on a-limy rock above a thousand feet high, having fhells half petrified on its fummit. On its top grow alfo the plants of the vallies, the feeds of which were probably dropped by birds, or brought by the winds. On doubling the first point of land to the eastward of Alicant, the bay and harbour of St. Paul prefents itself. Here the fhips come to load falt from the Mata, a great lake by the fea-fide, but having no visible. communication with it. The quantity of falt here, which, we are told, is the property of the king, is immense, and cofts little more than the labour of heaping it. The high bank, which separates the Mata from the fea, appears natural: the Jake is bounded on the land fide by mountains, and is formed by the torrents of rain water that rush down in winter; which evaporating gradually by the heat of the fun, added to the nature of the foil, become a mass of falt, fo plentiful that fome years the exports have amounted to near one hundred thousand tun weight, chiefly for Holland and the Baltic. We are informed that the foil and air in general, on the coafts of Valencia, Murcia, and Granada, is impregnated to a very uncommon degree with falt."

Letter XVI. describes the road from Alicant to the city of Valencia. The whole of this country is faid to be highly beautiful, but the plain of Valencia is particularly celebrated, and forms the subject of the next letter. Here nature, we are told, always fmiles, and the air is conftantly embalmed with the fragrant perfume of an infinite number of fruit-trees and odoriferous herbs.

Letter XVIII. recites a journey from Barcelona to the mountain of Montferrat; and Letter XIX. gives an account of a fingular mountain of foffil falt, near the town of Cardona in Catalonia. The rock which yields this falt is about a league in circumference, and nearly of the fame height with the adjacent mountains. The falt is commonly white from the bottom to the top, though in fome parts it is red. This the people of the country cut into pieces like bricks, and think it of ufe for pains in the fide, by applying it to the part after being moderately warmed. Sometimes it is of a light blue, but both this and the red colour disappear in grinding, the falt remaining white, and having no flavour nor tafte either of earth or vapour. This prodigious mountain of falt, divefted of any other fubftance, is, our author obferves, unparalleled in Europe. The river, which runs at its foot, is briny ; and when it rains, the faltnefs of the water increases, and kills the fish but this effect does not extend above three leagues. After many experiments which Don Guillermo Bowles made with the water of this river by evaporation, diftillation, and various

;

different

different proceffes, he never could discover in it the leaft grain of salt, which persuaded him that the falt was entirely decom→ pounded by motion, and diffolved into earth and water.

Letter XX. contains observations made by Don Guillermo Bowles, on the roundness of pebbles in the beds of rivers; Letter XXI. describes the hot wells at Caldas in Catalonia, and those of Caldetas, near the city of Mataro; Letter XXII. men tions remains of ancient volcanoes in Spain; and Letter XXIII. recites M. Bowles's return to Valencia and Castile; giving an account of a mine of fal gem at Mingranilla, with the fource of the Guadiana, and a mine of antimony near Santa Cruz de Mudela, in La Mancha.

'The volume concludes with an appendix, containing fupple→ ments to many of the Letters, with a lift of vegetables growing upon Mount Calpe, or the Hill of Gibraltar.

Through the whole work, Baron Dillon appears to have judiciously felected, and well arranged, the valuable materials on the natural history of Spain, contained in the observations of Don Guillermo Bowles; and befides blending the narrative with a variety of hiftorical and antiquarian anecdotes, he has in many parts greatly elucidated the fubject, as well as corrected several chemical errors, which occurred in his author. Exclufive of all its other advantages, the work is embellished with a number of engravings.

Mathematical Memoirs refpecting a Variety of Subjects; with an Appendix containing Tables of Theorems for the Calculation of Fluents. Vol. I. By John Landen, F. R. S. 4to. 18s. in boards Nourse.' THE HE purpose of these Memoirs, fays Mr. Landen, is to improve the various branches of fcience in which mathematical reasoning is neceffary, by illuftrating its use in treating of a variety of interefting fubjects :-and, thereby, furnishing fuch precedents as may be the means of enabling the reader, who may be curious either in analytics, geometry, or mechanics, to apply fuch reafoning to new fubjects; and to deduce, from clear principles, with as much facility as poffible, the most satisfactory conclufion the nature of the fubject may admit of, in any difquifition that he may be induced to attempt, to which any method of computation proposed to be explained in this work may be applicable.'

It is with real pleasure we congratulate the learned in those curious and important inquiries, who beft know how to estimate the value of them, on the prospect of enjoying the benefit refulting from the perufal of these other excellent mathematical works of this learned writer: and, recommending them to the work itself, we fhall briefly mention the contents of the prefent

volume, which confifts of nine Memoirs, and a large Appendix, containing a very great number of curious and useful theorems for finding fluents.

Memoir I. treats on the mechanic powers, as far as relates to equilibriums.

