terior epicycloid, described by the rolling of the same circle on the convex arc of the wheel (art. 541, fig. 182). The inher part of the wheel's teeth may in like manner be fashioned to the interior epicycloid formed by the rolling of any circle on the concave arc of the wheel, and the outer part of the pinion's teeth must be formed by the exterior epicycloid, described by the rolling of the same circle on the convex arc of the pinion. It is proved, that teeth of this shape, will always touch their common tangent in the point of contact; a perpendicular to which will constantly cut the line of the centres in the point of contact of the wheel and pinion, which is shewn (arts. 525 and 535) to be essential to a wheel driving a pinion equably; or vice versa.

It is true, and consistent with the above, that if the inner part of the pinion's teeth, and the outer part of the wheel's teeth, or the inner part of the wheel's teeth and the outer part of the pinion's teeth, be derived from the rolling of different circles instead of the same, as recommended in this extract from Imison, in all the cases considered by Emerson (8vo. Mechanics, probs. 23 and 25) and in art. 545 of Camus, yet still the intersection of those curves (for they can rarely touch) or the action of either of those curves on a point, in the circumference of the other wheel (or pinion) would produce equable motion, but this cannot be considered as favourable for avoiding friction, or practicable with teeth of the common construction, requiring in some cases hooked teeth, as Emerson has shewn, page 197, fig. 156, in order to produce equable motion; for want of attention to this distinction, Doctor Hutton (Math. Dict. II. 564) has represented Emerson and Camus as differing on a point wherein they are perfectly agreed.

It has been shewn (Camus, art. 538), that if the rolling or generating circle, in the first of the above cases, be assumed equal in diameter to the radius of the pinion, and in the latter case to the radius of the wheel, that the interior epicycloids in each case will be converted into straight or radial lines, and hence neither the wheel or pinion's teeth need be curved in their inner parts, but be radial within the pitch-lines, provided the outer part of the pinion's teeth be described by the rolling of a circle half as much in diameter as the

wheel; and the outer part of the wheel's teeth by a circle half the diameter of that of the pinion. Vide Camus, fig. 171, also Dr. Young's Syllabus, p. 49. Where the number of curves or teeth in a pinion amount to nine or more, (art. 552 and 553), they can be driven, without being touched by the teeth of the wheel (if sufficiently large) till after they arrive at the line of centres, of course the outer or epicycloidal part of the pinion's teeth here becomes unnecessary, and radial lines (having rounded ends, without the pitch-line, to avoid the accidents to which sharp corners might be liable, art. 554) answer the purpose of equable motion, as in figs. 191 to 194 of Camus. Under the like restriction, as to the numbers of teeth on the pinion and wheel, if the wheel's teeth are only to act before they arrive at the line of centres, their outer parts may be omitted, and straight teeth with rounded ends adopted for the wheel, as mentioned by Mr. Brewster, Ferg. Lect. IV. 217.

It must be plain from the above, that wheels and pinions constructed as Imison recommends, with teeth acting on each other, whose epicycloids are described by the rolling of an equal circle to the other respectively (being the same which Camus, Emerson, and others have recommended for acting on points, instead of the surfaces of teeth) cannot produce equable motion. We have no evidence offered by the writer in Imi son, that friction is considerably reduced, much less avoided altogether, by the form of teeth which he recommends, except (page viii.) where it is said, that mills on a very large scale have been so constructed, "the wheel works of which have been in use for more than seven years. without requiring any repairs," a circumstance which few persons acquainted with good wheelwork will deem extraordinary, or uncommonly favourable to that particular form of teeth. These remarks further say, "His (Mr. Brewster's) additions are by no means applicable to our present improved practice; for it is a fact, that the epicycloidal faces of the teeth of wheels and pinions ought not to act upon each other, but reciprocally upon those parts which are made radii, to produce their most beneficial effects: None of the examples given by Mr. B. however, pos sess these advantages "Now it happens, that Mr. Brewster, in pages 211 and 217, fig. 3, plate II, and fig. 2, plate III, expressly de

scribes and recommends plain or radial teeth for the pinion, and for the wheel also, in different cases; and that Brewster is consistent throughout with the deductions of Camus, before us, except in one unguarded expression in page 215, wherein he says (and we are sorry to find it copied into Gregory's Mechanics) that epicycloidal teeth will act upon each other without friction, the one tooth rolls upon the other;" for which position, not one argument or proof is adduced, but, on the contrary, his two following pages are employed on expedients for lessening the friction occasioned by the use of such teeth.

