and chances, several of which are quite new. The next article comprehends the different kinds of progressions, with the solution of various problems, arising out of them; also several tricks and games, founded on arithmetical combinations, are proposed and explained; which are followed by a selection of curious problems very proper for exercising young mathematicians. This part then concludes with whatever is most curious in political arithmetic, in regard to population, and the duration of human life, &c.

The second part of this volume is occupied by geometry. This part contains about seventy-five problems, which it is hoped will be found, in general, well chosen; and which we have endeavoured to render more interesting, both by the form of the enunciation, and by the elegance and simplicity of the solution. Among these, are some elegant and singular theorems, from which is deduced a generalization of certain celebrated properties, such as the 47th proposition of the first book of Euclid, which is demonstrated also by various transpositions of parts, exceedingly ingenious. We have likewise given some transmutations of rectilineal spaces into other forms; as, of the square into rectangles, merely by decomposition and the transposition of parts, which, though elementary and not difficult, are yet quite new. This part contains also a curious historical dissertation on the quadrature of the circle, with a great number of remarkable problems respecting the lunules of Hippocrates, and others formed in imitation. of them. Lastly, this volume is terminated by a collection of very curious problems, of which only the enunciation is given, being here proposed by way of exercise to young arithmeticians and geometri sians. In general, they are rather simple and elegant, than difficult. Some of them however are not unworthy the attention of the experienced geometrician or analyst.

The second volume begins with mechanics. In this part the reader is presented with a great number of interesting problems, much better selected in general than those in the former editions. An examination of several attempts to discover the perpetual motion, and various curious facts relating to that subject, will also be found in it. The whole is terminated by a brief historical account of the most remarkable machines, both ancient and modern; among the latter of which are the celebrated clocks of Strasburgh and Lyons; the machines invented by Truchet, Camus and Vaucanson; the machine of Marly, and the steam engine. On all these objects several new and interesting observations are offered.

The next part of the same volume contains Optics. This part we can assert has been much improved, as well in regard to arrangement, as to the accuracy and novelty of the matters, This subject is concluded with a short account of every thing new or worthy of being known in regard to microscopical observations.

This volume then terminates with the subjects Acoustics and Music. The principles of the formation and propagation of sound, the phenomena depending on them, an explanation of ancient and modern music, several curious facts relating to the effects of both, with questions respecting the mechanism of harmony, the properties of different instruments, and certain musical paradoxes, are the prin

cipal articles w ch compose this part, and which terminate the second

volume.

The following, or third volume, comprehends Astronomy, and Geography as far as it relates to the former science; also Chronology, Gnomonics. Navigation, Architecture, and Pyrotechny, or the art of making artificial fire works. To enter into a minute detail of the corrections and considerable additions made to these different treatises of Ozanam's book, would be too tedious. In general, they have been abridged and simplified; and the errors he committed have been corrected; for it must be owned that Ozanam, having but very little studied astronomy, possessed scarcely any knowledge of the physicoastronomical truths that were demonstrated even in his own time: nothing therefore can be more superficial than what he says in regard to the system of the universe. A view of that system, and of the bodies which compose it, has been substituted in its stead; and which it is hoped will afford satisfaction to the reader, both on account of the explanation given of the different phenomena, and of the singular comparisons employed to convey an idea of its immensity.

In regard to Chronology, we shall only remark, that this part, a few introductory observations excepted, is entirely the work of Ozanam, and required very few changes. The article on Gnomonics is almost all of it original, and contains several new problems, better chosen than those given in the work of that author. The succeeding part is also entirely new, and contains many curious problems con cerning the art of navigating and manoeuvring vessels. A pretty full account is here given of the celebrated problem respecting the longitude. The case is the same with the article Architecture, which has furnished matter for several curious questions, either in regard to building, or to measuring, or the art considered merely as an object of

taste.

The volume concludes with Pyrotechny. What Ozanam gave on this subject is abridged in some places, and improved in others.

