for the fake of brevity the general multiplier) this following, 5-1.5+39—1.9+3.%* 1.5.13 + 5+3 5+3 9+3.2+ 1.13 1.5.13. 5.17 13+3.23 5.9.17 + 4 &c. = +. 13-113+3.z3 &c.= 9.13.21 9+3.2+ 13+3.28 + 5.9.17 + + &c. + + 1.13 5.17 9.21 1.5.13 5.9.17 17-6.24 21-6.z 5.17 24 + -13 + 9z+ 9.21 3 1.13 9.13.21 + &c. 9.21 &c.; + X: 32 9.17 + + 48 Mr. Simplon's conclufion. And here without recurring at all to any general form, we have put down every figure that we actually made use of in the operation; and all the transformations we have here given are far more evident than that which Mr. Simplon found neceflary, in order to be able to reduce the original feries within the rank comprehended under his general formula. Our limits, however, will not allow us to enlarge further on this fubject. Mr. Clarke is indeed very fevere upon his antagonist; bringing charges which, if true, would make Mr. Landen appear very little indeed. For he fays, at p. 53d of his Supplement And now, gentle Reader, for your farther acquaintance with men, manners, and things, I fhall prefent you (by way of conclufion) with the tranflation of a few pages from the Ala Eruditorum of Leipzig, for September 1762 (p. 458.); and when you have well digefted, and ftrictly compared it with that gentleman's fecond Memoir (p. 23, &c.), particularly the 9th and roth Articles thereof, I would advise you to annihilate those wonderful infignia with which that memoir is fo profufely embellished; not only as a juft facrifice to the manes of J. F. De Tufchis de Fagnano and his venerable father, but that the fourrilous and ill-natured may not thereby take occafion to say, that a British Mathematician had afcribed the honour of a difcovery to himself, which he had "bafely pilfered" from a foreigner' . . . He He then puts down from the above-named Acts, the demonftration of a theorem, containing fome properties given by Mr. Landen in his fecond Memoir, who, in anfwer, fays, in the poftfcript of his Appendix... With refpect to what may have been difcovered by 7. F. De Tufchis de Fagnano and his father, I can, with the ftricteft regard to truth, aver, that I had never, by any means whatever, seen (or heard of) any of their Works before the publication of Mr. Clarke's Supplement: nor have I seen any of the Acta Eruditorum, or Diarium Eruditorum Italiæ, or the Works printed at Pefaro, mentioned in that pamphlet.—Its author, therefore, may take fhame to himfelf for the illiberality of his reflections!-If I have proved his want of skill, he himfelf has proved his want of candour.... And indeed we fee no reafon for not believing Mr. Landen, his method of investigating thefe properties being wholly different from what is tranflated by Mr. C. and bearing all the marks, or internal evidence, of originality. Abftrufe mathematics are now cultivated by able hands, in fo many different nations and languages, that few private persons have the opportunity of feeing all that is done on thefe fubjects. Mr. Clarke feems to us to have an advantage, which those that live in retired fituations can rarely poffefs, namely, that of confulting a good public library. If then he would have taken the trouble, with any tolerable share of candour and impartiality, to have given a fhort account of the invention and improvement of each formula, afcribed to their proper owners; it would have been an honour to himself, and an acceptable piece of service to the Public; as our English mathematicians efpecially are shamefully deficient in particular acknowlegements. ART. III. An Introduction to Natural Philofophy. Illuftrated with 125. HIS treatife, the Author tells us, is intended to give a clear account of the prefent ftate of Natural Philofophy to fuch as poffefs very little mathematical knowledge. That his grand object, throughout, has been to relieve the memory, and allift the understanding by concifenefs, and illuftrative arrangement. And notwithstanding the nature of the undertaking unavoidably required a deviation from thofe beautiful and general principles, which are obtained by ftrict mathematical reasoning, yet it is prefumed, he fays, that the ftudent will find nothing in this treatife which he will be under the neceffity of unlearning, when he attempts the perufal of thofe books, to which this is offered as an introduction. From these short extracts from the Author's own account of this performance, it will be feen, feen, that thofe branches of phyfics, which include the nature and laws of motion, mechanics, hydraulics, optics, and aftronomy, can be but curforily touched upon in this performance; and indeed this part was the leaft wanted, because we have already fo many excellent elucidations of thefe branches... What feemed chiefly wanting now, was fomething in an elementary form, adapted to the capacity of beginners, concerning the great difcoveries and improvements made by Dr. Priestley, and others, in Aerial Phyfics, Chemistry, and Electricity. On the two firft of thefe fubjects Mr. Nicholfon has been particularly explicit and as a fpecimen of his method of proceeding, we fhall, for the entertainment of our young philofophical Readers, felect his account of phlogifton, vol. ii. p. 160. The element, phlogifton, is by many chemifts termed fire; and in order to diftinguish it from heat, which they likewife call fire, the phlogifton is called combined fire, while heat is denoted by the term Elementary Fire. But this manner of expreffion prefuppofes a certain theory of fire, which is by no means established. We are ignorant whether heat be a mode or a subftance; and to ufe the fame term to exprefs both it and phlogifton, which, in fact, is no more than the principle of inflammability, muft tend to confuse our notions, and betray us into a persuasion, that we know more of the fubject than we really do. It will therefore be neceffary to keep as near the facts as poffible. Phlogifton is that by which bodies, when in contact with pure air, and heated to a certain degree, are put into a state of combuftion, during which they are in a great measure decompounded, and moft commonly, or perhaps univerfally, exhibit an appearance of flame. To vindicate the admiffion of the cause of inflammability, or phlogifton, among the elements, it will be neceffary to fhew, that it is a fubftance, and not a mere modification