observations have confirmed the general
result, the period being now estimated as slightly over 11 years on
the average, though subject to considerable fluctuations. A year later
(1852) three independent investigators, Sir _Edward Sabine_ (1788-1883)
in England, _Rudolf Wolf_ (1816-1893) and _Alfred Gautier_ (1793-1881)
in Switzerland, called attention to the remarkable similarity
between the periodic variations of sun-spots and of various magnetic
disturbances on the earth. Not only is the period the same, but it
almost invariably happens that when spots are most numerous on the
sun magnetic disturbances are most noticeable on the earth, and that
similarly the times of scarcity of the two sets of phenomena coincide.
This wholly unexpected and hitherto quite unexplained relationship
has been confirmed by the occurrence on several occasions of decided
magnetic disturbances simultaneously with rapid changes on the surface
of the sun.
A long series of observations of the position of spots on the sun
undertaken by _Richard Christopher Carrington_ (1826-1875) led to the
first clear recognition of the difference in the rate of rotation
of the different parts of the surface of the sun, the period of
rotation being fixed (1859) at about 25 days at the equator, and two
and a half days longer half-way between the equator and the poles;
while in addition spots were seen to have also independent “proper
motions.” Carrington also established (1858) the scarcity of spots in
the immediate neighbourhood of the equator, and confirmed statistically
their prevalence in the adjacent regions, and their great scarcity more
than about 35° from the equator; and noticed further certain regular
changes in the distribution of spots on the sun in the course of the
11-year cycle.
Wilson’s theory (chapter XII., § 268) that spots are depressions
was confirmed by an extensive series of photographs taken at Kew in
1858-72, shewing a large preponderance of cases of the perspective
effect noticed by him; but, on the other hand, Mr. _F. Howlett_,
who has watched the sun for some 35 years and made several thousand
drawings of spots, considers (1894) that his observations are decidedly
against Wilson’s theory. Other observers are divided in opinion.
299. =Spectrum analysis=, which has played such an important part in
recent astronomical work, is essentially a method of ascertaining the
nature of a body by a process of sifting or analysing into different
components the light received from it.
It was first clearly established by Newton, in 1665-66 (chapter IX., §
168), that ordinary white light, such as sunlight, is composite, and
that by passing a beam of sunlight—with proper precautions—through a
glass prism it can be decomposed into light of different colours; if
the beam so decomposed is received on a screen, it produces a band of
colours known as a =spectrum=, red being at one end and violet at the
other.
[Illustration: FIG. 97.—Fraunhofer’s map of the solar spectrum. (The
red end of the spectrum is on the left, the violet on the right.)]
Now according to modern theories light consists essentially of a series
of disturbances or waves transmitted at extremely short but regular
intervals from the luminous object to the eye, the medium through
which the disturbances travel being called =ether=. The most important
characteristic distinguishing different kinds of light is the interval
of time or space between one wave and the next, which is generally
expressed by means of =wave-length=, or the distance between any point
of one wave and the corresponding point of the next. Differences in
wave-length shew themselves most readily as differences of colour;
so that light of a particular colour found at a particular part of
the spectrum has a definite wave-length. At the extreme violet end of
the spectrum, for example, the wave-length is about fifteen millionths
of an inch, at the red end it is about twice as great; from which it
follows (§ 283), from the known velocity of light, that when we look
at the red end of a spectrum about 400 billion waves of light enter
the eye per second, and twice that number when we look at the other
end. Newton’s experiment thus shews that a prism sorts out light of a
composite nature according to the wave-length of the different kinds
of light present. The same thing can be done by substituting for the
prism a so-called =diffraction-grating=, and this is for many purposes
superseding the prism. In general it is necessary, to ensure purity
in the spectrum and to make it large enough, to admit light through a
narrow slit, and to use certain lenses in combination with one or more
prisms or a grating; and the arrangement is such that the spectrum is
not thrown on to a screen, but either viewed directly by the eye or
photographed. The whole apparatus is known as a =spectroscope=.
The solar spectrum appeared to Newton as a continuous band of colours;
but in 1802 _William Hyde Wollaston_ (1766-1828) observed certain dark
lines running across the spectrum, which he took to be the boundaries
of the natural colours. A few years later (1814-15) the great Munich
optician _Joseph Fraunhofer_ (1787-1826) examined the sun’s spectrum
much more carefully, and discovered about 600 such dark lines, the
positions of 324 of which he mapped (see fig. 97). These dark lines are
accordingly known as =Fraunhofer lines=: for purposes of identification
Fraunhofer attached certain letters of the alphabet to a few of the
most conspicuous; the rest are now generally known by the wave-length
of the corresponding kind of light.
It was also gradually discovered that dark bands could be produced
artificially in spectra by passing light through various coloured
substances; and that, on the other hand, the spectra of certain flames
were crossed by various _bright_ lines.
Several attempts were made to explain and to connect these various
observations, but the first satisfactory and tolerably complete
explanation was given in 1859 by _Gustav Robert Kirchhoff_ (1824-1887)
of Heidelberg, who at first worked in co-operation with the chemist
Bunsen.
Kirchhoff shewed that a luminous solid or liquid—or, as we now know, a
highly compressed gas—gives a continuous spectrum; whereas a substance
in the gaseous state gives a spectrum consisting of bright lines
(with or without a faint continuous spectrum), and these bright lines
depend on the particular substance and are characteristic of it.
Consequently the presence of a particular substance in the form of gas
in a hot body can be inferred from the presence of its characteristic
lines in the spectrum of the light. The _dark_ lines in the solar
spectrum were explained by the fundamental principle—often known as
Kirchhoff’s law—that a body’s capacity for stopping or absorbing light
of a particular wave-length is proportional to its power, under like
conditions, of giving out the same light. If, in particular, light from
a luminous solid or liquid body, giving a continuous spectrum, passes
through a gas, the gas absorbs light of the same wave-length as that
which it itself gives out: if the gas gives out more light of these
particular wave-lengths than it absorbs, then the spectrum is crossed
by the corresponding bright lines; but if it absorbs more than it gives
out, then there is a deficiency of light of these wave-lengths and the
corresponding parts of the spectrum appear dark—that is, the spectrum
is crossed by dark lines in the same position as the bright lines in
the spectrum of the gas alone. Whether the gas absorbs more or less
than it gives out is essentially a question of temperature, so that
if light from a hot solid or liquid passes through a gas at a higher
temperature a spectrum crossed by bright lines is the result, whereas
if the gas is cooler than the body behind it dark lines are seen in the
spectrum.
300. The presence of the Fraunhofer lines in the spectrum of the sun
shews that sunlight comes from a hot solid or liquid body (or from a
highly compressed gas), and that it has passed through cooler gases
which have absorbed light of the wave-lengths corresponding to the dark
lines. These gases must be either round the sun or in our atmosphere:
and it is not difficult to shew that, although some of the Fraunhofer
lines are due to our atmosphere, the majority cannot be, and are
therefore caused by gases in the atmosphere of the sun.
For example, the metal sodium when vaporised gives a spectrum
characterised by two nearly coincident bright lines in the yellow
part of the spectrum; these agree in position with a pair of dark
lines (known as D) in the spectrum of the sun (see fig. 97); Kirchhoff
inferred therefore that the atmosphere of the sun contains sodium. By
comparison of the dark lines in the spectrum of the sun with the bright
lines in the spectra of metals and other substances, their presence
or absence in the solar atmosphere can accordingly be ascertained. In
the case of iron—which has an extremely complicated spectrum—Kirchhoff
succeeded in identifying 60 lines (since increased to more than 2,000)
in its spectrum with dark lines in the spectrum of the sun. Some
half-dozen other known elements were also identified by Kirchhoff in
the sun.
The inquiry into solar chemistry thus started has since been prosecuted
with great zeal. Improved methods and increased care have led to the
construction of a series of maps of the solar spectrum, beginning
with Kirchhoff’s own, published in 1861-62, of constantly increasing
complexity and accuracy. Knowledge of the spectra of the metals has
also been greatly extended. At the present time between 30 and 40
elements have been identified in the sun, the most interesting besides
those already mentioned being hydrogen, calcium, magnesium, and carbon.
The first spectroscopic work on the sun dealt only with the light
received from the sun as a whole, but it was soon seen that by throwing
an image of the sun on to the slit of the spectroscope by means of a
telescope the spectrum of a particular part of the sun’s surface, such
as a spot or a facula, could be obtained; and an immense number of
observations of this character have been made.
301. Observations of total eclipses of the sun have shewn that the
bright surface of the sun as we ordinarily see it is not the whole,
but that outside this there is an envelope of some kind too faint to
be seen ordinarily but becoming visible when the intense light of
the sun itself is cut off by the moon. A white halo of considerable
extent round the eclipsed sun, now called the =corona=, is referred to
by Plutarch, and discussed by Kepler (chapter VII., § 145) Several
18th century astronomers noticed a red streak along some portion of
the common edge of the sun and moon, and red spots or clouds here
and there (cf. chapter X., § 205). But little serious attention was
given to the subject till after the total solar eclipse of 1842.
