confidered: and in thefe, instead of being well provided, you are totally deficient. You have funk from glory to dif from wealth to poverty. For the riches of a State, grace, I take to be the number, fidelity, and affection of its allies: in all which you are notoriously deficient. And by your • total infenfibility, while your affairs are thus falling into ruin, he is become fuccefsful, great, and formidable to all the Greeks, to all the Barbarians; and you deserted and • inconfiderable; fumptuous, indeed, in your markets; but ⚫ in every thing relating to military power, ridiculous.'—(ƒ)

Thus the renowned Demofthenes; who from the thirtieth, till the forty-fecond year of his life, endeavoured, tho' in vain, to alarm his carelefs countrymen with a sense of impending ruin. But fo fond were they of riches and luxury, fo funk in pleasure, and so lost to manhood, that altho' one of the greatest powers on the continent, who had already feized fome of their colonies, who had made great advances to ftrip them of all the reft, who had entirely feduced many of their allies, and over-awed those who remained unfeduced; when this power threatned them with hourly invafion, yet would they not interrupt trade, or abandon amusement, so much as to put themselves in a posture of defence; but trufting to the influence of money, their naval force, and the bravery of foreigners, were at laft furprized in their own territory, by Philip, who put the foreigners to flight, and enflaved the Athenians.

(f) Philippic the fourth, p. 137, 144, 148.

Philofophical Tranfactions. Vol. XLIX. Part I. for the Year 1755. 4to. 12s. Davis.

HIS volume is at least not inferior to any of those pub

Tlifhed, even within the laft four or five years, when

the reputation of the Philofophical Tranfactions of our Royal Society began to revive. Of the feveral papers which compofe this new collection, we shall mention the greatest part, for the information of our readers: omitting fome, rather for the fake of keeping the prefent article within moderate bounds, than from any perfuafion that the particulars we overlook are unworthy to remain in the company to which they have been introduced, by the Gentlemen to whom the management of these publications is intrusted by the Society.

Art.

Art. 1. De Preffionibus Ponderum in Machinis Motus.

This article is the work of that ingenious Mathematician Christian Hee. It is a short but curious performance, and the process is delivered in a very elegant manner.

Art. 2. An investigation of a general rule for the refolution of foperimetrical Problems of all orders. Sympfon, F. R. S.

By Mr. Thomas

Among the feveral branches of mathematical learning, this relating to ifoperimetrical problems, has, perhaps, been the leaft purfued. Mr. Mc. Laurin is almoft the only author who has confidered the fubject. The method laid down by that Gentleman is very easy, but not fo general as could be wifhed. Mr. Sympfon has here given us a far more general method than that of Mr. Mc. Laurin, and, at the fame time, obviated the difficulties attending the refolution of problems of this kind. Every one converfant in the mathematical principles of the Newtonian Philosophy, must be convinced that the me thods of finding the Maxima and Minima of quantities, are of the utmost importance; and tho' the term Ifoperimetrical, according to its proper acceptation, should be applied only to fuch problems as relate to finding the greatest Areas and Solids under equal perimeters, yet Mathematicians extend it much. farther, calling all thofe problems that relate to the finding the Maxima and Minima of Quantities, whether depending on a line, space, or body, ifoperimetrical.

Mr. Sympfon, from two Lemmas, deduces the following general Rule.

For the folution of Ifoperimetrical problems, of all orders, <take the Fluxions of all the given expreffions (as well that refpecting the Maximum or Mininum, as of the others, ⚫ whofe Fluents are to be given quantities) making that quan tity (*) alone variable, whofe Fluent (x) enters not into the faid expreffions; and having divided every where by the fecond Fluxion, (*) let the quantities thence arifing, join⚫ed to general Co-efficience, 1, e, f, g, &c. whofe values ⚫ will depend on the values given, (and may be either pofitive or negative) be united into one fum, and the whole be made equal to nothing; from which equation the true relation of and, and of x and y, will be given, let the < number of restrictions be what it will.'

This rule Mr. Sympfon has illuftrated by feveral examples, and, among the reft, that of finding the Solid of leaft refift ance, and the Curve of fwiftest descent.

Art. 4. A remarkable cafe of a Morbid Eye. By Mr. Spry, Surgeon, at Plymouth.

According to Mr. Spry, this disorder was a Carcinomà, which he having in vain endeavoured to remove by repeated bleedings at the arm, and once at the temporal artery, by epifpaftics, purgatives, mild and draftic dofes of mercury, a feton, fearifications, and a collyrium, the cure was at laft effected by excifion. Behind the difeafed eye, a cyft filling the whole orbit was found; which, upon being opened, difcharged, with confiderable force, a great quantity of pus like lymph, (as he expreffes it) when the tumor fubfided a good deal. The greateft part of this cyft being cut away, the remainder floughed off, and the woman got well in a month. The cafe is indiftinctly related. It seems to have been a protrufion of the eye from the cyft, and not a Carcinoma.

Art. 5. A Supplement to the account of a diftempered fkin, publifhed in the 424th Number of the Philofophical Tranfactions. By Mr. Henry Baker, F. R. S.

n;

In 1731 a lad of fourteen years of age was fhewn to the Society, having a difeafe of the fkin, fo different from any mentioned in the hiftory of difeafes, that Mr. Machin, the Society's fecretary, drew up an account of it, which was publifhed. The fame perfon is ftill alive, and in 1754 was in London, as a fhew, under the name of the Porcupine Man and not improperly, as the whole of his fkin, except his face, palms of his hands, and foles of his feet, is covered with a very thick-fet grove of dark brown cylindrical warts, fo firm and elaftic, especially when at their full fize, which is an inch, that they make a rustling noise when the hand is paffed over them.

