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The work alluded to is entitled " A new theory of the diurnal rotation of the earth, demonstrated upon mathematical principles, from the properties of the cycloid, and the epicycloid, by John Wood."

Beside the important curves obtained by cutting a cone in different manners, several curves of various origin and denominations are wellknown to have employed the attention of the most eminent mathematicians. Such are, among others, the cycloid and the epicycloid. The labours of Paschal, Huygens, Bernouille, &c. have, in some measure, consecrated the cycloid, and Mr. Wood's application of its principal property will, no doubt, render that curve still more celebrated, and more precious to science. That principal property of the cycloid is, that a body revolving along it describes unequal arcs in equal times; or (to use the very instance which has certainly given rise to all the researches on this subject, from those of Mersenne to the present theory) “the top of a carriage-wheel in motion moves with greater velocity than the bottom.” This results from the compound motion of the wheel, viz: a motion round its axis, and a motion along a horizontal plane. As this truth stands on the strong basis of demonstration, it may be assumed as a fundamental principle, the applications of which may become very numerous, and productive of the most satisfactory results.

Of this important property of the cycloid, two applications only seem to have been made, before Mr. Wood's ingenious idea of applying it to the diurnal rotation of the earth. Huygens obtained a very desirable object by making pendulums describe cycloidal, instead of circular arcs; and M‘Laurin, in his account of sir Isaac's Newton's discoveries, determined the path of a satellite to be an epicycloid of a certain description, arriving, as he himself observes, at the same result as the great Newton, though by a more circuitous route.

Mr. Wood's application, therefore, is altogether new and original. it consists in his considering the earth as a wheel, or, if you like it better, in considering the equator, and all the parallels of latitude as so many wheels, having a common axis, viz. the axis of the globe. The motion of every point on the earth's surface is, therefore, compounded of two motions, a rotary motion round the axis, and a progressive motion along the plane of the ecliptic. Hence, it follows that every such point must describe a curve of the epicycloidal kind. Upon this application the whole fabric of the author's ingenious theory is erected.

In the first book of his work wherein he demonstrates whatever belongs to the cycloid, and the epicycloid, he scarcely claims any other merit than that of having luminously arranged and developed the discoveries of his predecessors in the same career. Yet, even here, I observe several corollaries, and some propositions, entirely new. The twelfth proposition particularly deserves attention as immediately and cssentially connected with the inquiry. It serves to establish the ratio

of any one point in the upper hemisphere to that of the point diametrically opposite; and supplies a formula which, being applied in the second book to the motion of the earth, shows the difference of velocity of any point under the equator, at noon and at midnight, and at other corresponding hours. By this difference of velocity, the action of gravity is necessarily affected. Hence, a body is found to weigh less at noon than at midnight, &c. This consideration our theorist afterwards extends to the fluids which encompass the earth, and proves that the difference of gravity resulting from epicycloidal motion has upon such fluids an effect considerably greater than that of either the sun, or the moon. The Newtonian theory of the tides being, as is well known, unsatisfactory in some of its essential points; and the polar effusions of the amiable and justly celebrated St. Pierre not appearing adequate to their supposed effects, Mr. Wood easily evinces the insufficiency of former causes to account for the phenomena under consideration, and substitutes to them his fundamental principle, which, in the second chapter of the third book, he states to raise the tides about thirteen feet, twice every twenty-four hours. To the same cause he refers the trade-winds, and those stony substances which are said to have descended from Heaven. These he considers as volcanic products, projected from the earth and carried to an immense distance from the place of projection by the difference of velocity in opposite points of the globe, under the same parallel of latitude.

Time does not permit me to abridge or condense the train of reasoning used by the theorist. The inquisitive are referred to the work itself, where extent of research, and mathematical profundity and accuracy are eminently conspicuous.

This theory, Mr. Oldschool, though I do not yet assent to all the inferences of the author, I consider as a new and important link in the vast chain, which will probably constitute, at some future period, a satisfactory ensemble of physical knowledge. Its fundamental principle is not a gratuitous and merely explicative hypothesis; it does not substitute for the unknown cause of existing phenomena some obscure and indefinite agent, which, if not a reality, may, upon the whole, stand as the representative of truth. Here we have history and not romance. In effect, grant the diurnal and annual motion of the earth, every point of its surface must necessarily revolve with unequable velocity, and, of course, describe unequal arcs in equal times. And who will deny that difference of velocity must be attended with certain effects? Though itself an effect, it becomes for us an important cause, to which we may legitimately refer certain phenomena. And here, Mr. Oldschool, candour, perseverance, and patient investigation must be our guides. Let us spurn the fetters of antiquated error, and a servile acquiescence in all received doctrines—nullius jurare in verba magis

