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the analogous semi-axes of the two ellipsoids : the point thus assumed will be within the second ellipsoid, and its attraction may be calculated parallel to each of the three axes of that ellipsoid. In order to deduce the three attractions of the external point to the first ellipsoid, it is only necessary to multiply those of the second by the ratios between the products of the other two axes in the respective ellipsoids. If the proposed spheroid differ little from a sphere, the series which express the attractions become very convergent. In all cases the investigation is extremely elegant; and though in some particulars it is susceptible of improvement, it proves that Mr. Ivory is profoundly acquainted with the sublimer departments of analysis, and it will obtain for him an honourable rank among mathematical philosophers.
Two of the papers in the present volume, viz. the 5th and the 12th, contain Dr. Herschel's observations upon two comets which appeared in the winter of 1811-1812, with remarks on their probable construction. We are not converts to Dr. Herschel's theory respecting these singular bodies ; though it is but fair to remark that the celebrated Laplace has adopted it, as appears from a dissertation he has published in the Connaissance des Tems, pour l'an 1816. Herschel's hypothesis is, in brief, this :-he regards comets as small nebulæ formed by the condensation of the nebulous matter which is spread with so much profusion throughout the universe. Comets become thus, with regard to the solar system, what aëroliths are, probably, relatively to the earth. When these stars first become visible to us, they present a resemblance to nebulæ so perfect, that they are frequently confounded with them ; so that, it is only by their motion, or by an acquaintance with all the nebule comprised in the part of the sky where they appear, that we are able to distinguish them. For the full detail of this hypothesis, and some ingenious applications of it, to the two comets here observed and described, we must refer to Dr. Herschel's papers. .
The 16th paper in the volume, is “ On the attraction of such
lids as are terminated by Planes, and on Solids of greatest attraction. By Thomas Knight, Esq. The general problem here solved is thus enunciated :— Any solid, regular or irregular, terminated by plane surfaces, being given, to find, both in quantity and direction, its action on a point given in position, either within it or without it.' This general problem is considered under forty subordinate ones; and the discussion is thrown
; into five sections. 1. Of the attraction of planes bounded by right lines. 2.' Of the attraction of pyramids, and generally of any solids whatever that are bounded by planes. 3. • Of the attraction of prisms.' 4. ' Of the attraction of certain solids not terminated by planes.' 5. Of solids of greatest attraction.'
The investigation is conducted with tolerable accuracy, though not, we think, with much elegance, the whole being too much wire-drawn. We have not in the perúsal been struck with many novel or important results : but we confess we were rather surprised at Mr. Knight's observation, that the only person who had preceded him extensively in this line of inquiri, was Mr. Playfair. There is a strange propensity in the minds of some men to forget the obligations under which this class of investigations lies to the labours of Dr. Hutton in relation to Mount Schichallin, and the determination of the point of greatest atraction in a hill. The Philosophical Transactions, however, do not furnish the best place in which to manifest such negligence and forgetfulness, because it was in the early volumes of these Transactions that Dr. Ilutton's inquiries as to this very point were first given to the world.
The 15th paper in the present volume is also by Mr. Knight, and relates to the penetration of a hemisphere by an indefinite number of equal and similar cylinders.' Vivianu and Bossut, as is well known to matheinaticians, long ago developed soine curious propositions in reference to the piercing of hemispheres by cylinders They constitute individual cases of Mr. Knight's problem which is genral : viz. • To pierce ai hemisphere, perpendicularly on the plane of its base, with any number of equal and similar cylinders ; of such a kind, that, if we take away from the hemisphere those portions of the cylinders that are within it, the remaining part shall admit of an exact cubature : and if we take away, from the surface of the hemisphere, those portions cut out by the cylinders, the remaining surface shall admit of an exact quadrature. Mr. Knight here
' employs the word cylinder to denote any right prism with a symmetrical curvilinear base : and he exhibits a simple solution to the problem, by means of an elegant construction, which, we regret that we cannot render intelligible independent of a diagram.
