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dification before they can be applied to them. The science of dya Lamics, thus modified, is called mechanics.'

Conformably to these definitions, the subordinate divisions are thrown into the following order :

Dynamics. Sect. I. Measures of motion. 2. First law of motion. 3. Communication of motion by impulse. 4. Motion equably accelerated or retarded. 5. Motion of projectiles. 6. Motion, accelerated or retarded by variable force...... Mechanics 1. Centre of Gravity. 2. The mechanical powers, i. e. The Lever, the Balance, the Wheel and Axle, the Pulley, the Wedge, the Screw, the Funicular machine. 3. Friction. 4. Mechanical Agents. 5. Motion of machines. 6. Descent of heavy bodies on plane and curved surfaces. Centre of Oscillation. Heavy bodies descending on a cycloidal surface. 7. Rotation of bodies. Rotation about a fixed axis. Rotation on a moveable axis. Appendix to mechanics. Constructionof Arches. Strength of Timber.'

We should have thought it far better to assume Mechanics as the universal term, including Statics, Dynamics, Hydrostatics, and Hydrodynamics. Then the Professor might, after the example of the learned Author of the “ Mécanique Philo“ sophique,” have defined Statics as that part of Mechanics,

which, dropping the consideration of time, examines only the reciprocal actions of powers, applied to an inflexible system of

points or of bodies, when the efforts resulting from those " actions destroy one another, and the system remains immove

able.' Dynamics would then be defined, as that part of Meehanics in which time enters the consideration, and which has ' for its object that action of forces on solid bodies from which (motion results.'

Had our Author proceeded thus, he would have had a portion in the mechanics of solid bodies, which would have corresponded to that which he has rightly denominated Hydrostatics, in the mechanics of incompressible fluids. His doing otherwise, is to be regarded, however, as the result of some peculiarities in defining, not as a serious defect of knowledge. Those, peculiarities abound in the earlier portions of the first volume of the Outlines ;' so that we could easily, were it not an unpleasant task, fill pages with observations upon his strange manner of distinguishing Chemistry from Natural Philosophy, hypotheses from facts, solids from fluids, motions from powers, and his equally strange definitions and remarks in relation to the sutlicient reason, the form of pores', magnetism, velocity, laws of motion, &c. We have, indeed, been satisfied with scarcely any thing in the introductory part of the first volume, except the Professor's account of the benefits which may accrue from the science of Natural Philosophy; and this we quote with cordial approbation.

· The study of Natural Philosophy is accompanied with great advantages.

1. It extends man's power over nature by explaining the principles of the various arts which he practises.

• 2. It improves and elevates the mind, by unfolding to it the magnificence, the order, and the beauty manifested in the construction of the material world.

* 3. It offers the most striking proofs of the beneficence, the wis. dom, and the power of the CREATOR.'

Let not the reader suppose that all we have found worthy of approbation in the first volume, has been extracted above. They are peculiarities of manner of which we complain : the matter is often highly valuable ; the selections of propositions and corollaries, are made with great judgement, and the excellent practical applications, are such as could have proceeded from no mere theorist. We know not where to point for more useful information in equally small compass, than is to be found, under the subdivisions of Mechanical Agents, Motion of Machines, Motion of Water in conduit pipes and open canals, and Hydraulic engines, comprising those moved by the impulse, those by the weight, and those by the re-action of the water.

There is one particular in which these “ Outlines” are distinguished from all other synopses of philosophical lectures with which we are acquainted. Generally, when the Author leaves a proposition undemonstrated, he refers to other works in which demonstrations are given ; or, when he does not present the requisite details or explanations, he points to other performances in which they may be found. This is calculated to be extremely beneficial, especially as the Professor's references are judiciously selected, and not very numerous. This part of the plan admits of an obvious and easy improvement, which we hope Mr. Playfair will introduce into a new edition. It is simply to mark with an asterisk, that, among the several works specified in any class of references, which the student may most advantageously consult. In cases where a young man has opportunity of turning to many books on every subject, as when he has access to a college library, he will often be bewildered by a multiplicity of references. And, in other cases, where the magnitude of a library depends upon the extent of an individual's pecuniary means, a few of these friendly asterisks may save a deserving lover oi knowledge many a guinea and many a sigh..

It is time we should turn to the second volume, with which, as a whole, we have been much more pleased than with the first. It is entirely devoted to the subject of Astronomy, and is di

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vided into two parts; the first relating to what has been usually denominated plane astrononıy; the second, to physical astronomy. The arrangement of both parts is logical, and well calculated for the cominunication of knowledge. Considering the limits to which Professor Playfair lias confined himself, he has given a tolerably perspicuous view of the best means of developing the true system of astronomy. He has also interspersed several of the most elegant formula for computation, and has tabulated some of the most important results. The first part is terminated by a valuable Appendix on the method of determining by ob

servation, the constant coellicients in an assumed or given (function of a variable quantity ;' in which Tobias Ma er's process for determining the co-efficients by equations of condition, a process which has been most successfully employed by all subsequent astronomers, is succinctly, but elegantly and clearly explained.