The fourth volume is entirely devoted to Physics or Natural Philosophy. The first division of this volume, which forms the eleventh of the work, is a kind of Philosophical Miscellany, in which are collected the most curious questions of every kind. It commences with a necessary introduction, which contains an accurate account of every thing known and best approved in regard to the properties of fire, of air, of water, and of earth. A view is then taken of the different branches of Natural Philosophy in general: experiments on air, hydraulie and hydrostatic recreations; the history of thermometers, barometers and hygrometers, with the method of constructing them; remarkable problems in physical astronomy solved according to their real principles; curious observations on the divisibility of matter, the tenuity of odours, and that of light, &c; questions respecting comets, an account and examination of some singular and ingenious opinions on that subject; explanation and history of intermittent springs, phenomena of ice, the method of producing it. the analysis of paper kites, &c., are the principal articles which compose this eleventh part: a proper idea of which can only be formed by consulting the table of

.contents.

D 3

6

AVhat

What regards experimental philosophy could not be terminated better than by a particular treatise on the magnet. Every thing new and most curious respecting the phenomena of this singular production of nature, its different properties, the advantages derived from it, the amusements and principal tricks performed by their combination, with artificial magnets, &c. form the subject of this treatise.

Electricity holds too distinguished a rank among the phenomena of nature not to find a place in a work of this kind. This subject will be found treated at full length, if the number of facts and experiments made known be considered; and with great precision, if attention be paid to the manner in which they are explained. An interesting part of this short treatise is contained in what is said on the analogy be tween thunder and electricity. The different amusements performed by means of this singular property of bodies have not been neglected; and something is said also on the cures effected by electricity.

Electricity, the source of so many curious phenomena, is followed by Chemistry. The principles of this science are first explained in a succinct manner, and an accurate idea is given of the different substances, the mutual play and action of which produce its principal phenomena. After this introduction, the simplest and most curious experiments in Chemistry are described and explained, according to the principles before laid down. Sympathetic inks, and the amuse. ments which can be performed by their means, are not forgotten; nor are metallic vegetations. This part concludes with a dissertation on the philosopher's stone, on potable gold, and on palingenesy; also chemical problems, of which a curious, instructive and philosophical kind of history is given.

This volume is terminated by two supplements; one of which treats on the different kinds of phosphorus, both natural and artificial; and the other on the pretended perpetual lamps. But we have not been so prolix as Ozanam, or rather the author of the pitiful compilation contained in the fourth volume of his work. We hope, or rather can with confidence assert, that we have related, in much less room, a great many more things, and in a much more correct manner, respecting the different kinds of phosphorus, than has been done by the author of that treatise, inserted in the edition of the Mathematical Recreations, published after Ozanam's death. In regard to the perpetual lamps, after giving an historical account of them, we shew in a very few pages, and according to the principles of sound philosophy, that they are to be considered as a chimera, only worthy of being placed in the same class as Palingenesy and the divining rod.

We must not here omit to mention a peculiar advantage which mathematicians and philosophers will derive from this work: we allude to the various and extensive tables, which they have often occasion to make use of; and for want of which, calculators are often at no small loss. These are as follow:

Vol. I. A table of the feet of different countries, as compared with the Parisian foot.

A table of the ancient measures of capacity as compared with those of Paris.

• Vol. II.

• Vol. II. A table of the specific gravities of the most usual substances. In various respects it is more extensive than that of Muschenbroek, and certainly more correct.

A table of the different weights, both ancient and modern, as well as foreign, compared with the French pound.

Vol. III. A table of the longitudes and latitudes of the principal places of the earth, more extensive than any ever yet given.

A table of the itinerary measures, both ancient and modern. A table of the eclipses visible on the horizon of Paris, till the year 1800 +.

Vol. IV. A table of the degrees of heat, or cold, at which different substances melt or congeal.

A table of the different degrees of heat or cold observed in different places of the earth, or necessary for certain operations.

