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A cycle of celestial objects : for the use of naval, military, and private astronomers (Volume 1) online

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Zanotti. Bologna ephemerides. Catalogue of 414 zodiacal stars.

1783. Wargentin. Transits of Venus in 1761 and 1769 in Sweden.

Tables of Jupiter's satellites.

Lexell. Solar parallax. Lunar occupations. Cometary orbits. On

the great comet of 1770.

Mayer, C. Transits of Venus in 1761 and 1769, at Schwesinyen.

D'Alembert. Planetary theory. Figure of the earth. Precession

of the equinoxes.

Euler. Analytical treatment of the planetary motions. Theory of

the moon. Solar and lunar Tables.

1784. Frisi. On gravity, hydraulics, mechanics, and electricity.

Cassiuilll. (DeThury). The French arc of meridian. Refractions.

1786. Ludlara. Occupations and eclipses. Transit of Venus in 1769.

Ximenes. Transit of Venus in 1761. History of Tuscan astronomy.

1787. Boscovich. Optics. Degree of the meridian at Rimini. Invents a

prismatic micrometer.

Mason. Degree of the meridian in North America. Lunar Tables.

Transit of Venus in 1761 at the Cape of Good Hope.

1788. Fouchy. On the lunar atmosphere. Transits of Mercury.

Maraldi II., J. D. Theory of Jupiter's satellites.

Lapaute, Madame. Planetary Tables. Parallactic angles. On the

cometary theory.

1789. Roy. Geodesy. Trigonometrical survey of England.

Dagelet. Sidereal observations. Astronomer to La Perouse.

1790. Favre. Mathematical and astronomical inquiries.

1792. Le Gentil. Refractions. Transit of Venus in 1?G9 in India.
Hell. Solar parallax. Transit of Venus in 1769 in Lapland.

Smeaton. Improvements in various astronomical instruments. Adapts

an equatoreal micrometer and clock.
Dunn. Probability of a lunar atmosphere. On comets. Transit of

Venus in 1761.

1793. Bailly. History of astronomy. Theory of Jupiter's satellites. On

the zodiacal stars.
Mudge. Improvements in reflecting telescopes and chronometers.

1794. Saron. Orbit of Uranus. Cometary orbits.
Condorcet. On analysis and integral calculations.

Du Sejour. Inquiry into parallaxes. Irradiations. Inflections.
Celestial motions.


Pingre. Transit of Venus in \7til at Rodrigues ; and that 0/1769
at St. Domingo. On chronometers.

1797. Maraldi III., J. P. Astronomical observations at Peri naldo.

1798. Wales. Astronomer to Cook. Transit of Venus in 1769 at Hudson's

Bay. On ad-fected equations.

1799. Borda. An improved reflecting circle. On navigation.

Le Monnier. Solar and lunar Tables. Zodiacal charts.

Moutucla, History of mathematics. Observations at Cayenne.

Liesganig. An arc of the meridian in Hungary.

1800. Ramsden. Numerous improvements in the construction of astro-

nomical instruments.

Cousin. Differential and integral calculus. Physical astronomy.

Bandhri. Commentary on Aratus.

1801. Bory. Nautical astronomy, and its instruments.

1802. Swanberg. Measure of an arc in Lapland.

1803. Fontana. Integral calculus. Indefinite equations.

Jeaurat. Tables of Jupiter. Chart of his sixty-four stars of the

Pleiades. On dissecting the angle.

1804. Mechaiu. Grand arc of the meridian. Comets. Cometary orbits.

1805. Robinson. On light. The orbit of Uranus.

1806. Horsley. Solar atmosphere and parallax.

Coulomb. General mathematics and physics. Magnetism.

1807. Berthoud. Improvements in horology, and marine chronometers.

Lalande, J. Planetary tables. Lunar librations and parallax.

Atwood. Theory of motion. Rotation of bcdies.

1809. Cavallo. Atmospheric electricity. On micrometers.

Dupuis. Researches into ancient astronomy.

-""ISIO. Cavendish. Density of the earth. Prismatic micrometer.

Hornsby. On solar parallax. Transit of Venus in 1769.

1811. Maskelyne. On local attraction. Establishes the Nautical Almanac.
The Greenii'ich stars.

Nouet. Tables of Uranus. A meridional arc in Egypt.

Bougainville. Integral calculus. Nautical astronomy.