The portion of these “ Outlines," however, which we hare examined with the greatest pleasure, is that which relates to Physical Astronomy. Persons in general have been too apt to regard this department of science as absolutely unapproachable, except by a very profound mathematician. The work which contains the most complete and elahorate development of the principles and discoveries in this department of astronomy, namely, the “ Mecanique Celeste” of Laplace, is far too abstruse to be read by any but masters of the exact sciences. The elegant introduction to it by Biot, in his “ Astronomie de Phy

sique,” has never been widely circulated in this country. The perspicuous and satisfactory treatises by Frisi, i. e, the “ Cosinographia,” and “ Theoria Diurna Motûs,” are seldom found, except in the libraries of our colleges and public institutions. And the accurate, and, in some respects, profound essay on playsical astronomy, given by Professor Vince in the second volume of his quarto Treatise, is, by reason of the expense of that work, necessarily excluded from the libraries of the majority of students. We are, therefore, glad to find, in the latter of the volumes before us, a sketch of the principles and of the most important discoveries of physical astronomy, which is at once concise and perspicuous, and which, though it does not furnish a demonstration of every proposition advanced, gives so satisfactory an exhibition of some investigations, and so clear a view of the principles on which others are conducted, that instead of deterring a student, it will stimulate him to fạrther examination of the subject in the treatises wherein it is fully discussed.

Professor Playfair's view of physical astronomy occupies about one hundred and twelve pages, and is exhibited in eight sections. 1. On the forces which retain the planets in their orbits. 2. The forces which disturb the elliptical motions of the

planets, and of the moon. 3. Disturbances in the motions of the primary planets, from their actions on one another. 4. Disturbances in the motions of Jupiter's satellites from their mutual actions, with the general result from the theory of the planetary disturbances. 5. Attraction of spheres and spheroids, 0. Figure of the earth. 7. Precession of the equinoxes, variation of the diurnal rotation and of the obliquity of the ecliptic. 8. Physical explana ion of the plenomena of the tides, ana' coneluding remarks on the principle of universal gravitation.

We shall extract soine instructive passages from the commencement of the second section :

“When there are only two bodies that gravitate to one another, with forces inversely as the squares of their distances, it appears from the last section that they move in conic sections, and describe about their common centre of gravity, equal areas in equal times, that centre either remaining at rest, or moving uniformly in a right line. But if there are three bodies, the action of any one on the other two, changes the nature of their orbits, so that the determination of their motions becomes a problem of the greatest difficulty, distinguished by the name of THE PROBLEM OF THREE BODIES.

• The solution of this problem in its utmost generality, is not within the power of the mathematical sciences, as they now exist. Under certain limitations, however, and such as are quite consistent with the condition of the heavenly bodies, it admits of being resolved. These limitations are, that the force which one of the bodies exerts on the other two, is, either from the smallness of that body, or its great distance, very inconsiderable in respect of the forces which these two exert on one another.

The force of this third body is called a disturbing force, and its effects in changing the places of the other two bodies are called the disturbances of the sysiem.

• Though the small disturbing forces may be more than one, or though there be a great number of remote disturbing bodies, the computation of their combined effect arises readily from knowing the effect of one; and therefore the problem of three bodies, under the conditions just stated, may be extended to any number

• Two very different methods have been applied to the solution of this problem. The most perfect is that which embraces all the effects of the disturbances at once, and, by reducing the momentary changes into fluxionary or differential equations, proceeds, by the integration of these, to determine the whole change produced in any finite time, whether on the angular or the rectilineal distance of the bodies.' This method gives all the inequalities at once, and as they mutually affect one another

• The other method of solution is easier, and more elementary, but inuch less accurate. It supposes the orbit disturbed, to be nearly known, and proceeds to calculate each inequality by itself, independently of the rest. It cannot, therefore, be exact, and gives only a first approximation to the quantities sought: but being far simpler

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than the other, it is much better suited to the elements of science. It is also the original method, and that which was first applied by Sir ISAAC Newton, to explain the irregularities of the moon's motion. The same has been followed and improved, by CALENDRINI, in his Commentary on the third Book of tħe Principia; by Frist in his Cosa mographia ; and by Vince in the second volume of his Astronomy. The other method was not invented till several years

later, when it occurred nearly about the same time to the three first geometers of the age, CLAIRAUT, EULFR, and D'ALEMBERT. It was followed also by Mayer, and several others, but particularly by LAPLACE, who, in the Mecanique Celeste, has given a complete investigation of the inequalities both of the primary and secondary planets.

I shall explain the resolution of the forces that is in some measure common to both methods; and shall shew how their effects are to be estimated in some simple instances, going from thence to the enumeration of the results. I begin with the moon's irregularities, as the easiest case of the problem.'

These he traces with considerable perspicuity, stating the most important propositions, and enumerating many curious particulars, especially those which tend to confirm the assumed theory of gravitation. We have room to specity only one of them. Clairaut after solving the problem which relates to the motion of the apsides of the lunar orbit, on comparing the result with observation, met with the same difficulty that Newton had experienced, and

· Found that his formula gave only half the true motion. He therefore imagined that gravity is not inversely as the squares of the distances, but follows a more complicated law, such as can only be expressed by a formula of two terms. In seeking for the co efficient of the second term, he was obliged to carry his approxination farther than he had done before ; in consequence of which the co-efficient he sought for came out equal to nothing, and the motion of the apsides was found to be completely explained by the supposition that the force of gravity is inversely as the square of the distance.

Another striking confirmation, as well as application, of this universal theory, is given at p. 282, when our Author is treating of comets, and the way in which their orbits are atfected by the disturbing forces of the planets. He also presents a few observations on the improbability that any perceptible alteration in the motion of the planets, or indeed any sensible effect upon them, should be produced by comets. This subject, by the way, is treated in a very satisfactory manner, by Delambre, in his quarto Astronomie, tome jii. p. 404-6, and in the Abrégé, p. 564. Tbe latter work is frequently cited by the Professor.

After developing the principal effects of the disturbing forces of the planets upon the several parts of the solar system, he

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