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rily precluded any great advances in astronomy, either in the theory or the practice of the science; not to mention the powerful impediments to all free inquiry, arising from the blind zeal and ignorance of intolerant theologians. A more liberal spirit, however, has since been evinced, which, aided by the new analyses and other discoveries in mathematics, and by great improvements in our telescopes and other instruments for observation, has carried the science of astronomy to a high de gree of precision and consequence. Hence we have attained an accurate estimate and calculation of the motions, the affections, and the phænomena, of the great bodies in the universe; the distances, magnitudes, and mutual actions, of the various bodies in the planetary system; and even the discovery of several. new planets, satellites, comets, and thousands of stars never before seen or suspected. Hence the aberration of the stars, the motion of light, the measure and figure of the earth, the distances and magnitudes of the sun and the other planets, the nutations of the stars, the returns of comets, the transits of Venus and Mercury, the nature of the sun and of light, the discovery of the three primary planets, Herschel, Piazzi, and Olbers, and many satellites; new and accurate instruments for land and sea these and many other valuable acquisitions have given, as we have just observed, a new appearance and importance to the science of astronomy. It is to these novel and valuable acquisitions that the History now advances.
Astronomy may be properly divided into two grand parts; viz. the one practical, or that which is purely dependent on observations and common elementary geometry; the other-which may be denominated its physical branch-that which appertains to the affinities and affections of matter, and to the modern and improved analysis. Both of these have, in the eighteenth century, contributed in a great degree to perfect the science of astronomy. The former, restricting itself to observations of natural phænomena alone, collected and presented facts for the basis of an accurate theory; the other, penetrating further, investigated the mechanical causes of the phenomena presented, and subjected them to calculation. For example: in the theory of the moon, the practical or astronomical observer labours to determine her different inequalities or deviations from a regular path in the heavens, according to her various aspects and wanderings, both with respect to the earth and the sun. These being attained, the astronomer was, next enabled to calculate experimentally the several equations in the moon's motions; and hence Mayer derived his theory and tables of the moon, which approach so near to the truth. In the mean while, our physical astronomers and profound analysts, such as Euler, Clairaut, d'Alembert, Lagrange, Laplace, commencing with the principle of the mutual attraction of the celestial bodies on each
other, particularly the combined action of the sun and earth on the moon, laboured to determine the curve which she describes about our globe, and thence to establish rules for calculating her motions.
The History commences with the first of these divisions, or the practical branch; it describes the numerous and important observations and discoveries which have been made within the period referred to; and subjoins an account of the more remarkable astronomers. This section is introduced by a particular description of the solar system, beginning with the sun, and afterward noticing the several planets in their order. In all these descriptions, and the whole of this astronomical part, the editor, M. Lalande, who has taken the principal share in its composition, perpetually disgusts and fatigues the reader by his incessant vanity in referring to his own works and opinions in almost every page and passage.
Having run through the discoveries and circumstances of the planets and their satellites, the History then proceeds, in the second article, to those relating to the fixed stars, and explains the observations and conjectures concerning their numbers, parallax, distances, magnitudes, catalogues, motions changeable and periodical, new stars, double, triple, &c. stars, groups, clusters, and nebulosities, milky way, construction of the hea vens, or stellar disposition. The third article treats of the mo tions of the sun, or rather of the earth, as affected by her mutual attractions with the moon, with Jupiter and Venus, and with comets, and also by the possible resistance of an ethereal medium; discussing the questions of the equations of those bodies, the eccentricity of the earth's orbit, the length of the year, and whether permanent or variable, as also her distance from the sun. It is here stated, as the opinion of Euler and other philosophers, that some ethereal fluid must occupy the planetary regions; that this medium, however rare or attenuate it may be, must give some small resistance to the earth and the other planets in their motions through it; the consequences of which must be, that every planet must revolve in a progressive approximation to the sun, and occupy a shorter period in every successive revolution, till at length it must of necessity fall into the solar substance, and be absorbed; first the planet Mercury, next Venus, then the earth, and so on, in the order of their position.
Art. IV treats of the moon's motions considered astronomically, or of the inequalities discovered by observations. Under this head, the lunar observations, the discoveries, and the tables of calculation, of many astronomers are described; and particularly those of Tycho Brahe, Kepler, Horrox, Halley, Mayer, Mason, Burg, Bouvard.
In the fifth article commences the physical consideration of
the celestial motions; and first the physical theory of those of the moon, as determined by Newton in his Principia, and the principles of universal gravitation, as applied to the mutual influences of the sun, moon, and earth. These three bodies are considered in their various positions; and the effects they produce on the moon's orbit and motions are exemplified in the quantity of different equations and variations of her orbit, her nodes, apses, &c. The same subject is further continued inthe next article, and in a more dilated manner, as well as with. more accuracy. The problem is here rendered general, under the name of the problem of the three bodies, in which it is proposed to determine what course three bodies will assume, of given masses, and which shall mutually influence one another, after being projected with given velocities, from given places in given directions. The History announces the various success of several authors in their contemplations on the general state of this problem, and their particular applications to the delicate variations in her motions, as influenced by the attrac tions of the earth and the sun, considered strictly according to Newton's law-viz. in the inverse ratio of the square of the distances a law which has been fully confirmed by a comparison of the results of physical and analytical calculations with the most accurate astronomical observations. These calculations and observations have given rise to the construction of several sets of very accurate lunar tables, which are still employed in the calculation of her phases, as those of Euler, Clairaut, d'Alembert, Mayer, &c. And among the chief authors who distinguished themselves in these abstruse inquiries, are enumerated Clairaut, d'Alembert, Euler, Walmesley, Lagrange, Simpson, Frisi, Fontaine, Lambert, Laplace.
