puted to be 200,000; befides these, about one-fourth as many are, in confequence of thefe fisheries, employed on fhore, in the building of hips, making nets, curing the fish, &c. &c. "Therefore, fuppofing us only to come-in for one-half of what the Dutch enjoy, we thail gain, befides emyloyment to upwards of 12,000 artificers, an acceffion of 100,000 feamen, two-thirds of which would be always on our coafts, ready to man our fleets on every emer gency. A moit noble refource! This fhews, in the strongest manner, the abfolute neceffity there is for the free import and export of grain and provifions; becaule, from this only can provifions and wages become lower, and upon the lownefs of thefe depends the acceffion of the riches and power attendant on ex tenfive fisheries. The fame caufes will produce the fame effects in the English and Irish fisheries, fo.as to enable them to contribute their share to the grandeur and increafe of the British maritime power." The other objects of domeftic improvement here infifted on, are the methods of manning the navy, the execution of the laws in Scotland, and a reviñion of the laws in England repecting the poor; an object of the firft magnitude, refpecting the internal police of this kingdom. The tenth and laft fection contains confiderations on Eat India affairs; but, for the particulars of this, and alfo of the author's appendix, relative to the emancipation of flaves, we muft refer the inquifitive reader to the performance ite felf. W. A Treatife concerning Porifms. By Robert Simfon, M. D. In which the Author hopes that the Dotine of Porifms is juffici ently explained, and for the future will be fafe from Oblivion. Tranflated from the Latin by John Lawson, B. D. 4to. 25. 16d. Nourfe, &c. Mr. Lawfon has here only given five fheets of Dr. Simfont treatife; fenfible of the confined fale of publications on fo abAracted a fubject, though not without hopes that the lovers of geometry will encourage the tranflation of the whole, for the following reafons: ift, On account of the great curiofity of the fubje&t, which has lain in total obfcurity and oblivion ever fince the time of Pappus Alexandrinus, as will be feen in the Preface. 2d, On account of the great abilities of the author, the late Dr. Simfon, who has always been efteemed the firft geometer of the ages Lastly. Laftly, On account of the peculiar circumftance of this and the Doctor's other Pofthumous Pieces, viz. that they are not to be purchased for money, they having been printed at the expence of that noble Patron of mathematical learning, the Right Honourable the Earl Stanhope, only to be difpofed of in Prefents. It is out of regard to the fcience of geometry, and to pro duce the neceffary encouragement for continuing the tranfla tion of this valuable work, that we fhall quote the author's preface entire; well perfuaded that our geometrical readers will think themfelves not a little obliged to us, for fome elucidation of a fubject, to which many, if not moft, of them are ftrangers. ***There is nothing to be found among the antient geometers concerning Porifms, except what Pappus has preferved. And Fermat, in his Var. Oper. Math. page 116, afferts that the Moderns did not fo much as know them by name, or only gueffed at what they were. Yer I find that before Fermat Albertus Girardus thought of explaining and restoring them, who, in his Trigonometry written in French and publifhed at the Hague r629, after enumerating the forms of rectilineal figures, which have four, five, or fix fides, add this, "Le tout, quand il n'y a que deux lignes qui paffent par un point, comme jadis eftoyent les Poritmes d'Euclid, qui font perdus, lefquelles j'efpere de mettre bien tot en lumiere, les ayant reftituez il y a quelques années en ça.' And again in the Mathematical Works of Simon Stevin, which Girardus published, amended and augmented at Leyden 1634, after he had faid in page 459 that Euclid very seldom used compound ratio, he fubjoins, Mais il eft à estimer qu'il en a plus efcrit en ces trois livres de Porifmes qui font perdus, lefquelles, Dieu aidant, j'espere de mettre en lumiere, les ayant inventez de nouveau." From which it appears that Girardus, a man uncommonly skilled in mathematics, thought that he had restored the Porifins; but what he had written concerning them was never published, and unlefs perhaps it lies concealed in fome library in Holland, it is to be esteemed as loft. But from the first of thetè quotations it feems that he took fome propofitions concerning quadrilateral figures and others and their affections for: Porifms, and that therefore he did not understand their nature. "After Girardus Ishmael Bullialdus, in his third geometrical exercitation, which with the two former was published at Paris 1667 endeavoured to explain the Porifms; but although he received fome things concerning them from Fermat, for he cites Fermat's words which were afterwards printed in his renovated doctrine of Porifms among his various mathematical works at Tholofe 1679; yet Bullialdus could by no means clear up the matter. Now in this book of Fermat's, which was published after his death, there are found a few things, but it feems they are all that he had committed to writing concerning Porifms. From which it appears, that to this most fagacious man alone any thing was known concerning their nature from the time that Pap pus lived. But fince he confefles that he penetrated into the fecrets of is matter almoft without any other affiftance than what he was fur ained with from that corrupt definition which Pappus juftly blames the junior geometers for giving of a Porifin, viz, that a Porifm is that which is deficient in hypothefis from a local theorem; it is certain that he did not fufficiently understand what Porifins were. For Fermat is by no means right in affirming that this definition fpecifically difoo vers the nature of a Porifin, fince there are innumerable Porisms which by no means depend upon a local theorem, and have nothing common with loci. Fermat indeed promifes in the fame writing that he will fome time or other restore the whole three books of Porilms, and bring to light (thefe are his words) other wonderful and unknown matters; but this was too rafhly fpoken, for there are many of Euclid's Porifms of which there is not any ftep or veftige extant; and Fermat has not enucleated the first of the first book, which alone Pappus has preferved entire. *There is no occafion to relate here what Charles Renaldine has on this fubject in his book De Refolutione et Compofitione