It has been common for writers on the mechanic powers to found their demonftrations of the properties of fuch powers, in respect to equilibriums, in which no motion is concerned or takes place, on a principle drawn from bodies in motion; which is prepofterous and unnatural. They infer, from the doctrine of motion, that as thofe bodies are equipollent in the congress and reflexion, whofe velocities are reciprocally as their innate forces; so, in the use of mechanic inftruments, those agents are equipollent, and mutually fuftain each the contrary preffure of the other, whofe velocities, estimated according to the determination of the forces, are reciprocally as the forces.' But this is certainly taking for granted what ought to be proved as a theorem, inftead of being employed as a principle, in the proof of equilibriums. In this Memoir, therefore, this ingenious writer has refcued the doctrine of equilibriums from this opprobrium, he having clearly demonftrated them, in all the mechanic powers, from the preffures of bodies, or tensions of cords, independent of all motion whatever. In the courfe of this Memoir, the author has given føme new properties, besides demonftrating all the principal common ones, and pointing out the mistakes and inaccuracies in writers of fome eminence. It has not been uncommon for the nature and properties of the wedge to be miftaken; fome writers having fuppofed, that the wedge refifted by a force acting at right angles to its fides, whilft others confidered the refifting force as acting in a direction parallel to the back of the wedge: whence it is, that their conclufions have been different. Thefe diverfities Mr. Landen fets in a proper light, and more clearly diftinguishes between the nature of preffure and percuffion than any writer that we have ever before known to treat of those heterogeneous forces. In cleaving of wood, he obferves, the resistance oppofing the force of the mallet (fuppofing the fides of the wedge perfectly polished, and its edge a geometrical line) is the attraction of colefion in the particles of the wood to be separated; and this being a kind of preffive force acting against the fides of the wedge, it is extremely abfurd to attempt to compare it with the Fercullive force of a mallet on the back of a wedge, as fome writers have done. For the greatest finite preffive force muft give way to the leaft percuffive one, as a large ship on the ftocks is readily lifted by a wedge driven in below by a man with the ftroke of a mallet; nor can there poffibly be an equi

librium

librium between two fuch different forces. Any percuffive force, acting on a moveable body, generates a finite quantity of motion in an indefinitely small particle of time; but the time will be finite, in which any given preffive force whatever, a&ting on the fame body, can generate or deftroy the fame quan tity of motion. Therefore, a body being urged in a certain direction by any preffive force whatever, and in the contrary direction by any percuffive one, the preffive force will be fome finite time in deftroying the quantity of motion which the percuffive one generated in an inftant. Confequently, how great foever the preffive force may be, and how small foever the percuffive one, the body will be moved by this laft force, at leaft for fome fhort time. Indeed, after the ftroke is given, the preffive force may quickly prevail, and force back the body, which the impulse of the other force had driven forward and this would often be the cafe with respect to cleaving of wood, if the fides of the wedge were perfectly smooth. For, after the ftroke of the mallet, the wedge, unlefs its weight were equivalent to the force of the attraction of the parts of the wood to be feparated, would prefently be forced back from the place to which the mallet had driven it. And it is chiefly the roughnefs of the fides of the wedge, and of the parts of the wood in contact with them, which in that operation hinders the wedge from receding. It is that roughness too, and the bluntnefs of the edge, which fometimes prevent the wedge from being moved forward by the ftroke of the mallet: for, were it not obftructed by fuch roughness and bluntnefs, it would, according to what we just now observed, be always driven forward even by the very leaft percuffive force.

Memoir II. Of the Ellipfis and Hyperbola.

This Memoir is on a subject of very difficult and intricate calculation; it being on the relations between elliptic and hyperbolic arcs, and the fluents of fome fluxions affignable by them. In the application of certain theorems given by mathematicians for the calculation of fluents by means of fuch arcs, there being required the difference to be taken between a hyperbolic arc and its tangent; and as this difference is not directly attainable when the arc and its tangent both become infinite, which happens when the whole fluent is wanted, although fuch fluent be at the fame time finite; therefore in that cafe those theorems fail, a computation by them being then impracticable without fome farther help. To fupply this defect, our author confidered as a point of fome importance in geometry, and his endeavours have been attended with a happy fuccefs; he having here affigned, by means of fuch arcs, the ultimate difference between the hyperbolic arc and its tangent,

the

the point of contact being supposed to be removed to an infinite diftance from the vertex of the curve, which is indeed the difference between the afymptote and the curve infinitely extended from the vertex. Many other curious properties are also here determined, fuch as a general expreffion for the length of any conic hyperbola by means of two elliptic arcs; also the affigning of a right line which shall be equal to the difference between two certain elliptic arcs, &c.

Memoir III. Of the Defcent of a Body in a Circular Arc.

In this fhort Memoir Mr. Landen determines the whole time of defcent or vibration in any circular arc, and the relation of the times in different parts of the arc, by fluents expreffed in terms of elliptic arcs, as found in the preceding Memoir.

Memoir IV. Of the Centrifugal Force of the Particles of a Body, arifing from its Rotation about a certain Axis paffing through its Center of Gravity.

In this Memoir we are taught how to find a great many folids having various permanent axes of rotation, about any of which the solid may be made to revolve; a subject very difficult and important in mechanico-philofophical confiderations.

Memoir V. or a new Method of obtaining the Sums of certain Series, contains the investigation of several difficult and useful fluents, befides that of many very intricate forms of feries by means of circular arcs and logarithms.

Memoir VI. treats of a remarkable new property of the cycloid, which fuggefts a new method of regulating the motion of a clock.

Memoir VII. treats of the motion of a body which keeps al ways in the fame given plane, whilft it is acted on by any force or forces urging it continually to change its direction in that plane. Here the general theorems containing the relation of fuch forces, with their directions and the nature of the curve in which the body moves, are investigated in a clear and easy manner, and applied in a variety of curious and useful instances of different curves, whether their planes be vertical, horizontal, or oblique; and the nature of the forces is illuftrated by many curious cafes, among which are thofe in which they are determined by the revolution of planes, flender tubes, or rods; alfo by fome theorems in the case of a body moving in a medium, whofe refiftance is proportional to any power of the ve locity of the projectile. Among a number of other curious confequences that may be drawn from this memoir, we also perceive, without any regard to the area of the trajectory defcribed, the phyfical ground of the celebrated bishop Ward's method of determining the place of a planet in its orbit: which method, it is here fhewn, is not merely an hypothesis, as it is

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