Observations made then and at the two following eclipses of 1851 and
1860, in the latter of which years photography was for the first time
effectively employed, made it evident that the red streak represented
a continuous envelope of some kind surrounding the sun, to which the
name of =chromosphere= has been given, and that the red objects,
generally known as =prominences=, were in general projecting parts of
the chromosphere, though sometimes detached from it. At the eclipse of
1868 the spectrum of the prominences and the chromosphere was obtained,
and found to be one of bright lines, shewing that they consisted of
gas. Immediately afterwards M. _Janssen_, who was one of the observers
of the eclipse, and Sir _J. Norman Lockyer_ independently devised a
method whereby it was possible to get the spectrum of a prominence at
the edge of the sun’s disc in ordinary daylight, without waiting for an
eclipse; and a modification introduced by Sir _William Huggins_ in the
following year (1869) enabled the form of a prominence to be observed
spectroscopically. Recently (1892) Professor _G. E. Hale_ of Chicago
has succeeded in obtaining by a photographic process a representation
of the whole of the chromosphere and prominences, while the same method
gives also photographs of faculae (chapter VIII., § 153) on the visible
surface of the sun.
The most important lines ordinarily present in the spectrum of the
chromosphere are those of hydrogen, two lines (H and K) which have
been identified with some difficulty as belonging to calcium, and a
yellow line the substance producing which, known as =helium=, has only
recently (1895) been discovered on the earth. But the chromosphere when
disturbed and many of the prominences give spectra containing a number
of other lines.
[Illustration: FIG. 98.—The total solar eclipse of August 29th, 1886.
From a drawing based on photographs by Dr. Schuster and Mr. Maunder.]
The corona was for some time regarded as of the nature of an optical
illusion produced in the atmosphere. That it is, at any rate in great
part, an actual appendage of the sun was first established in 1869 by
the American astronomers Professor _Harkness_ and Professor _C.
A. Young_, who discovered a bright line—of unknown origin[168]—in
its spectrum, thus shewing that it consists in part of glowing gas.
Subsequent spectroscopic work shews that its light is partly reflected
sunlight.
The corona has been carefully studied at every solar eclipse during
the last 30 years, both with the spectroscope and with the telescope,
supplemented by photography, and a number of ingenious theories of its
constitution have been propounded; but our present knowledge of its
nature hardly goes beyond Professor Young’s description of it as “an
inconceivably attenuated cloud of gas, fog, and dust, surrounding the
sun, formed and shaped by solar forces.”
302. The spectroscope also gives information as to certain motions
taking place on the sun. It was pointed out in 1842 by _Christian
Doppler_ (1803-1853), though in an imperfect and partly erroneous way,
that if a luminous body is approaching the observer, or _vice versa_,
the waves of light are as it were crowded together and reach the eye at
shorter intervals than if the body were at rest, and that the character
of the light is thereby changed. The colour and the position in the
spectrum both depend on the interval between one wave and the next, so
that if a body giving out light of a particular wave-length, _e.g._
the blue light corresponding to the F line of hydrogen, is approaching
the observer rapidly, the line in the spectrum appears slightly on
one side of its usual position, being displaced towards the violet
end of the spectrum; whereas if the body is receding the line is, in
the same way, displaced in the opposite direction. This result is
usually known as =Doppler’s principle=. The effect produced can easily
be expressed numerically. If, for example, the body is approaching
with a speed equal to 1∕1000 of light, then 1001 waves enter the eye
or the spectroscope in the same time in which there would otherwise
only be 1000; and there is in consequence a virtual shortening of the
wave-length in the ratio of 1001 to 1000. So that if it is found that a
line in the spectrum of a body is displaced from its ordinary position
in such a way that its wave-length is apparently decreased by 1∕1000
part, it may be inferred that the body is approaching with the speed
just named, or about 186 miles per second, and if the wave-length
appears increased by the same amount (the line being displaced towards
the red end of the spectrum) the body is receding at the same rate.
Some of the earliest observations of the prominences by Sir J. N.
Lockyer (1868), and of spots and other features of the sun by the same
and other observers, shewed displacements and distortions of the lines
in the spectrum, which were soon seen to be capable of interpretation
by this method, and pointed to the existence of violent disturbances in
the atmosphere of the sun, velocities as great as 300 miles per second
being not unknown. The method has received an interesting confirmation
from observations of the spectrum of opposite edges of the sun’s
disc, of which one is approaching and the other receding owing to the
rotation of the sun. Professor _Dunér_ of Upsala has by this process
ascertained (1887-89) the rate of rotation of the surface of the sun
beyond the regions where spots exist, and therefore outside the limits
of observations such as Carrington’s (§ 298).
303. The spectroscope tells us that the atmosphere of the sun contains
iron and other metals in the form of vapour; and the photosphere,
which gives the continuous part of the solar spectrum, is certainly
hotter. Moreover everything that we know of the way in which heat is
communicated from one part of a body to another shews that the outer
regions of the sun, from which heat and light are radiating on a very
large scale, must be the coolest parts, and that the temperature in
all probability rises very rapidly towards the interior. These facts,
coupled with the low density of the sun (about a fourth that of the
earth) and the violently disturbed condition of the surface, indicate
that the bulk of the interior of the sun is an intensely hot and highly
compressed mass of gas. Outside this come in order, their respective
boundaries and mutual relations being, however, very uncertain,
first the photosphere, generally regarded as a cloud-layer, then the
=reversing stratum= which produces most of the Fraunhofer lines, then
the chromosphere and prominences, and finally the corona. Sun-spots,
faculae, and prominences have been explained in a variety of
different ways as joint results of solar disturbances of various kinds;
but no detailed theory that has been given explains satisfactorily more
than a fraction of the observed facts or commands more than a very
limited amount of assent among astronomical experts.
[Illustration: FIG. 99.—The great comet of 1882 (ii) on November 7th.
From a photograph by Dr. Gill.]
304. More than 200 comets have been seen during the present century;
not only have the motions of most of them been observed and their
orbits computed (§ 291), but in a large number of cases the appearance
and structure of the comet have been carefully observed telescopically,
while latterly spectrum analysis and photography have also been
employed.
Independent lines of inquiry point to the extremely unsubstantial
character of a comet, with the possible exception of the bright central
part or =nucleus=, which is nearly always present. More than once,
as in 1767 (chapter XI., § 248), a comet has passed close to some
member of the solar system, and has never been ascertained to affect
its motion. The mass of a comet is therefore very small, but its bulk
or volume, on the other hand, is in general very great, the tail
often being millions of miles in length; so that the density must be
extremely small. Again, stars have often been observed shining through
a comet’s tail (as shewn in fig. 99), and even through the head at no
great distance from the nucleus, their brightness being only slightly,
if at all, affected. Twice at least (1819, 1861) the earth has passed
through a comet’s tail, but we were so little affected that the fact
was only discovered by calculations made after the event. The early
observation (chapter III., § 69) that a comet’s tail points away from
the sun has been abundantly verified; and from this it follows that
very rapid changes in the position of the tail must occur in some
cases. For example, the comet of 1843 passed very close to the sun at
such a rate that in about two hours it had passed from one side of the
sun to the opposite; it was then much too near the sun to be seen, but
if it followed the ordinary law its tail, which was unusually long,
must have entirely reversed its direction within this short time. It
is difficult to avoid the inference that the tail is not a permanent
part of the comet, but is a stream of matter driven off from it in
some way by the action of the sun, and in this respect comparable with
the smoke issuing from a chimney. This view is confirmed by the fact
that the tail is only developed when the comet approaches the sun,
a comet when at a great distance from the sun appearing usually as
an indistinct patch of nebulous light, with perhaps a brighter spot
representing the nucleus. Again, if the tail be formed by an outpouring
of matter from the comet, which only takes place when the comet is
near the sun, the more often a comet approaches the sun the more must
it waste away; and we find accordingly that the short-period comets,
which return to the neighbourhood of the sun at frequent intervals (§
291), are inconspicuous bodies. The same theory is supported by the
shape of the tail. In some cases it is straight, but more commonly it
is curved to some extent, and the curvature is then always _backwards_
in relation to the comet’s motion. Now by ordinary dynamical principles
matter shot off from the head of the comet while it is revolving round
the sun would tend, as it were, to lag behind more and more the farther
it receded from the head, and an apparent backward curvature of the
tail—less or greater according to the speed with which the particles
forming the tail were repelled—would be the result. Variations in
curvature of the tails of different comets, and the existence of two
or more differently curved tails of the same comet, are thus readily
explained by supposing them made of different materials, repelled from
the comet’s head at different speeds.
The first application of the spectroscope to the study of comets was
made in 1864 by _Giambattista Donati_ (1826-1873), best known as the
discoverer of the magnificent comet of 1858. A spectrum of three bright
bands, wider than the ordinary “lines,” was obtained, but they were
not then identified. Four years later Sir William Huggins obtained a
similar spectrum, and identified it with that of a compound of carbon
and hydrogen. Nearly every comet examined since then has shewn in its
spectrum bright bands indicating the presence of the same or some
other hydrocarbon, but in a few cases other substances have also been
detected. A comet is therefore in part at least self-luminous, and some
of the light which it sends us is that of a glowing gas. It also shines
to a considerable extent by reflected sunlight; there is nearly always
a continuous spectrum, and in a few cases—first in 1881—the spectrum
has been distinct enough to shew the Fraunhofer lines crossing it. But
the continuous spectrum seems also to be due in part to solid or liquid
matter in the comet itself, which is hot enough to be self-luminous.