tri_but let us not yield too much to the enthusiasm of novel conceptions. We cannot hope to develop all the mysteries of nature, but we may hope continually to approximate towards the focus of complete philosophic illumination. Shall I confess it? Our light in many branches of physics appears to me yet crepuscular. Let, therefore, each votary of science endeavour to contribute a few rays, and let those rays be made to converge in one point. The great Newton has observed the lunar and solar influences upon the tides: St. Pierre has proved alternate effusions from the poles: both these are demonstrated to be insufficient for the production of the phenomena attributed to their agency; and a new cause occurs to the sagacious mind of Mr. Wood. Why not admit all those agents as concurring in the coinpletion of the result under consideration, the tides? Why that singular propensity of the human mind to refer as many effects as possible to one single cause? We call this simplifying, and simplicity is, according to us, the true march of nature. The very structure of animals and vegetables, and the complex agency of their various organs, evince the contrary. I know that I directly oppose one of the rules of philosophizing: but that rule was made by one intent upon a theory, where a single principle predominates; and I may well contest its legitimacy. Even in intellectual and moral researches, this exclusive spirit is observable. Helvetius ascribes every thing to education; doctor Gall of Vienna every thing to nature; and he finds the morality of man in certain prominences, and depressions of the head. Here we have the materialists, there the idealists. Many attempts have been made to refer the “ Beautiful and Sublime" each to a single fundamental principle. Medicine has not been free from this spirit of system. In short, as every religious sectary pretends to have God in his chapel, so every philosopher will have the truth, and the whole truth on his side. But this is idle digression.

To conclude-Mr. Wood shall long be remembered in the scientific world as having exploded the opinion hitherto generally received, that, every twenty-four hours, each point on the surface of the earth revolves from west to east, all round, with an equable motion, thereby describing, during every successive hour, an arc of fifteen degrees; and as having clearly demonstrated that each such point describes epicycloidal arcs, and, of course, moves with a velocity that continually changes. The discovery of this important fact would alone suffice to insure him a niche in the temple of fame. The ingenious application of his fundamental principle to the tides, the trade-winds, and other phenomena, whether it be considered as entirely satisfactory, or only as a happy accession to the materials already extant for the formation of a general theory of nature, also entitles him to the gratitude of the learned. Newton himself, the inodest, the truly great and good Newton, would, no doubt, if living, think himself indebted to Mr. Wood for rectifying aberrations which even his sublime genius could not avoid—because it is the lot of man to err—and that Newton was diffident of the truth of some points in his “ Theory of Universal Gravitation," is well known to those who have read his life.

In unavoidable haste, but with truest esteem,
I am, Mr. Oldschool,
Your obedient servant and subscriber,

L. H. GIRARDIN.

FOR THE PORT FOLIO.

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To Benjamin West, Esq. historic painter to the king of Great Bri

tain, London. DEAR SIR, ' In reading your very sensible and entertaining letter to Mr. Peale, lately published in The Port Folio, I was much struck with the information you gave him of the limited patronage of the art you have exercised with so much honour to yourself and country, in Great Britain. , It led me to inquire into the cause of it. I submit to your judgment the result of this inquiry.

In proportion as nations become civilised and refined, they become artificial in every thing. Nature is banished from their buildings, dresses, manners, and, above all, from the human countenance. But even in this state, from an indestructible instinct in the human mind, she does not lose her charms, and, in spite of fashion and habit, never fails to please whenever she is exhibited, particularly in the works of the painter and the statuary. Let us examine this principle by the taste of three of the nations of Europe.

In Italy, where nature has been completely driven from her empire, an artificial uniformity pervades every face ; hence painting and statuary, which restore a part of that empire, are universally admired in that country. In France nearly the same artificial uniformity appears in the human face, and hence her general taste for those arts, as they are called, which revive the knowledge and beauties of Nature in that preeminent part of her works.

In Great Britain Nature still retains a large portion of her dominion over manners and character as expressed in the character. “ The Volto Sciolto, with the pensieri stretti," of lord Chesterfield, is occasionally seen, it is true, in the higher ranks of British society, but the expressions of the understanding and of the passions in the countenance are to be met with in their full force in all the middle and lower walks of life in the inhabitants of that country. It is for this reason that they do not crowd an exhibition room, nor spend large sums of money in purchasing the representations of thoughts and passions which are familiar to them in their daily intercourse with each other. The country gentleman stands in no need of boxes of flowering shrubs in his parlour, to remind him that “ Nature still lives,” to use the words of Mr. Cowper; but they constitute a delightful part of the ornament of the house of a citizen, whose eyes are met in all other places, with the artificial and mercenary productions of the hand of man.

In support of the assertion that Nature still lives in the expression of the passions in Great Britain, I shall remind you of a fact you mentioned to me, at a late hour, by your hospitable fireside in the winter of 1769. Upon your landing at Dover, in England, after spending several years in Italy, the first object, you informed me, that arrested your notice was the sight of two boys fighting upon the shore. You beheld it, you said with great pleasure. It was an open and natural expression of the passion of anger, and formed a striking contrast to the composed manner in which you had been accustomed to see the same passion vent itself by means of the stiletto, and other instruments of death in the country you had left.

If the explanation I have given of the fact contained in your letter be just, it will account for the little encourage

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