on the other hand acknowledge the greater experience, joined with the soundest mathematicul knowledge, in the author of the Hydrostatics. A few brief remarks on the progess of the latter science will serve to introduce our observations on the style, manner, and design of the works before use, as applying in a general point of view to both. From the nature of the subjects, it is evident that we cannot enter into any particular details of their respective contents... The science of Hydrostatics has been cultivated from very remote antiquity: it seems most probable that its origin may be traced up to the ancient Egyptians, who both in securing the advantages and guarding against the evil of the overflow of the Nile, were driven to the invention of various expedients, which an habitual observance of the powers and properties of a body of water would soon suggest. But the earliest instance upon record of any attempt to reduce the subject to philosophical principles, is to be found in the researches of Archimedes. His treatise "De Insidentibus Humido," contains a very definite developement of some of the leading principles of the science, and several inventions which are ascribed to him show the same powers of genius which were displayed in his geometrical speculations. A modern improvement upon this work, entitled, "Archimedes Promotus," by Marinus Ghetaldus, seems to have afforded the principal materials from which the subsequent works of Oughtred, &c. were composed. But the science never assumed any thing like a perfect and experimental form till it was prosecuted by Pascal, who was the first to reduce it to sound principles, founded on experiment, in his "Traité de 'Equilibre des Liqueurs, et de la Pésanteur de l'Air.” He was followed by the distinguished M, Mariottel whose work on the Motion of Fluids was published at Paris in 1686, These writers were the first to rescue the science from the mysticism of the schoolmen, and while it remained in those trammels it was not likely to make much progress. It was not to be expected that much advance could be made in our acquaintance with the laws of fluids, when the very nature of their pressure was hardly understood or admitted, and when it was strenuously denied that they possessed the power of gravitating in proprio loco. This last question was soon decided by experiments, which to any ordinary apprehension would have been quite conclusive; but such was the force of prejudice, that it was long before those imbued with the subtleties of the schools, would admit that a portion of liquid, in the midst of a mass of the same liquid, was affected by gravity. Not more absurd, nor more inveterate, seems to

have been the belief in the fuga vacui, and the mysterious power of suction. When Toricelli, the ingenious disciple of Galileo, performed the famous experiment of filling a sealed glass tube with mercury, and inverting it, the resulting fact was so strikingly beautiful, and so completely decisive of the weight of the atmosphere, that the bare announcement of it ought to have been sufficient to convince any person of common understanding. The supporters of" Nature's horror of a Vacuum," were for a time sadly perplexed; they were indeed unable to reply, but yet determined to maintain their opinion. At length a champion arose, and defying the power of argument, Father Linus gravely asserted, that the mercury was suspended from the top of the barometic tube by invisible threads! It was not till the age of Newton that science and experiment can be said to have completely triumphed over the conceits of scholastic theory. In a portion of the Principia," some of the higher principles of the science are investigated with the usual sagacity and profound mathematical skill of our illustrious philosopher. If in some points succeeding inquirers have maintained the existence of discrepancies between his conclusions and the facts, it must be at the same time admitted, that on such extremely complicated subjects as the theory of waves, &c. it is not surprising that there should be many conditions in the real experimental problem which may not have been sufficiently taken into account, and still more which are probably yet uninvestigated. Euler, Venturi, and D'Alembert, with many other philosophers of eminence, have since contributed to the perfection of the science; and in particular, the modern French writers, as Bossuet and Biot, have furnished us with complete treatises on the subject, as well as several of our own countrymen.

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The French writers on this, as well as other branches of mathematical science, have hitherto been justly entitled to the praise of a superior degree of elegance and simplicity in their mode of treating the subject. They adopt a more simple and improved form of algebraic expression, which is often of considerable importance in pointing out to the learner the relation between different parts of the subject, and tending to convey a more connected and symmetrical idea of its theories. But with these advantages they generally unite the evils of a most tiresome diffuseness, and unnecessary detail of particulars, which might as well, or indeed much better, have been left to the sagacity of the learner to make out. Again, we often observe in them a departure from the models of geometrical strictness; which tends to obscure the views of

