terminates this portion of his investigations by the following instructive and interesting conclusion. One general result of these investigations is, that both in the system of primary and secondary planets, two elements of every orbit remain secure against all disturbance; the mean distance and the mean motion, or, which is the same, the transverse axis of the orbit and the time of the planet's revolution. Another result is, that all the inequalities in the planetary motions are periodical, and observe such laws that each of them after a certain time runs through the same series of changes. Every inequality is expressed by terms of the form A sin nt or A cos nt; where A is a constant co-efficient, and a certain multiplier of ✰ the time, so that nt is an arc of a circle which increases proportionally to the time. Now, though nt is thus capable of indefinite increase, since sin nt never can exceed the radius or 1, the maximum of the inequality is A. Accordingly, the value of the term A sin nt first increases from o to A, and then decreases from A to o; after which it becomes negative, extends to= A, and passes from thence to o again, the period of all those changes depending on n the multiplier of t. If into the value of any of the inequalities, a term of the form, A tan nt, A or of the form A x nt were to enter, the inequality so sin nt expressed, would continually increase, and the order of the system might finally be displaced. LA GRANG and LA PLACE, in demonstrating that no such terms as these last can enter into the expression of the disturbances of the planets, made known one of the most important truths in physical astronomy. They proved that the system is stable; that it does not involve any principle of destruction in itself, but is calculated to endure for ever, unless the action of an external power is introduced This accurate compensation of the inequalities of the planetary motion, depends on three conditions, belonging to the primitive and original constitution of the system. I. That the eccentricities of the orbits are all inconsiderable, or contained within very narrow limits. ' II hat the Planets al move in the same direction, as both primary and secondary do from west to east. II. That the planes of their orbits are but little inclined to one another. 'But for these three conditions, terms of the kind mentioned above, would come into the expression of the inequalities, which might therefore increase without 1 mit. These three conditions do not necessarily arise out of the nature of motion or of gravitation, or from the action of any physical cause with which we are acquainted. Neither can they be considered as arising from chance; for the probability is almost infinite to one, that without a cause particularly directed to that object, such a conformity could not have arisen in the motions of 31 different bodies scattered over such a vast extent. The only explanation therefore that remains is, that all this is the work of intelligence and design, directing the original constitution of sy tem and expressing such motions on the parts as were calculated to give stability to the whole. the This, as far as it goes, is excellent. But the principle of gravitation will enable us to take another step, and that a very momentous one. It is demonstrable from this principle, not only that there existed originally a Designing Agent, but that the universal system requires, his perpetual intervention. This has been shown conclusively by many writers, but by none, perhaps, more indubitably than by Professor Vince in his "Observations on the Cause of Gravitation" which we reviewed some years ago. It seems reasonable (says Mr. Vince) to admit a Divine Agency at that point where all other means appear inadequate to produce the effect. And as mechanical operations, in whatever point of view they have been considered, do not appear sufficient to account for the preservation of the system (to say nothing of its formation), we ought to conclude, that the Deity, in his government, does not act by such instruments; but that the whole is conducted by his more immediate agency, without the intervention of material causes.' A mathematical writer in a celebrated northern journal, laboured hard to weaken this consolatory inference: but, happily, he failed in the attempt by neglecting (whether from ignorance or intention we cannot say) to distinguish between motive and accelerating force. There is much valuable matter in the remainder of these “Outlines, but we have not room to speak of more than a -single topic, viz. the variation of the obliquity of the ecliptic. The position of the ecliptic is incessantly changing by reason of the action of the planets. The variations in the obliquity of the ecliptic, thus produced, are among the number of the secular inequalities which have long periods, and, after reaching a maximum, return in a contrary direction. As far back as observation goes, the obliquity of the ecliptic has been diminishing, and is doing so at present, by 52" in a century; it will not, however, always continue to diminish, but in the course of ages will again increase, oscillating backwards and forwards on each side of a mean, from which it never can depart far. The secular variation of the obliquity was less in ancient times than it is at present; it is now near its maximum, and will begin to decrease in the 22d century of our era. LA GRANGE has shewn, that the total change of the obliquity, reckoning from that in 1700, must be less than 50 23'; Mem. Acad. de Berlin, 1782. p. 284. Also that the changes in the inclinations of the planetary orbits, are all periodical, and cannot carry the planes of those orbits beyond the limits of the zodiac, or 8° on either side of the ecliptic. By the retrogradations of the nodes of the ecliptic and the planetary orbits, the precession of the equinoxes is diminished by a small quantity, which is at present about 07 281 annually. Ibid. p. 281. All this is quite independent of the figure of the earth, and would be the same though the earth were truly spherical.' These variations in the obliquity, with their limits and peculiarities, will become still more manifest to the student, on his applying the curious theorem given by Laplace for that purpose. Let t denote the number of years from 1750, to be regarded as negative before, and as positive after that epoch; then will the obliquity be always nearly expressed in sexigesimal measures by the formula, 23°28/23" 051191/2184 [1cos (t. 1394645)] 3347 0496 sin. (t. 3211575). It is interesting to observe how the sentiments of astronomers have vacillated on this subject. Copernicus and Kepler were both of opinion, not only that the obliquity varied, but that the variation had limits. The former assigned them between 23° 56' and 23° 28′; the latter, between 26° 5' and 22° 20′,- -2 most remarkable