1813. Lagrange. On the propagation of sound. Gravitation of the planets.

Analytical functions. On libration, Jupiter 1 s satellites. Attrac-
tion of spheroids. Variations of the elliptic elements.

1814. Flinders. Nautical astronomy. Local magnetism.

1815. Wollaston, F. Transit of Venus in 1769. Stellar zones. Catalogue

of circumsolar stars. S : *vC<A>Yuu*>*** ^\ ^ ^ V

1817. Messier. Catalogue of clusters and nebulae. Comets and eclipses.

1818. Cagnoli. Conic sections. Occnliations. Catalogue of stars.

1819. Playfair. Mathematical and astronomical disquisitions.
-^1821. Vince. On fluxions. Infinite series. System of astronomy.

Mudge, General. The great English arc of the meridian. Gec-

detical operations.

"" 1822. Herschel, Sir W. Extensive telescopic discoveries in planets, nebula;,
double stars, $c. Improver of metallic mirrors, telescopes, micro-
meters, and every means of observation.


1822. Delambre. Tables of Jupiter, Saturn, and Uranus. Grand French

arc of the meridian. On refractions. Solar tables. An elaborate
history of astronomy.

1823. Lambton. Grand arc of the meridian in India.

Hutton. On the mean density of the earth.

1825. Burckhardt. Tables of the moon. Cometary theory. Orbits of the

new planets.

1826. Bode. Celestial maps, and index of 17,240 stars. Gradations of

the planetary distances.
Frauenhofer. Researches in physical optics. Optical improvements.

Piazzi. Discovery of Ceres. Catalogue of 7646 stars.

^.1827. Woodhouse. On the transit instrument. System af astronomy.

Calandrelli. On stellar parallax. Opusculi Astronomici.

Laplace. Analytical investigations. Secular inequalities of the solar

system. Theory of Saturn's ring. Orbit of Uranus. Theory of
the tides. Mechanique celeste.

1828. Wollaston, W. Invents the goniometer and dip-sector. Various

experiments on light. On horizontal refractions. Finite extent
of atmosphere.

1829. Young. Vision, light, colours. Physical optics. Nautical astronomy.
-^1831. Fallows. Catalogue of 275 southern stars.

Pons. Cometary observations.

Forster. Observations on refraction. Pendulum experiments*.

1832. . Zach. Solar tables. Catalogue of 1830 zodiacal stars. Tables of

aberration and nutation. On local attraction.

Oriani. Perturbations of Mercury and Ceres. The lunar theory.

Groombridge. Tables of refraction. Catalogue of 4243 circum-

polar stars.

Le Gendre. On the integral calculus. Method of least squares.

Elliptic numbers. Various geodetical operations.

1833. Harding. Discovered the planet Juno. Compiled a Celestial Atlas.

Brioschi. Practical astronomy and geodetical operations.

Caturegli. Places of the four new planets. Table of zodiacal stars,

with constants. Sologna ephemerides.

* In recording the untimely death of my zealous and scientific friend,
Captain Forster, who was drowned from a canoe in the River Chagres, Isthmus
of Darien, I cannot but regret the being unable also to state the period of
demise of another seaman, the skilful Spanish astronomer, Don Jose Joaquin
de Ferrar. This gentleman was a bright ornament of that powerful navy,
which, in our own times, has passed away; and he must be placed in the very
foremost rank of maritime savans. Proofs of his scientific talents may be
seen in the Memoirs of the Royal Astronomical Society of London, where his
papers on cometary orbits and solar parallax exhibit an intimate acquaintance
with the subject; and his process for obtaining the longitude of the Havannah
in Vol. IV. is so truly admirable, that I cannot but recommend it to the
reader's attention. His able discussion of the transit of Venus in 1 769, in
Vol. V., is dated from Cadiz, so late as 29th December, 1815.


1834. Soldner. Astronomical and geodetical operations. Astronomische


Burg. Lunar tables. Ephemerides of Vienna.

1835. Brinkley. Tables of refraction. Stellar parallax.

Troughton. Numerous improvements in the structure and graduation

of astronomical and geodetical instruments.

Kater. Convertible pendulum. Floating collimators.

183G. Pond. Mural circle observations, by direct and reflected vision.

Gambart. Cometary orbits, and general phenomena.

Ramage. Improvements in reflecting telescopes.

1837- Colebrooke. Researches in Hindu astronomy.

Tiarks. Nautical astronomy. Chronometric measures.

