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evil tendency; for, more than any other case, it brings the Church itself into disgrace: in a word, it is positive schism.

I much fear, that no inconsiderable countenance has been given to these irregularities, by certain practices of a similar nature, which have recently been tolerated in the establishment itself. It is much to be lamented, that they should have been sanctioned by something like necessity; or rather is it to be lamented, that the existing evils were not remedied in a less objectionable manner, Το the great number of private chapels in the metropolis is to be imputed the great increase of dissenting meeting-houses; for so radically evil are their construction and establishment, that they tend only to disgust the serious rich, and expel the poor. It is a subject only for private speculation; and as the rich alone can pay; to them only is accommodation offered. But it is an horrid subject for speculation. If the minister engages in it himself, he too commonly accommodates his doctrines to his audience; seeking to please rather than to instruct, his motives are apt to be suspected, and very little utility can be expected from ins ministry. If, on the other hand, he be merely engaged by the proprietor, he is commonly sought out, not for sterling qualifications, so much as for popular manners and an airy elocution; as is sufficiently proved by the vapid characters which commonly occupy such situations. But the most weighty objection to these establishments is, that they are fashionable religious assemblies for the rich. The poor are excluded: and it is no -less lamentable, that, in a considerable part of the metropolis, and in some other large .towns, the middling and lower classes have no accommodation whatever for religious worship. They are thus driven to the conventicle. It is even to be wished that they should go there, for better is it they should so engage in the duties of religion, than not to do it at all. pp. 32-34.

- It appears then that a once striking mark of Christianity, is now reversed, and "the poor have not the Gospel "preached unto them." Why then, "what hold have we on the consciences of the poor? what should imbue them with 'virtue? what should render them comfortable? The impolicy of this neglect is so obvious and gross, that we agree with our author in thinking it is to be wished that this class should worship where it can. As Bishop Horsley has observed, speaking of the omission of religious services on Sunday afternoons, "the worser part "of those who were at Church in the morning, go now to the ale-house; the better part to the conventicle,"

We add a note from the Bishop of London's Lect. viii. Vol. I. p. 205.

"There is a most dreadful want of this nature in the western part of this great metropolis. From St. Martin's in the Fields to Mary-le-Bone church, inclusive, a space containing, perhaps, 200,000 souls, there are only five parish churches, St. Martin's; St. Anne's, Soho; St. George's, Hanover Square; and the very small church at Maryle-bone. There, are, it is true, a few chapels interspersed in this space; but what they can contain is a mere trifle, compared to the whole number of inhabitants in those parts; and the lowest classes are almost entirely excluded from them. The only measure that can be of any essential service, is the erection of several spacious parish churches, capable of receiving very large congregations, and attordng decent accommodations for the lower and inferior, as well as for the higher orders of the people. In the reign of Queen Anne, a considerable sum of money was voted by parliament for fifty new churches. It is most devoutly to be wished that the present parliament would, to a certain extent at least, foliow so honourable an example It is, I am in every point of view, political, mozal, and religious, well worthy the attention of the British legislature. A suflicient number capital and in other parts of the kingdom, of new parish churches, erceted both in the where they are wanted, for the use of the members of the Church of England of all conditions, would very essentially conduce to the interests of Religion, and the security and welfare of the Established Church."

sure,

The semi official sentiments of this pamphlet have induced us to consider it with attention: we have hinted at some of its errors with candour, meaning that our remarks should be of use in proper time and place. Some of its observations we have readily strengthened, and enforced; they accord with our own remarks, and we heartily wish them effectual success.