305. The work of the last 30 or 40 years has established a remarkable
relation between comets and the minute bodies which are seen in the
form of =meteors= or =shooting stars=. Only a few of the more important
links in the chain of evidence can, however, be mentioned. Showers of
shooting stars, the occurrence of which has been known from quite early
times, have been shewn to be due to the passage of the earth through a
swarm of bodies revolving in elliptic orbits round the sun. The paths
of four such swarms were ascertained with some precision in 1866-67,
and found in each case to agree closely with the paths of known comets.
And since then a considerable number of other cases of resemblance or
identity between the paths of meteor swarms and of comets have been
detected. One of the four comets just referred to, known as Biela’s,
with a period of between six and seven years, was duly seen on several
successive returns, but in 1845-46 was observed first to become
somewhat distorted in shape, and afterwards to have divided into two
distinct comets; at the next return (1852) the pair were again seen;
but since then nothing has been seen of either portion. At the end of
November in each year the earth almost crosses the path of this comet,
and on two occasions (1872, and 1885) it did so nearly at the time when
the comet was due at the same spot; if, as seemed likely, the comet had
gone to pieces since its last appearance, there seemed a good chance of
falling in with some of its remains, and this expectation was fulfilled
by the occurrence on both occasions of a meteor shower much more
brilliant than that usually observed at the same date.
Biela’s comet is not the only comet which has shewn signs of breaking
up; Brooks’s comet of 1889, which is probably identical with Lexell’s
(chapter XI., § 248), was found to be accompanied by three smaller
companions; as this comet has more than once passed extremely close to
Jupiter, a plausible explanation of its breaking up is at once given
in the attractive force of the planet. Moreover certain systems of
comets, the members of which revolve in the same orbit but separated by
considerable intervals of time, have also been discovered. Tebbutt’s
comet of 1881 moves in practically the same path as one seen in 1807,
and the great comet of 1880, the great comet of 1882 (shewn in fig.
99), and a third which appeared in 1887, all move in paths closely
resembling that of the comet of 1843, while that of 1668 is more
doubtfully connected with the same system. And it is difficult to avoid
regarding the members of a system as fragments of an earlier comet,
which has passed through the stages in which we have actually seen the
comets of Biela and Brooks.
Evidence of such different kinds points to an intimate connection
between comets and meteors, though it is perhaps still premature to
state confidently that meteors are fragments of decayed comets, or that
conversely comets are swarms of meteors.
306. Each of the great problems of sidereal astronomy which Herschel
formulated and attempted to solve has been elaborately studied by the
astronomers of the 19th century. The multiplication of observatories,
improvements in telescopes, and the introduction of photography—to
mention only three obvious factors of progress—have added enormously
to the extent and accuracy of our knowledge of the stars, while the
invention of spectrum analysis has thrown an entirely new light on
several important problems.
William Herschel’s most direct successor was his son _John Frederick
William_ (1792-1871), who was not only an astronomer, but also made
contributions of importance to pure mathematics, to physics, to the
nascent art of photography, and to the philosophy of scientific
discovery. He began his astronomical career about 1816 by re-measuring,
first alone, then in conjunction with _James South_ (1785-1867), a
number of his father’s double stars. The first result of this work was
a catalogue, with detailed measurements, of some hundred double and
multiple stars (published in 1824), which formed a valuable third term
of comparison with his father’s observations of 1781-82 and 1802-03,
and confirmed in several cases the slow motions of revolution the
beginnings of which had been observed before. A great survey of nebulae
followed, resulting in a catalogue (1833) of about 2500, of which
some 500 were new and 2000 were his father’s, a few being due to other
observers; incidentally more than 3000 pairs of stars close enough
together to be worth recording as double stars were observed.
[Illustration]
307. Then followed his well-known expedition to the Cape of Good Hope
(1833-1838), where he “swept” the southern skies in very much the
same way in which his father had explored the regions visible in our
latitude. Some 1200 double and multiple stars, and a rather larger
number of new nebulae, were discovered and studied, while about 500
known nebulae were re-observed; star-gauging on William Herschel’s
lines was also carried out on an extensive scale. A number of special
observations of interest were made almost incidentally during this
survey: the remarkable variable star η _Argus_ and the nebula
surrounding it (a modern photograph of which is reproduced in fig.
100), the wonderful collections of nebulae clusters and stars, known as
the _Nubeculae_ or _Magellanic Clouds_, and Halley’s comet were studied
in turn; and the two faintest satellites of Saturn then known (chapter
XII., § 255) were seen again for the first time since the death of
their discoverer.
An important investigation of a somewhat different character—that
of the amount of heat received from the sun—was also carried out
(1837) during Herschel’s residence at the Cape; and the result agreed
satisfactorily with that of an independent inquiry made at the same
time in France by _Claude Servais Mathias Pouillet_ (1791-1868). In
both cases the heat received on a given area of the earth in a given
time from direct sunshine was measured; and allowance being made for
the heat stopped in the atmosphere as the sun’s rays passed through it,
an estimate was formed of the total amount of heat received annually by
the earth from the sun, and hence of the total amount radiated by the
sun in all directions, an insignificant fraction of which (one part in
2,000,000,000) is alone intercepted by the earth. But the allowance for
the heat intercepted in our atmosphere was necessarily uncertain, and
later work, in particular that of Dr. _S. P. Langley_ in 1880-81, shews
that it was very much under-estimated by both Herschel and Pouillet.
According to Herschel’s results, the heat received annually from the
sun—including that intercepted in the atmosphere—would be sufficient
to melt a shell of ice 120 feet thick covering the whole earth;
according to Dr. Langley, the thickness would be about 160 feet.[169]
308. With his return to England in 1838 Herschel’s career as an
observer came to an end; but the working out of the results of his
Cape observations, the arrangement and cataloguing of his own and his
father’s discoveries, provided occupation for many years. A magnificent
volume on the _Results of Astronomical Observations made during
the years 1834-8 at the Cape of Good Hope_ appeared in 1847; and a
catalogue of all known nebulae and clusters, amounting to 5,079, was
presented to the Royal Society in 1864, while a corresponding catalogue
of more than 10,000 double and multiple stars was never finished,
though the materials collected for it were published posthumously in
1879. John Herschel’s great catalogue of nebulae has since been revised
and enlarged by Dr. _Dreyer_, the result being a list of 7,840 nebulae
and clusters known up to the end of 1887; and a supplementary list
of discoveries made in 1888-94 published by the same writer contains
1,529 entries, so that the total number now known is between 9,000
and 10,000, of which more than half have been discovered by the two
Herschels.
309. Double stars have been discovered and studied by a number of
astronomers besides the Herschels. One of the most indefatigable
workers at this subject was the elder Struve (§ 279), who was
successively director of the two Russian observatories of Dorpat and
Pulkowa. He observed altogether some 2,640 double and multiple stars,
measuring in each case with care the length and direction of the line
joining the two components, and noting other peculiarities, such as
contrasts in colour between the members of a pair. He paid attention
only to double stars the two components of which were not more than
32″ apart, thus rejecting a good many which William Herschel would
have noticed; as the number of known doubles rapidly increased, it was
clearly necessary to concentrate attention on those which might with
some reasonable degree of probability turn out to be genuine binaries
(chapter XII., § 264).
In addition to a number of minor papers Struve published three separate
books on the subject in 1827, 1837, and 1852.[170] A comparison of
his own earlier and later observations, and of both with Herschel’s
earlier ones, shewed about 100 cases of change of relative positions of
two members of a pair, which indicated more or less clearly a motion
of revolution, and further results of a like character have been
obtained from a comparison of Struve’s observations with those of later
observers.
[Illustration:
FIG. 101.—The orbit of ξ _Ursae_, shewing the relative positions
of the two components at various times between 1781 and 1897, (The
observations of 1781 and 1802 were only enough to determine the
direction of the line joining the two components, not its length.)]
William Herschel’s observations of binary systems (chapter XII., § 264)
only sufficed to shew that a motion of revolution of some kind appeared
to be taking place; it was an obvious conjecture that the two members
of a pair attracted one another according to the law of gravitation,
so that the motion of revolution was to some extent analogous to that
of a planet round the sun; if this were the case, then each star of a
pair should describe an ellipse (or conceivably some other conic) round
the other, or each round the common centre of gravity, in accordance
with Kepler’s laws, and the apparent path as seen on the sky should be
of this nature but in general foreshortened by being projected on to
the celestial sphere. The first attempt to shew that this was actually
the case was made by ξ _Ursae_, which was found to be revolving in a
period of about 60 years.
Many thousand double stars have been discovered by the Herschels,
Struve, and a number of other observers, including several living
astronomers, among whom Professor _S. W. Burnham_ of Chicago, who
has discovered some 1300, holds a leading place. Among these stars
there are about 300 which we have fair reason to regard as binary,
but not more than 40 or 50 of the orbits can be regarded as at all
satisfactorily known. One of the most satisfactory is that of Savary’s
star ξ _Ursae_, which is shewn in fig. 101. Apart from the binaries
discovered by the spectroscopic method (§ 314), which form to some
extent a distinct class, the periods of revolution which have been
computed range between about ten years and several centuries, the
longer periods being for the most part decidedly uncertain.
