6 as Haafner subjoins, may be dangerous for vessels;' yet the latter, if he may be trusted, found no difficulty in approaching the place in a crazy open boat, in the worst season, though we are taught, that never traveller comes near In conclusion, if Jacob Haafner be a real character, he is a man totally destitute of every principle of honour and truth; if a mere nom de guerre, the book may be considered as having been got up by the French government for the mean and odious purpose of creating a false and unfavourable impression of the British character on the continent, and fixing an unmerited stigma on the British name in India. This must be our apology for noticing it at all; and this, we trust, our readers will admit to be sufficiently valid. ART. VII. Traité Elémentaire d'Astronomie Physique, par J. B. Biot, Membre de l'Institut de France, &c. Avec des Additions relatives à l'Astronomie Nautique, par M. de Rossel, ancien Capitaine de Vaisseau, Rédacteur et Co-opérateur du Voyage de d'Entrecasteaux. Seconde Edition, destinée à l'Enseignement dans les Lycées impériaux et les Ecoles secondaires... An Elementary Treatise on Physical Astronomy, &c. Paris. 1810. 3 vols. 8vo. pp. xxxvi. 1727. and 41 Plates. A LTHOUGH the volumes before us constitute the second edition of a work of no superlative merit, yet it has many claims on our attention. In magnitude it nearly triples the former edition, and may, therefore, be considered rather as a new than an improved work. Since its first appearance, the author has received many suggestions for modification and improvement, from Laplace, Delambre, Pictet, Prevost, Maurice, Arago, Chaix, Rodrigues, Berrouer, Mathieu, Bouvard, and Rossel; his performance, therefore, may be contemplated as a fair specimen of the maximum of producible talent in France on this interesting subject. It contains, besides, many striking instances of the prevailing wish among Frenchmen of science to extirpate from the continent the notion that any such beings as philosophers now exist in Great Britain. And it developes some of the arts to which even a man of respectable talents will have recourse, in order to derive all possible pecuniary advantage from his character, by swelling out his work to double its requisite size. M. Biot, M. Biot, in his prefatory sketch of the object of his treatise, supposes the student to possess no absolute knowledge of astronomy, or even of cosmography. He farther supposes the existence of all the prejudices respecting the figure of the earth and the celestial motions which spring from the uncorrected testimony of the senses; and he endeavours to lead his pupil, by a gradual process of observation and reasoning, to the true mechanism of the system of the world, including, of course, the motion of the earth, the laws of Kepler, and the explication of the various phenomena which depend upon attraction. The work is divided into four books, of which we shall speak in their order. Book I. contains twenty-three chapters, which treat of the heavens viewed astronomically; the roundness of the earth; the atmosphere; instruments necessary in astronomical observations; use of the transit instrument; equality of celestial revolutions, and their use in measuring time; determination of the meridian by the measure of time; direction of the axis of apparent celestial rotation; mural quadrant, and its use in determining the height of the pole; exact determination of the laws of diurnal motion, including proofs of its uniformity; principal circles of the celestial sphere; terrestrial poles and equator; determination of the figure of the earth; with the exact measure of its magnitude; mode of fixing the position of the different points of the earth's surface; investigation of the physical consequences which result from the universality of the diurnal motion; physical consequences of the compression of the earth's polar axis, including the variations in the length of the second's pendulum; atmospherical refractions; parallaxes; description and use of the repeating circle; instruments used at sea; sextant; reflecting circle; and mariner's compass. These subjects, with the notes, occupy the whole of the first volume. In this volume we meet with some excellencies, and not a few peculiarities. Among the former, we must specify the note on the subject of refraction; and among the latter, the omission of the English measurers in the chapter on the determination of the earth's figure and magnitude The progress of sentiment, and change of conduct, on this point, are somewhat curious. At first, the English measurers and the French academicians met at Dover to adjust their plan of operations; they then kept up a friendly correspondence, and the French liberally extolled the superior accuracy of the English operations; afterwards they praised the accuracy of the English measures, but with a saving clause in favour of their own; as was the case with Puissant in his Géodésie,' who, after stating some remarkable intances of correctness in General Roy and Colonel Mudge, says, ' Neanmoins, " jusqu'à jusqu'à présent rien n'égale en exactitude les opérations géodésiques qui ont servi de fondement à notre système métrique;' and, lastly, an elaborate chapter is written on the measure of the earth, in which there is no more notice taken of the most correct of all trigonometrical surveys, carried on uniformly with great science and skill, and extreme public benefit, for 27 years, than if it had never commenced, This is rendered still more extraordinary by M. Biot's commendation of Messrs. Mason and Dixon's measure of a degree in Pennsylvania, though we will venture to say there is no respectable mathematician in Europe who is not aware of the extreme inaccuracy of the American results. Dr. Maskelyne, in the Philosophical Transactions for 1768, (from which the French authors obtained their account of Mason and Dixon's belles opérations,') informs us, that Mr. Henry Cavendish 'having mathematically investigated several rules for finding the attraction of the inequalities of the earth, has, upon probable suppositions of the distance and height of the Allegany mountains from the degree measured, and the depth and declivity of the Atlantic ocean, computed what alteration might be produced in the length of the degree, from the attraction of the said hills, and