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ART. X. Théorie de l'Action Capillaire; par M. Laplace; Supplément au dixieme [sic] livre du Traité de Mécanique Céleste. pp. 65. 4to. Paris. 1806. Supplément, pp. 80. 1807.

[pp. 107-112] [original article in PDF format]

  1. THE paucity of the continental publications which have of late found their way into Great Britain, and the well earned celebrity of the author of this essay, will afford us a sufficient apology, for devoting to it a larger share of our attention, than a work of so abstruse a nature would otherwise have required. It is not our object to present our readers with a full account of every improvement which may be made in science; we shall be more anxious to give a trite representation of the tone and spirit of the works which we may notice, and of the merits and demerits of the authors, as compared with those of their predecessors and contemporaries: and in these respects we apprehend that the essay before us may be considered as affording an unexceptionable specimen of the most refined labours of a man, who appears to be placed, by the suffrages of a majority of the literary world, at [107] the head of all the science of his country, and perhaps even of his age.

  2. The first impression, produced by a cursory perusal of Mr Laplace's works, is that of an admiration of their profoundness and a consciousness of the difficulty of sufficiently appreciating them. But with a laudable condescension for the want of ability or of leisure, in such of his readers as are willing to be satisfied with a superficial view of his subject, Mr. Laplace has generally recapitulated, in language sufficiently familiar, and often peculiarly elegant, the final results of his sublime researches. This recapitulation has facilitated the labour, not only of partially studying, but also of abridging and reviewing him. We have seen analyses published by his countrymen, and criticisms by our own, which have born evident marks of the touches of his own masterly hand: it has been found much easier to take Mr. Laplace's own account of his discoveries, than to examine the proofs of those discoveries themselves; and praise, when there was so little danger of its being considered as extravagant, has been wisely lavished without reserve, in order to obviate any suspicion that, might be entertained of a general backwardness to bestow approbation.

  3. We do not believe that ten persons in the universe have read Laplace's Mécanique Céleste as it ought to be read. What may be the number of mathematicians in this country who are capable of such a study, we shall not undertake to determine: but we will venture to assert, from our knowledge of the comparative state of the cultivation of the sciences in different countries, that there are as many individuals in Great Britain, who, at a certain time of their lives, could enter into it without difficulty, as in all the world besides. The country of Newton, of Cotes, of Maclaurin, and of Waring has not exhausted itself. There will be occasional fluctuations in the scientific pursuits of its inhabitants: at one time they will be the first in mathematics, at another in chemistry, at a third in optics, and at a fourth in practical astronomy; but in the true groundwork of all natural philosophy, they will perhaps always remain unrivalled; that is, in the manner of instituting and conducting their researches, whether experimental or simply theoretical: they will view their objects in the truest light; they will grasp them by the right handle: they will touch the secret spring, by which the door of truth will be unbarred, while others will exert all the powers of machinery in order to force it open by direct violence. The algebra of invention, which Dr. Hooke proposed to form into a science, has been tacitly [108] studied by his successors; and it has enabled them not only to keep pace, at a small expense of labour, with the complicated efforts of their contemporaries in other countries, but in many important instances completely to anticipate them.

  4. An ostentatious parade of deep investigation, which leads almost to nothing, has too often filled the works of the mathematicians of the continent; and we are sorry to be obliged to include Mr. Laplace in the number of those, who appear to have been more influenced on some occasions, by the desire of commanding admiration, than of communicating knowledge. The habit of affecting an unnecessary abstraction, may in part have arisen from the nature of the symbols, in which fashion has determined that the reasoning of modern mathematicians should be enveloped. We have sometimes been amused, in the perusal of this essay, with observing, that after an expression had travelled, with considerable fatigue, through several pages of Greek, Roman, and Italic characters, it was transformed, by proper substitution, into an equation belonging simply to a circle, from which it would have been just as easy to have set out at once: that a complicated fluxion, when its fluent had been determined, produced a much simpler theorem, which was a necessary consequence of the mere mechanical laws of the decomposition of force; and what is of much more importance, we have discovered that an equation, involving a complete absurdity, has been left in its algebraical dress, when a translation into common language would have shewn that it implied an impossibility, and that the premises, from which it was derived, were therefore inadmissible. In short, almost the only novelty of any consquence contained in the whole essay, is a formula for determining the depression of a fluid like mercury in a very wide tube, deduced from an approximation which appears to be very ingenious, but which is in great measure arbitrary. We should have hoped, from Mr. Laplace's powers of calculation, for at least an approximate, if not a correct, solution of the general problem relating to the form of the surface of a cohesive fluid: we have no reason to think such an approximation impossible; we even conjecture that there must be a certain method of obtaining it, although a very laborious one. The point, on which Mr. Laplace seems to rest the most material part of his claim to originality, is the deduction of all the phenomena of capillary action from the simple consideration of molecular attraction. To us it does not appear, that the fundamental principle, from which he sets out, is at all a necessary consequence of the established properties of matter; and we conceive that his mode [109] of stating that principle is but partially justified, by the coincidence of the results derived from it with experiment, since he has not demonstrated that a similar coincidence might not be obtained by proceeding on totally different grounds.