310. William Herschel’s telescopes represented for some time the utmost
that could be done in the construction of reflectors; the first advance
was made by Lord _Rosse_ (1800-1867), who—after a number of less
successful experiments—finally constructed (1845), at Parsonstown in
Ireland, a reflecting telescope nearly 60 feet in length, with a mirror
which was six feet across, and had consequently a “light-grasp” more
than double that of Herschel’s greatest telescope. Lord Rosse used the
new instrument in the first instance to re-examine a number of known
nebulae, and in the course of the next few years discovered a variety
of new features, notably the spiral form of certain nebulae (fig. 102),
and the resolution into apparent star clusters of a number of nebulae
which Herschel had been unable to resolve and had accordingly
put into “the shining fluid” class (chapter XII., § 260). This last
discovery, being exactly analogous to Herschel’s experience when he
first began to examine nebulae hitherto only observed with inferior
telescopes, naturally led to a revival of the view that nebulae
are indistinguishable from clusters of stars, though many of the
arguments from probability urged by Herschel and others were in reality
unaffected by the new discoveries.
[Illustration: FIG. 102.—Spiral nebulae. From drawings by Lord Rosse.]
311. The question of the status of nebulae in its simplest form may
be said to have been settled by the first application of spectrum
analysis. Fraunhofer (§ 299) had seen as early as 1823 that stars had
spectra characterised like that of the sun by dark lines, and more
complete investigations made soon after Kirchhoff’s discoveries by
several astronomers, in particular by Sir William Huggins and by the
eminent Jesuit astronomer _Angelo Secchi_ (1818-1878), confirmed this
result as regards nearly all stars observed.
The first spectrum of a nebula was obtained by Sir William Huggins in
1864, and was seen to consist of three _bright_ lines; by 1868 he had
examined 70, and found in about one-third of the cases, including that
of the Orion nebula, a similar spectrum of bright lines. In these cases
therefore the luminous part of the nebula is gaseous, and Herschel’s
suggestion of a “shining fluid” was confirmed in the most satisfactory
way. In nearly all cases three bright lines are seen, one of which is a
hydrogen line, while the other two have not been identified, and in the
case of a few of the brighter nebulae some other lines have also been
seen. On the other hand, a considerable number of nebulae, including
many of those which appear capable of telescopic resolution into
star clusters, give a continuous spectrum, so that there is no clear
spectroscopic evidence to distinguish them from clusters of stars,
since the dark lines seen usually in the spectra of the latter could
hardly be expected to be visible in the case of such faint objects as
nebulae.
312. Stars have been classified, first by Secchi (1863), afterwards in
slightly different ways by others, according to the general arrangement
of the dark lines in their spectra; and some attempts have been made to
base on these differences inferences as to the relative “ages,” or at
any rate the stages of development, of different stars.
Many of the dark lines in the spectra of stars have been identified,
first by Sir William Huggins in 1864, with the lines of known
terrestrial elements, such as hydrogen, iron, sodium, calcium; so that
a certain identity between the materials of which our own earth is made
and that of bodies so remote as the fixed stars is thus established.
In addition to the classes of stars already mentioned, the spectroscope
has shewn the existence of an extremely interesting if rather
perplexing class of stars, falling into several subdivisions, which
seem to form a connecting link between ordinary stars and nebulae,
for, though indistinguishable telescopically from ordinary stars,
their spectra shew _bright_ lines either periodically or regularly. A
good many stars of this class are variable, and several “new” stars
which have appeared and faded away of late years have shewn similar
characteristics.
313. The first application to the fixed stars of the spectroscopic
method (§ 302) of determining motion towards or away from the observer
was made by Sir William Huggins in 1868. A minute displacement from its
usual position of a dark hydrogen line (F) in the spectrum of Sirius
was detected, and interpreted as shewing that the star was receding
from the solar system at a considerable speed. A number of other stars
were similarly observed in the following year, and the work has been
taken up since by a number of other observers, notably at Potsdam under
the direction of Professor _H. C. Vogel_, and at Greenwich.
[Illustration: FIG. 103.—The spectrum of β _Aurigae_, shewing the K
line single and double. From a photograph taken at Harvard.]
314. A very remarkable application of this method to binary stars has
recently been made. If two stars are revolving round one another, their
motions towards and away from the earth are changing regularly and
are different; hence, if the light from both stars is received in the
spectroscope, two spectra are formed—one for each star—the lines of
which shift regularly relatively to one another. If a particular line,
say the F line, common to the spectra of both stars, is observed when
both stars are moving towards (or away from) the earth at the same
rate—which happens twice in each revolution—only one line is seen; but
when they are moving differently, if the spectroscope be powerful
enough to detect the minute quantity involved, the line will appear
doubled, one component being due to one star and one to the other.
A periodic doubling of this kind was detected at the end of 1889 by
Professor _E. C. Pickering_ of Harvard in the case of ζ _Ursae_, which
was thus for the first time shewn to be binary, and found to have the
remarkably short period of only 104 days. This discovery was followed
almost immediately by Professor Vogel’s detection of a periodical shift
in the position of the dark lines in the spectrum of the variable
star Algol (chapter XII., § 266); but as in this case no doubling of
the lines can be seen, the inference is that the companion star is
nearly or quite dark, so that as the two revolve round one another the
spectrum of the bright star shifts in the manner observed. Thus the
eclipse-theory of Algol’s variability received a striking verification.
A number of other cases of both classes of spectroscopic binary stars
(as they may conveniently be called) have since been discovered. The
upper part of fig. 103 shews the doubling of one of the lines in the
spectrum of the double star β _Aurigae_; and the lower part shews the
corresponding part of the spectrum at a time when the line appeared
single.
315. Variable stars of different kinds have received a good deal of
attention during this century, particularly during the last few years.
About 400 stars are now clearly recognised as variable, while in a
large number of other cases variability of light has been suspected;
except, however, in a few cases, like that of Algol, the causes of
variability are still extremely obscure.
316. The study of the relative brightness of stars—a branch of
astronomy now generally known as stellar =photometry=—has also been
carried on extensively during the century and has now been put on
a scientific basis. The traditional classification of stars into
magnitudes, according to their brightness, was almost wholly arbitrary,
and decidedly uncertain. As soon as exact quantitative comparisons of
stars of different brightness began to be carried out on a considerable
scale, the need of a more precise system of classification became felt.
John Herschel was one of the pioneers in this direction; he suggested
a scale capable of precise expression, and agreeing roughly, at any
rate as far as naked-eye stars are concerned, with the current usages;
while at the Cape he measured carefully the light of a large number
of bright stars and classified them on this principle. According to
the scale now generally adopted, first suggested in 1856 by _Norman
Robert Pogson_ (1829-1891), the light of a star of any magnitude bears
a fixed ratio (which is taken to be 2·512 ...) to that of a star of
the next magnitude. The number is so chosen that a star of the sixth
magnitude—thus defined—is 100 times fainter than one of the first
magnitude.[171] Stars of intermediate brightness have magnitudes
expressed by fractions which can be at once calculated (according to a
simple mathematical rule) when the ratio of the light received from the
star to that received from a standard star has been observed.[172]
Most of the great star catalogues (§ 280) have included estimates of
the magnitudes of stars. The most extensive and accurate series of
measurements of star brightness have been those executed at Harvard
and at Oxford under the superintendence of Professor E. C. Pickering
and the late Professor Pritchard respectively. Both catalogues deal
with stars visible to the naked eye; the Harvard catalogue (published
in 1884) comprises 4,260 stars between the North Pole and 30° southern
declination, and the _Uranometria Nova Oxoniensis_ (1885), as it is
called, only goes 10° south of the equator and includes 2,784 stars.
Portions of more extensive catalogues dealing with fainter stars, in
progress at Harvard and at Potsdam, have also been published.
[Illustration: FIG. 104.—The Milky Way near the cluster in Perseus.
From a photograph by Professor Barnard.]
317. The great problem to which Herschel gave so much attention, that
of the general arrangement of the stars and the structure of the
system, if any, formed by them and the nebulae, has been affected in a
variety of ways by the additions which have been made to our knowledge
of the stars. But so far are we from any satisfactory solution of
the problem that no modern theory can fairly claim to represent the
facts now known to us as well as Herschel’s earlier theory fitted the
much scantier stock which he had at his command. In this as in so
many cases an increase of knowledge has shewn the insufficiency of a
previously accepted theory, but has not provided a successor. Detailed
study of the form of the Milky Way (cf. fig. 104) and of its relation
to the general body of stars has shewn the inadequacy of any simple
arrangement of stars to represent its appearance; William Herschel’s
cloven grindstone, the ring which his son was inclined to substitute
for it as the result of his Cape studies, and the more complicated
forms which later writers have suggested, alike fail to account for
its peculiarities. Again, such evidence as we have of the distance of
the stars, when compared with their brightness, shews that there are
large variations in their actual sizes as well as in their apparent
sizes, and thus tells against the assumption of a certain uniformity
which underlay much of Herschel’s work. The “island universe” theory
of nebulae, partially abandoned by Herschel after 1791 (chapter XII.,
§ 260), but brought into credit again by Lord Rosse’s discoveries
(§ 310), scarcely survived the spectroscopic proof of the gaseous
character of certain nebulae. Other evidence has pointed clearly to
intimate relations between nebulae and stars generally; Herschel’s
observation that nebulae are densest in regions farthest from the Milky
Way has been abundantly verified—as far as irresoluble nebulae are
concerned—while obvious star clusters shew an equally clear preference
for the neighbourhood of the Milky Way. In many cases again individual
stars or groups seen on the sky in or near a nebula have been clearly
shewn, either by their arrangement or in some cases by peculiarities of
their spectra, to be really connected with the nebula, and not merely
to be accidentally in the same direction. Stars which have bright
lines in their spectra (§ 312) form another link connecting nebulae
with stars.