1838. Bowditch. Translator and commentator of the Michanique Celeste.

1839. Lalande, Le Fran9ais. Horary tables. Catalogue of 50,000 stars.

Rigaud. Life of Bradley. Critical views on astronomical history. *-

1840. Olbers. Cometary orbits. Discoverer of Pallas and Vesta.

Gregory, O. Various useful works on mechanics, mathematics, geo-

metry, and astronomy.

Poisson. Planetary perturbations. Attraction of the spheroids.

On the precession of the equinoxes.

Littrow. Various researches in physical astronomy. On comets.

From this hasty sketch it results, that astronomy has
advanced from its infancy to full maturity by successive stages,
every one of which is an honour to the age of its advent.
But the last and present century have witnessed its most rapid
approach to perfection. The mechanical improvements which
have been introduced into the construction of instruments, within
that period, have induced a corresponding accuracy of observa-
tion, and given a fresh energy to observers, by the gratification
which the assurance of working securely confers. Every link in
the great chain has been ably overhauled, and all the details
proved to be in admirable connection : the altitude of the pole, the
obliquity of the ecliptic, the declination of the stars, their right
ascension, the longitude of the sun, and the elements of refrac-
tion, have a mutual and harmonious dependence on each other.
The amazing extension that has been given to analysis, has
raised the celestial mechanics from the heresies of hypothesis to
a rivalry with the most complete of the abstract sciences, show-
ing the vast progression between the heliacal risings of old, and
those astonishing modern discoveries by which future centuries
are anticipated. In a word, so important have the labours of


the last hundred years been, that, independent of the surprising
discoveries which have resulted, a complete system of the plane-
tary motions might be deduced from the observations made
during this period; and, as Bowditch remarks, " If all the pre-
vious observations, even from the most remote antiquity, were lost,
the effect on the tables of the sun, planets, and satellites, would
hardly be perceived, since the great accuracy of modern observa-
tions more than compensates for the shortness of the epoch."
And independent of utilitarian bearings, astronomy has the
highest claims upon reason : " Though it should not," says
Fontenelle, "be absolutely necessary for the purposes of geo-
graphy, navigation, and even for the cultivation of divinity, yet it
is highly worthy of the attention of every rational being, for the
noble and sublime spectacle which it presents to the mind."




SURVEY this midnight scene:
What are earth's kingdoms to yon boundless orbs,
Of human souls, one day, the destined range !

ALTHOUGH the CYCLE is strictly a sidereal one, its contem-
plated use will be materially enhanced if introduced by a few
preliminary words on the Solar System, or that assemblage of
celestial bodies which consists of the sun, the planets which
revolve round him, their satellites, and the numerous comets
which traverse space, and mark the wondrous extent of the sun's
influence. This group so strongly manifests the intelligent design
of an Omnipotent Being, who is at once the Creator and Main-
tamer, and furnishes such an index to other visible systems, that
it could not be omitted in a work like this. And indeed it is
both right and necessary to show our colours, since the irregular
cruisers already alluded to, despising alike the aids of deduction
and induction, will not allow us to abandon what is evidently
unsearchable, and reason upon what may be really discernible,
without direct charges of impiety. But their interpretation of
the creation is guided by their own degree of knowledge: and
they lose sight of the necessity of proportioning a miracle to
its end. The opening of the book of Genesis is a description
of the creation of the earth, not the universe, so revealed as to
accommodate the ineffable ideas of the Creator to the limited
understanding of the creature: and the doctrine of a plurality
of worlds, rolling in silent grandeur in the remote and un-
explorable dominions of the boundless empire, is rational, as
irresistibly manifesting the power and grandeur of the all-
glorious ENS ENTIUM. Much must ever remain above our
comprehension, but we are not therefore to limit the powers
of the Creator; and until the anti-Newtonians can better


handle the argument, we are likely to continue under the delu-
sion of viewing

This world

Pois'd in the crystal air, with all its seas,
Mountains, and plains, majestically rolling
Around its noiseless axis.

The mind must be deficient in culture, which is not filled
with the utmost exultation on contemplating matters of certainty,
and not of speculation. The worlds which compose the solar
system, from revolving in complex and intricate paths, seem, at
a first view, to be subject to strange anomalies and irregularities;
nevertheless, all these apparent discrepancies have been resolved,
after many ages, into the most beautiful order, and for every
deviation yet detected by observation, a proper compensation has
been found to exist.

