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that the former have already been occasionally touched upon in the preceding chapter.
This book is divided into twelve sections or articles, the first of which treats of astronomical refractions, and of the physical hypotheses proper for representing them. In this article are some misrepresentations, as usual, by Lalande, in disfavor of the English. In stating the medial quantity of the terrestrial refraction, which he rightly does, at one-twelfth of the arc intercepted between the two stations, he suppresses the names of the philosophers (captain Mudge and Mr. Dalby) by whose observations this quantity has been settled. He mentions, indeed, the observations of the English general Roy, as it would seem, because his limits are very wide-viz. between the third and the twenty-fourth of the intercepted arc-but omits that of the French measurer Legendre, who erroneously fixed it at onefourteenth; carefully announcing, nevertheless, that of Delambre, because he came near the mark-viz. one-eleventh.The second article treats of the figure of the earth, such as is given by astronomic measurements, executed in the course of the eighteenth century. The figure of the earth is one of the most important considerations both in geography and astronomy. The question is, whether it be that of a globe or of a spheroid; and, if the latter, what degree of an ellipse it possesses, and whether a lengthened or a flattened one? It is clear, however, that, if the earth be not a perfect globe, it differs but very little from such a figure. This difference is to be determined in two ways, viz. by actual mensuration, and by calculation on the theory of universal gravitation. By both these methods it has been demonstrated that the form of the earth is spheroidal, and of that kind which is in a small degree flatted . at the poles. It is the first of these methods which is discussed in the present article, viz. by measuring the lengths of the degrees of latitude, and by the length of the pendulum in different latitudes; and the other method is treated of in the next, or third, article. The present is indeed a very important and interesting chapter, containing a very particular account of all the measurements that have been made of the earth, in some degree, perhaps, too minute and particular for a general history. It offers us the different opinions of different mathematicians concerning the elliptic form of the earth, the accurate method of estimating it by the Newtonians, and the erroneous one of the Cassinians; together with the disputes produced by these differences, which gave rise to the test of so many actual measurements. The result of the calculations, from the whole of these, is, that the earth is a flatted globe, and that the degree of flattening, being the 334th part, is the polar axis to the equatorial diameter, is in the proportion of 333 to
The third article, then, contains the history of the figure of the earth, as deduced from calculations on the principle of attraction; and on the ring of Saturn.--While some astronomers and mathematicians had been employed to determine, by actual measurements and observations, the carth's configuration, and the length of a pendulum in different latitudes, others occupied themselves in deciding upon the same facts in their cabinets alone, by physical calculations on the laws of gravity and centrifugal force. The first among these latter were Newton and Huygens, who had even produced their calculations before the new process, undertaken in France and other parts for ascertaining the form of the earth by measurement, was carried into execution.
Newton, from his principle of universal attraction between the particles of matter in the earth, combined with that of the centrifugal force arising from the earth's rotation, computed the flattened form of the earth, and the ratio of the axis to the equatorial diameter, as 230 to 231, or more rigidly, on the same principles, as 229 to 230.
But Huygens, unfortunately for himself, not approving, and consequently not adopting, Newton's law of the universal attraction of matter, conceived all the parts as of equal weight, though at unequal distances from the centre: this erroneous principle, combined in his calculations with the law of the centrifugal force, gave him a false conclusion-viz. the ratio of
578 to 579 for that of the earth's two diameters.
The differences in these results, and the erroneous notions of Cassini and some other astronomers in contending for the elongation instead of compression of the earth at its poles, gave rise to the laborious measurements described in the preceding article. After such actual survey, however, many other philosophers repeated the physical computations on the Newtonian principles with ample success: and, among these, the more remarkable are Stirling, Clairaut, Bouguer, Maclaurin, Euler, Daniel Bernouilli, d'Alembert, Lagrange, Legendre, and Laplace. The joint conclusions, from the calculations of such eminent men, are, that the earth is flattened towards the poles, and elevated about the middle or equator, in consequence of the diurnal rotation on its axis: that the degree of compression, however, is very small, or the total form very little differing from an exact globe, being not more than the 230th part, which is the quantity that would have arisen by supposing the earth to be everywhere homogeneous, and to have been at first fluid; but as the earth is evidently of very unequal density, the flattening must be less than the 230th part, but by no means so small as the 577th: that, from a comparison of the lengthening of pendulums in different latitudes, and other circumstances, the most probable degree of flattening is fixed at 4th, whence
the length of the terrestrial meridian is computed, and consequently the metre or standard of the new measures: that there are probably various errors in all the practical measures that have hitherto been taken of the degrees of the meridian, partly from inattention to small celestial angles, and partly from the effects of the hollows of the seas, mountains on the earth, and more dense matters within its bowels,, in disturbing the plumbline. The article concludes with adverting to the application which Laplace has made of the same mode of calculation to the ring of the planet Saturn: by supposing this ring to consist of a very thin fluid, carried off by a very rapid rotation to a vast distance from the body of the planet, till the centrifugal force is a counterbalance to its gravity, he finds the method applies very well to its motions around the planet.
The fourth article treats on the aberration of the stars and planets, which is an effect in consequence of the progressive motion of the rays of light, combined with the motion of the observer, or of the earth in its orbit. This fine discovery was made by Dr. Bradley, about the year 1727 or 1728, with regard to the fixed stars; and the same was afterwards applied by Clairaut to the sun and planets, the effect of which ought to be considered, whenever very nice calculations of their relative places are examined into.