A good many converging lines of evidence thus point to a greater
variety in the arrangement, size, and structure of the bodies with
which the telescope makes us acquainted than seemed probable when
sidereal astronomy was first seriously studied; they also indicate the
probability that these bodies should be regarded as belonging to a
single system, even if it be of almost inconceivable complexity, rather
than to a number of perfectly distinct systems of a simpler type.
318. Laplace’s nebular hypothesis (chapter XI., § 250) was published a
little more than a century ago (1796), and has been greatly affected by
progress in various departments of astronomical knowledge. Subsequent
discoveries of planets and satellites (§§ 294, 295) have marred to some
extent the uniformity and symmetry of the motions of the solar system
on which Laplace laid so much stress; but it is not impossible to give
reasonable explanations of the backward motions of the satellites
of the two most distant planets, and of the large eccentricity and
inclination of the paths of some of the minor planets, while apart
from these exceptions the number of bodies the motions of which have
the characteristics which Laplace pointed out has been considerably
increased. The case for some sort of common origin of the bodies of the
solar system has perhaps in this way gained as much as it has lost.
Again, the telescopic evidence which Herschel adduced (chapter XII., §
261) in favour of the existence of certain processes of condensation in
nebulae has been strengthened by later evidence of a similar character,
and by the various pieces of evidence already referred to which connect
nebulae with single stars and with clusters. The differences in the
spectra of stars also receive their most satisfactory explanation as
representing different stages of condensation of bodies of the same
general character.
319. An entirely new contribution to the problem has resulted from
certain discoveries as to the nature of heat, culminating in the
recognition (about 1840-50) of heat as only one form of what physicists
now call =energy=, which manifests itself also in the motion of
bodies, in the separation of bodies which attract one another, as
well as in various electrical, chemical, and other ways. With this
discovery was closely connected the general theory known as the
=conservation of energy=, according to which energy, though capable
of many transformations, can neither be increased nor decreased in
quantity. A body which, like the sun, is giving out heat and light is
accordingly thereby losing energy, and is like a machine doing work;
either then it is receiving energy from some other source to compensate
this loss or its store of energy is diminishing. But a body which goes
on indefinitely giving out heat and light without having its store of
energy replenished is exactly analogous to a machine which goes on
working indefinitely without any motive power to drive it; and both are
alike impossible.
The results obtained by John Herschel and Pouillet in 1836 (§ 307)
called attention to the enormous expenditure of the sun in the form of
heat, and astronomers thus had to face the problem of explaining how
the sun was able to go on radiating heat and light in this way. Neither
in the few thousand years of the past covered by historic records, nor
in the enormously great periods of which geologists and biologists take
account, is there any evidence of any important permanent alteration in
the amount of heat and light received annually by the earth from the
sun. Any theory of the sun’s heat must therefore be able to account
for the continual expenditure of heat at something like the present
rate for an immense period of time. The obvious explanation of the sun
as a furnace deriving its heat from combustion is found to be totally
inadequate when put to the test of figures, as the sun could in this
way be kept going at most for a few thousand years. The explanation
now generally accepted was first given by the great German physicist
_Hermann von Helmholtz_ (1821-1894) in a popular lecture in 1854. The
sun possesses an immense store of energy in the form of the mutual
gravitation of its parts; if from any cause it shrinks, a certain
amount of gravitational energy is necessarily lost and takes some
other form. In the shrinkage of the sun we have therefore a possible
source of energy. The precise amount of energy liberated by a definite
amount of shrinkage of the sun depends upon the internal distribution
of density in the sun, which is uncertain, but making any reasonable
assumption as to this we find that the amount of shrinking required to
supply the sun’s expenditure of heat would only diminish the diameter
by a few hundred feet annually, and would therefore be imperceptible
with our present telescopic power for centuries, while no earlier
records of the sun’s size are accurate enough to shew it. It is easy to
calculate on the same principles the amount of energy liberated by a
body like the sun in shrinking from an indefinitely diffused condition
to its present state, and from its present state to one of assigned
greater density; the result being that we can in this way account for
an expenditure of sun-heat at the present rate for a period to be
counted in millions of years in either past or future time, while if
the rate of expenditure was less in the remote past or becomes less in
the future the time is extended to a corresponding extent.
No other cause that has been suggested is competent to account for
more than a small fraction of the actual heat-expenditure of the sun;
the gravitational theory satisfies all the requirements of astronomy
proper, and goes at any rate some way towards meeting the demands of
biology and geology.
If then we accept it as provisionally established, we are led to the
conclusion that the sun was in the past larger and less condensed than
now, and by going sufficiently far back into the past we find it in a
condition not unlike the primitive nebula which Laplace presupposed,
with the exception that it need not have been hot.
320. A new light has been thrown on the possible development of the
earth and moon by Professor G. H. Darwin’s study of the effects of
tidal friction (cf. § 287 and §§ 292, 293). Since the tides increase
the length of the day and month and gradually repel the moon from
the earth, it follows that in the past the moon was nearer to the
earth than now, and that tidal action was consequently much greater.
Following out this clue. Professor Darwin found, by a series of
elaborate calculations published in 1879-81, strong evidence of a past
time when the moon was close to the earth, revolving round it in the
same time in which the earth rotated on its axis, which was then a
little over two hours. The two bodies, in fact, were moving as if they
were connected; it is difficult to avoid the probable inference that
at an earlier stage the two really were one, and that the moon is in
reality a fragment of the earth driven off from it by the too-rapid
spinning of the earth, or otherwise.
Professor Darwin has also examined the possibility of explaining in
a similar way the formation of the satellites of the other planets
and of the planets themselves from the sun, but the circumstances
of the moon-earth system turn out to be exceptional, and tidal
influence has been less effective in other cases, though it gives a
satisfactory explanation of certain peculiarities of the planets and
their satellites. More recently (1892) Dr. _See_ has applied a somewhat
similar line of reasoning to explain by means of tidal action the
development of double stars from an earlier nebulous condition.
Speaking generally, we may say that the outcome of the 19th century
study of the problem of the early history of the solar system has
been to discredit the details of Laplace’s hypothesis in a variety of
ways, but to establish on a firmer basis the general view that the
solar system has been formed by some process of condensation out of an
earlier very diffused mass bearing a general resemblance to one of the
nebulae which the telescope shews us, and that stars other than the
sun are not unlikely to have been formed in a somewhat similar way;
and, further, the theory of tidal friction supplements this general
but vague theory, by giving a rational account of a process which
seems to have been the predominant factor in the development of the
system formed by our own earth and moon, and to have had at any rate an
important influence in a number of other cases.
AUTHORITIES AND BOOKS FOR STUDENTS.
I. GENERAL.
I have made great use throughout of R. Wolf’s _Geschichte der
Astronomie_, and of the six volumes of Delambre’s _Histoire de
l’Astronomie_ (_Ancienne_, 2 vols.; _du Moyen Age_, 1 vol.; _Moderne_,
2 vols.; _du Dixhuitième Siècle_, 1 vol.). I shall subsequently
refer to these books simply as _Wolf_ and _Delambre_ respectively.
I have used less often the astronomical sections of Whewell’s
_History of the Inductive Sciences_ (referred to as _Whewell_), and
I am indebted—chiefly for dates and references—to the histories of
mathematics written respectively by Marie, W. W. R. Ball, and Cajori,
to Poggendorff’s _Handwörterbuch der Exacten Wissenschaften_, and
to articles in various biographical dictionaries, encyclopaedias,
and scientific journals. Of general treatises on astronomy Newcomb’s
_Popular Astronomy_, Young’s _General Astronomy_, and Proctor’s _Old
and New Astronomy_ have been the most useful for my purposes.
It is difficult to make a selection among the very large number of
books on astronomy which are adapted to the general reader. For
students who wish for an introductory account of astronomy the
Astronomer Royal’s _Primer of Astronomy_ may be recommended; Young’s
_Elements of Astronomy_ is a little more advanced, and Sir R. S. Ball’s
_Story of the Heavens_, Newcomb’s _Popular Astronomy_, and Proctor’s
_Old and New Astronomy_ enter into the subject in much greater detail.
Young’s _General Astronomy_ may also be recommended to those who are
not afraid of a little mathematics. There are also three modern English
books dealing generally with the history of astronomy, in all of which
the biographical element is much more prominent than in this book: viz.
Sir R. S. Ball’s _Great Astronomers_, Lodge’s _Pioneers of Science_,
and Morton’s _Heroes of Science: Astronomers_.
II. SPECIAL PERIODS.
_Chapters I. and II._—In addition to the general histories quoted
above—especially _Wolf_—I have made most use of Tannery’s _Recherches
sur l’Histoire de l’Astronomie Ancienne_ and of several biographical
articles (chiefly by De Morgan) in Smith’s _Dictionary of Classical
Biography and Mythology_. Ideler’s _Chronologische Untersuchungen_,
Hankel’s _Geschichte der Mathematik im Alterthum und Mittelalter_, G.
