the superior part of the tube, which is not immediately in contact with the liquid. Besides, the surface of the liquid inclosed in the tube would, when it is concave, be drawn vertically downwards, by the vertical columns of the liquid adhering to it; and when this surface is convex, as in that of mercury in a glass tube, and of a drop of water at the extremity of a tube, it would be pressed perpendicu larly, in each of its points, by the weight of the superior columns of the liquid. This surface would not, then, be the same in these two cases, and the capillary phænomena would not follow the same laws; which deduction is contrary to experience. It must therefore be acknowleged that these phænomena do not solely depend on the action of contact, but on an attraction extending beyond, and decreasing with an extreme rapidity.'

-M. LA PLACE then contends that the viscosity of fluids, instead of being the efficient cause of capillary phænomena, is a disturbing cause; and that those phænomena are strictly conformable to the theory only in fluids that are endowed with a perfect fluidity. He moreover adds that to the viscocity of water are owing several considerable differences which are observed by philosophers, between the heights of that liquid, in capillary glass tubes of the same diameter.

In the latter part, the author developes very justly, from the history of the infinitesimal calculus, the reasons which induced former philosophers to endeavour to explain the forms of fluids as arising from certain forces of tension and elasticity. He then notices the unsatisfactory investigations of Segner; and lastly those of Dr. Thomas Young, inserted in the Philosophical Transactions for 1805.

ART. XV. Supplément au IIIme Volume, &c.; i. e. A Supplement to the Third Volume of the Treatise on Celestial Mechanics. 4to. pp. 24. Paris. Imported by De

f

By M. LA PLACE.

Boffe. Price 38.

WE WE have here a short but by no means an unimportant addendum to the second book of the Mécanique Celeste. In that book, the author discussed the important question of the Orbit of a body revolving round a primary, but disturbed in its motion by the action of other bodies. M. LA PLACE'S mode of determining the position of the disturbed body is by assigning three expressions for the radius-vector, the longitude, and the latitude. These expressions are not finite, but under the form of a series, the terms of which involve the sines and cosines of the time: but they also involve quantities which are considered as constant, namely the six elements of the orbit, the axis major, the excentricity, the inclination, the APP. REV. VOL. LX. longitude

M m

530 La Place's Supplement to his 3d Vol. of Mécanique Céleste.

:

It

longitude of the node, the longitude of the epoch, and the longitude of the perihelion. Now these elements are not all accurately constant, but are subject to slight variations. becomes, then, a problem of no inconsiderable moment, to assign expressions for estimating the values of these variations for then, at a given time, we can correct the elements, and substitute them so corrected into the three expressions for the radius vector, longitude, and latitude. The differentials of the six elements are stated in the Mécanique Céleste, Liv. 2. pages 327, 347, 348, 363, and 365; and the differential of the major axis was originally given by La Grange in the Berlin Memoirs for 1781, pp. 219, and 236. It is of this form ; =2. d R, where R is a quantity that can be resolved into a series of sines and cosines of the form m. k. cos. (gt + A), R and A being functions of the six elements of the orbit. Now M. La Grange observed, from the expression for R and from its differential d R being restricted to the co-ordinates of the disturbed orbit, that the expres

sion () could only contain terms of the form

whence he concluded that the variations of

could only be periodic, and consequently that neither the mean distance nor the velocity of the mean motion was subject to any kind of secular variation.

At p. 330, &c. in proving the same important result, M. LA PLACE pursues the same track of reasoning: but this result, according to the proofs of these two great mathematicians, is to be admitted as true only when the squares and products of the disturbing masses are neglected. M. Poisson, however, has extended the truth of the result to the case in which the squares of the disturbing masses are not neglected; and one object of the present supplement is to demonstrate this material fact. The proof is facilitated by the new forms which M. LA PLACE here gives for the variations of the elements, nearly after the following manner :

*The symbol A, used by La Grange, is the inverse of the mean distance, and corresponds to used by LA PLACE ; and the sym

I

a

bol corresponds to the R of the Mécanique Céleste.

If represents the mean motion of the planet m, then it is shewn, p. 331. of Mécanique Celeste, that

=3. fandt. d R.

In the tract before us, the author takes the finite variation of this expression, makes R to vary only what is relative to m, and for the finite differences or variations of the axis major (a), the excentricity (e), the longitude of the perihelion (w), &c. substitutes the integrals of da, de, da, &c. He then, from the value of R, shews that do R contains only periodic quantities, or that it is nothing when we regard only secular quantities of the order of the squares of the planetary masses; and the same he proves to be true for d RfdR: consequently,

since

=3. fandt. d R

d=3 an. dt. d. dR + 3a2 (ndt. d R.fd R)

or the variation is nothing, considering only the secular quantities which, by a double integration, acquire a denomin→ ator of the order of the square of the planetary masses.