Article V treats on the precession of the equinoxes, and the nutation of the carth's axis. These are two effects, which arise from the inclination of the terrestrial axis to the plane of the ecliptic, and from the spheroidal form of the earth, by which the sun and moon act unequally on the protuberant matter about the earth's equator: effects, the quantity of which has been discovered by observation, and confirmed by physical calculation on Newton's principle of universal gravitation; of the truth of which, therefore, this coincidence is an additional proof. The precession of the equinoxes is the retrograde motion of the nodes of the earth's equator, after the rate of fifty seconds per year; and is the cause of the apparently continual change of place in the fixed stars, as to longitude. The nutation of the earth's axis is its libration from side to side, being drawn from its true parallelism by the action of the sun and moon, by which it is made to describe a small oval, in the course of eighteen years seven months, which, among the fixed stars, has its longest diameter 18", and the shortest 13". This was determined by observation, by Dr. Bradley, in the year 1737; though it was conceived, a priori, by Newton, long before, and calculated by him, on his principle of universal attraction, as well as could be done by the accuracy of the data then known; viz. the quantity of the earth's ellipticity, and the ratio of the actions of the sun and moon. Since these data have been better known, the effects have been more accurately computed by
later philosophers, as d'Alembert, Euler, Simpson, Silvabelle, Frisi, Walmesley, Laplace.
In article VI, on the diminution of the obliquity of the ecliptic, it is shown that this decrease would be at the rate of about 50′′ in a hundred years, if we acknowledge the accuracy of the ancient observations, since it is stated by Ptolemy at 23° 51', and its present obliquity is 23° 28'. But as the first quantity is probably too great, the rate is stated with more accuracy at 33" per 100 years. This gradual diminution is traced from the ancients, through the Arabs, and the more modern astronomers, to the present time. It is shown that it arises chiefly from the actions of the planets Jupiter and Venus, the effects of which are computed as near as can be by Euler and Laplace; and whence it appears that the decrease of the obliquity will not continue perpetually, or till the ecliptic coincide with the equator, but only to a certain term; after which it will increase again to another term, so as to re-acquire its greatest quantity. The obliquity is also subject to a periodical variation, in eighteen years seven months, owing to the nutation of the earth's axis.
Article VII gives the discovery and theory of the satellites of the planets Saturn, Jupiter, and Herschel. The satellites have been useful in calculating the masses of their respective primary planets. Those of Jupiter, in particular, have also been of eminent service, in determining the progressive motion of light, and its velocity, as well as the longitude of places on the earth. It is not to be wondered at, therefore, that the most eminent astronomers have assiduously applied themselves to accurate observations on these secondary planets, and to a construction of tables for computing their motions and places; as Galileo, Reineri, Marius, Peiresc, Hodierna, Borelii, Cassini, Bremer, Maraldi, Bradley, Wargentin, Bailly, Euler, Lagrange, Laplace, Delambre, Herschel.
Article VIII discusses the subject of comets. These have been chiefly interesting, since it was announced by Newton, that comets are a kind of bodies which revolve about the sun like planets, but in very long or eccentric orbits. In consequence, Dr. Halley first predicted the time of the return of a comet, which it accordingly fulfilled in the year 1759; and this is the only comet which has yet answered to prediction. The labours of the chief astronomers who have written on the subject of comets are here minutely described.
In the ninth article, the history treats of those comets which can so nearly approach the earth, as to produce danger of its destruction. This article seems to have been written, in consequence of the great alarm excited at Paris, in the year 1773, by a paper on the same subject then written by Lalande; when it was found necessary, in order to calm the public mind,
for the lieutenant of police to require from that astronomer a memcir, to certify the public that there was no danger to be apprehended from any such kind of accident. The memoir, when written, was referred to M. Montucla, the official censor of books for that period, who gave his certificate to this effect: I have read, by order of the chancellor, a manuscript, entitled, "Reflexions on such Comets as can approach the Earth," and I have found nothing in it that can authorise the imaginary terrors concerning such approximation; while, on the contrary, the pamphlet seems rather calculated to appease them, by showing that such a dreadful accident, though a thing possible, is of that order of possibilities to which no reasonable being pays any attention, on account of the extremely small degree of chance of its taking place, according to the laws of probability.'
The tenth article treats of the libration of the moon, of our poles of rotation, and of the singular circumstance by which she revolves once round her own axis. in exactly the same time as she fulfils her period round the earth.
The two remaining articles of this book are on the flux and reflux of the sea; in which, after slightly noticing the vague ideas of former philosophers upon this subject, of the ancients, of Descartes, Galileo, Baliani, Wallis, &c., M. Montucla advances to an explanation of the true cause, or that which consists in the mutual attraction between the earth and the two luminaries-the sun and moon. He then adds, that, on the same principles, more particular and ample explanations have been. given by D. Bernouilli, Maclaurin, Euler, d'Alembert, and Laplace.
The History now enters on the seventh book of this part of the work, which contains, in so many articles, the history of astronomical tables, of ephemerides, of calendars, of instruments, of observatories, and of judicial astrology.-The first and second articles are simply catalogues of astronomical tables and of ephemerides, with sometimes a line or two of remarks upon them, of little consequence.
The third article treats of the Gregorian calendar. The first reformation of the Julian calendar, by pope Gregory XIII, and its adoption by the catholics, was treated of in the first volume of this History. In the present article, therefore, the historian only adverts to the time and manner of adopting the correction and change, by the protestant states of Europe, with the contests. that occurred on the occasion. The new calendar was first admitted into Germany, Switzerland, Denmark, and Sweden, in 1700; but into England, not till the year 1752; since which time, a difference of 11 days continued between the old and new style, till the year 1800; and, since then, another interçalary day being at that period omitted, the difference between