The directions from Imison (page x.) for the form of a lifting-cog, cam, or wiper, is in every respect improper for lifting a forge hammer; it will neither elevate it equally (owing to the generating circle being twice the proper size for that purpose) nor with the duly decelerated motion, in order to its being rebounded by the strong spring provided over it for that purpose, as Mr. Brewster has remarked in page 250; while this, as well as 'Imison's lifters for stampers, are liable to the more serious objection, of requiring large masses of matter to start at once into their full motion, instead of beginning the same progressively from a state of rest (as in the action of a common crank) which would not fail of soon shaking any machine to pieces; as Gregory has well observed, Mechanics II. 264.

The importance of a correct theory in the construction of mechanical instruments must vindicate our intention in these remarks, and our judgment in allotting them. the space they occupy in our pages. We are indeed very desirous of distinguishing the additions, prefixed, not only unnecessarily but unwisely to M. Camus's work, from the work itself; which is extremely respectable and correct, and manifests great ability in its author. We proceed now to mention briefly the remaining subjects of which it treats.

At pages 38 and 68 the proper length of the teeth of wheels is considered, and at page 54 the space between them, necessary for their easy working together. At page 59 we have the additional friction between bodies, not perfectly hard, when shoved along, instead of being drawn over each other, adduced as a reason why wheels ought to drive each other, by acting after passing the line of centres, when

the teeth are sliding out of each other, in-、 stead of sliding in, as in this action before the line of centres; and the proportionate number of teeth is investigated (page 60) so that their action may take place after passing the line of centres. The plates of the teeth of wheels are said (page 70) to be accurately drawn, that clock and watchmakers may imitate them by the eye, in finishing the teeth of wheels, too small to be set out as these have been. The nature of spherical epicycloids, or those formed by a point fixed in the convex surface of a right cone, the summit of which cone is affixed to that of another right cone, on which the first cone rolls, are considered; and the same are applied (page 76) to determine the proper form of the teeth of crown-wheels and trundles, or crownwheels and pinions, (page 89); the same being applicable to bevelled-wheels, which were probably not in use in our author's time. The last chapter is upon calculating the trains of clocks, orrerys, or other machines, with a number of wheels; among the examples, the calculations of which are given at length, is that of the train proper for a clock to beat seconds and carry wheels, on whose arbors three hands can be placed, for seconds, minutes, and hours, without any unnecessary wheels; for an astronomical clock, of which the great wheel shall revolve in a mean year, within 1" 14" of the truth, when worked from the hour-wheel of a correct clock; and, for another to revolve in the mean synodical revolution of the moon within less than 15, worked from the minutewheel of a clock: the application of diophantine or indeterminate algebraical processes to all these kinds of questions is well explained. We confidently recommend this translation of M. Camus's work to the English Mechanic, who cannot fail of profiting by the correct information which it conveys, and which circumstance made it the more necessary, for us to point out the errors of the additions which are here made to it.

The Geography of Strabo comprises almost all the history of science from Homer to the age of Augustus: it marks the origin of nations, and their migrations; the founding of cities, the establishment of empires and states, the histories of eminent persons; and includes an immense collection of events which in vain may be sought elsewhere. The French Government interested itself in forwarding this publication: the minister of the interior committed the undertaking to M. de la Porte du Theil and M. Coray, whose labours have presented us in the present volume with the three first books of their author.

Besides the translation, a large body of notes critical and grammatical annexed, is an honourable evidence of their erudition and sagacity.

A translation of Strabo, designed to be truly useful, requires many geographical elucidations. This department was assigned to M. Gossellin, a well-known savant in ancient geography. The introduction also is by this gentleman.

The state of Strabo's text, the ambiguity of some of his descriptions or expressions, and the diversity of subjects which he treats, render a concise, yet accurate, version extremely difficult. This difficulty is peculiarly felt, when terms of sentiments refer to ancient philosophical opinions, now utterly unknown and inconceivable, or to historical incidents not allied to any other from which assistance might be derived, or to physical and mathematical data, which perhaps the writer himself but slightly understood.