In the seventh article is treated, in particular, the secular equation of the moon, called her acceleration. This effect in the moon's motion was discovered by Dr. Halley, in computing some ancient eclipses recorded by Ptolemy and other authors. From Dr. Halley's calculations, and several others made since his æra, compared with the records, of ancient observations, it has been uniformly found that there is a certain difference between the two, and that pretty regularly in proportion to the interval of time elapsed between them, in such a manner as to evince the fact of a gradually quicker or accelerated state of that planet's motion in her orbit. To discover the cause of this ap pearance has employed the talents and labours of several of our first philosophers, as Euler, Lagrange, Laplace. Is the change really an acceleration in the motion of the moon herself? or is it only apparent, arising from a real retardation in the motion of the earth? either of which events would have the same effect, since it is by the revolutions of the earth that those of the moon are measured in an inverse ratio, the moon's motion ap
pearing to be so much the quicker, in an exact proportion as that of the earth is slower. After a variety of fruitless attempts to discover the cause of this appearance, by several of the philosophers we have just enumerated, it at length occurred to Laplace, that the gradual diminution in the eccentricity of the earth's orbit might occasion a decrease in her comparative motion with the moon, and consequently produce the effect in question. Accordingly on trial, by a nice calculation of the result of this cause, he found it exactly to correspond to the quantity given by observation, and thus established the fact beyond any further doubt.
Art. VIII treats on the moon's parallax, as observed and computed by different astronomers. Ptolemy made the quantity of the horizontal parallax to be between 54 and 103", according to the different distances of the moon from the earth: at present, by more accurate determinations, the limits are 53′ 28′′ and 61′26′′.
The ninth article treats of the eclipses of the sun and moon, in which an explanation is given of the nature and principles of these eclipses, and an account of some of the best writers and writings on these subjects. Upon this occasion, as on many others, occurs a remarkable instance of the editor's partiality to the French astronomers, and injustice to the English, in speaking of the method of constructing solar eclipses, and exhibiting their appearance and path on the earth. He here ascribes the first performances of the kind to J. D. Cassini, and refers, for the publication of it, to a memoir of Cassini in 1706. He afterward enumerates several other persons as having followed in the like practice, without so much as noticing the ori ginal publisher of such constructions and exhibitions, viz. Flamsteed, the first astronomer-royal of England, who invented the method in 1676, and published it at large in 1680, in the first volume of Sir Jonas Moore's System of Mathematics—namely, in that part which is entitled the Doctrine of the Sphere,' the whole of which was written by Flamsteed, and in the preface to which piece he explains the date and circumstances of the invention. Indeed Sir Christopher Wren had practised the same method sixteen years earlier, but never made it known till after Flamsteed produced his to the public.-In the next article is treated the method of finding the longitude of places on the earth, from the eclipses of the sun and moon, as also from the occultations of stars by the moon. In this article again the editor Lalande makes no mention of the English astronomers, although we know that they had the principal share in the bu siness, and that it was Flamsteed who first proposed and practised it, as may be seen in his treatise above quoted.
Art. XI illustrates the transits of Venus and Mercury over the face of the sun, and the sun's parallax deduced from observa
tions of these planets. The transits of the two inferior planets over the sun's disc are phænomena whose observation was reserved for modern astronomy, since some such instrument as the telescope was necessary to their notice. Such a notice, however, was not merely a matter of curiosity; for they determined, first, the sun's parallax, and, in consequence, the relative magnitude of all the bodies in the solar system, with the relative extent of their orbits. The transits of Mercury are very frequent, but those of Venus more rare, though these latter are of greater consequence in astronomical decisions. Since the use of telescopes, astronomers have lost few opportunities of observing such transits. The first on record is one of the planet Mercury, the 7th of November, 1631, by Gassendi; and the first of Venus was noticed by Horror, in England, the 24th of November, 1639. But the most profitable observations of the transits of Venus were those made in the years 1761 and 1769, in which phænomena most of the nations of Europe interested themselves in a high degree, many of them expediting astronomical missions to all parts of the world where observations could be made to most advantage. The consequence of all their labours has been the determination and conclusion of the sun's parallax at S"; whence it necessarily follows, from a comparison of this with the earth's diameter, that the distance of the earth from the sun is about ninety-five and a half millions of miles. Hence also are deduced most of the leading facts in the solar system; such as the magnitudes of the orbits of all the planets, their diameters, bulk, solid contents, densities, and the theory of eclipses, &c.
The twelfth article treats of the theory of the principal or primary planets, the peculiarities and circumstances attending the motions and properties of each, separately considered; and the history of the discovery of the Herschel-the other two newly discovered primary planets, Piazzi and Olbers, not being noticed, as having only been detected since this book was printed. An interesting account is here given also, from Laplace, of the cause of the secular equations of Jupiter and Saturn, experienced by astronomical observations, and which he shows are periodical, balancing and renewing themselves in certain intervals.
We now arrive at the sixth book of this fifth general part of the work. This division contains the history of physical astronomy; under which title are comprehended those parts of the science which require especially the examination of physical causes, and the calculations dependent on them-as refraction, the flattened figure of the earth, the diminution of the obliquity of the ecliptic, the satellites, the comets, the libration of the moon, the flux and reflux of the sea, &c.: though, so connected are the physical and practical branches of astronomy,