conjecture, considering the time in which it was advanced. Afterwards, in the seventeenth century, and at the beginning, of the eighteenth, philosophers in general aimed to prove that the obliquity was constant. Thus, Professor Bernard, of Oxford, in a paper published A. D. 1684, in No. 163, of the Philosophical Transactions, endeavoured to prove there was no diminution: and Flamstead, by transmitting that paper to the Royal Society unaccompanied by any remark, seemed to concur in the opinion. Dom. Cassini, Lahire, and even Lemonnier, so late as 1745, took the same side of the question. In 1716, when M. de Louville presented to the French Academy of Sciences a paper in which he attempted to prove that the obliquity was actually diminishing, that paper was not adinitted into their memoirs, because ALL the astronomical Academicians thought differently from Louville. Malgré toutes les raisons de M. de Louville (said Fontenelle, in the History of the Academy for 1816) les autres astronomes de l'académie • sont demeurés attachés à l'obliquité constante de l'ecliptique de 23° 29'.' The disquisition being thus excluded from the Paris Memoirs, was inserted in the "Acta Eruditorum," of Leipsic, for June 1719. Such, however, is now the state of physical astronomy, that if a person were to call in question the fact of the variations of the obliquity, he would be ex pected next to deny the rotation of the earth, or that the moon exhibited mutable phases. But, looking back at the extent of what we have written, we must now return for one moment to the Professor Playfair's work, and then conclude. After remarking that the existing law of gravitation has been wisely selected out of an infinite number;' he hints at the existence of a still more general principle, and thus terminates his work : 'If we consider how many different laws seem to regulate the other phenomena of the material world, as in the action of Impulse, Cohesion, Elasticity, Chemical Affinity, Crystallization, Heat, Light, Magnetism, Electricity, Galvanism, the existence of a principle more general than any of these, and connecting all of them with that of Gravitation, appears highly probable. The discovery of this great principle may be an honour reserved for a future age, and science may again have to record names which are to stand on the same levels with those of NEWTON and LAPLACE. About such ultimate attainments it were unwise to be sanguine, and unphilosophical to despair.' This is language and sentiment worthy a Professor of Natural Philosophy. It would be well, we think, if the ingenious writer in the Edinburgh Review, whose whimsical dreamings relative to a formula which should comprise the trajectories described by every particle of matter in the universe we detailed in our December Number, could attend a course of Mr. Playfair's lectures. It only remains for us to remark, that neither of these volumes contains the science of optics. Whether it is that this branch of knowledge does not constitute a portion of the Edinburgh course, or that the learned Professor means to treat it separately, are questions on which we must leave those of our readers who may be so inclined to speculate, till either a new volume from the same Author, or a preface to a new edition, furnish the requi site information Art. VI De la Traite et de l'Esclavage des Noirs et des Blancs. Par un Ami des Hommes de Toutes les Couleurs. pp. 84. Paris. Adrien Egron, Imprimeur. 1815. On the Slave Trade and the Slavery of Blacks and Whites. By a Friend of Men of all Colours. BUONAPARTE has abolished the Slave Trade in France. With respect to the motives which have dictated this absolute decree of the Usurper's, in contempt of all the opposing interests and other obstacles which we were taught to believe stood in the way of justice and humanity, there is, probably, but one opinion. Unsusceptible of any passion but ambition, the mind of such a man is not to be diverted from its oneness of object by any consideration of so remote a policy as that of morality, or by any such weakness of feeling as giving way to the opinions of others, or to the convictions of his own mind, one degree beyond what it has become expedient to do, or to feign. All that we can know of such a man are-his acts. The relation which those acts have to his settled purpose, only a mind of equal capacities of good and evil is competent always to detect: while the hidden motive of his actions is frequently veiled from every eye but that of Omniscience. Nothing, however, could be a more ludicrous misapprehension, or could betray more completely an inability to understand the staff and texture of such a mind, than the idea that any compunctious visitations of conscience, or any relentings towards good, were likely to prompt him to the inconsistency of virtue. If there were room in the thoughts of Buonaparte, at this crisis of his fortunes, for any other purpose than that of evident policy, one would be apt to believe that his adoption of this measure was in calm, magnanimous derision of the Potentates and Statesmen assembled in Congress, to deliberate, among other things, upon this point of simple humanity: who, after detaining Europe in anxious suspence for so long a period, have brought forth a Declaration on the subject, which declares nothing so clearly as the guilt of all the parties implicated in this hypocritical toleration of the traffic. In the language of this eloquent pamphlet, we may render it thus :-- We know that the Slave Trade is a crime, but let us agree to commit the crime for five years longer.' Upon this famous Declaration the simple decree of Buonaparte's is a covert satire, whether designed or not, of the keenest description. Buonaparte abolishes the Slave Trade in France. Henry the Eighth abolished popery in this kingdom. The circumstance by which the lives and liberties of millions may be preserved, is not to be the less rejoiced in, because hypocrisy, or turbulent ambition, blindly working the counsels of Providence, was the agent. How often do we find the means which the Almighty selects for accomplishing the mightiest good, those which we should have deemed both unlikely and unfit; those which human wisdom would have disdained to employ; or to which human pride would have revolted from the idea of being indebted! The instrument is, perhaps, detestable. The man can claim no gratitude for the benefit he confers. The Almighty accepts the unavailing efforts, the very will and wishes of humble goodness; but He employs the rod of the oppressor, and the sword of the conqueror, to do his work They are fitter weapons for such harsh and unhewn materials as they are employed upon. He makes the wrath of man to praise him. It is little, after all, that the combined efforts of patriots and philanthropists seem capable of effecting: the circumstances of the world are against men, who have to |