The learned authors announce, in addition to their notes on these and other subjects, geographical, historical, and biographical, prolegomena, including a life of Strabo himself; with notices of the principal editions, MSS. and other authorities which they have consulted. In the introJuction, M. Gossellin offers general and

estimating the ancient road stadia: he explains the errors which have arisen from miscalculations of these measures; and supposes that stadia of different lengths were adopted in different countries. There were stadia of 700 to a degree, others 1111 1-3; others 666 2-3; others 500; others 833 1-3 to a degree, each of which is treated by M. G. in distinct chapters. In short, this gentleman supposes that, as the length of leagues and miles differs in various parts of Europe, yet these names are still retained; so, antiently, the stadium was not uniformly the same, and to this diversity he ascribes those obvious contradictions which occur in ancient writers, and the difficulty experienced by the moderns in verifying the distances they mention between one place and another.

M. Gossellin, by applying different stadia, as circumstances determine, has brought many intervals of distance within a little of those expressed by the historians, and other writers of antiquity.

The Romans borrowed the stadia, with their geography, from the Greeks, but without distinguishing those used by Eratosthenes and Hipparchus, from those adopted in the Olympic games; and by their erroneous methods of rendering them into Latin, says M. G., they have deprived them of intelligibility. This he shews in several undeniable instances.

After having ascertained the respective proportions of these measures, and detected the sources of many errors, from the days of the Alexandrian school to our own, the learned investigator states the manner in which they ought to be applied, and shews their importance in our endeavours to understand many intricate passages of Strabo. He next reduces the ancient measures to modern; and explains the use of sixteen schemes, annexed to this introduction, which explain the relation of measures of length in Greek stadia and Roman miles.

Scheme 1. shews the relative proportions of the six kinds of stadia already mentioned. 2. The proportions of degrees, minutes, and seconds of a great circle to the foregoing stadia. 3. Proportion of these stadia to marine leagues, twenty to a degree. 4. Stadia in fathoms, feet and inches; also stadia in Roman miles; Roman miles in feet and inches,

&c. &c. M. G. has also adopted those measures to a degree of longitude, in the parallel of lat. 36°. Six hundred Roman miles, in the opinion of Pliny, were equal to 4,800 Olympic stadia; which gives in longitude in this parallel, 9°. 53'. 18". These tables are useful in assigning distances where none are mentioned by antient writers. The last six plates of this series contain more extensive distances, on the respective stadia ascertained by our author, and which he proves to have been acknowledged by the Greeks themselves, as employed among them by their astronomers, geographers, and travellers.

By means of this method M. Gossellin demonstrates, that the major part of the distances transmitted to us by the writers of Greece and Rome, far from being so erroneous as they have usually been thought, are, on the contrary, sufficiently coincident with the present state of our geographical knowledge. He infers also, that hereby we may rectify numerous passages in antient writers, which hitherto have been considered as altogether mistaken, or corrupted, or entangled with inextricable difficulties. "Ifit were possible," adds M. G.," that my method should be complained of as too favourable to the antients, I would answer, that the rules of criticism imperiously demand, on every occasion, such an interpretation of these authors, as places their intention, and the sense of their words, in the most favourable point of view; and that in geography, when a measure is exact, or nearly exact, to whatever standard it may be referred, we are not allowed to fancy that it is an error."

Our readers will appreciate the validity. of these remarks: we fear that while we vindicate antient writers from one defect, we attribute to them another, and perhaps a worse, we mean that confusion to which they must have been aware they subjected their readers, by omitting to determine to what stadia they referred. We fear, too, that by similar adoptions of convenient scales of measurement, we may make any thing of any thing.

After these tables M. G. places illustrations of the different points attributed to the winds among the ancients; accompanied by what we may call the compasscard of the Romans, compared with the compass-card of the moderns.

This volume is ornamented and eluci

dated by five geographical charts, constructed by M. Gossellin, shewing, 1. the geographical system of Eratosthenes ; 2. the geographical system of Hipparchus; 3. the Mediterranean sea, according to Polybius; 4. the Northern Hemisphere, according to the Hypothesis of Strabo; 5. the geographical system of Strabo.

The typographical execution of this volume is entitled to great applause. We do not find that the translation has hitherto been subjected to any close or critical examination, but we doubt not that it may be considered as of great utility in the study of antient geography and statistics.

Le Danger des mauvais Livres, c.The Danger of bad Books, a Sermon on Rev. x. 10. 8vo. pp. 44. Geneva, Bonnant, 1806.

