this distinguished astronomer to the undertaking, or develop the principles by which he was guided in its execution, than by translating a portion of his first chapter. After remarking that the solution of one of the simplest problems which could well be proposed, viz. the determination of the hour of the day by the observation of a star, presupposes, independently on the uniformity of the diurnal motion, the knowledge of the precession, the aberration, the nutation, the refraction, and, if the body observed were a planet, of the parallax, and all the planetary inequalities, he proceeds thus:

" Hence it results that the student who would devote himself to the science of astronomy, is reduced to this alternative, either to read and reflect for a long time before he can make the simplest observation, or to observe for a long time without at all comprehending the reductions of every kind which he is obliged to apply to the immediate results of his observations: it cannot be till after some months' application, that he will be able to assign any reason for the practice which he has adopted blindly and on the word of his preceptor.

This inconvenience must have been thought inevitable, and so it is to a certain point, since no astronomer either ancient or modern, in the numerous treatises we possess, has taken any care to subject himself to a more satisfactory and luminous order; but each contents himself, for the most part, with an exposition more or less methodical, of phenomena and of processes, supposing throughout, the observations carefully made and carefully reduced, without showing how those reductions are made; a matter, indeed, respecting which many authors have kept the most profound silence.

Yet this inconvenience will be considerably diminished, if he who would become an astronomer will apply himself first to observations. A study of a few hours will suffice for the acquiring of those ideas which have led to the invention of the principal astronomical instruments: a noviciate of a few days will suffice to familiarize the use of those instruments, to observe with precision the passage of a star over the different wires of a telescope, to regulate a pendulum, to measure a zenith distance, to compute the first reductions; and, in fine, to keep a register in which may be found in succession all the data which will conduce, step by step, to the explication of the system of the world, and to the calculation of all the celestial motions.

Thus, observation will precede theory, and the theories will spring by degrees from the computation of the observations. shall take for data only the most striking phenomena, such as an attentive observer cannot fail to remark: I shall suppose the student to possess only the most elementary knowledge of mathematics: I shall, however, suppose him capable of raising himself above prejudices, and of rectifying by reason the errors of his senses: but, he must be equally freed from ali contrary notions, which VOL. III. N. S. 2 F

cannot be regarded as less than prejudices in him, if he have adopted them without mature examination: he shall doubt of every thing, and only yield to evidence; and yet he shall discover, of himself, by the observations, the system of astronomy, such as it was sixty years ago, that is to say, before the modern analysis had explained and computed the celestial motions, even to the minutest irregularities.

It has been said, with much reason, that Astronomy is the daughter of Time. We are not in a state to explain clearly, or to predict a phenomenon, till it has been frequently observed; and astronomy has several phenomena which only return at very long intervals; nor is that the only cause which has retarded the course of this science. The progress of inventors was very slow, because they did not enjoy the aids which are now within our reach. In the state of perfection which the mechanical arts and the analytical science have now attained, fifty years would be sufficient to elevate astronomy, nearly to the point of perfection it has now reached, even if it had been little, or not at all, cultivated previously.

By profiting by our actual knowledge, and availing ourselves of the invention of telescopes, and the progress of horology, we shall show by what process a geometer might now discover all that we know of astronomy. But, if the reader cannot make the observations himself, we shall imagine that he can consult the collections which have been made during the last fifty years: he may take the observations simply as the observer has disposed them in his registers; he may compare those of different astronomers; and he will at once be convinced that they have all desirable authenticity.

Without adopting any hypothesis, any system, he shall only reason from incontestible facts. If he have an observatory at command, or possess instruments, his own observations, should he continue them solely for a few years, will enable him to find the same theories, to deduce the same consequences; but with a little less precision and certainty, in proportion as the interval has been

short.

We shall suppose, then, that a young man, struck with the regularity of the celestial motions, devotes his nights for a year or two to the observation of the stars and planets; that during the days he observes the transits and the altitudes of the sun's upper and lower limbs, especially at the meridian; that he employs himself in finding rules for the solution of such problems in spherical astronomy as thus occur: he will not even need for some time to regard the earth as a globe; this knowledge will long be useless. He will ascertain which of the phenomena are regular, and the small irregularities which affect them; and though he may not, at first, perceive the causes, he will at least possess the measure and the rules of the calculus which will determine them nearly to the minuter circumstances. Thus will he learn astronomy, such as it was sixty years ago, and with this approximate

knowledge, he may find mathematically the small corrections which reduce the science to its present state.

To the observations made, more than half a century ago, by Lacaille and Bradley, we shall join those which Dr. Maskelyne published regularly for more than forty years, and the work in which all the recent observations of M. Piazzi are registered; and, finally, those of the Board of Longitude, published annually in the Connaissance des Tems.

According to this plan, we shall admit nothing which is not decisively proved; we shall even vary the proofs as often as we shall judge necessary. Thus we shall cause to pass in review all the parts of astronomy; we shall present them in a different order from the authors who have preceded us; but the form alone will be changed.

Some authors justly celebrated, have pursued a method nearly similar to those in treatises of geometry or algebra, and have attempted to invent the science for their readers. Thus they became exposed to the reproach of giving long treatises but little complete. The reason probably is, that in geometry and analysis, if all the theorems are essentially connected with some preceding theorem, we do not always see the necessity of passing from the first to those which are corollaries; since the same theorem may have a great number of consequences, which have little analogy to one another, and of which we do not see the utility: while in astronomy the phenomena to be explained occur continually as we proceed. Our treatise, therefore, will be complete when the whole is explained, and when we possess rules of computation for every particular. Thus we shall treat of nothing useless; we shall omit nothing essential; and we shall not be detained longer upon the subject, than if, after the example of Lacaille, we had at once supposed the observer at the centre of the sun.