C. Lewis’s _Astronomy of the Ancients_, and Epping & Strassmaier’s
_Astronomisches aus Babylon_ have also been used to some extent.
Unfortunately my attention was only called to Susemihl’s _Geschichte
der Griechischen Litteratur in der Alexandriner Zeit_ when most of my
book was in proof, and I have consequently been able to make but little
use of it.
I have in general made no attempt to consult the original Greek
authorities, but I have made some use of translations of Aristarchus,
of the _Almagest_, and of the astronomical writings of Plato and
Aristotle.
_Chapter III._—The account of Eastern astronomy is based chiefly on
Delambre, and on Hankel’s _Geschichte der Mathematik im Alterthum und
Mittelalter_; to a less extent on Whewell. For the West I have made
more use of Whewell, and have borrowed biographical material for the
English writers from the _Dictionary of National Biography_. I have
also consulted a good many of the original astronomical books referred
to in the latter part of the chapter.
I know of no accessible book in English to which to refer students
except _Whewell_.
_Chapter IV._—For biographical material, for information as to the
minor writings, and as to the history of the publication of the _De
Revolutionibus_ I have used little but Prowe’s elaborate _Nicolaus
Coppernicus_, and the documents printed in it. My account of the _De
Revolutionibus_ is taken from the book itself. The portrait is taken
from Dandeleau’s engraving of a picture in Lalande’s possession. I have
not been able to discover any portrait which was clearly made during
Coppernicus’s lifetime, but the close resemblance between several
portraits dating from the 17th century and Dandeleau’s seems to shew
that the latter is substantially authentic.
There is a readable account of Coppernicus, as well as of several other
astronomers, in Bertrand’s _Fondateurs de l’Astronomie Moderne_; but I
have not used the book as an authority.
_Chapter V._—For the life of Tycho I have relied chiefly on Dreyer’s
_Tycho Brahe_, which has also been used as a guide to his scientific
work; but I have made constant reference to the original writings:
I have also made some use of Gassendi’s _Vita Tychonis Brahe_. The
portrait is a reproduction of a picture in the possession of Dr.
Crompton of Manchester, described by him in the _Memoirs of the
Manchester Literary and Philosophical Society_, Vol. VI., Ser. III. For
minor Continental writers I have used chiefly _Wolf_ and _Delambre_,
and for English writers, _Whewell_, various articles by De Morgan
quoted by him, and articles in the _Dictionary of National Biography_.
Students will find in Dreyer’s book all that they are likely to want to
know about Tycho.
_Chapter VI._—For Galilei’s life I have used chiefly Karl von Gebler’s
_Galilei und die Römische Curie_, partly in the original German form
and partly in the later English edition (translated by Mrs. Sturge).
For the disputed questions connected with the trial I have relied as
far as possible on the original documents preserved in the Vatican,
which have been published by von Gebler and independently by L’Épinois
in _Les Pièces du Procès de Galilée_: in the latter book some of the
most important documents are reproduced in facsimile. For personal
characteristics I have used the charming _Private Life of Galileo,
compiled chiefly from his correspondence and that of his daughter
Marie Céleste_. I have also read with great interest the estimate of
Galilei’s work contained in H. Martin’s _Galilée_, and have probably
borrowed from it to some extent. What I have said about Galilei’s
scientific work has been based almost entirely on study of his own
books, either in the original or in translation: I have used freely the
translations of the _Dialogue on the Two Chief Systems of the World_
and of the _Letter to the Grand Duchess Christine_ by Salusbury, that
of the _Two New Sciences_ by Weston (as well as that by Salusbury), and
that of the _Sidereal Messenger_ by Carlos. I have also made some use
of various controversial tracts written by enemies of Galilei, which
are to be found (together with his comments on them) in the magnificent
national edition of his works now in course of publication; and of the
critical account of Galilei’s contributions to dynamics contained in
Mach’s _Geschichte der Mechanik_.
_Wolf_ and _Delambre_ have only been used to a very small extent in
this chapter, chiefly for the minor writers who are referred to.
The portrait is a reproduction of one by Sustermans in the Uffizi
Gallery.
There is an excellent popular account of Galilei’s life and work in the
_Lives of Eminent Persons_ published by the Society for the Diffusion
of Useful Knowledge; students who want fuller accounts of Galilei’s
life should read Gebler’s book and the _Private Life_, which have
been already quoted, and are strongly recommended to read at any rate
parts of the _Dialogue on the Two Chief Systems of the World_, either
in the original or in the picturesque old translation by Salusbury:
there is also a modern German version of this book, as well as of the
_Two New Sciences_, in Ostwald’s series of _Klassiker der exakten
Wissenschaften_.
_Chapter VII._—For Kepler’s life I have used chiefly _Wolf_ and the
life—or rather biographical material—given by Frisch in the last
volume of his edition of Kepler’s works, also to a small extent
Breitschwerdt’s _Johann Keppler_. For Kepler’s scientific discoveries
I have used chiefly his own writings, but I am indebted to some extent
to _Wolf_ and _Delambre_, especially for information with regard to his
minor works. The portrait is a reproduction of one by Nordling given in
Frisch’s edition.
The _Lives of Eminent Persons_, already referred to, also contains an
excellent popular account of Kepler’s life and work.
_Chapter VIII._—I have used chiefly _Wolf_ and _Delambre_; for the
English writers Gascoigne and Horrocks I have used _Whewell_ and
articles in the _Dict. Nat. Biog._ What I have said about the work of
Huygens is taken directly from the books of his which are quoted in
the text; and for special points I have consulted the _Principia_ of
Descartes, and a very few of Cassini’s extensive writings.
There is no obvious book to recommend to students.
_Chapter IX._—For the external events of Newton’s life I have relied
chiefly on Brewster’s _Memoirs of Sir Isaac Newton_; and for the
history of the growth of his ideas on the subject of gravitation I have
made extensive use of W. W. R. Ball’s _Essay on Newton’s Principia_,
and of the original documents contained in it. I have also made some
use of the articles on Newton in the _Encyclopaedia Britannica_
and the _Dictionary of National Biography_; as well as of Rigaud’s
_Correspondence of Scientific Men of the Seventeenth Century_, of
Edleston’s _Correspondence of Sir Isaac Newton and Prof. Cotes_, and
of Baily’s _Account of the Rev^{d.} John Flamsteed_. The portrait is a
reproduction of one by Kneller.
Students are recommended to read Brewster’s book, quoted above, or
the abridged _Life of Sir Isaac Newton_ by the same author. The Laws
of Motion are discussed in most modern textbooks of dynamics; the
best treatment that I am acquainted with of the various difficulties
connected with them is in an article by W. H. Macaulay in the _Bulletin
of the American Mathematical Society_, Ser. II., Vol. III., No. 10,
July 1897.
_Chapter X._—For Flamsteed I have used chiefly Baily’s _Account of the
Rev^{d.} John Flamsteed_; for Bradley little but the _Miscellaneous
Works and Correspondence of the Rev. James Bradley_ (edited by
Rigaud), from which the portrait has been taken. My account of Halley’s
work is based to a considerable extent on his own writings; there is a
good deal of biographical information about him in the books already
quoted in connection with Newton and Flamsteed, and there is a useful
article on him in the _Dictionary of National Biography_. I have made a
good deal of use in this chapter of _Wolf_ and _Delambre_, especially
in dealing with Continental astronomers; and for special parts of
the subject I have used Grant’s _History of Physical Astronomy_,
Todhunter’s _History of the Mathematical Theories of Attraction and the
Figure of the Earth_, and Poynting’s _Density of the Earth_.
_Chapter XI._—Most of the biographical material has been taken from
_Wolf_ from articles in various encyclopaedias and biographical
dictionaries, chiefly French, and from Delambre’s _Eloge_ of Lagrange.
The two portraits are taken respectively from Serret’s edition of the
_Oeuvres de Lagrange_ and from the Academy’s edition of the _Oeuvres
Complètes de Laplace_. Gautier’s _Essai Historique sur le Problème des
Trois Corps_ and Grant’s _History of Physical Astronomy_ have been the
books most used for my account of the scientific contributions of the
various astronomers dealt with; I have also consulted various modern
treatises on gravitational astronomy, especially Tisserand’s _Mécanique
Céleste_, Brown’s _Lunar Theory_, and to a less extent Cheyne’s
_Planetary Theory_ and Airy’s _Gravitation_. For special points I
have used Todhunter’s _History_, already referred to. Of the original
writings I have made a good deal of use of Laplace’s _Mécanique
Céleste_ as well as of his _Système du Monde_; I have also consulted
a certain number of his other writings and of those of Lagrange and
Clairaut; but have made no systematic study of them.
Students who wish to know more about gravitational astronomy but
have little knowledge of mathematics should try to read Airy’s
_Gravitation_; Herschel’s _Outlines of Astronomy_ and Grant’s
_History_ (quoted above) also deal with the subject without employing
mathematics, and are tolerably intelligible.
_Chapter XII._—The account of Herschel’s career is taken chiefly from
Mrs. John Herschel’s _Memoir of Caroline Herschel_, from Miss A. M.
