This accurate compensation of the inequalities of the planetary motions depends on three conditions, belonging to the primitive and original constitution of the system. 1. That the eccentricities of the orbits are all inconsiderable, or contained within narrow limits:2. That the planets all move in the same direction, as both primary and secondary do from west to east:-3. 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 limit. 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 thirty-one 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 constitutions of the system, and impressing such motions on the parts as were calculated to give stability to the whole.

Having thus stated our opinion of these "Outlines" as a whole, we shall now notice one or two incorrect expressions, and point out some instances in which we think the work may be improved, sincerely hoping that Mr. Playfair will soon have an opportunity, in a new edition, of correcting the one, and re-considering the other. The definitions of motions given in articles 20 and 40 of the first volume are at variance with each other; and the latter only we conceive to be correct. In Art. 50, the word indefinitely, should be substituted for infinitely; and in Art. 54, " the product of the mass, multiplied by the velocity," should have been the product of the mass and the velocity. A few other instances of this kind might be pointed out, but they are of too trifling a nature to require enumeration. The following, however, requires more particular notice:

Mr. Playfair denotes the number that expresses the circumference of a circle of which the diameter is 1, by ; the strength of a ligneous fibre by s; the length of a beam, projecting horizontally from a wall, by ; and the weight, which is just sufficient to break

The terms here referred to are of the form Atan nt,

where A is any constant coefficient, and n a certain multiplier of t the time, so that at is an arch of a circle, which increases proportionally to the time. Now if any of these terms were to enter into the value of any of the inequalities, its value would continually increase, and the order of the system might finally be destroyed.

the beam, when suspended from its extremity, by W. Then, at page 153 of vol. i. he observes:

In a cylindric beam, of which the radius is r,

In a cylindric tube, the radius of the external surface being r, and of the internal r',

The strength of the tube is, therefore, to the strength of the same quantity of matter, formed into a solid cylinder of the same length as

rto

This is not only obscure, but the conclusion is erroneous. The radius r of the solid cylinder, used in the first formula, is not equal to that of the external surface of the cylindric tube of the same length and quantity of matter, employed in the second, and therefore, they should not have been denoted by the same letter r. To avoid the obscurity and error, which we conceive to have arisen from this cause, let R be the radius of the external surface of the tube, then the second formula becomes

and consequently the relative strength of the solid cylinder to that of the cylindric tube is as

But rand (R2-2) are the areas of the sections of the two cylin drical beams, which, as well as the strengths of their ligneous fibres and lengths, are the same in both, by hypothesis; and therefore their relative strengths are as r to ; and not as to 12, as inadvertently stated by the Professor.

To the propositions respecting the strength of Timber, given in the first volume, the two following Theorems might be added with advantage; and their practical nature renders them important. If WV denote the number of hundred-weights, which laid on the middle of an oak beam, supported at both ends, is just sufficient to break it; 1, the length of the beam; b, its breadth; and d, its depth; then W= 100bd. Fir is a little weaker than oak; and about 4th of this weight may be safely supported in practice,

Again, let S denote the quantity which a beam of fir will sink, when supported as before, and loaded with w pounds placed on the middle; the other letters remaining as in the preceding Theorem ; then S=__2013 Oak sinks a little more than fir. These

10000000bd3

two theorems have been deduced from Dr. Young's Lectures on Natural Philosophy.

The measurement of altitudes by means of the barometer has long been regarded as an important physical Problem; and many of the most eminent philosophers, both of the last and present age, justly considering the barometrical formula as a valuable instrument in obtaining a physical knowledge of the globe, have been Occupied in contributing towards its perfection. Professor Playfair, in his historical notices on this subject, contained in Art. 338, vol. i. has not included any reference to M. Biot's Essay, inserted in the 2d edition of his d'Astronomie Physique;" though this work was published in the year prior to the first volume of the work before us. This omission, however, may be satisfactorily accounted for, from the difficulty and delay in obtaining the new French publications at that period. As M. Biot has taken all the quantities into his investigation that are likely to affect the accuracy of the result, and has also rendered the formula very simple, we have adapted it to English measures, and shall insert it for the use of such of our readers as feel interested in the subject.

If A represent the required altitude in fathoms, t and t denote the temperatures of the air at the two stations, in degrees of Fahrenheit's Thermometer above the freezing point; H the height of the barometer at the lower station, and ǹ at the higher, both being reduced to the same temperature; then,

which gives the difference of altitude of the two stations, independently of the latitude of the place of observation. But when it is thought necessary to take this correction into the account, let the latitude be denoted by ; and then the formula becomes

H

▲=10057-3(1+0·002837 cos24) (1+1) log.