When he had the fmall-pox, the warts fell off, but they foon fhot up again; to get rid of which he has been twice. falivated while the mercury did its office, he had hopes of a recovery, for his fkin became fmooth and white; but no, fooner did the ptyalifm cease, than his warty integuments reappeared.

Mr. Baker further informs us, that he sheds them annually, either in the autumn or winter, when he ufually loofes blood, to prevent a little fickness, which otherwife accompanies their fall. At other times he is remarkably healthy.

He has had fix children, who all, in nine weeks after their birth, acquired the fame rugged covering with himself; but

* See that cafe at large, Review, vol. XIII. p. 329. feq.

REV. Sep. 1756.

T

they

they are now dead, except one boy, who has also had the fmall-pox, during which time the warts fell off; after which he attended his father in London..

It appears, therefore, (adds Mr. Baker) past all doubt, that a race of people may be propagated by this man, having fuch rugged coats as himfelf: and if this should ever happen, and the accidental original be forgotten, it is not • improbable they might be deemed a different fpecies of mankind. A confideration which would almost lead one to imagine, that if mankind were all produced from one and the fame ftock, the black fkins of the Negroes, and many other differences of the like kind, might poffibly have been ori⚫ginally owing to fome fuch accidental caufe.'

Art. 6. Extract of the fubftance of three letters from Ifaac Famineau, Efq; his Majesty's Conful at Naples, to Sir Francis Hofkins Eyles Stiles, Bart. F. R. S. concerning the late eruption of Mount Vefuvius.

Mr. Jamineau, in thefe letters, has defcribed the late eruption of Vesuvius from its first appearance. The lava first began to run down the fide of the mountain on the 3d of December, 1754. from an opening on the eaft fide; but the matter • foon ceased running from this orifice, and burft out from a much greater one, about two hundred yards below it. From this there afterwards flowed no matter; but the lava has run from it within, tho' very near the surface, to a third • furnace, whence the liquid fire now pours out. This channel of fire after falling from the third furnace, with great fury, a few yards, is covered by the hard exterior surface of the lava, which cools and incrufts on its furface, as its courfe is on a level, or gently declining ground, till it comes within ten yards of the top of a steep declivity. Here the fire collects, as in a refervoir, to fupply a cascade, which rushes down from thence in a channel of more than twenty < feet wide, and about two hundred yards in length, with a

fall of at least fifty feet, divided upon fuch length. After ⚫ which the ftream is lefs rapid, but grows wider, and has al· ready forced its courfe for four miles from the fource, where it affords a very different scene from what it presented from its firft eruption. For there it runs over a country already 6 deftroyed: the cafcade looks like melted gold, and tears off large bodies of old lava, which float down the stream, ⚫ till the intenseness of the heat lights them from the bottom. But, in the lower country, the channel is divided into leffer ftreams, running with lefs rapidity; whence, notwithftanding its flowness, it drives the ftrongeft ftone fences be

• fore

fore it, and lighting the trees like torches, affords a most extraordinary, tho' difmal, fpectacle.'

In another letter Mr. Jamineau obferves, that the ftream described above, is but a branch of the main river, and when compared to the principal one, only a trout fiream. The largest begins in a cafcade of a mile in length; and tho' the declivity is rather lefs than that already defcribed, is equally rapid, from the great quantity of lava. The breadth of this burning river was about fixty feet at the top, but by having melted down an ifland that divided its ftream, about two hundred yards from the top of the cascade, its breadth is there near one hundred yards.

Art. 8. An account of a mountain of iron ore, at Taberg in Sweden, in a letter to Mr. Peter Collinfon, F. R. S. by Peter Afcanius, M. D. Tranflated from the Latin by Mr. Emanuel Mendes da Cofta, F. R. S

An affiduous enquirer into the works of nature, will often meet with productions which abundantly demonftrate the infufficiency of most of those systems which the luxuriant imáginations of Naturalifts have framed, to account for their origin and formation. The article above-mentioned prefents us with an object of this kind; and fufficiently fhews, that not one of all the various hypothefes invented by different authors, is fufficient to account for the formation of mountains.

This mountain, or rock of iron ore, is fituated in a mountainous part of the country, covered with fand, near forty leagues diftant from the fea. It is an entire mafs of rich iron ore; its perpendicular height above four hundred feet, and its circumference three English miles. Oppofite to it is a valley, through which flows a fmall river. No ore is found be-yond the foot of it, nor on the neighbouring plain; so that it appears as if the mountain had been artificially laid on the fand, for it has no roots, or, like other mountains, its fubftance does not penetrate the ground. There are many perpendicular and horizontal fiffures all over the mountain, which are filled with fand reduced to a kind of fine mud-like pafte; not impregnated with the least particle of the iron ore of the mountain, but remaining of the fame purity and nature as it is found on the fea beaches. In the interior fiffures of the mountain, bones of ftags, and other animals, are found imbedded in the fand.

From the above defcription it is evident, that no hypothefis hitherto proposed to explain the formation of mountains, will be fufficient to account for the origin of this mountain of iron.

Qur