the student in this way: instead of stating distinctly, in the way of separate propositions, the different points to be investigated, they adopt a continuous style of writing, which leaves the learner in doubt as to what he is proving; he goes on without knowing when he has arrived at one point, or when he is proceeding to the next; when he is to consider himself beginning an investigation, or where he is to stop: Some writers of the English school in avoiding these defects have gone into the opposite extreme. They have indeed been sufficiently clear in dividing their subject, and have shown the most consummate judgment in the selection of their materials: but they have not sufficiently consulted either the apprehensions of students, or even the proper powers of language, in the excessive brevity of their enunciations. And this has been especially observable in the more elementary definitions and first principles of the sciences; in laying down which it will be readily admitted the greatest possible degree of caution is requisite; and in which no inconsiderable share of metaphysical precision, in regard to the ensurance of clearness of ideas, is very essential. These important parts are, in some treatises which we could name, hurried over, and the writer seems impatient to get afloat on algebraic symbols and computations; to measure and number what is as yet very imperfectly understood in its nature. Besides these faults displayed by many writers of the English school, there is another which, though of less real importance, is yet not the less deserving of criticism. This is in the form of their algebraic expressions. The language of analysis is as much under the dominion and laws of good taste as ordinary language. In ordinary speech an argument loses nothing of its force from being conveyed in language appropriately chosen, and disposed with an attention to elegance, or at least to the avoiding of harshness and awkwardness; but, on the contrary, will certainly gain in the degree of its impression by such regard to style. Thus, in analytical language we may certainly express an equation with the same precision, although it be composed of terms which have a harsh and unsymmetrical appearance, and which have been deduced from other theorems not given upon any uniform principle of investigation, as if all such considerations were attended to. But, on the other haud, we may consult better taste without losing the least degree of precision or force; and the question is by no means solely one of mere taste. There are no inconsiderable advantages to be gained by the learner, in having the different elementary parts of

a subject laid before him in such a form, that he may after+ wards, with the greater facility, view them as combined in new relations, and forming parts in a more general doctrine. But the same laws of good taste apply in a more especial degree to the mode in which an investigation or demonstration is conducted: it is here that the resources of the mathematician are peculiarly called into play; and while his more substantial qualities of sound knowledge and profound combination are exercised, there is, at the same time, the amplest field for the display of tasteful invention, in selecting that line of proof which leads to the conclusion, either by the fewest steps, or by the combination of the simplest and apparently most unconnected data, or in such a way as shall render the whole most symmetrical with some other kindred investigation, or some comprehensive system of propositions.

Too many writers of the English school hitherto, while eminent in the more sound and fundamental requisites, have been very deficient in the less requisite but still desirable qualification of elegance. There is too often a clumsiness and want of arrangement about their mode of proof; and their different demonstrations seem heaped together without apparent connexion with each other. Our continental neighbours have sometimes gone to the opposite excess; and for the sake of symmetry have sought to express the simplest truths as parts of the most general enunciation, thus producing unnecessary amplication.

The authors of both the works before us seem to have kept very nearly in the mean between the opposite extremes just spoken of. They have confessed themselves under considerable obligations, the one to Bossuet and Biot, the other to Poisson and Le Grange, in their treatises on the subject, of which they have made great use; but in doing so, they have been far from mere copyists. They have by no means adopted the French style of treating the subject; they have avoided its faults, and adopted its excellencies; they have retained the brevity of the English school, without its obscurity, and have given to the style of mathematical investigation a considerable portion of the French elegance. And in the descriptive statements, and enunciations of their propositions, they have avoided the vapid diffuseness of some writers of the foreign school, without losing their precision of detail. The mathematical processes are conducted chiefly in the algebraical style, and in a large portion of them the reader will not fail to discover much of that neatness which constitutes the principal claim to attention in the eye of

the critic, and is so peculiarly desirable in reference to the purposes of instruction, and the intellectual exercise of the learner..

The excellencies of such able works as the present will be the more duly appreciated, when we recollect the great want hitherto experienced of good systematic books on these branches of science. The short treatise, by the late Professor Vince, on Hydrostatics, has been justly censured for too great brevity, and a want of clear arrangement. It has on these accounts, we believe, been very little used as a book of instruction in the university from which it emanated, where its place has been much better supplied by the MS. treatises drawn up by the different tutors for the particular use of their respective classes. In the sister university, so far as hydrostatics have been studied at all, it has generally been by the aid of Vince's treatise. The larger work of Parkinson is hardly suited to elementary instruction; and the French treatises are but ill adapted to the taste of the English learner or teacher. The scientific productions of the former nation seem as if intended for the drawing-room: those of our own country have till of late seemed as if designed for the workshop. To produce a work really calculated for the study and the lecture-room, would require something of a medium which, as we have already observed, we think the authors now before us in particular, and the present school of mathematical writers in England, in general, have happily adopted. And (by the way be it observed) this school with all its improve-. ments, borrowed from the most modern resources, has originated almost entirely in one of our ancient, monkish, moth-eaten, superannuated universities; which have afforded so wide a field of sage animadversion to the advocates of modern economical improvements. In reference to the treatises on Mechanics, the well-known abilities of Mr. Whewell are such as pre-eminently to qualify him for the task he has undertaken; and they are displayed to the greatest advantage in the work before us, whether we regard it in respect to the style of general explanation, to the form of mathematical investigation, or the selection of subjects. This last is, perhaps, of all others the most important in an elementary treatise. It is a point on which the greatest judgment must be exercised, and which nothing but an habitual acquaintance with the wants and proper objects of learners can enable a writer to accomplish with any degree of success. Mr. W. has extensive experience to aid his abstract knowledge of the subject; and by means of a judicious application of both, he has produced a treatise, which we have no hesitation in say