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also obtain the parallax of the sun after another manner, without observing it immediately, and from the knowledge of an inequality of the lunar motions which is connected with that parallax. To conceive such connection it must be recollected that the inequalities of the lunar motions have determinate relations with the positions of the earth and sun. The calculus makes these relations known; the observations de termine the extent of the inequalities; and combining those data, we may deduce the value of the elements on which the inequalities depend, for we have the expression of their dependence and the measure of their action. The whole is reduced to finding inequalities in which that action is, in some sort, comprehended, or in which it is incessantly reproduced, in such manner that it may be inferred exactly by a great number of observations. There exists in the motion of the moon an inequality of this kind, which depends upon the sun's parallax, or upon its distance from the earth ; and on determining that by observation, M. Laplace has thence deduced the value of the parallax equal to 26". 4205 (8.-560243 sexiges.) which is nearly the same as the result deduced from the transits of Venus. It is probable that this result of the theory is even more exact than that which has been derived from the observations upon those transits.'

Such coincidences of results, deduced from totally independent methods, are extremely interesting; and every fresh instance has the effect of banishing to a greater distance than ever, all possible doubt of the sufficiency and correctness of the great principle of universal attraction, according to the inverse ratio of the square of the distances. We have long been in possession of a simple and satisfactory method of determining the moon's parallax from the usual theory of gravity, which is brought to our recollection by the preceding quotation; and which, though we know not how to ascribe it to its proper author, we cannot refrain from transcribing from our port-folio, as we think it far too ingenious to remain unknown.

Let S be the space in feet fallen in 1 second, by a heavy body in vacuo at the equator; V the versed-sine of the arc described by the moon, in the same time, to radius 1; R the radius of the equator in feet, ratio of the distance of the moon's and earth's centre, to the semidiameter of the latter that of X to 1: then, by the general law of gravitation, the space descended by the moon in 1", is S

But the same space is evidently s = VRX. Therefore
S

S
and X =

Now at the equator,
X2

S = 16.10185, its logarithm 1.2088645
Log. R= -

- 7.3211900
Log. V =-

: 7.5492882

The

VRX =

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( )!

The sum of the two latter taken from log. S, and the remainder divided by 3, gives 1.7787954 = log. of 60 08906 ; its arithmetical complement is = log. tan, of 57'12."34 the approximate horizontal parallax.

Now, let x + 1 be the distance of the centres of the moon and earth, divided by their centres of gravity in the ratio of x to 1. Imagine a sphere of the same dimensions as the earth placed at that centre, and to exert the same attractive force on the moon as our earth actually does, the periodic time remaining unaltered : then must the density of this sphere be diminished in the ratio of 22 to (x + 1)2 that its nearer distance from the moon may be compensated by the defect of density and attraction. Now, if an inhabitant of this fictitious earth were supposed to compute its distance from the moon in the manner above explained, the quantities V and R would be the same as in the former computation; but his S would be to our S, as x2 to (x + 1)? ; and thence his X' would be to our X, as iš to (x + 1)*; that is, X' = X. This

It is the distance from the fictitious earth, or from the common centre of gravity: but (D) the distance from our earth is 1+1 X, greater, as was supposed, in the ratio of x + 1 to r; that is, D =

X. But, Newton, from the phænomena of the tides, estimated the ratio of x+1 to x, at 40-788 to 39.788 (Princip. lib.ii. prop. 37.cor. 6.) So that the log, of 3, 2+1

0.0035934;

V which added to 1.7787954, the log. of X for an immovable earth gives 1.7823888 = log. of 60.5883 radii of the equator, whence the horizontal parallax there = 56'44;"07.

M. Biot having unnecessarily swelled his book by the introduction of extraneous discussions, finds, unfortunately, that he has too much matter for two volumes, but not enough for three; he therefore has recourse to his earlier publications, and the communications of his friends, to eke out his last volume. Thus, we are favoured with 216 pages of Additions, such as, first, a tedious disquisition on the measure of altitudes by the barometer and thermometer, taken from his former work on that subject; then a treatise on dialling, by M. Berroyer, professor of mathematics at the college of Sens; then an essay . Sur le mouvement de translation du systême planétaire,' by M. Biot himself, who concludes that we have no evidence whatever of any such motion; then, a tract on the rectification of a transit instrument, of course closely connected with physical astronomy; then, an essay on the length of the se

cond's

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cond's pendulum in different latitudes, furnished in part by M. Mathieu ; then, the Description et usage du Comparateur,' an instrumeut desigred for the purpose of measuring and comparing distances, such as the metre, accurately, but which will be of no use to those who are acquainted with the ingenious means employed by Mr. Bird, in determining the length of toises, &c.;* and, lastly, an ingenious and scientific method of determining the orbits of comets, by M. Laplace. This article, peculiarly interesting so soon after our evening's skies have been decorated by the most splendid comet which has been seen here for more than a century, has, we observe, found its way into one of our philosophical journals.

In conclusion, we are presented with a treatise on nautical astronomy, abridged from a former piece by • M. de Rossel. This treatise, which occupies 230 pages, is, with the exception of a few neat formulæ and useful tables by Borda and others, nearly as unscientific as the well-known production of Mr. Hamilton Moore; and an author must be reduced to wretched shifts before he could congratulate himself and bis readers, as M. Biot does, on its insertion.