THE subject of this discourse in the present state of society is distinguished by its importance: much mischief has been done by bad books; and in no instance, unhappily for morals, is the maxim that "evil communications corrupt good man"ners," more completely justified. The general spread of instruction in reading among us; the infinite number of opportunities for gratifying that inquisitive disposition which is interwoven in human nature, and of which books are the object; the readiness of concealment which attends smaller works; the facility of lending and borrowing, with the gratification of perusal enhanced by secrecy : these and many other circumstances sufficiently known, render the circulation of bad books extremely dangerous to individuals, and equally pernicious to the state.

We include in this description whatever is contrary to religion and good morals, ́ to the prosperity of the commonwealth, to loyalty, to liberty, to public tranquillity, to peace among individuals, to personal security, and, we may add, to personal enjoyment. Writings which, by affecting undue seriousness, slide into austerity; which produce melancholy, even from the very principles and radices of chearfulness; which propagate discontent, peevishness, moroseness, distraction of mind, misanthropy, under whatever appellations they may be disguised, are, in our opinion, little less censurable than those more obviously criminal performances,

which promote levity, frivolity, indifference to mportant objects, dislike to reflection, inconsideration, alienation of mind from the duties of a person's station, and that ruinous perversion of sentiment, which when it is once effectually rooted in the heart, resists the efforts of reason and nature, of affection, prudence, patriotism, and even of piety itself.

To all these kinds of books, though not intended in the present discourse, the character maybe attributed which distinguished that described in the text adopted by the worthy author: "sweet as honey in the mouth, but bitter as gall when received into the stomach." The discourse opens with the following apostrophe.

"MEDICINES FOR THE SOUL! Such was the expressive inscription which a king of Egypt placed over the door of his library. It belongs, no doubt, to well selected books; but, alas! how many of those which appear in our days would be more aptly described as poisons!" Those of this poisonous class M. Cellerier, the preacher, treats with the severity they deserve; and, what must have been uncommonly gratifying to himself, his persuasions were attended with the happiest success; for we learn from credible authority, that the Committee of Subscribers to the Institution for the instruction of Catecumens in Geneva, in consequence of this discourse, took measures, though attended with considerable expense, to prevent the circulation of dangerous books, by remonstrating with those who trafficked in them, and by inducing these traders to relinquish their profits, and give up their disgraceful commodities that they might be committed to the flames. Many dealers in such trash, and many who lent them out to read, many young persons, and some parents, of their own accord, brought out and destroyed whatever they could discover of a like kind: an acceptable sacrifice to piety! a happy result of their pastor's admonitions to "imitate those generous christians of Ephesus, who, touched by grace, burnt at the feet of the Apostles those pernicious books which they had formerly prized! go," says he, "at your departure from this sacred place, deliver up whatever of this nature you may happen to possess to those who watch for your souls! and thus fulfil ye their joy!"

"Go,

Collection des Ecrits de Gustave III. Roi de Suède, &c.- Collection of the political, literary, and dramatical Writings of Gustavus III. King of Sweden: to which is annexed his Correspondence, &c. 4. vol. 8vo. Stockholm.

Unquestionably in the strict rules of criticism, the intrinsic merit of a work ought to be the sole object of consideration; yet, from immemorial prescription, candid critics have been indulged in occasional deviations from so narrow a path. We shall plead the privilege, while we gratify our feelings, and we trust those of our readers, by paying a scanty but sincere tribute to the memory of the royal author of the volumes before us. The works of crowned heads will not come every day under our cognizance; and when they do, we may safely be allowed to speak favourably of a deceased sovereign.

Few thrones have been graced with more dazzling virtue than that of Sweden. Nature in those hardy climes seems to have cast the souls of kings in her noblest mould. The still increasing wreath of glory has been transmitted with the diadem through a succession of heroes, from Gustavus Vasa who emerged from the dungeons of Denmark, and from the mines of Dalecarlia, to free his country from a foreign yoke, to the present dauntless monarch, who stands erect and unappalled amidst the crush of empires. In this honourable list we find the name of Gustavus III. worthy of such predecessors and worthy of such a descendant; he too freed his country, if not from foreign bondage, yet from foreign influence, and from domestic factions equally baneful, and equally opposite to true liberty. He fell, at length, by the blow of an assassin; a royal victim to the sanguinary tyrants of Europe! The achievements of the king belong to history; the work before us, with which only we are concerned, unfolds the man.

As a man of letters Gustavus would have been eminent had he ranked among ordinary citizens; for, to its merit alone must be attributed the adjucation of a prize by the Academy of Stockholm, to an essay which he had composed. It appears that no suspicion was entertained of the real author, till after a length of time the nong claimance of the prize induced a conjec