But there is another cause of danger to the Church, which this author has not noticed; we mean INGRATITUDE: for what can be more ungrateful than to suffer a man to starve on a pitiful income of 6 or 7001. per annum who understands Divinity better than all who ever went before him, and whose talents, did people but credit them, would relieve our belief from such a variety of heavy articles, that he must truly be a most unreasonable Atheist, Deist, Socinian, Arian, Mahometan, Jew, or Pagan, who could possibly stumble at those which would re

main? Can any thing be more detrimental than the supineness of the Rev. Dr. W. Gretton, Archdeacon of Essex, in not recommending Francis Stone, M. A. F. A. S. Rector of Cold Norton, to competent exaltation ! We freely acknowledge, that we discover so many cardinal virtues, and so great predominance of them, such as modesty, humility, deference to superiors, candour, readiness to learn, abhorrence of filthy lucre, and a multiplicity of others, in a single sermon, that we see not how

Jewish Prophecy the Sole Criterion to distinguish between genuine and spurious Christian Scripture, &c. A discourse preached before the Rev. Dr. W. Gretton, Archdeacon of Essex, at Danbury, July 8, 1806; by Francis Stone, M. A. F. S. A. Rector of Cold Norton, Essex.

By the favour of Archidiaconal appointment, I am nominated-p. 3.

This genealogy (Luke) is surely very oddly placed, as well as most abruptly introduced. St. Luke, we know, was the friend and companion of St. Paul ; and what St. Paul's opinion was about such genealogies we learn very clearly from his epistles, I. Tim. i. 4. Titus iii. 9. This makes it highly improbable, that any of his intimates should attempt to trace out any genealogy at all.―p. 6.

But to proceed to establish the strict, literal, and only humanity of Jesus, p. 7, in submitting to your serious consideration, a very grand impasture practised on Christians, to the extent of the two first chapters of Matthew's Gospel, which abound with misapplications and misrepresentations of prophecies, p. 12.

This gives birth to what, in their hypermetaphysical dialect, they term the hypostatic union, asserting that in Christ two natures were united, the divine and the human.

21.

I have been the more particular in exposing the forged miracle, because it gives birth to that absurd hypothesis, the Arian trinity, which ended in the establishment of that most senseless doctrine of human invention, the Athanasian trinity in unity. p. 27. That monster of error and absurdity. p. 31.

I mean the mistaken idea, too generally reeived of the atonement of divine wrath, by -the death of Christ. p. 32.

Let us divest ourselves of a misplaced attachment to the erroneous theology and fabulous theogony, of the middle of the 10th santury. p. 30.

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Antiquated errors of the Church of England : extracted from the Articles, published by Authority; repeatedly signed by every Clergyman, before he can hold a living: and constantly alluded to in the daily Prayers of the Establishment.- -To be abolished.

Almighty God, our heavenly father, who hast purchased to thyself an universal church by the precious blood of thy dear son; mercifully look upon the same; and at this time so guide and govern the minds of thy servants, the bishops and pastors of thy flock, that they may lay hands suddenly on no man, but faithfully and wisely make choice of fit persons to serve in the sacred ministry of thy church. And to these which shall be ordained to any holy function, give thy grace and heavenly benediction; that both by their life and doctrine they may set forth thy glory, and set forward the salvation of all men, through Jesus Christ our Lord, amen.

So that two whole and perfect natures that is to say, the God-head and nan-hood, were joined together in one person never to be divided; whereof is one Christ. Art. 2.

The three creed, Nice creed, Athanasius's Apostle's creed, ought thoroughly to be recreed, and that which is commonly called the ceived and believed for they may be proved by most certain warrants of holy scripture. Art. 8.

Christ who truly suffered, was crucified, dead, and buried, to reconcile his father to us.-Art. 2. And there is none other satisfaction for sin but that alone. Art. 31.

The book of consecration of archbishops, and bishops, of priests, and deacons, hath not any thing that of itself is superstitious, or ungodly. Art. 36.