  5. The first part of the work, when compared with the second, presents us with a happy specimen of a power of accommodating observations to opinions previously formed. MM. Haüy and Trémery, at the request of the author, made some experiments on the ascent of fluids in capillary tubes, and between plates of glass; and these experiments very satisfactorily confirmed the measures somewhat hastily set down by Newton in one of his queries. But before the publication of the second part, Mr. Laplace had read a later essay on the same subject, in which the measures were made exactly twice as great as those of Newton: his obliging and accurate friend Mr. Gay Lussac then furnished him with a new series of experiments, considerably diversified, which even went a little beyond the last result. We entertain no doubt of Mr. Gay Lussac's correctness; and we also acquit Mr. Haüy of any intention to deceive; because we know that certain precautions are necessary to the experiments, which he probably omitted : but it would have been better if Mr. Laplace had begun by consulting a greater number of authors, and considering whether Mr. Haüy's measures agreed sufficiently well with the majority of them, to deserve publication.

  6. We are far from wishing to undervalue any of Mr. Laplace's labours. We readily allow a very high degree of merit to a variety of improvements which he has made in several departments of natural philosophy; but we have reason to believe, that, like another Hercules, he has often been enriched at the expense of a multitude of his predecessors: nor can we endure that the track, which he has followed, should be pointed out as the royal road to eminence, while its characteristic marks are often difficulty, obscurity, and perplexity. His works discourage, at the same time that they astonish a student: and we are persuaded, from experience, that it is often much easier to find out a new and a straighter path to the point at which he has arrived, than to retrace the same footsteps which he has already trodden. It is observed of Archimedes, by his philosophical biographer, that although we might labour long without success, in endeavouring to demonstrate from our own invention, the truth of his propositions; yet so smooth, and so direct, is the way by which he leads us, that when we have once travelled it, we fancy that we could readily have found it without assistance: since either his [110] natural genius, or his indefatigable application, has given to every thing that he attempted the appearance of having been performed with ease. Had Archimedes lived in modern France, how different would have been the manner in which he must have courted the approbation of his countrymen and his critics!

  7. Mr. Laplace is not the only mathematician who has sometimes been led aside by a predilection for the algebraical modes of notation. One of the most eminent of his colleagues, whose name ought perhaps to stand at least on a level with his own, has employed a vast profusion of calculation, on a partial solution of a problem relating to the strength of columns, when no one of the circumstances on which his determination is founded can possibly occur in practical cases; while the solution itself, from its length and intricacy, appears to have been rendered but too liable to accidental inaccuracy. We have known more than one author of celebrity in our own country applaud himself on the happy adoption of appropriate symbols, at the very moment that he was quoting erroneously, and reasoning inconclusively. Even the clear and explicit language of the simple and natural Smeaton, when translated by force into algebraical characters, has been converted into absolute nonsense. We have seen an ingenious attempt to deduce, from very intricate considerations of a fluxional nature, the same conclusions, respecting another case in practical mechanics, as may confessedly be derived, in the most simple manner, from a geometrical construction: and such has been the multiplicity of the steps which have been required for the purpose, that the author, although one of our best mathematicians, has by some accident taken a wrong turning, and presented an erroneous result. We confess that there are many calculations, in which the introduction of algebraical symbols, at a certain stage, is, practically speaking, absolutely indispensable; but we have always observed that the further the verbal reasoning, or the geometrical representation could be carried, the more simple, elegant, and satisfactory was the solution : and on the other hand, that the unnecessary adoption of literal characters has almost uniformly tended to divert the mind from the true state of the inquiry, and to suspend the exercise of the judgment, while the eye and the memory only were occupied in the mechanical process of manufacturing a work of science. We do not, however, wish to have it understood, that we consider an acquaintance with the refinements of modern analysis as by any means superfluous in the pursuit of natural philosophy : we are persuaded, on the contrary, that those, who enter with ardour [111] on a life of science, could not pursue a more eligible path, than to proceed, with the assistance of modern elementary treatises, from the academical study of the great British mathematicians, to the profound and masterly works of Euler, which stand, in our opinion, immediately next to those of Newton, with respect to mathematical elegance and address, however inferior they may be in philosophical solidity. With this preparation, if they should fortunately escape the contagion of a rage for abstraction and prolixity, their road through the works of the modern astronomers, opticians, and mechanicians, in the very first class of which we willingly rank the Mécanique Céleste of Laplace, would lie almost on a uniform declivity. After such a course of study, their further labours, in any one department of science which they might select, could not fail of being highly honourable to themselves and ornamental to their country.

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September 2006

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