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« considered : and in these, instead of being well provided,

you are totally deficient. You have sunk from glory to disgrace, from wealth to poverty. For the riches of a State I take to be the number, fidelity, and affection of its allies :

in all which you are notoriously deficient. And by your « total insensibility, while your affairs are thus falling into <ruin, he is become fuccessful, 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.:-)

Thus the renowned Demosthenes ; who from the thirtieth, till the forty-second year of his life, endeavoured, tho' in vain, to alarm his carelefs countrymen with a sense of impending ruin. But so fond were they of riches and luxury, lo funk in pleasure, and so lost to manhood, that altho' one of the greatest powers on the continent, who had already seized some of their colonies, who had made great advances to strip them of all the rest, who had entirely seduced many of their allies, and over-awed those who remained unseduced ; when this power threatned them with hourly invasion, 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 last surprized in their own territory, by Philip, who put the foreigners to fight, and enslaved the Athenians,

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

Philosophical Transactions. Vol. XLIX. Part I. for the Year 1755. 4to.

Davis.

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years, when

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

lished, even within the last four or five the reputation of the Philosophical Transactions of our Royal Society began to revive. Of the several papers which compose this new collection, we shall mention the greatest part, for the information of our readers: omitting fome, rather for the sake of keeping the present article within moderate bounds, than from any persuasion 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 Pressionibus Ponderum in Machinis Motus. This article is the work of that ingenious Mathematiciant 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 resolution of

Isoperimetrical Problems of all orders. By Mr. Thomas Sympson, F. R.S.

Among the several branches of mathematical learning, this relating to isoperimetrical problems, has, perhaps, been the least pursued. Mr. Mc. Laurin is almost the only author who has considered the subject. The method lạid down by that Gentleman is very easy, but not so general as could be wished. Mr. Sympson 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 resolution of problems of this kind. Every one conversant in the mathematical principles of the Newtonian Philosophy, must be convinced that the mes thods of finding the Maxima and Minima of quantities, are of the utmost importance; and tho' the term Iloperimetrical, according to its proper acceptation, should be applied only to such problems as relate to finding the greatest Areas and Solids under equal perimeters, yet Mathematicians extend it much farther, calling all those problems that relate to the finding the Maxima and Minima of Quantities, whether depending on a line, space, or body, isoperimetrical.

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

· For the solution of Isoperimetrical problems, of all orders, ( take the Fluxions of all the given expressions (as well that r respecting the Maximum or Mininum, as of the others, • whose Fluents are to be given quantities) making that quan

tity (*) alone variable, whose Fluent (x) enters not into

the said expressions; and having divided every where by the ' fecond Fluxion, (*) let the quantities thence arisings join' ed to general Co-efficience, 1, e, f, s, &c. whose values • will depend on the values given, (and may be either positive

or negative) be united into one fum, and the whole be ( made equal to nothing; from which equation the true re• lation of x and j, and of x and y, will be given, let the < number of restrictions be what it will.'

This rule Mr. Sympson has illustrated by several examples, and, among the reit, that of finding the Solid of leaft refifte ance, and the Curve of swiftest descent.

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Art. 4. A remarkable case of a Morbid Eye. By Mr. Spry,

Surgeon, at Plymouth. According to Mr. Spry, this disorder was a Carcinoma, which he having in vain endeavoured to remove by repeated bleedings at the arm, and once at the temporal artery, by épispastics, purgatives, mild and drastic dotes of mercury, a seton, fearifications, and a collyriurn, the cure was at last effected by excision. Behind the diseafed eye, a cyft filling the whole orbit was found; which, upon being opened, discharged, with confiderable force, a great quantity of pus like lymph, (as he expreffes it) when the tumor subsided a good deal. The greateft part of this cyst being cut away, the remainder floughed off, and the woman got well in a month. The case is indistinctly related. It seems to have been a protrusion of the eye from the cyst, and not a Carcinoma. Art. 5. A Supplement to the account of a distempered skin, púb

lished in the 424th Number of the Philosophical Transactions. By Mr. Henry Baker, F.R.S.

