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same spirit. Another part contains a detailed account of the dis asters which have befallen Germany; all which, says Mr. Burdon, ' were the blessed results of Bonaparte's conquests in Italy, or, properly speaking, of the first coalition against French liberty. We too can glow at the name of liberty: but we cannot couple that sacred name with the name of Frenchmen; we can bestow no praise on the cause which attracts so much of Mr. Burdon's admiration ;--that cause whose notorious and avowed object was the subversion of established governments, and the dethroning of legitimate kings. We apprehend, and the justice of our apprehensions is proved by the experience of ages, that liberty or universal equality is but a name; an ideal blessing which exists only in the declamation of school-boys, in the imagination of poets, in the dreams of a visionary philosopher. Its theory is delightful; but the depravity of human nature, or some other cause, has ever prevented its being carried into practice. It is a phantom in the pursuit of which the blood of thousands has been spilt; which misguided enthusiasm is delighted to chase, but
Hæret hians, jam jamque tenet, similisque tenenti
Before Mr. Burdon is dismissed, it must be allowed that there are several parts of his work which, to those who do not happen to have read them before, will doubtless afford amusement: such are, in particular, the ceremony of the presentation of Bonaparte to the directory, page 85; the description of the passage of the Alps, page 155; &c. &c. We shall conclude by wishing, not for the sake of his glory, but of our own instruction, that Bonaparte may meet with a more able historian.
ART. V.-Elements of Mechanical Philosophy, being the Substance of a Course of Lectures on that Science. By John Robison, LL.D. Professor of Natural Philosophy in the University of Edinburgh, Fellow of the Royal Society of Edinburgh, of the Imperial Academy of Sciences at St. Petersburgh, and of the Philosophical Societies of Manchester and New York, &c. Vol. I. including Dynamics and Astronomy. 8vo. 11. 1s. Boards. Cadell. 1804.
ALTHOUGH the business of critics is with books, and not with their authors, yet, as it was likely to happen, the character of Dr. Robison excited within us a curiosity to see what was said by him on a subject, by general acknowledg ment, arduous and intricate. The plan, the conduct, the use
fulness, and the merits, of his work, may be understood from the subjoined analysis and our occasional comments: these are given nearly as they were suggested by progressive perusal.
The title page announces the contents of the present volume to be Dynamics and Astronomy, but the former subject is treated with considerable restriction: no application is made of the doctrine of powers and moving forces, to the motion of bodies along inclined planes, to the motion of bodies connected by levers, &c.; and consequently the present volume contains nothing concerning the centres of oscillation, gyration, &c. It should seem the main object of the author is, to illustrate and to familiarize the philosophy of Newton; and to show, in the motions and perturbations of the planets, in the figure of the earth, and in the phenomenon of the tides, the universality of the law of gravitation.
In the order and mode of demonstration Dr. Robison treads very nearly in the steps of our great philosopher; as continued quantity, as curves and variable motion, were to be the subjects of discussion in the 'Principia,'Newton prefixed his first section, by which he taught how continued quantity was to be measured and estimated. He stated his axioms and rules geometrically. The author of the present work begins it with certain propositions concerning prime and ultimate ratios or limits, and proves them by the aid or intervention of diagrams. This doctrine of prime and ultimate ratios, or of limits, by its nature, if we may so express ourselves, is not without great difficulties. It is very perplexing and embarrassing to beginners: the doctrine has not been clearly and accurately propounded. Newton is not able to satisfy the doubts and objecting inquiries of the true searcher after truth; and the obscurity of his doctrine is not dissipated by the light that Dr. Robison has thrown upon it if he was clear, he would be very brief; but, in our opinion, he has done nothing to remove the ancient prejudices concerning the connection or concomitancy of brevity and obscurity.
Preliminary propositions concerning limiting ratios, or concerning that method in fact by which continued quantity is to be estimated, very properly precede any discussion relative to force and velocity. These are mere terms, the creatures of definition; and from the definitions to know their value and mathematical measure, recourse must be had to fluxions, or to the differential calculus, or to the method of limits: thus the symbol for the velocity is, the symbol for the force isor
and particular instances being given, to know how to ex press in algebraic terms the value of such symbols, we must ap ply the rules of the mentioned calculi. Dr. Robison begins, and properly enough, with uniform motions; and deduces the
common and known formulas that subsist between the spaces, velocities, and times. He then passes on, to the consideration of variable motion; and here, in our opinion, the learned professor uses more words than are necessary: indeed, in certain, passages, he seems not entirely free from the thraldom and mystical influence of words;-he talks about a body having a potential velocity, and a certain determination; and this is the more remarkable, since extracts will be exhibited by us not only of clear and accurate argumentation, but in which the author insists on the necessity of using words of a precise signification.
The professor's proposition concerning the method of estimating the velocity, we do not much approve of: from this proposition it is deduced, as a corollary, that the velocities are in the ultimate ratio of the spaces described in equal moments of time. The author then adds: 'It often happens, that we cannot ascertain this ultimate ratio, although we can measure the spaces described in very small moments. We are then obliged to take these as measures of the velocity.' This passage either we do not rightly understand, or, if we do understand it, it is manifestly wrong: if, in the language of the modern mathematicians, the space be a function of the time, or if =t, what is the case in which we cannot compute
After the composition of motions, which is well explained and illustrated, Dr. Robison proceeds to show, after Newton, that the areas are proportioned to the times; that the velocity varies inversely as the perpendicular; &c.: he also deduces the several expressions for the force, a body moving in a right line towards the centre of force, or describing a curve line round the centre of force; that is, he proves expressions such as these, ƒ= = = = ‚F=
chord of curve. chord of curve.