Mathema tica, for it is by no means fubfervient to the knowledge of Porifms. And these are the only authors, as far as I know, who have made any mention of Porifins, at least who have in any manner attempted to explain them. And though the celebrated David Gregory, in his preface prefixed to Euclid's works, fuppofed "That it would not be difficult infome fort to restore the Porifins, when the Greek text of Pappus fhould fee the light," yet his colleague, the learned Halley, not lefs converfant in the geometry of the antients than Gregory, after having publifhed the Greek text as much corrected as he could, ingenuously fabjoins the following words to Pappus's defcription of Porifms: Thus much for the defcription of Porifms, which can neither be ufeful to me nor the reader, nor can it otherwife: both on account of the want of the scheme of which mention is made; from whence many right lines here treated of without any alphabetical marks, or any other characteristic distinction, are confounded one with another, and alfo because of fome things omitted and tranfpofed, or otherwife vitiated, in the expofition of the general propofition; from whence I am not able to guess what Pappus ineant. Add moreover a mode of expreffion too -concife, and which ought never to be used on a difficult fubje&t, fuch Pas this is. "But after I had read in Pappus that the Porifms of Euclid were a moft curious collection of many things which related to the analyfis of the more difficult and general problems, I was earnestly desirous of knowing fomething about them; wherefore often and by various ways I endeavoured to understand and to restore as well Pappus's general propofition, lame and imperfect as it was, as alfo the first Porifin of the first book, which, as was faid before, is the only one out of the three books which remains entire; but my labour was in vain, for I made no proficiency. And when thefe thoughts had confumed much of my time, and at length had become very troublesome, I firmly refolved never to make any further enquiry for the future, especially as that beft of geometers Halley had given up all hopes of understanding Them. Therefore as often as they occurred to my mind I endeavoured to put them by. Yet afterwards it happened that they feized me un awares, awares, forgetful of my refolution, and detained me fo long till fome light broke in which gave me hopes of at least finding out Pappus's general propofition, which indeed not without much investigation I at length restored. Now this foon after, together with the first Porifm of Book I. was printed in the Philofophical Tranfactions for 1723, No. 177. "But because at that time I did not fufficiently understand the na ture of a Porifm, I think proper now to deliver it more explicitly, that this kind of propofitions, and the way by which they are investigated, which geometers from the time that Pappus lived have been ignorant of, may be restored to geometry, and may bring no contemptible in ereale thereto. And because Pappus's defcription of Porifins is not eafily to be understood without a fpecimen of them, therefore I have thought proper to premife fome eafy Porifms to the explication which Pappus offers of them; and then to Pappus's defcription of them to fubjoin fome of Euclid's Porifms, namely, fuch as I could diftinguish to be fuch, either from Pappus's general propofition, or his defcription of Poritms; or laftly, by help of his lemmas for the Porifms. After thefe follow four of Fermat's propofitions changed into the form of Porifins, for the remaining one of his five is concerning the parabola; and I have demonstrated it in my Conic Sections, Prop. 19. B. V. 2d Ed. There are fome other things added, the chief of which were propofed to me, and the conftruction of fome of them given, by that excellent geometer, Matthew Stewart, Profeffor of Mathematics in the University of Edinburgh, by whom this matter has already been well, and I hope for the future will be much, cultivated." In hopes that the learned and ingenious tranflator will meet with proper encouragement to compleat an English version of Dr. Simfon's treatise, we referve our opinion of its execution and importance to a future article. W. Thoughts General Gravitation, and Views thence arifing as to the State of the Univerfe. 1s. Cadell. It is the general error of fpeculative minds to be more attentive to what paffes within themselves than to the observations and discoveries of others, even on fubjects of their immediate contemplation. Hence it is that these profound thinkers, after a world of reflection, make wonderful difcoveries of things known to every body but themselves. Not that the prefent writer has made any other difcovery, in the prefent pamphlet, than that he knows very little of the profeffed fubject of it. The late facetious author of Tom Jones fomewhere ludicrously obferves, that every writer will probably treat his fubject the better for knowing fomething about it. With this lage remark, therefore, we take leave of this thinker on general gravitation; recommending him the next time he fits down to write on any fubject, to read what has already been written it. W. Mount Mount Pleasant: a Defcriptive Poem. To which is added an Ode. 4to. 2s. Johnfon. To this poem is prefixed the following modeft and pertinent preface. "The following Poem was written fome years ago, at a very early period of life, without the least intention of publication. It is not however by way of an apology, that this circumftance is mentioned; the author being fully covinced, that an excufe for obtruding a new publication on the world is always fuperfluous; a good one being in no need of it, and an indifferent one receiving no addition to its value, from any circumstance that can be alledged in its favour." Mount Pleafant is an agreeable eminence near Liverpool, which commands the profpect defcribed in this poem. A fpecimen of the writer's talent for poetical defcription is given in the following lines. "Far as the eye can trace the profpect round, Ply round the fhores, nor tempt the dangerous main, Defcriptive of Merfey's prefent ftate, we have the following. "Far to the right, where Merfey duteous pours Where in foft tints the fky with ocean blends, And on the weaken'd fight, the long, long prospect ends." Again, drawing a comparison between the plains of this and thofe of warmer climates, the poet exultingly gives the proference to those of our own country. "Yet lovelier fcenes the varied profpect cheer, Where Ceftria's plains in long extent appcar; YOL. VI. S There |