In 1731 a lad of fourteen years of age was shewn to the Society, having a disease of the skin, so different from any mentioned in the history of diseases, that Mr. Machin, the Society's secretary, drew up an account of it, which was published. The same person is still 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 skin, except his face, palms of his hands, and soles of his feet, is covered with a very thick-set grove of dark brown cylindrical warts, fo firm and elastic, especially when at their full size, which is an inch, that they make a rustling noise when the hand is passed over them.

When he had the small-pox, the warts fell off, but they foon shot up again; to get rid of which he has been twice, salivated : while the mercury did its office, he had hopes of a recovery, for his skin became smooth and white; but no, sooner did the ptyalism cease, than his warty integuments reappeared.

Mr. Baker further informs us, that he sheds them annually, either in the autumn or winter, when he usually looses blood, to prevent a little fickness, which otherwise 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 same rugged covering with himself; but

• See that case at large, Review, vol. XIII. p. 329. feq. Rev. Sep. 1756.

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they are now dead, except one boy, who has also had the small-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, havring such rugged coats as himself: and if this should I ever

happen, and the accidental original be forgotten, it is not . improbable they might be deemed a different species of man• kind. A confideration which would almost lead one to ima• gine, that if mankind were all produced from one and the • fame itock, the black skins of the Negroes, and many other differences of the like kind, might possibly have been ori

ginally owing to some such accidental cause.' Art. 6. Extract of the substance of three letters from Isaac

Jamineau, Esq; his Majesty's Conful at Naples, to Sir Francis Hoskins Eyles Stiles, Bart. F. R. S. concerning the late eruption of Mount Vesuvius.

Mr. Jamineau, in these letters, has described the late eruption of Vesuvius from its first appearance. The lava first began to run down the side of the mountain on the 3d of December, 1954. from an opening on the east side; but the matter • soon ceased running from this orifice, and burst 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 chan

nel 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 incrusts on its surface, as its 6 course 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 reservoir, to supply a cascade, which crushes 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 such length. After " which the stream is less rapid, but grows wider, and has al• ready forced its course for four miles from the source, where • it affords a very different scene from what it presented from • its first eruption. For there it runs over a country already • destroyed: the cascade looks like melted gold, and tears off

lärge 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 lesser streams, running with less rapidity; whence, notwithstanding its flowness, it drives the strongest stone fences be

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<fore it; and lighting the trees like torches, affords a most • extraordinary, tho' dismal, spectacle.'

In another letter Mr. Jamineau observes, that the stream described above, is but a branch of the main river; and when compared to the principal one, only a trout ftream. The largest begins in a cascade of a mile in length; and tho' the declivity is rather less than that already described, 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 island that divided its stream, 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, át Taberg in

Sweden, in a letter to Mr. Peter Collinson, F.R.S. by Peter Ascanius, M. D. Translated from the Latin by Mr. Ema , nuel Mendes da Costa, F. R. S.

An affiduous enquirer into the works of nature, will often meet with productions which abundantly demonstrate the ina suficiency of most of those systems which the luxuriant imáginations of Naturalists have framed, to account for their origin and formation. The article above-mentioned presents us with an object of this kind; and sufficiently shews, that not one of all the various hypotheses invented by different authors, is fufficient to account for the formation of mountains.

This mountain, or rock of iron ore, is situated in a mountainous part of the country, covered with fand, near forty leagues distant from the sea. It is an entire mass of rich iron ore; its perpendicular height above four hundred feet, and its circumference three Engliíh miles. Opposite to it is a valley, through which flows a small river. No ore is found beyond the foot of it, nor on the neighbouring plain; so that it appears as if the mountain had been artificially laid on the sand, for it has no roots, or, like other mountains, its subftance 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 paste; not impregnated with the least particle of the iron ore of the mountain, but remaining of the same purity and nature as it is found on the sea beaches. In the interior fissures of the mountain, bones of stags, and other animals, are found im-. bedded in the sand.

From the above description it is evident, that ho hypothesis hitherto proposed to explain the formation of mountains, will be l'ufficient to account for the origin of this mountain of iron.

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