The latter part of this supplement is occupied in the correction of an error. In the theory of Jupiter and Saturn, [Mécanique Céleste, Liv. vii.] estimation is made of the fifth powers of the excentricities and of the inclinations of the Orbits; and the terms dependent on these powers were computed by M. Burckhardt. M. LA PLACE, however, has since ascertained that the inequality resulting from these terms had been taken with a contrary sign; and he here rectifies the formulæ. He observes; hence results a slight change in the mean motions and the epochs of these planets [Jupiter and Saturn]; and this change accords with the observation which Ebn-Junis made at Cairo in 1007, from their mutual conjunction: an observation which does not differ more from the formulæ, than by a quantity much less than the error to which it is liable. The antient observations cited by Ptolemy are equally represented by my formulæ. This agreement shews that the mean motions of two of the largest bodies of the solar system are at present well known, and have not undergone, since the days of Hipparchus, any sensible alteration; and it ensures for a long time, the accuracy of the tables which M. Bouvard has constructed after my theory, and which the Board of Longitude has just published.'

ART. XVI. Voyage par terre de Santo Domingo, &c. ; i. e. Travels from the Capital of the Spanish Part of Saint Domingo to Cape François, the Capital of the French Part of that Island; with a Report of the State of the Mines of the Spanish Colony, translated from Don Juan Nieto, Mineralogist to His Catholic Majesty. To which is subjoined a Detail under the Title of My return to France. By DORVO SOULASTRE, formerly Advocate and ex-Commissary of the Government at St. Domingo. 8vo. pp. 407. Paris. 1809. Imported by Dulau and Co. Price 10s.

HAD

AD we not been aware of the existence in Paris, as well as in London, of the precious art of book-making, this publication would have let us into the secret. M. SOULASTRE dedicates his book, with no little appearance of consequence, to Prince Cambatérès; and he adds an introduction which, like the title, is calculated to convey the idea that the work consists of a description of a journey through the interior of St. Domingo. Of a thick volume, however, only 89 pages are appropriated to that subject; a few are added on the state of the mines; and the remaining three fourths, intitled "Mon retour en France," contain a visit to the isle of Cuba, where the author, observing the tomb-stone of Captain Ducloz, cannot refrain from devoting 173 pages to that gentleman's history. The materials, therefore, which ought to have been compressed into a small pamphlet, are thus spun out into an 8vo volume; and the reader, who is deliberately searching for an addition to his stock of geographical and statistical information, finds himself transported into the regions of imagination, and his sympathy assailed by a tale of romantic adventures.

Nevertheless, that part of the book which treats of the island of St. Domingo is not altogether deficient in interest. The author was an Army-Commissary in the small expedition which sailed from Brest for St. Domingo, in February 1798, under General Hédouville. They reached their destination, the town of St. Domingo, in safety, and marched across the island in a north-west direction to Cape François, having traversed nearly the whole of the Spanish quarter. The reason for sending the expedition to a harbour at such a distance from the Cape was to shew the inhabitants of the Spanish quarter (then lately ceded to France, and a cession which was by no means popular,) that a French force had arrived, and was acquainted with the roads and passes. Ten days after the termination of this march, an earthquake took place at the Cape, which the author thus describes: (page 22.)

On the preceding evening, the clouds had sunk extremely low, the horizon appeared close to us, and the heat had become insupportable.

We

We could not be said to breathe, we panted; and although not making the least movement, we were covered with copious perspira tion, which ran off at the points of our fingers. We remained in this painful condition till one o'clock in the morning, when the want of air became complete, and our difficulty in breathing was similar to that of an animal placed under an air-pump. The consternation now became general: every one ran from his residence, and fled either into the streets or the open country. We heard from a distance the lowing of cattle, the howling of dogs, and plaintive cries from every breathing animal. Gradual shocks were then felt from east to west during thirty-nine seconds. Several walls fell, some houses were shattered, springs were dried up in some places, and reappeared in others. After all was quiet in the earth, it thundered, and a smart degree of cold ensued, followed by a very heavy fall of rain.'

It appears that the French were greatly struck with the fertility of this island. Throughout their whole march, they did not see a single barren spot: but the ground was every where covered either with grass or with beautiful trees. Nowhere could nature be more rich or more splendid, but nowhere could her stores be less improved by art; and in the course of the first ninety miles, they saw only one village and a few detached habitations. The face of the country, though often hilly, discovered many extensive plains; and it is watered by nume rous streams, and by four large rivers, the Ozanna, Isabella, Grand Yacqui, and Yuna: but all these advantages are lost at present; the inhabitants cultivate nothing except for the supply of their immediate wants, and they have no trade but in cattle, which roam at large in these vast pastures, and attain a size that is seldom equalled in Europe. The earth abounds with mines of gold, and of various other metals. The French found several families occupied in separating the grains of gold from the sands of the Rio Verde; and the report of the mineralogist, Nieto, mentions with confidence several gold mines imperfectly wrought, which seemed to him de la plus grand richesse. M. SOULASTRE, strongly impressed with the advantages that may be derived from a spirited improvement of St. Domingo, recommends the adoption of speedy measures to that effect. He advises that the bay of Samana should be surveyed, and a harbour constructed in it; that the inland communication by roads and canals should be improved; and that the mines should be wrought on the European plan.

The Spanish settler (for he has no title to the name of planter) consumes his time in great indolence and poverty. A wretched cabin, with hammocks slung at the corners, a few spots of ground cultivated for vegetables or tobacco, and some tattered clothes, constitute the sum of his property. His wife works while he reclines at ease, and it is even too much trouble for him to attend