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parison greatest at or near the Moon's surface. But as we recede from the Moon, and approach to the Earth, this force decreases, while the other augments; and at one point between the two planets, these forces are exactly equal, so that a heavy body, placed there, must remain at rest. If, therefore, a body is projected from the Moon towards the Earth, with a force sufficient to carry it beyond this point of equal attraction, it must necesfarily fall on the Earth. Nor would it require a very great impulse to throw the body within the sphere of the Earth's superior attraction. Supposing the line of projection to be that which joins the centres of the two planets, and supposing them to remain at rest; it has been demonstrated, on the Newtonian estimation of the Moon's mass, that a force of projection moving the body 12,000 feet in a second, would entirely detach it from the Moon, and throw it upon the Earth. This estimate of the Moon's mass is, however, now admitted to be much greater than the truth; and upon M. De la Place's calculation, it has been hown that a force of little more than one half the above power would be sufficient to produce the effect. A projectile, then, moving from the Moon with a velocity abour three times greater than that of a cannon ball, would infallibly reach the Earth ; and there can be little doubt that such forces are exerted by volcanoes during eruptions, as well as by the production of steam, from subterranean heat. We may easily imagine such cause of motion to exist in the Moon, as well as in the Earth. Indeed, several observations have rendered the existence of volcanoes there extremely probable. In the calculation just now referred to, we may remark, that no allowance is made for the resistance of any medium in the place where the motion is generated. In fact, we have every reason to believe, from optical confiderations, that the Moon has no atmosphere.

A body falling from the Moon upon the Earth, after being impelled by such a force as we have been describing, would not reach us in less than two days and a half. It would enter cur -atmosphere with a velocity of nearly 25,000 feet in a second ; but the resistance of the air increasing with the velocity, would foon greatly reduce it, and render it uniform. We may remark, however, that all the accounts of fallen stones agree in attributing to the luminous bodies a rapid motion in the air, and the effects of a very considerable momentum to the fragments which reach the ground. The oblique direction in which they always fall, muit tend greatly to diminish their penetrating power.

While we are investigating the circumstances that render this account of the matter highly probable, we ought not to omit one


confideration, which lies wholly in the opposite scale. The greater part of these fingular bodies have first appeared in a high state of ignition; and it does not seem easy to conceive how their passage through so rare a fluid as the atmosphere could have generated any great degree of heat, with whatever rapidity they may have moved. Viewing as we do, the hypothesis of their lunar origin as by far the most probable in every other respect, we will acknowledge that this circumstance prevents us from adopting it with entire fatisfaction. And while we see so many invincible objections to all the other theories which have been offered for the solution of the difficulty, we must admit that the supposition least liable to contradiction from the facts, is nevertheless sufficiently exceptionable, on a single ground, to warrant us in concluding with the philosophical remark of Vauquelin, • Le parti le plus fage qui nous reste à prendre dans cet etat des • choses, c'est d'avouer franchement, que nous ignorons entiere'ment l'origine de ces pierres, et les causes qui ont pu les. produire.'

If, however, a more extensive collection of accurate observations, and a greater variety of specimens, mall enable us to reconcile the discrepancy, and to push ftill farther our inquiries into the nature of the new substance, a knowledge of the internal structure of the Moon may be the splendid reward of our investigations. And, while the labours of the Astronomer and Optician are introducing new worlds to our notice, Chemistry may, during the ninteenth century, as wonderfully augment our acquaintance with their productions and arrangement, as she has already, within a much shorter period, enlarged our ideas of the planet which we inhabit.

Art. XIII. Analytical Insitutions : In Four Books. Originally written

in Italian by Donna Maria Gaetana Agneli, Professor of the Mathe. maticks and Philosophy in the University of Bologna. Translated into English by ihe late Rev. John Colson, M. A. F. R. S. and Lu. cafian Professor of the Mathematicks in the University of Cambridge. Now first printed from the Translator's Manuscript, under the inspec. tion of the Rev. John Hellins, B. D. F. R. S. and Vicar of Porter'sPury in Northamptonshire. 2 Vol. 4to. London. 1801. Sold by Wingrave.

A WORK on the most profound of the mathematical sciences,

from the pen of a lady, can hardly fail to be an object of attention. It has indeed been so among the learned on the conDd3


tinent for many years, and the author of it considered as one who, without taking into account the indulgence due to her sex, is entitled to rank high among the mathematicians of the 18th cen. tury. We regret, however, that of the history of a person so extremely interesting, but few particulars have yet come to our knowledge. The editor of the translation before us has collected some anecdotes; one of which, extracted from the President de Broffes's letters from Italy, is truly fingular, and, though of undoubted authenticity, calls to mind the marvellous stories which are told of Pica di MIRANDOLA, and the Admirable CREIGHTON.

De Broffus, in passing through Milan (about the year 1740), was carried to a converzatione on purpose to meet Signora Agnesi, whom he describes as a young lady about 18 or 20, who, though she could hardly be called handsome, had a fine complexion, with an air of great fimplicity, softness, and female delicacy:

• There were,' says he, about thirty people in the room, many of them from different countries in Europe, who formed a circle round the lady and a little fitter who accompanied her. The count Belloni ad. dresied her in a fine Latin speech, with the formality of a college decla. mation. She answered with great readiness and ability in the same lan.' guage ; and they then entered into a disputation (itill in Latin) on the origio of fountains, and on the causes of the ebbing and flowing which is observed in some of them like the tides in the fea. She spoke on this Subject like an angel, and I never heard it treated in a manner that gave me more satisfaction.