A Treatise on the Teeth of Wheels, Pinions, &c. demonstrating the best forms which can be given them for the various purposes of Machinery; such as Mill-work, Clock-work, &c. and the art of finding their numbers: translated from the French of M. Camus, with additions; illustrated by 15 plates, 144 pp. Price 10s. 6d. J. Taylor, 1806. THE work before us is a translation of Books x. and xi, of the second edition of M. Camus's Cours de Mathématique, print ed in 1767, in which the divisions of the original work are very properly retained for the use of those who may wish to consult it. The preface informs us that M. Camus not having treated the generation of cycloid and epicycloid curves, and their practical application to the Teeth of Wheels, &c. the same is now fully done by an extract from the new edition of Imison's Elements of Science and Art; this follows in nine pages; two pages more are added, (by the writer in Imison,) as an . answer to Mr. Brewster's animadversions in his late edition of Ferguson's Lectures, on this part of Imison's work; these constitute the additions noticed in the title. Few subjects have been more generally misunderstood, than the effect of cycloidal and epicycloidal curves when applied to the Teeth of Wheels. It has too generally been imagined, from the generation of these curves by a rolling motion, we suppose, that, when applied to the teeth of wheels, they occasioned them to roll, instead of slide or rub, upon each other; thereby avoiding wear of the machine, and loss of power in friction between the teeth. But M. Camus, in the work before us (like Emerson and English mathematical writers in general, whom we remember to have read) has expressly employed himself on a different problem, viz. to discover that form for the Teeth of Wheels and Pinions, which shall enable the one to drive or move the other with a uniform angular velocity, if its own be such. We well know that teeth, improperly formed, will occasion a wheel moving uniformly round, to drive its pinion with an alternately accelerated and retarded motion, to the hindrance of many operations required to be performed by machinery, and destructive in its jerking effect upon the machinery itself. Different modifications of the cycloidal and epirycloidal curves have been found to efVOL. I. [Lit. Pan. Nov, 1806.]

fect in every case an equable motion between two wheels acting on each other; to which M. Camus (page 2, 10, 21, and 57) limits the properties of the teeth he recommends; while at page 59 he expressly states, that teeth thus formed will rub or slide against, instead of rolling upon, each other. Dr. Young, in his Syllabus of Lectures at the Royal Institution, Art. 180, says, "it appears to be impossible to produce an equable motion, and at the same time wholly to avoid friction, although some of the best authors have supposed, that both these objects were attained by the epicycloidal teeth." In a note upon this, the Doctor investigates the quantity of sliding or rubbing reciprocally sustained by these teeth for equalizing motion. This statement shews the increase of this effect, as the teeth are larger, or their action extends beyond the line of the centres. But, to our great suprise, this extract from Imison asserts, that wear, or loss of power by friction, is avoided, by using cycloidal or epicycloidal teeth in different cases; while in other essential parts of the theory, these additions are directly at variance with the conclusions of M. Camus. We conceive it, therefore, necessary to examine more particularly, the pretensions of the writer in Imison; first remarking that M. Camus, in art. 536, figs. 178 and 179, has given as good a description, or generation, of an epicycloid as can be written; while the passage from Imison intended to mend it, (page vii.) is an unmeaning jargon of indefinite words. Its inconsistency fur ther appears in page viii. line 17 and 26, where the diameter and the radius of circles are confounded with their arcs; and page xii. line 13, where the term cycloid is applied to the curve, called by all mathematicians the involute of a circle!

An attentive reader of M. Camus will readily perceive, that for producing equable motion, the acting faces of the teeth of wheels and pinions, intended to act before and after they have passed the line of centres, must each consist of two portions of different epicycloids, joined at the pitch-line; the inner part of the pinion's teeth (or so much thereof as is within the pitch-line) may conform to the interior epicycloid, derived from the rolling of any circle on the concave arc of the pinion, or its pitch-line; and the outer part of the wheel's teeth must be formed by the ex

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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

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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 respective| ly (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 Imison, 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 uncom monly favourable to that particular form These remarks further say, of teeth. "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 radu, to produce their most beneficial effects: None of the examples given by Mr. B. however, possess these advantages." Now it happens, that Mr. Brewster, in pages 211 and 217, fig. 3, plate II. and fig. 2, plate III. expressly den

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 63 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, instead 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.

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Géographie de Strabon, &c. Strabo's Geography, translated from Greek into French. Tom. I. 4to. pp. 513, with five Maps. Paris, from the Imperial Press, 1805.

We hope that at some time, not far distant, British literature may boast of its Strabo. Report says, that after the lapse

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