: and he distinguishes properly, as Dalembert has done before him, between the measure of the force, the body moving in a polygon, and the measure, the body moving in a curve.
In the second section the author defines dynamics to be 'that department of physico-mathematical science, which contains the abstract doctrine of moving forces; that is, the necessary results of the relations of our thoughts concerning motion and the causes of its production and changes.' This passage is rather obscure and vague: what does the author mean by the causes of its production'? The next passage will inform us changes of motion are the only indication of the agency, the only marks of the kind, and the only measures of the intensity of those causes.' We know nothing then of causes: we can indeed talk about them, by making terms stand for effects; and dynamics
in fact, treat only of effects, of spaces described, and of the mathematical laws of their description-But, considering the great and general merit of the performance before us, we seem to ourselves degenerating into petty and peevish criticism; we turn, therefore, with satisfaction, to certain passages in which the author's perspicuity, accuracy, and mental vigour, eminently shine forth.
'These mechanical affections of matter have been very generally called powers or forces; and the body conceived to possess them is said to act on the related body. This is figurative or metapho rical language. Power, and force, and action, cannot be predicated in their original strict sense, of any thing but the exertions of animated beings; nay, it is perhaps only the exerted influence of the mind on the body which we ought to call action. But language began among simple men; they gave these denominations to their own exertions with the utmost propriety. To move a body, they found themselves obliged to exert their strength, or force, or power, and to act. When speculative men afterwards attended to the changes of motion observed in the meetings or vicinity of bodies, and remarked that the phenomena very much resembled the results of exerting their own strength or force; and when they would express this occurrence of nature, it was easier to make use of an old term, than to make a new one for things which so much resem bled; because there are always such differences in other circumstances of the case, that there is little danger of confounding them, We are not to imagine that they thought that inanimate bodies exerted strength, as they themselves did. This was reserved for much later times of refinement.-In the progress of this refinement, the word power or force was employed to express any efficiency what ever; and we now say, the power of aqua fortis to dissolve silver -the force of argument-the action of motives, &c. &c.
To this notion of conveniency we must ascribe, not only the employment of the words power and force, to express efficiency in general, but also of the terms attraction, repulsion, impulsion, pressure, &c. all of which are metaphorical, unless when applied to the actions of animals. But they are used as terms of distinction, on account of the resemblance between the phenomena and those which we observe when we pull a thing toward us, push it from us, kick it away, or forcibly compress it.
Much confusion has arisen from the unguarded use of this figu rative language. Very slight analogies have made some animate all matter with a sort of mind, a wore Vuyy, while other resemblances have made other speculatists materialize intellect itself.
The very names which we give to those powers which we fancy to be inherent in bodies, shew that we know nothing about them. These names either, like magnetism, express a relation to the par ticular substances which we imagine possess the power, or they express something of the effect which suggested their existence.→ Of this last kind are cohesion, gravity, &c. They are almost all verbal derivatives, and should be considered by us merely as abbre viated descriptions or hints of the phenomena, or as abbreviated
references to certain bodies, but by no means as any explanation of their nature. The terms are the worse by having some meaning. For this has frequently misled us into false notions of the manner of acting. Perhaps the only strict application of the term action is to the effect produced by our exertions in moving our own limbs. But we think that we move other bodies, because our own body, which is the immediate instrument of the mind, is overlooked, like the plane in the hand of the carpenter, attending to the plank which he dresses.' P. 90.
And again, when he tells us not to trouble ourselves about the intimate nature of forces:
The only safe procedure is to consider all the forces which we observe in action as mere phenomena. The constitution of our mind makes us infer the agency of a cause, whenever we observe a change. But, whether the exertion of force shall produce motion or heat, we know not, except by experience, that is, by observation of the phenomena. Nor will speculations about the intimate nature of these forces, and their manner of acting, contribute much to our useful knowledge of mechanical nature. We gain all that is possible concerning the nature of those faculties which accompany matter, or are supposed to be its inherent properties, by noticing the laws according to which their exertions proceed. Without a knowledge of these laws, the other knowledge is of no value.' P. 94.
The three laws of motion,-to which, in our opinion, much greater importance than is necessary has been attached,-are discussed by the author in a very masterly manner. After stating the various opinions concerning the first law, and the proofs that have been attempted of it, he adds the following excellent observation:
All these differences of opinion may be completely settled, by adhering to the principle, that "every change is an effect." It is a matter of fact, that the human mind always considers it as such. Therefore, the law is strictly deduced from our ideas of motion and its causes; for, even if it were essential to matter gradually to diminish its motion, and, at last, come to rest, this would not inva lidate the law, because our understanding would consider this diminution as the indication of an essential, or, at least, a universal property of matter. We should ascribe it to a natural retarding force, in the same way that we give this name to the weight of an arrow discharged straight upwards. The nature of existing matter would be considered as the cause, and we should estimate the law of its action as we have done in the case of gravity; and, as in that case, we should still suppose that were it not for this particular property, the material atom would continue its motion for ever undiminished.' P.104.
The remarks on the second law, which is properly charac terized as a tautological proposition, are not less excellent. The author does not directly say the law is nugatory, but we fancy we discern a struggle between his good sense and his ve