900

In order to facilitate the application of this formula, M. Biot has reduced it into Tables, which render its use extremely easy. We cannot help suggesting to the masterly author of these volumes that a section on Time might be properly introduced into the second volume, more fully explaining the derivation of the different species, their relation to each other, and their respective uses in astronomical, nautical, and civil calculations. This appears

to us to be the more desirable, as we are not acquainted with any work in our language that can be satisfactorily referred to on that subject.

It was not the author's intention that his work alone should be sufficient for the student who is desirous of attaining an intimate acquaintance with the principles of Natural Philosophy; yet there are three classes for whose use it is well adapted. It will, agreeably to his intention, be found an excellent guide to those who attend his lectures; and it deserves to be recommended as a remembrancer to such as have already acquired a considerable knowledge of the subject; and also as a directory to those who possess a good scientific library.

ART. IX. Secret Memoirs of Napoleon Buonaparte, preceded by an Historical Survey of the character of this extraordinary Personage, founded on his own words and actions, by one who never quitted him for fifteen years. Second Edition, to which is added an account of the Regency at Blois, and the Itinerary of Buonaparte, from the period of his residence at Fontainbleau, to his Establishment on the Island of Elba. London, Colburn. 1815. We have perused this work withconsiderable interest, as communicating much information relative to the strange being whom it professes to depict. It does not, indeed, throw any new light on the more prominent features of his character, which are sufficiently marked by the operations which he has directed, and which will form so melancholy a portion of modern history. But it discovers to us many minute shades, and nice lines in his moral complexion, in which the fire and the terrors of his spirit break forth, and enable us to view him in his privacy with a sort of horrible distinct

ness.

The chief constituents of his character, as represented by this author, are a vague, headlong and intemperate craving for notoriety -a desperate and concentrated selfishness-a "love of life," and an unprincipled disregard of the lives of others. Those who shall in future times endeavour to analyse, without prejudice, the character of Buonaparte, will perhaps find it extremely inadequate to the results it has produced. His most determined admirers will hardly allow to him the merit of enlarged policy; and even his professional reputation is tarnished with the charge of a needless and unskilful profusion of human blood. As a singular anomaly in the annals of the world-as a noxious and heterogeneous compound of mental and moral qualities, he may indeed be called an

extraordinary person; but in the page of history, he will hardly obtain the honors of true greatness; or even the miserable credit of consistency in Evil Wisdom. As he is pourtrayed in this volume, we are irresistibly reminded of the well-known aphorism; and are prompted again to marvel at the slight stock of sagacity and talent which suffices to govern nations. What Tacitus observes of barbarian valor in the field of battle, may be applied to Buonaparte: Virtus (we do not use the word in a moral sense) velut extra ipsum. The mind of this Destroyer seems to want stability and firmness; to be rather led by impulse, than regulated by reason; while every action of his life, and his relations with every object about him, appear subservient to his appetite for glory. The most philosophic of Roman Historians has considered the pursuit of fame as an incentive to virtue; but how far is the benignant love of the guardian Deity, from the selfish and savage triumph of the Pagan Idol!

The author relates at length the intrigues of Buonaparte against Moreau; and we have an interesting narrative of the imprisonment and murder of Pichegru. These are already so familiar to the public, that we must reserve our space for other subjects. The four Mamelukes, who strangled Pichegru, are supposed to have afterwards fallen victims to the sanguinary caution of the Despot.

Buonaparte's attention to the minuter springs of human conduct and opinion, forms a very essential ingredient of his policy. Hence proceeded the system of mutual inspection, which fettered the freedom of thought; the slavery of the press, and the studied perversion or suppression of the materials of authentic history. The same spirit, but differently directed, will be visible in the subsequent passages:

No sooner did he become Consul, than the expression of his countenance was enlivened, his voice was less harsh, his eye became mild, and his manner much less repulsive. Did he confer any favor, did he promote any one to an office, it was done with courtesy, often adding even some obliging expressions. The beauties of language were little familiar to him; he was a stranger to those brilliant obscurities, those neat inversions so necessary to statesmen, who should take care that their modes of speech do not always express what they ought to say, but what they wish others to understand. To remedy this dearth of oratorical powers, he formed to himself a dictionary of chosen words and phrases, which he arranged and moulded according to time, place, person, and circumstances. His speeches of form were always arranged before-hand; he knew what would be said to him, and he was prepared with an answer. Thence came that barrenness of ideas, that pompous gallimaufry, to which his miserable courtiers gave the appellation of sublime. Many times have I seen him study the style