Our demonstrations generally commence by the manner of synthesis; the purely analytical method not being always either the easiest or the shortest. When the problems appear susceptible of an easy construction, which will speak to the eyes, we shall employ it in preference; such construction may furnish us with the fundamental equations: but if analysis can afterwards simplify that formula, and present it in a shape better fitted for computation, or should facilitate the combinations and lead to more general and fertile results, we shall not permit those advantages to escape.

That this word analysis, however, may not alarm any of my readers; let it be remarked, that astronomy, if we omit the pla netary perturbations, requires only the knowledge of the most elementary theorems of geometry, the simplest rules of algebra, a few of the chief properties of the conic sections, the two fundamental theorem of the differential and integral calculus, and above all, spherical trigonometry, which astronomy itself has called into existence, and which we shall deduce even from our observations with the aid of rectilinear trigonometry.'

We have made this long extract unhesitatingly, because it will be interesting, not only as it serves to develop the plan of Delambre's work, but as it explains the means which, in the estimation of this experienced astronomer, may best be pursued to attain a knowledge of his favourite science. We shall now proceed to examine, with as much minuteness as our limits will allow, the several parts of the treatise; first presenting an outline of the contents of each volume, and then pointing to the more ingenious and valuable portions of it.

The first volume is divided into nineteen chapters, from the first of which, containing an introductory sketch of the plan, the preceding quotation has been translated. In the following chapters the Author treats, in succession, of the observations which first appear requisite, the pendulum and astronomical telescope, observation of the sun, gnomonics, ancient and modern instruments, plumb-line and level, vernier, micrometer and reticle, circles, quadrants, and transit instruments: to these succeed a sketch of spherical trigonometry, with its application to gnomonics, and an explication of the trigonometry of the Greeks and these again are employed in the investigation of refraction, twilight, and parallax, in the formation of a catalogue of stars, in tracing the annual course of the sun, the diurnal motion, and the method of corresponding altitudes.'

In this volume we find many particulars worthy of notice, but can specify only a few. Thus, on the subject of trigonometry, the Author exhibits a very perspicuous view of that of the Greeks, and demonstrates the celebrated formula of Napier with great simplicity and elegance. He also deduces a variety of formulæ presenting the relations between four, five, and six parts of spherical triangles, and tending to simplify the differential expressions of these triangles. Of those differentials he exhibits a more complete and methodical collection than we have hitherto seen; and he adds a very curious table for the verification of trigonometrical formulæ. He also lays before the reader some ingenious rules to facilitate trigonometrical mnemonics.

From the application of trigonometrical theorems to the observations of the stars, the general uniformity of their motion is inferred, at the same time that some minor irregularities lead to the detection and determination of what is denominated refraction. This subject our Author treats copiously and elegantly. The construction given originally by Cassini, leads immediately to the formula of Bradley, namely, rp tan (z-qr), r being the refraction that corresponds to the zenith distance z, p and q co-efficients to be determined by observation. He examines the different formule of Simpson, Boscovich, Laplace,

&c.; and with regard to that of Simpson, first published in his "Dissertations," in 1743, he remarks, that though it is only an approximation, it is one of the best; that it will serve very well for observations upon all such heavenly bodies as do not go beyond 78° in zenith distance; and that when it ceases to be exact, all others, even the most refined, become doubtful. He suggests ready means of comparing other formula with this of Simpson, furnishes a valuable comparative table of refractions according to a variety of theorems; and, lastly, points out convenient means of deducing from observation the requisite constant quantities, and indeed of drawing a table of refractions from observations alone, without recurring to any abstract theory,

Thus far the Author has proceeded as though the astronomical observer were posited at the centre of the celestial motions. But may an astronomer assume this as a probable hypothesis? or must he abandon it? In order to free the student from the delusions of sense, and lead him to the discovery of the true state of things, Chevalier Delambre pursues, through the latter half of his first volume, a most masterly train of induction, of which we would fain give a perspicuous sketch. He investigates the formula which relate to parallax, giving them the requisite developments to ensure exactness and facilitate computations. The theory he here presents is entirely trigonometrical, the parallax depending solely upon the distances either of the observer, or of the heavenly body, from the centre of motion. The formulæ at once indicate the circumstances which best conduce to the discovery of the relation which subsists between those two distances, and this relation is all which their use requires. Hence the student is taught to infer, with certainty, that the fixed stars have not any diurnal parallax; and is prepared to form and arrange a catalogue of them by their right ascensions

and declinations.

This catalogue, however, is not to be regarded as possessing all possible precision, since the observer has not yet any idea of aberration, of nutation, or even of the precession: nevertheless, the precautions suggested ensure the relative positions of the fixed stars from all but almost imperceptible errors, and these may be removed, and the catalogue perfected, by means of the method of reductions. To this, our Author proceeds by comparing two well-known and authentic catalogues, the one prepared by Piazzi, in 1800, the other by Lacaille, in 1750. From this comparison he deduces the precession, and even the general formulæ which may afterwards be applied to each particular star. These formula, deduced solely from observation, are explicable by a conical motion of the axis of the equator about