of the parts of bodies; and that it is fo univerfally fimilar to itself as to be eafily distinguished in all the various bodies which are combuftible. For this purpofe, let us attend to all the circumftances attending combuftion, and from thence make our inferences. First, All combustible fubftances, which can be exposed to great heat in clofe veffels, cannot, in that fituation, be calcined or burnt; and in the open air the calcination is more quickly effected accordingly as the fupply of pure air is greater. Secondly, If a combuftible fubftance be inflamed, and afterwards included in a veffel, with a small quantity of atmospherical air, the combuftion lafts for a certain time, and then ceafes; this time, and confequently that part of the mafs which becomes calcined, is greater or lefs according to the quantity of pure air included; and, at the end of this time, the air is found to be decompofed, part being fixed and precipitated, and the remainder, which is about four-fifths of the original quantity, is fo changed, as to be unfit for the purpofe of affifting combuftion, and is in fome degree noxious. Thirdly, Sulphur may by combuftion be deprived of its inflammable principle, by which means it is converted into the vitriolic acid; and again, the vitriolic acid, being properly treated with any inflammable fubftance, may regain the phlogifton, and be converted into fulphur, which fulphur is poffeffed of the fame properties, however different the properties of the inflammable fubftances may have been by which the phlogifton was furnished. Laftly, The calces of fixed compounds, as metals, may be restored to their original state, by being treated with fome inflammable fubftance; and the metal is in all cafes the fame, however various the phlogiftic fubftances may have been by which it was revived. The natural deduction from the fe facts appears to be, that phlogifton is a fubftance which is very fimple and fimilar to itfelf. For what can the enclofing a combuftible body in a clofe vefle! do, but prevent the difperfion of fome fubftance? If calcination be no more than a change in the arrangement of the parts of bodies, why fhould not heat affect [effect] this as well in clofe as open veffels? Is it not evident in the fecond inftance, that the phlogifton becomes combined with the decompounded fluid air, and caufes it to depofite one of its principles in the form of fixible air, while the calcination of the i flamed body goes forward; and does not the combuftion cease when the remaining principle, or principles of the air, being faturated, are incapable of receiving any more phlogifton? When fulphur, by combuftion, is tranfmuted into vapours, which, when condenfed by means of water, and afterwards concentrated, are found to be the vitriolic acid, ought we not to conclude, that this very inflammable fubftance is converted into a fubftance which is not at all fo, by having loft one of its principles, namely, phlogiston? But when, on the other hand, the converfe of the problem is effected, by producing fulphur from a wellmanaged combination of the vitriolic acid with the inflammable principle of fome other body, we can hardly entertain a doubt of the exiftence of this fubftance, and at the fame time learn, from its effects, that it is fimilar in all inflammable bodies. And this fimilarity of the phlogifton is ftill more evident from the reduction of the calces of metals; for if a metalline calx be properly treated with any inflammable fubftance, the external air being excluded, the metal, from which the calx was originally inade, will be reproduced. The phlogifton of inflammable bodies being feparable only when those bodies are in contact with others with which it can combine, it is not probable that we fhall ever be able to obtain it in an uncombined and detached ftate. But it is by no means proper to speak decifively on a fubject in which so much remains yet to be investigated.' He proceeds then to give a very clear account of the other fimples and compounds, which is both useful and entertaining; but we cannot pretend to defcend to particulars. We, however, recommend the work particularly to thofe who have not leifure or 'opportunity for confulting many books, and still are defirous of having fome acquaintance with thefe fubjects. Agr. IV. Part the First of an Introduction to the Writing of Greek after the Manner of Clarke's Introduction to Latin. For the Uie of Winchester College. By G. J. Huntingford, A. M. Fellow of New College, Oxford. The Third Edition, with confiderable Improvements. 8vo. 25. Oxford, printed. Dodley. 1782. ART. V. Part the Second of an Introduction to the Writing of Greek ; being select sentences from Xenophon's. Cyropædia, for the Ufe of Winchefter College, By G, J. Huntingford, Fellow of New College, Oxford. Svo. 2s. 6d. Oxford, printed. Sold in London by Dodfley. WE E could not procure thefe little books at their first publication, from which circumftance we conclude, that they were confined folely to the use of Winchester college. We fhould otherwife have beftowed on them, much earlier, the notice to which they are justly intitled, from their claim to originality: a claim which would have inclined us to commend them, even if the Author had failed in his attempt. Mr. Huntingford, in printing these publications, has very judicioufly followed Mr. Warton*, in the rejection of accents. We know no reason, why they fhould ever deform the pages of Greek literature. To ftudents, they are only unneceffary puzzles; and to the learned, they seem of little ufe; and that little is, perhaps, fanciful-if we except, however, that the accents have frequently afforded them opportunities of difplaying their erudition. The mode of giving the examples in Greek and English we highly approve; but ftill we do not feel fatisfied. We cannot help withing that a Latin tranflation had likewise been added. The two languages are now united by the strongest ties, and will adhere more clofely every day: a connection furely very defireable, and which cannot, indeed, be avoided, as long as Mr. Warton published his learned and elegant edition of Theocritus without accents; and they have also been rejected by Mr. Tyrr whit, in the editions of Babrius, Orpheus, and Plutarch, with which he has favoured the literary world. they |