That branch of science which relates strictly to our own
system, and compares the laws of motion as observed in the
heavens, with its known laws on the surface of the earth, is
usually termed Physical Astronomy: it treats of the planetary
orbits, or the curves which the planets describe around the sun;
of their rotation about their own axes, and also of their figures,
which, as well as their motions, are modified by gravitation.
This sublime study may be said to have arisen in the seventeenth
century, when Newton rejected all the complex machinery
which had hitherto been adopted; and it was accompanied by
the invention of logarithms, the fluxionary calculus, the science
of dynamics, the theory of central forces, and the great law of
gravity. When to these brilliant developments are added the
discovery of the telescope, the microscope, barometer, and ther-
mometer, and the application of the pendulum to time-keepers,
the claim of that age to intellectual superiority must be fully
admitted. It was the art of printing, however, which by leap-
ing at once into maturity, like Pallas from the brain of Jupiter,
had paved the way for this by facilitating the intercourse of
minds; and there is a near connection between the extended
emulation it occasioned, and the accelerated progress of know-
ledge. It drew the speculative world from wild and visionary
theories to rational inquiry, and made the productions of the
human mind imperishable.



By duly recognising the powerful influence of gravitation, the
orbits of the planets are capable of being determined with singular
precision, because by reason of the great distances of these bodies
from one another, and the near approach of their figure to that
of a sphere, they are such, that their mutual actions are nearly the
same as if their masses were collected at their respective centres
of gravity; so that they may be regarded as so many material
points gravitating towards one another according to a given law.
But the computation of the effects of gravity on the rotatory
motion of the planets, cannot be accomplished with the same
precision, from our being, as yet, imperfectly acquainted with
the law by which their densities vary from their centres towards
their surfaces, and also from our ignorance of the actual figure
of their surfaces.

Newton accounted for the movements observed in the solar
system, from the principles of gravitation combined with the
laws of matter and motion, deduced from observations on
terrestrial matter. Hence he saw that the sun, situated in the
midst of the planets, attracts them all towards himself, while
they also attract the sun; but from the greater mass of the
latter, the effect of the planets is comparatively small. Had no
other impulse been given to each of these bodies, they would
have come together in consequence of their mutual attraction.
But a proper impulse was given to each planet in a direction
perpendicular, or nearly so, to a line joining the sun and planet.
These impulses must have been given at the creation ; for they
required, to use the words of Newton, " the Divine Arm to
impress them according to the tangents of their orbits."" And
surely none but the OMNIPO* NT CREATOR who framed the
universe, could have so beautitally proportioned, as well as
originated, the adverse centripetal and centrifugal forces, thus
wonderfully called into action. The celestial motions exhibit at
once the existence of a power acting under different circum-
stances; a power originally impressed upon the bodies, and a
power continually acting upon them. And the motive forces
indicate an external cause; for no internal powers of a material
body can give it motion, or when in motion alter its state.

To arrive at a comprehensive view of the systematic order of


the solar system, from our excentric station in it, we must reject
many of the fallacies and prejudices dictated by the mere senses.
The distinction between supposition and demonstration consists
both in object and degree; the former rests frequently on little
or no reality, and is therefore altogether unlimited in its com-
pounds; but the end of the latter being perfect congruity, it is
necessarily restrained to matter-of-fact. It is thus that, on ex-
amining the apparent revolutions of the inferior planets, not-
withstanding their approximation to regularity of appearance, it
becomes evident that no strictly regular and constant motion can
be deduced from these appearances, which could be referred to
the earth as a centre. Still less could the greater changes of
the superior ones be thus explained, for it is evident that, in con-
sequence of the eartli's revolving around the sun within their
orbits, they will appear successively in every point of the ecliptic.
Their apparent revolutions are subject to all the changes of direct
and retrograde motions observed in Mercury and Venus; but the
discovery of the real cause was made when the motion of the
earth itself had been assumed, instead of adhering to the ancient
absurdity of assigning to the whole universe, a diurnal rotation
of inconceivable rapidity around us. It is true, that Philolaus
is asserted to have taught the annual motion of the earth round
the sun, and Hicetas, of Syracuse, the diurnal rotation on her
own axis*; yet it is clear that neither of these conclusions was
adopted, for the system of Ptolemy was the generally received
one for many ages. Philosophers were, therefore, sadly per-
plexed with the apparently inexplicable epicycloidal maze; and
the erudite Riccioli, a constrained maintainer of terrestrial im-
mobility, distracted by the puzzling combinations required to
keep the earth in the centre, dexterously cites the Rabbinical
opinion, which allots to each planet an intelligence, or a conning