A table of the dilatation of metals.

A table of the heights of different places, and of several mountains above the level of the sea, both in the old continent, and in America.

Such then is the plan of this new edition of the Mathematical Recreations; and we may venture to assert that, in its present state, it is not unworthy the attention of the best informed mathemati cians and philosophers. Persons of every class, by perusing it, may find amusement and instruction; and the questions proposed or solved will afford them an agreeable opportunity of exercising their genius and talents in the various sciences.'

Prefixed to Vol. I. are historical accounts of Ozanam and Montucla. The latter was undoubtedly a man of talents, and of considerable acquirements: but, fairly estimating his labours, and chiefly his History of the Mathematics, we should hesitate to pronounce him, with his biographer, one of the most considerable mathematicians of the 18th century.

Though this edition is much more copious, accurate, and instructive than the original, yet it is less amusing, as it contains less Recreation. Some of the problems, methods, and receipts of M. Ozanam are very entertaining: they please from their absurdity; and to those who love to contemplate a strange mixture of science and superstition, of ingenuity and credulity, they are not altogether without instruction. Most of these are, however, expunged from the present edition; and we thought that the first problem, "Une Abbesse aveugle visi tant ses Réligieuses qui sont disperseés également dans hurt Cellules," &c. &c. had, for reasons of decorum, been omitted, till we found the blind abbess in the middle of the first volume.

For

In this English edition, these tables have been entirely changed; the weights, measures, &c. being given as compared with a British standard. TRANS.'

In the translation, this table has been omitted and a new one of the eclipses visible at London, for many years to come, has been given in its stead. TRANS.'

other problems, however, we have sought in vain; for instance: to prepare an ointment that will cure a wound at a distance.' This ointment is almost as valuable as that which was designed to re-unite the cleft body of the hero of La Mancha; and the composition is as curious as the ointment itself is valuable. Take of the usnea or moss of the skull of a man that was hanged, two ounces; mummy, human blood, of each half an ounce; earth worms washed in water or wine, and dried, two ounces and a half; human fat, two ounces; the fat of a wild boar, and the fat of a bear, of each half an ounce; oil of linseed and oil of turpentine, of each two drachms,' &c. Then again, the methods of curing the cholick and tooth-ache are extremely ingenious and entertaining: Thomas Bartholin says, his uncle was cured of a violent cholick by applying a dog to his belly, which was thereupon seized with it; and that his maid-servant was cured of the tooth-ache by clapping the same dog to her cheek, and when the dog was gone from her, he howled and made such motions, as gave them to know he had got the maid's tooth-ache.-M. Montucla, however, does not exclude the divining Rod, but relates a pleasant story or two concerning it.

For having chastened and purified the collection from those parts which might raise indecorous laughter, M. Montucla has made ample compensation, by the variety of amusing and useful information with which he has diversified and enriched his volumes; and they are well adapted to lie on the tables or chairs of our parlours, since they may be taken up for five minutes and again laid down, after we have learnt to construct a dial, or to make a rocket, or to compute with our fingers.

We have already said that the present work is well calculated to teach useful things in an agreeable manner. Science loses not always its dignity, by losing its formality; and Demonstration may gain possession of the understanding, although it does not make its regular and tactical approaches by lemma, proposition, and corollary. Yet this production is artful without the appearance of art: since, by holding out gratification to the characteristic propensities of the juvenile mind, it impels youth to the quest of knowlege, it gently induces the indolent to join in the pursuit, and, by addressing the uninformed in common language and familiar phrases, insinuates instruction. We do not think, indeed, as has been remarked that these Recreations will unbend the mind; unless they are supposed to unbend it on the same principle on which we unstring a bow, to preserve its elasticity and vigour *.

ART. R.W.

P. 308,

One or two small criticisms may be conveyed in a note. vol. 1. we meet an odd word squarralle,' and again, p. 439, vol. 4.