No. 17 of the volume before us, is one which we are astonished to see inserted in the Philosophical Transactions. It is entitled, “Observations on the Measurement of three Degrees of the Meridian, conducted in England by Lieut. Col. William Mudge. By Don Joseph Rodriguez.' It is written appa
, rently for the unworthy object of casting discredit upon a great and important national work; though, happily, the attack being made on an impregnable fortress, and being moreover conducted very unskilfully, has failed altogether. Don Rodriguez, however, a foreigner, and one who had been united with some of the French mathematicians in measuring a degree in the neighbourhood of Barcelona, is permitted, during a war between the two nations, to occupy, in the Transactions of the Royal Society, thirty pages, in drawing an unfair comparison between the talents and skill of the French and those of the English observers ; in pretending to detect an error of four and a half seconds in a series of zenith distances, where no such error was to be found ; and in attempting to make it appear that nothing as to this important and interesting class of investigations, was effected previously to the French Revolution, nor after it, except by the French themselves! We have no inclination to assume a harsh tone even on such an occasion : yet we must say, that nothing but great weakness of judgement, or great unworthiness of motive, in those who, in 1812, had the management of the Royal Society publications, could have permitted the insertion of so despicable a dissertation as this. Nor do we wish to dwell upon so ungracious a topic; especially, as we have reason to believe that the few members of the council,' who thus committed themselves, have long ago been ashamed of their conduct, and, because the public decision has been some time formed upon this question. Dr. Gregory's animadversions upon Don Rodriguez, in No. 159 of Nicholson's Philosophical Journal, and No. 179 of Tilloch's Philosophical Magazine, have exposed the general fallacy of that writer's reasonings, and proved that it is absolutely impossible in the nature of things that there can be an error of the magnitude the Don pretends, or indeed any appreciable error. The Chevalier
. Delambre also, who has entered very candidly into this question, in the Connaissance des Tems, pour l'an 1816, gives it as his opinion that such an error in the observations, is highly improbable; and complains that Don Rodriguez's examination is partial, and not sufficiently far extended. Indeed, the only person, so far as we know, who bas ventured to state in public his approbation of Don Rodriguez's attempt, and his belief in the accuracy of his charges, is Dr. Thomas Thomson. But what pretensions Dr. Thomson has to intermeddle in a question of astronomy, or what satisfaction he can derive from permitting himself to be made the tool of others in such a question, we are at a loss to conjecture. Some years ago be published a book on chemistry, which, to the best of our recollection, was neither much admired, nor much censured : last winter he delivered some prosing, somnific lectures on the same subject in the Surrey Institution : he is also the Editor of a Journal of Natural Philosophy, in which he has already attained some celebrity for not knowing the meaning of the word genie, and for the acrimony with which he animadverts on those of his chemical correspondents who do not agree with him; and he has produced a crude book of Travels into Sweden, and a cruder History of the Royal Society * But all this, makes him neither an astronomer, nor a judge of astronomical matters : and we really regret for his own sake that any considerations (we have no desire to unravel them) should have tempted him to take part in a discussion to which he is so obviously incompetent.
The last paper we have now to notice, is No. 19, 'On a periscopic Camera Obscura and Microscope. By William Hyde
. Wollaston, M. D. Sec. R.S.' 'This gentleman, three or four years ago, drew the attention of the public, to what he regarded as a new construction of spectacles, under the denomination of periscopic, but what is, in fact, only a revival of the meniscus glass, which had heen employed seventy years ago for the same purpose. The Doctor's object was to increase the field of distinct vision ; an object which was in some measure obtained, though the construction necessarily produces some disadvantages. The benefits, however, resulting from his contrivance, became augmented when applied to the Camera Obscura. Hé makes the lens a meniscus, with the curvatures of its two surfaces nearly in the ratio of two to one; and this meniscus is so placed, that its concavity is presented to the objects, and its convexity towards the plane on which the images are formed. The aperture of the lens he makes four inches, its focus at about twenty-two. He places also a circular opening, two inches in diameter, at about one-eighth of the focal length of the lens from its concave side, for the purpose of determining both the quantity and the direction of the rays that are to be transmitted. This construction is throughout ingenious, and will doubtles, be found preferable to the common Camera Obscura.
Dr. Wollaston then proceeds to adopt the ‘ periscopic principle' to the improvement of the microscope and the camera lucida : but we have not room to detail the peculiarities of their respective constructions. Indeed, we think the whole paper, though by no means void of ingenuity, is rather fitter for insertion in a monthly philosophical journal, than in the Philosophical Transactions.
Art. VI. Sermons, designed chiefly for the use of Villages and Fami
lies. By Thornhill Kidd. 8vo. pp. 442. price 8s. 12mo. price 5s.
Pontefract printed. Gale, Curtis, and Co. London. 1814. IN our last number we had occasion to remark the very small
proportion of works, bearing the indefinite title of Sermons, which are adapted to domestic or social reading. It is far from improbable, indeed, that many an excellent volume of the kind desired, may, from the want of the attraction of a name, or from some circumstance of arbitrary recommendation, have been suffered to sink into oblivion. Even when possessed of acknowledged merit, Sermons are not likely to obtain that lasting attention, which might preserve them beyond the period of ephemeral existence. There exists a prejudice which leads us to hold indiscriminately in light estimation compositions of which there is so immense a quantity constantly produced ; and Dissenters may, perhaps, be suspected to extend to written Sermons, the impatient dislike with which they endure the repetition of discourses delivered by the preacher. Yet it might be sufficient to rescue this class of compositions from this disadvantage, that there are so few who have excelled, while so many have easily attained mediocrity, if it were not that the title of Sermons' has become too generally a sign of ephemeral or uninteresting productions, to awaken attention, and that where the title of a work affords no clue to the judgement, few readers are competent to select for themselves, or to appreciate those of distinguished excellence.
It will, however, be readily allowed that we have but few collections of Sermons, adapted to families and to village reading. They require in the author a peculiar talent; or, if we were called upon to give in one word the leading and almost sufficient qualification for this peculiar mode of instruction, we should rather say, provided there be a moderate degree of real talent, simplicity of mind. By this, we mean a rarer attribute than genius ;-a simplicity, which, averse to exaggerate the truth, or any part of the truth, in order to render it impressive, refuses, on the other hand, to abate or qualify the truth in any of its properties, to render it more palatable, but preserves a directness of aim, and trusts for success to the authority which enforces the message:-a simplicity which will not permit the mind to content itself with the mechanical discharge of the sacred functions, how successful soever, or with the achievement of mere correctness of method or of system, but which is ever prompting the energies of feeling to secure, with the assent of the understanding, the effectual sympathy of the hearers, in relation to subjects of common and of infinite interest. Whatever admiration may be excited by the powers of oratory, the Vol. II. N.S.