Clerke’s _The Herschels and Modern Astronomy_, from the _Popular
History of Astronomy in the Nineteenth Century_ by the same author,
and from Holden’s _Sir William Herschel, his Life and Works_. The last
three books and the _Synopsis and Subject Index to the Writings of Sir
William Herschel_ by Holden & Hastings have been my chief guides to
Herschel’s long series of papers; but nearly every thing that I have
said about his chief pieces of work is based on his own writings. I
have made also some little use of Grant’s _History_ (already quoted),
of _Wolf_, and of Miss Clerke’s _System of the Stars_.
Students are recommended to read any or all of the first four books
named above; the _Memoir_ gives a charming picture of Herschel’s
personal life and especially of his relations with his sister. There is
also a good critical account of Herschel’s work on sidereal astronomy
in Proctor’s _Old and New Astronomy_.
_Chapter XIII._—Except in the articles dealing with gravitational
astronomy I have constantly used Miss Clerke’s _History_ (already
quoted), a book which students are strongly recommended to read; and in
dealing with the first half of the century I have been helped a good
deal by Grant’s _History_. But for the most part the materials for the
chapter have been drawn from a great number of sources—consisting very
largely of the original writings of the astronomers referred to—which
it would be difficult and hardly worth while to enumerate; for the
lives of astronomers (especially of English ones), as well as for
recent astronomical history generally, I have been much helped by the
obituary notices and the reports on the progress of astronomy which
appear annually in the _Monthly Notices_ of the Royal Astronomical
Society.
I add the names of a few books which deal with special parts of modern
astronomy in a non-technical way:—
_The Sun_, C. A. Young; _The Sun_, R. A. Proctor; _The Story of the
Sun_, R. S. Ball; _The Sun’s Place in Nature_, J. N. Lockyer.
_The Moon_, E. Neison; _The Moon_, T. G. Elger.
_Saturn and its System_, R. A. Proctor.
_Mars_, Percival Lowell.
_The World of Comets_, A. Guillemin (a well-illustrated but uncritical
book, now rather out of date); _Remarkable Comets_, W. T. Lynn (a very
small book full of useful information); _The Great Meteoritic Shower
of November_, W. F. Denning.
_The Tides and Kindred Phenomena in the Solar System_, G. H. Darwin.
_Remarkable Eclipses_, W. T. Lynn (of the same character as his book
on Comets.)
_The System of the Stars_, A. M. Clerke.
_Spectrum Analysis_, H. Schellen; _Spectrum Analysis_, H. E. Roscoe.
INDEX OF NAMES.
_Roman figures refer to the chapters, Arabic to the articles. The
numbers given in brackets after the name of an astronomer are the
dates of birth and death. All dates are_ A.D. _unless otherwise
stated. In cases in which an authors name occurs in several articles,
the numbers of the articles in which the principal account of him or
of his work is given are printed in clarendon type thus_: =286=. _The
names of living astronomers are italicised._
Abul Wafa. _See_ Wafa
Adams (1819-1892), XIII. 286, 287, 289
Adelard. _See_ Athelard
Airy (1801-1892), X. 227 _n_; XIII. =281=, =282=
Albategnius (?-929), II. 53; III. =59=, 66, 68 _n_; IV. 84, 85
Albert (of Prussia), V. 94
Albertus Magnus (13th cent.), III. 67
Alcuin (735-804), III. 65
Alembert, d’. _See_ D’Alembert
Alexander, II. 31
Alfonso X. (1223-1284), III. =66=, 68; V. 94
Al Mamun, III. 57, 69
Al Mansur, III. 56
Al Rasid, III. 56
Alva, VII. 135
Anaxagoras (499 B.C.?-427 B.C.?), I. 17
Anaximander (610 B.C.-546 B.C.?), I. 11
Apian (1495-1552), III. =69=; V. 97; VII. 146
Apollonius (latter half of 3rd cent. B.C.), II. =38=, 39, 45, 51,
52 _n_; X. 205
Arago, XII. 254
Archimedes, II. 52 _n_; III. 62
Argelander (1799-1875), XIII. 280
Aristarchus (earlier part of 3rd cent. B.C.), II. =24=, =32=, 41,
42, 54; IV. 75
Aristophanes, II. 19
Aristotle (384 B.C.-322 B.C.), II. 24, =27-30=, 31, 47, 51, 52;
III. 56, 66, 67, 68; IV. 70, 77; V. 100; VI. 116, 121, 125, 134;
VIII. 163
Aristyllus (earlier part of 3rd cent. B.C.), II. =32=, 42
Arzachel (_fl._ 1080), III. =61=, 66
d’Ascoli, Cecco (13th cent.), III. 67
Athelard (beginning of 12th cent.), III. 66
Auzout (?-1691), VIII. =155=, 160; X. 198
Bacon, Francis (1561-1627), VI. 134; VIII. 163
Bacon, Roger (1214?-1294), III. =67=; VI. 118
Bailly, XI. 237
_Ball_, XIII. 278 _n_
Bär, Reymers (Ursus) (?-1600), V. 105
Barberini (Urban VIII.), VI. 125, 127, 131, 132
_Barnard_, XIII. 294, 295
Baronius, VI. 125
Barrow, Isaac, IX. 166
Bayer, XII. 266
Bede, III. 65
Begh, Ulugh. _See_ Ulugh Begh
Bellarmine, VI. 126
Bentley, IX. 191
Berenice, I. 12
Bernouilli, Daniel (1700-1782), XI. 230
Bernouilli, James (1654-1705), XI. 230
Bernouilli, John (1667-1748), XI. 229, 230
Bessel (1784-1846), X. 198 _n_, 218; XIII. 272, =277-278=, 279, 280
Bille, V. 99
Bliss (1700-1764), X. 219
Bond, William Cranch (1789-1859), XIII. 295
Borelli (1608-1679), IX. 170
Bouguer (1698-1758), X. 219, =221=
Boullian. _See_ Bullialdus
Bouvard, XI. 247 _n_; XIII. 289
Bradley (1693-1762), X. 198, =206-218=, 219, 222-226; XI. 233;
XII. 257, 258, 263, 264; XIII. 272, 273, 275, 277
Brahe, Tycho (1546-1601), III. 60, 62; V. 97, 98 _n_, =99-112=;
VI. 113, 117, 127; VII. 136-139, 141 _n_, 142, 145, 146, 148;
VIII. 152, 153, 162; IX. 190; X. 198, 203, 225; XII. 257; XIII. 275
Brudzewski, IV. 71
Bruno, VI. 132
Bullialdus (1605-1694), XII. 266
Bunsen, XIII. 299
Burckhardt (1773-1825), XI. 241
Bürg (1766-1834), XI. 241
Bürgi (1552-1632), V. =97=, =98=; VIII. 157
Burney, Miss, XII. 260
_Burnham_, XIII. 309
Caccini, VI, 125
Caesar, II. 21; III. 67
Callippus (4th cent. B.C.), II. =20=, =26=, 27
Capella, Martianus (5th or 6th cent. A.D.), IV. 75
Carlyle, XI. 232
Carrington (1826-1875), XIII. 298, 302
Cartesius. _See_ Descartes
Cassini, Count (1748-1845), X. 220
Cassini, Giovanni Domenico (1625-1712), VIII. =160=, =161=; IX. 187;
X. 216, =220=, 221, 223; XII. 253, 267; XIII. 297
Cassini, Jacques (1677-1756), X. =220=, =221=, 222
Cassini de Thury (1714-1784), X. 220
Castelli, VI. 125
Catherine II., X. 227; XI. 230, 232
Cavendish (1731-1810), X. 219
Cecco d’Ascoli (1257?-1327), III. 67
_Chandler_, XIII. 285
Charlemagne, III. 65
Charles II., X. 197, 223
_Charlois_, XIII. 294
Christian (of Denmark), V. 106
Christine (the Grand Duchess), VI. 125
Clairaut (1713-1765), XI. 229, 230, =231=, 232, =233-235=, 237, 239,
248; XIII. 290
Clement VII., IV. 73
_Clerke_, XIII. 289 _n_
Clifford, IX. 173 _n_
Colombe, Ludovico delle, VI. 119 _n_
Columbus, III. 68
La Condamine (1701-1774), X. 219, =221=
Conti, VI. 125
Cook, X. 227
Coppernicus (1473-1543), II. 24, 41 _n_, 54; III. 55, 62, 69;