* Hicetas, or Nicetas, who seems to have flourished three or four hundred
years before our era, is expressly mentioned by Cicero Acad. Qucest. lib. n.
as a maintainer of this doctrine. The passage is: "Nicetas, according to
Theophrastus, considers that neither the sun, the moon, nor the stars are at
all in motion; but that the earth, by rolling round its axis (circum axem),
produces the same apparent effect as if it were immovably at rest, and the
firmament itself in motion." See likewise Diogenes Laertius, lib. viii., c. 7.


angel, to direct its arbitrary course. These difficulties were
cleared off by the Copernican theory, it is true; yet the apparent
movements and stations of them are curious, and very difficult to
calculate, even when limited to the elliptic motion. Cassini
treated them very ably in an essay, Du mouvement apparent des
Planetes a Regard de la Terre; which is inserted in the Me-
moires deTAcademie Roy ale des Sciences, for 1709, with large
plates illustrating the involutions performed by Mercury, Venus,
Mars, Jupiter, and Saturn. A careful reduction of the first of
these shewing the meandering movements of Mercury with
respect to the earth, between the years 1708 and 1715 will
explain the tenour of this argument:

Such was the perplexity of astronomers, when the mecha-
nical application of gravitation threw its powerful light over the
question, and reduced the spiral loops and complicated curves to
order and harmony. It is true that all the salient cosmical pheno-
mena may be accounted for by other laws, as well as by that of uni-


versal gravity; but no other supposition possesses the simplicity
of the Newtonian theory, or proves satisfactory in the remoter
consequences the mutual planetary perturbations. Of motive
powers inherent in matter, the reciprocal attraction or tendency
towards each other of every particle of such matter, is allowed
to be universal; and to be the most regular, and at the same
time the most comprehensive in its effects, and the most incom-
prehensible in its cause, of all the powers or qualities of matter.
It may be urged, and with propriety, that astronomical truth
does not admit of that species of evidence which belongs to
experimental science, because many of its conclusions rest on
analogical argument; but it is the purest and most simple appli-
cation of that mode of proof, and, when profoundly investigated,
produces conviction scarcely less satisfactory than positive de-
monstration. Our only absolute knowledge of gravity, as a
force, is the measure of its intensity estimated by the velocity
which it imparts to matter: and respecting the ratio of decre-
ment in the force, if gravity is applicable to particles of any kind
diverging from the centre, then their dispersion, if reckoned on
the surfaces of concentric spheres, would be inversely as the
squares of their respective diameters. This application of me-
chanical principles, in their free and uncontrolled condition, is
the basis of what some rabid philosophists stigmatize as the
Newtonian heresy.

These same philosophists have, however, indulged too freely
in their epithets and denunciations. " The harmony of a sci-
ence," says Bacon, "supporting each part the other, is and
ought to be the true and brief confutation and suppression of all
the smaller sort of objections." Now the planetary perturba-
tions need not be sneered at, because, from the absence of
minute ancient details, an accurate solution of problems which
require long epochs is still beyond the reach of the subtle
analysis hitherto employed; and it should moreover be kept in
view, that those which depend on the variation of orbital
elements, and are called secular, are so named merely for the
convenience of the term, for the centenary periods are no
more connected with these influences, than is the course of a
ship with the log-line by which its course is measured; or the


wonderful succession of distinct vicissitudes which occur in a
dream, with the momentary instant of time in which they are
presented to the imagination, by the mysterious and unfathomable
powers of the mind. But though a certain assumption of some of
the less perceptible elements is thus necessarily made, such has
been the advancement of the exact sciences, that a single second
of time, and even a fraction of one, now claims the zealous
astronomer's attention. Nay, more: a second in arc, a quantity
entirely microscopic to the human eye, provides data for the
inductive process, of which the recent disputes between the late
Bishop of Cloyne and the late astronomer royal, as to whether
such an observed difference in a star's place were referable to
parallax or to southern motion, afford an example in point.
But improved means and methods of observation and reduction,
promise, ere long, to bring all difficulties to an issue: in the
interim, we can but register phenomena with the utmost pre-
cision, and by allowing for the influences which we are ac-
quainted with, reduce them to that state in which the result
may be compared with observation, to test its truth or fallacy;
or, by the regularity of the deviation, indicate some new modifi-
cation of the influences, and thus lead us more closely to the

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