the defect of attraction of the Atlantic, and finds the degree may have been diminished from 60 to 100 toises from these causes.' Yet this is the degree which our Gallic lovers of 'exactitude' prefer to any of those measured in England! Our author has a diffuse though interesting chapter on atmospherical refractions, which is the more valuable as it is now known that M. Lambert's theory, hitherto almost generally received, is erroneous. In this he traces the cause of several curious phænomena which depend on variable refractions, and among others that which is known to their mariners under the name of mirage, and which the French army frequently observed in their expedition to Egypt. The surface of the ground of Lower Egypt is a vast plain, perfectly horizontal. Its uniformity is not otherwise broken than by some eminences, on which are situated the towns and villages, which, by such means, are secured from the inundations of the Nile. In the evening and morning the aspect of the country is such as comports with the real disposition and distance of objects; but when the surface of the earth becomes heated by the presence of the sun, the ground appears as though it were terminated at a certain distance by a general inundation. The villages beyond it appear like islands situated in the midst of a great lake. Under each village is seen its inverted image as distinctly as it would appear in water. In proportion as this apparent inundation is approached, its limits recede, the imaginary lake, which seemed to surround the villages, retires; lastly, it disappears entirely, and the illusion is reproduced by another town or village more distant. Thus, as as M. Monge, from whom I have borrowed this description, remarks, every thing concurs to complete an illusion which is sometimes cruel, especially in the desert, because it presents the image of water, at the time when it is most needed.' " The second book of this treatise is devoted to what is technically called the theory of the sun,' and is divided into eighteen chapters, occupying 342 pages. The distribution and arrangement of subjects will appear from the following enumeration. Proper motions of the stars, and the means of determining them; application to the sun, with the theory of its circular motion; calendar; manner of referring the position of the stars to the plane of the ecliptic; progressive diminution of the obliquity of the ecliptic; precession of the equinoxes; nutation; second approximation to the sun's motion, with the theory of its apparent elliptical motion ; mode of determining the exact position of the solar ellipse upon the plane of the ecliptic, with the origin of mean time, &c.; exact determination of eccentricity from observations of the equation of the centre; use of equations of condition' for the simultaneous determination of the elements; construction of solar tables; inequality of solar days, and the equation of time; spots of the sun, their form, and rotation; inequality of days and seasons in different climates; temperature of the earth; hypothesis of the earth's annual motion; precession of the equinoxes considered as the effect of the displacing of the terrestrial equator; use of the theory of the sun, and the motions of the equator, ecliptic, and equinoxes, in chronological researches, with some curious applications. This book contains much valuable matter, though not always exhibited in the best form. In the fourth chapter there is a short but useful note on the method of determining the longitude and latitude of a heavenly body, the right ascension, declination, and obliquity of the ecliptic being given; as well as the method of solving the converse problem. Let the obliquity of the ecliptic, d the declination of a star, or other body, a its right ascension, & its latitude, its longitude; then the following formulæ are deduced from the principles of spherical astronomy: sin. λ= sin. w cos. d sin. a + cos. w sin. d. cos. a sin. a tan. /= These two formulæ may be accommodated to the logarithmic calculus, by taking an auxiliary angle & such that tan. & = : for then exterminating sin. a from the first and tan. d, by means of the usual expressions for sines and cosines of sums and differences, there result tan. d sin. Again, to find the declination and right ascension the formulæ are similar, viz. tan. A tan. / tan. a sin. d sin. ∞ cos. A sin. + cos. w sin. λ . sin. (+) tan. a = cos. I Here, in like manner, taking a subsidiary angle, so that tan. Ø1 the resulting formulæ are, sin. / > sin. d sin. λ tan. a tan. / cos. (p cos. 1 sin. (pl sin. The angle of position S may be determined by either of the following theorems, viz. sin. S = sin. cos. a The preceding formula will answer for all positions of the stars, by making the sines, cosines, or tangents, positive or negative, according to the value of the arcs to which they correspond: they are very convenient in application, and, we think, preferable, on the whole, to the rules of Dr. Maskelyne for the same purpose, given in the first volume of Vince's Astronomy. sin. cos. l cos. d or sin. S = " One of the most remarkable results to which the theory of attraction has led, is that of the oscillation of all the irregularities of the planetary system within certain limits which they never pass. The variation in the obliquity of the ecliptic is an example of this kind; and M. Biot, in common with many other mathematicians, French and English, ascribes the discovery of this fact to M. Laplace, while, in truth, he has only the merit of affixing the last link to an interesting chain of deduction. Our countryman, Thomas Simpson, has the honour of forming the first; for, in the resolution of some general problems in physical astronomy, in his Mis cellaneous Tracts,' applying his results to the lunar orbit, he concludes, by showing that the effect of such terms or forces as are proportional to the cosine of the arch, is explicable by means of the cosines of that arch and of its multiples, (no less than the effects of the other terms that are proportional to the cosines of the multiples thereof,) a very important point is determined; for, since it appears thereby that no terms enter into the equation of the orbit but what by a regular increase and decrease do after a certain time return again to their former values, it is evident from thence that the |