=IV.= _passim_; V. 93-97, 100, 105, 110, 111; VI. 117, 126, 127,
129; VII. 139, 150; IX. 186, 194; XII. 257; XIII. 279
_Cornu_, XIII. 283
Cosmo de Medici, VI. 121
Cotes (1682-1716), IX. 192
Crosthwait, X. 198
Cusa, Nicholas of (1401-1464), IV. 75
D’Alembert (1717-1783), X. 215; XI. 229, 230, 231 _n_, =232-235=,
237-239, 248
Damoiseau (1768-1846), XIII. 286
Dante, III. 67; VI. 119 _n_
_Darwin_, XIII. 292, 320
Da Vinci. _See_ Vinci
Dawes (1799-1868), XIII. 295
Delambre, II. 44; X. 218; XI. 247 _n_; XIII. 272
Delaunay (1816-1872), XIII 286, 287
De Morgan, II. 52 _n_
Descartes (1596-1650), VIII. 163
Diderot, XI. 232
Digges, Leonard (?-1571?), VI. 118
Digges, Thomas (?-1595), V. 95
Donati (1826-1873), XIII. 304
Doppler (1803-1853), XIII. 302
_Dreyer_, XIII. 308
_Dunér_, XIII. 302
Ecphantus (5th or 6th cent. B.C.), II. 24
Eddin, Nassir (1201-1273), III. =62=, 68; IV. 73
Encke (1791-1865), X. 227; XIII. 284
Eratosthenes (276 B.C.-195 or 196 B.C.), II. =33=, 45, 54; X. 221
Euclid (_fl._ 300 B.C.), II. 33, 52 _n_; III. 62, 66; VI. 115; IX. 165
Eudoxus (409 B.C.?-356 B.C.?), II. =26=, 27, 38, 42, 51
Euler (1707-1783), X. 215, 226; XI. 229, =230=, 231 _n_, =233-236=,
237, 239, 242, 243; XIII. 290
Fabricius, John (1587-1615?), VI. 124
Ferdinand (the Emperor), VII. 137, 147
Fernel (1497-1558), III. 69
Ferrel, XIII. 287
Field (1525?-1587), V. 95
Fizeau (1819-1896), XIII. 283
Flamsteed (1646-1720), IX. 192; X. =197=, =198=, 199, 204, 207 _n_,
218, 225; XII. 257; XIII. 275, 281
Fracastor (1483-1553), III. =69=; IV. 89; VII. 146
Fraunhofer (1787-1826), XIII. =299=, 311
Frederick II. (of Denmark), V. 101, 102, 106
Frederick II. (the Emperor), III. 66
Frederick II. (of Prussia), XI. 230, 232, 237
Galen, II. 20; III. 56; VI. 116
Galilei, Galileo (1564-1642), II. 30 _n_, 47; IV. 73; V. 96, 98 _n_;
=VI.= _passim_; VII. 135, 136, 138, 145, 151; VIII. 152-154, 157,
163; IX. 165, 168, 170, 171, 173, 179, 180, 186, 190, 195; X. 216;
XII. 253, 257, 263, 268; XIII. 278, 295
Galilei, Vincenzo, VI. 113
_Galle_, XIII. 281, 289
Gascoigne (1612?-1644), VIII. =155=, 156; X. 198
Gauss (1777-1855), XIII. =275=, =276=, 294
Gautier (1793-1881), XIII. 298
Genghis Khan, III. 62
George III, XII. 254-256
Gerbert (?-1003), III. 66
Gherardo of Cremona (1114-1187), III. 66
Gibbon, II. 53 _n_
Giese, IV. 74
Gilbert (1540-1603), VII. 150
_Gill_, XIII. 280, 281
_Glaisher_, XIII. 289 _n_
Godin (1704-1760), X. 221
Goodricke (1764-1786), XII. 266
Grant, XIII, 289 _n_
Grassi, VI. 127
Gregory, James (1638-1675), IX. =168=, 169; X. 202
Gregory XIII., II. 22
Gyldén (1841-1896), XIII. 288
Hainzel, V. 99
_Hale_, XIII. 301
Halifax, John. _See_ Sacrobosco
Halifax (Marquis of), IX. 191
_Hall_, XIII. 283 _n_, 295
Halley (1656-1742), VIII. 156; IX. =176=, =177=, 192 _n_; X. 198,
=199-205=, 206, 216, 223, 224, 227; XI. 231, 233, 235, 243;
XII. 265; XIII. 287, 290
Hansen (1795-1874), XIII. 282, 284, =286=, 290
_Harkness_, XIII. 301
Harriot (1560-1621), VI. 118, 124
Harrison, X. 226
Harun al Rasid, III. 56
Helmholtz (1821-1894), XIII. 319
Hencke (1793-1866), XIII. 294
Henderson (1798-1844), XIII. 279
Heraclitus (5th cent. B.C.), 11, 24
Herschel, Alexander, XII. 251
Herschel, Caroline (1750-1848), XII. 251, 254-256, 260
Herschel, John (1792-1871), I. 12; X. 221; XI. 242; XII. 256;
XIII. 289 _n_, =306-308=, 309, 316, 317, 319
Herschel, William (1738-1822), IX. 168; X. 223, 227; XI. 250;
=XII.= _passim_; XIII. 272, 273, 294, 296, 306-311, 317, 318
Hesiod, 11, 19, 20
Hevel (1611-1687), VIII. =153=; X. 198; XII. 268
Hicetas (6th or 5th cent. B.C.), II. 24; IV. 75
_Hill_, XI. 233 _n_; XIII. =286=, 290
Hipparchus (2nd cent. B.C.), I. 13; II. 25, 27, 31, 32, =37-44=,
45, 47-52, 54; III 63, 68; IV. 73, 84; V. 111; VII. 145
Hippocrates, III. 56
Holwarda (1618-1651), XII. 266
Holywood. _See_ Sacrobosco
Honein ben Ishak (?-873), III. 56
Hooke (1635-1703), IX. =174=, 176; X. 207, 212
Horky, VI. 121
Horrocks (1617?-1641), VIII. =156=; IX. 183; X. 204
_Howlett_, XIII. 298
_Huggins_, XIII. 301, 304, 311-313
Hulagu Khan, III. 62
Humboldt, XIII. 298
Hutton (1737-1823), X. 219
Huygens (1629-1695), V. 98 _n_; VI. 123; VIII. =154=, =155=, =157=,
=158=; IX. 170-172, 191
Hypatia (?-415), II. 53
Ibn Yunos. _See_ Yunos
Ishak ben Honein (?-910 or 911), III. 56
James I., V. 102; VII. 147
James II., IX. 192
_Janssen_, XIII. 301, 307 _n_
Joachim. _See_ Rheticus
Kaas, V. 106
Kant, XI. 250; XII. 258, 260; XIII. 287
_Kapteyn_, XIII. 280
_Kelvin_, XIII. 292
Kepler (1571-1630), II. 23, 51 _n_, 54; IV. 91; V. 94, 100, 104,
108-110; VI. 113, 121, 130, 132; =VII.= _passim_; VIII. 152, 156,
160; IX. 168-170, 172, 175, 176, 190, 194, 195; X. 202, 205, 220;
XI. 228, 244; XIII. 294, 301, 309
Kirchhoff (1824-1887), XIII. =299=, =300=, 311
Kirkwood (1815-1895), XIII. 294, 297
Koppernigk, IV. 71
Korra, Tabit ben. _See_ Tabit
Lacaille (1713-1762), X. =222-224=, 225, 227; XI. 230, 233, 235;
XII. 257, 259
La Condamine (1701-1774), X. 219, =221=
Lagrange (1736-1813), IX. 193; XI. 229, 231 _n_, 233 _n_, 236, =237=,
238-240, =242-245=, 247, 248; XII. 251; XIII. 293, 294
Lalande (1732-1807), XI. =235=, 241, 247 _n_; XII. 265
Lambert (1728-1777), XI. 243; XII. 265
Lami, IX. 180 _n_
Landgrave of Hesse. _See_ William IV.
_Langley_, XIII. 307
Lansberg (1561-1632), VIII. 156
Laplace (1749-1827), XI. 229, 231 _n_, =238-248=, =250=; XII. 251,
256; XIII. 272, 273, 282, 286-288, 290, 293, 297, 318-320
Lassell (1799-1880), XII. 267; XIII. =295=
Lavoisier, XI. 237
Legendre (1752-1833), XIII. =275=, 276
Leibniz, IX. 191, 193
Lemaire, XII. 255
Leverrier (1811-1877), XIII. 282, 284, =288=, =289=, 290, 293, 294
Lexell (1740-1784), XII. 253
Lindenau, XI. 247 _n_
Lionardo da Vinci. _See_ Vinci
Lippersheim (?-1619), VI. 118
Locke, IX. 191
_Lockyer_, XIII. 301, 302
_Loewy_, XIII. 283 _n_
Louis XIV., VIII. 160
Louis XVI., XI. 237
Louville (1671-1732), XI. 229
Lubbock (1803-1865), XIII. 286, 292
Luther, IV. 73; V. 93
Machin (?-1751), X. 214
Maclaurin (1698-1746), X. =196=; XI. 230, 231; XII. 251
Maestlin, VII. 135
Maraldi, X. 220
Marius (1570-1624), VI. =118=; VII. 145
Martianus Capella. _See_ Capella
Maskelyne (1732-1811), X. =219=; XII. 254, 265
Mason (1730-1787), X. 226; XI. 241
Matthias (the Emperor), VII. 143, 147
Maupertuis (1698-1759), X. 213, =221=; XI. 229, 231
Maxwell (1831-1879), XIII. 297
Mayer, Tobias (1723-1762), X. 217, =225=, =226=; XI. 233, 241;
XII. 265
Melanchthon, IV. 73, 74; V. 93
Messier (1730-1817), XII. 259, 260
Meton (460 B.C.?-?), II. 20
Michel Angelo, VI. 113
Michell, John (1724-1793), X. 219; XII. 263, 264
_Michelson_, XIII. 283
Molyneux (1689-1728), X. 207
Montanari (1632-1687), XII. 266
Müller. _See_ Regiomontanus