We have now reached the end of our analysis ; and if it should be thought that we have extended our remarks too far, we must beg our readers to recollect that we have been sketching the contents of nearly 1800 pages; the joint labour of a dozen of the most celebrated men in France. We have no time to dwell minutely upon the disadvantages attending M. Biot's method of employing sometimes the centesimal, at others, the sexigesimal division of the circle; or those which arise from his frequently transcribing results from Laplace's - Mécanique Céleste,' without sufficiently developing the principles on which they depend. Altogether, however, the work contains much that is valuable; and we regret sincerely that from a desire to swell out his treatise to undue dimensions, and an obvious unwillingness to do justice to our countrymen, he should have compelled us to blend so much censure with our commendation.

See Philosoph. Transac. vol. Iviii; or New Abridgment, vol. xii. pa. 577.

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ART. VIII. Portugal. A Poem ; in Two Parts. By Lord George

Nugent Grenville. London, Longman, &c. 4to. pp. 120. 1819. OUR poets seem resolved not to resign to our soldiers all the

laurels of the Peninsula. Though we have not thought fit to introduce to our readers many of those modern Tyrtæi, we have not been inattentive observers of the tuneful campaign which has been prosecuted with almost as much vigour as the actual warfare.

However deficient these effusions may be in poetical merit, (and they are, in general, lamentably so,) they are not without a value of another kind : if they be not calculated to excite the public feeling, they may at least be adınitted as some evidence of it. They furnish an humble testimony of the popularity of the cause of the Peninsula, and of the revived military pride of this country. You shall better discover,' Lord Bacon somewhere says, ' how the wind blows by throwing up a straw than by casting up a stone.'

If, for this reason, we have regarded with complacency, even the weakest efforts of the muses militant, it will readily be believed, that we heard with great satisfaction the first rumours of the work before us : they were on many accounts calculated to excite no ordinary expectations. A younger branch, it was said, of a noble family (whose political opinions on the subject of the peninsular contest are notoriously hostile to our own) was, during a residence of some months in Portugal and Spain, so affected by the evidence of facts, as to have abjured the tenets of his House, professed himself a convert to the general opinion, and produced an ample and tuneful recantation.

What precise degree of credit should be attached to these rumours we cannot take upon us to say. Twice, with the most patient attention, have we read every line of this poem, and twice have we risen from the perusal, perplexed in the extreme.'

Lord George Nugent Grenville has, it is certain, published a poem under the title of Portugal; but though the stream of verse is sufficiently smooth, it is so prodigiously deep that our plummets have, in very few places indeed, been able to find the bottom; and, notwithstanding much intense study, we frankly confess, that had it not been for some extraneous assistance, which shall be hereafter gratefully noticed, we could not have ventured to offer any opinion on the merit of a work, which we could by no means flatter ourselves that we had duly comprehended.

The darkness is indeed so complete and uninterrupted, that we, at once, perceived that it was not produced by an involuntary confusion of ideas, but must have arisen from a regular and systematic design, formed on mature consideration, and executed with the most nebulous felicity. At first we suspected that this obscurity might K 4

have

have been somewhat too freely admitted as a source of the sublime; but this could only have dimmed particular passages. Then it occurred to us that the noble author had collected all the fragments of all the exercises which he had formerly sung in the academic bowers of Brazen-nose, and that we had here the disjecti membra poetæ' hastily put together; but this, too, appeared to be an untenable hypothesis ; for though it would explain much of the incoherence, it could not account for the total absence of light under which the whole appears to labour.

Another solution of the difficulty remains, and we are inclined to believe that it may be the true one. The author appears, under circumstances of peculiar delicacy-his feelings are at variance with those of his relatives, and what candour urges him to speak, the partialities of private kindness make him desirous of concealing. Appreciating, therefore, as we sincerely do, the painful struggle in which he was involved, we are inclined not merely to excuse, but almost to admire the dutiful confusion and pious obscurity in which he has buried his contending feelings.

But this mighty maze' is not, as we have already hinted, "without a plan;' and it is but justice to Lord George Nugent Grenville, to say, that he himself provides us with the clue, by prefixing a kind of preface raisonné to the whole, a detached argument to each of the parts, and explanatory notes to individual passages.

From all these sources we learn that his lordship has actually been (as rumor stated) in Portugal, and that the outline of his poem was suggested by a walk, which, one fine evening, he took in that country. Of these circumstances we entreat the reader not to lose sight; for we confess, that in the keenness of appetite with which we opened the book, we proceeded at once to the poetry, and had actually read it through without guessing at these, and other facts, which we afterwards gleaned from the several commentaries, and the knowledge of which rendered our second perusal much more easy

and delightful. The poem opens with an address to Portugal, spoken by his lordship on the rock of Cintra, about sun-set, on an autumnal evening in 1810, in which he tells her that our feelings of enthusiasm,

-when faery hands have wrought

Those ruddiest hues by poet Fancy taught,' should not indispose us towards the consideration of the cause of Portugal in all its bearings, the character of its assertors, with reference to its worse, as well as its better properties'-—and having thus clearly explained his moral sensations, he proceeds to a description of the scenery around him, which, we believe, for strength of

touch

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