! The Count then desired me to enter with her on the discussion of any other subject I chofe, provided that it was connected with matbematicks or natural philosophy. After making the best apology I could to the lady for my want of sufficient skill in the Latin language to make me worthy of conversing in it with her, we entered, first, on the manner in which the impressions made on the senses by corporeal objects are communicated to the brain or general fenforium ; and afterwards on the propagation of light, and the prismatic colours. Another of the copi. pany then discoursed with her on the transparency of bodies, and on cur. yilinear figures in geometry, of which laft I did not understand a word.

! She spoke wonderfully well on all these subjects, though she could not have been prepared before hand, any more than we were. She is much attached to the philosophy of Newton; and it is marvellous to see a person of her age so conversant with fuch abstruse subjects. Yet, however much I was surprised at the extent and depth of her knowledge, I was still more amazed to hear her speak Latin with such purity, ease and accuracy, that I do not recollect any book in modern Latin writtea in to classical a style as that in which she pronounced these discourses. The conversation afterwards became general, every one speaking in the language of his own country, and the answering in the same language ; Ther knowledge of languages is prodigious. She told me that she waz


sorry that the conversation of this visit had taken so much the formal turn of an academical disputation, and that the very much diliked Ipeak. log on such subjects in numerous companies, where, for one that was amused, twenty were probably tired to death.-1 was forry to hear that the intended to go into a convent and take the veil, not from want of fortune, for the is rich, but from a religious and devout turn of mind, which disposes her to fhun the pleasures and vanities of the world.'* .

After her work of the Instituzioni Analytiche was published, the was made professor of mathematics and philofophy in the University of Bologna. But neither the admiration the everywhere met with, nor the entreaties of her friends, could prevent her from executing the resolution she had taken of secluding herself from the world. After the death of her father, she retired to a convent of blue nuns, remarkable for the autterity of its rule ; and ended her days in one of those retreats, in which mittaken piety has so often buried the charms and accomplishments, the virtues and the talents which might have adorned and improved fociety. The fate of Pascal and Agneli will remain a melancholy proof, that the most splendid abilities, and the highest attainments in literature and science, cannot always defend the mind against the inroads of superstition and fanaticism.

Mr Hellins, the editor of the present work, has quoted Monfucla's encomium on this extraordinary woman, to which we must beg leave to add another of still higher authority, that of her countryman Frifi, who has excelled so much both in pure and mixt mathematics, 5 DOMINA MARIA CAJETANA AGNESIA Ana. lyticas Institutiones edidit anno 1748, opus nitidiffionum, ingeniofillin mum, et certe maximum quod adhuc ex fæemine alicujus calamo prodierit.' Frisi Opera, Præf. tom. imus. A French mathematician of great eminence, M. Bofiut, has alto beltowed on the Institu. zioni Analytiche the most unequivocal praise, by translating the 20 volume of it into French, and inserting it in his course of mathe. maticks, professedly as the best treatise he could furnille on the ele. ments of the differential and integral calculus.

It is to the liberal and enlightened patronage of Baron Maferes. to which the mathematical sciences are already under so high ob ligations, that we are indebted for the prefent translation of this work into English. The translation was made many years ago by the late Professor Colson, the ingenious commentator on the Fluxions of Newton. Baron Maferes, who in his youth had known Colson, and had reason to suppose from his conversation. DI 4

that • In the edition of de Brosses which we have seen, the lady's name is spelt, throughout, Agnery. The Monthly Review, from which Mr Hellins made his extract, seems to have corrected this errur very Arspos by spelling it Anglese,

that he had written a treatise on the higher geometry, as an addi. tion to the commentary just mentioned, was desirous of discover. ing this manuscript, and of giving it to the world. In his search he found, not the work he looked for, but the translation just mentioned; and after removing some pecuniary difficulties, which, without such generous assistance, would probably have for ever withheld it from the world, he obtained a copy of it, and put it into the hands of Mr Hellins, who undertook to become the editor.

In reviewing a book that comes before the public with so many extrinsic circumstances in its favour, an effort is required to preserve impartiality, and particularly, in the present case, to prevent our admiration of the author from influencing our opinion of her work. We have perused it accordingly, keeping this cau. tion continually in view ; and the favourable judgement we have nevertheless to report, is formed, we flatter ourselves, entirely on the intrinsic merit of the book.

The Analytical Institutions are divided into four books. The first contains the analysis of finite quantities, and occupies the whole of the first volume. The remaining three make up the ad volume, and treat of the analysis of infinitely small quantities. Each of these books is divided into sections; and a running margin renders the whole very convenient to peruse and to consult.

The First book begins, of course, with the ordinary rules of algebra, the solution of fimple equations, &c.; and in this most elementary part we do not perceive any peculiar excellence, except the uncommon clearness with which every part of the Institutions is written. It is in treating of variable magnitudes, or of the application of algebra to geometry, that the peculiar elegance of Donna Agneli's analysis first begins to appear. The subject of Loci, in itself so beautiful and interesting a part of geometry, could not fail to attract the attention of one who pursued that science merely for the love of it. The examples which she gives are well chosen ; the analysis of them is always ingenious, and conveys much instruction concerning the methods and principles of investigation. This part of the work is indeed eminently calculated to improve the student of geometry; and though other treatises on the same subject, more complete and systematic, have appeared since this was written, we do not bclieve that their exists, at the present moment, any one so well adapted to communicate folid and practical instruction in this branch of analysis, or so likely to sharpen the invention of a beginner, and to make him well acquainted with the resources of his art.

These observations are also applicable to the construction of determinate problems, by the intersection of Loci, in which great


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