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that those were the ftigmata promised him, and made by the blessed Virgin; and in this condition was he exposed to public view at the great altar.

« In the mean time the poor brother, simple as he was, conceiving that the blessed Virgin's voice was no other than that of the sub-prior, began to suspect the fraud. On this it was thought proper to dispatch him by poison; and, at fis receiving the communion, they gave him a hoft fprinkled with sublimate corrosive; but the acridity made him cast it out of his mouth; immediately the monks seized him, and bound him as a facrilegious person. To save his life, the poor creature promised that he would never reveal the secret, and confirmed his promise on another hoft; but some time after, finding means to make his escape, he went, and, on oath, made a deposition of the whole affair before the Magistrates. The process lafted two years, and terminated in the burning of four Dominicans before one of the gates of Berne, on the first of May 1509, 0. S. the sentence being pronounced by a bishop delegated from Rome.'

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An easy Introdu£tion to the Theory and Practice of Mechanics ; con

taining a Variety of curious and important Problems investigated with the greatest facility, by the Application of one general Property of the Center of Gravity, without having recourse to the Conposition and Revolution of Forces. By Samuel Clarke. 40. 6s. Nourse.

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HOEVER examines attentively the methods followed

by Nature in all her operations, will be foon convinced, that they are all founded on a few general principles, fertile indeed, and capable of producing eliects imporble to be equalled by the faint attempts of human lagacity. We should, however, labour to imitate Nature as far as the limited faculties of our mind will admit, and, consequently, endeavour to found the several arts and sciences on as few principles as pollible. This is what our Author has attempted in the work before us, with regard to Mechanics. He has founded the whole on one general principie, namely, 'that The Center of Gravity of a body, or the common Center of Gravity of a system of bodies, will, when the bodies are at rejt, be in the lowest place posible. A principle to evident in itself, and so plainly pointed out by Nacure, that it is amazing, how it could have so long escaped che notice of Man hematicians.

Our Author, after premising two useful Lemmas, proceeds to the solution of a great variety of curious and important problems, without having recourse to any other principle than that already mentioned, the lowest descent of the common Center of gravity of a system of bodies. And it is very pleasing to observe, through the whole course of these investigations, the conclufions exadly coincide with those given by Sir Isaac Newton, Bernoulli, Parent, Varignon, and others, in their folutions to the same kind of problems, derived from the resolution and composition of forces: at the same time Mr. Clark's operations are attended with less apparatus, and performed with much greater facility. The Reader will find instances of this kind in pages 7, 9, 23, 29, and that remarkable one, page 84, relating to the investigation of Roberval's balance.

But conciseness and facility are not the only advantages that flow from this fertile principle: the ingenious Author has given solutions to several problems, where recourse cannot be had to the composition and division of forces, tho' easily investigated by the general principle made use of throughout the whole work. Instances of this kind occur in pages 23, and 28, as well as in other parts of this treatise.

We are, therefore, of opinion, that the work before us will prove very useful to those who are desirous of being acquainted with the theory and practice of Mechanics ; as it contains the common properties of heavy bodies sustained on inclined planes, those of the several sorts of levers, the screw, the wedge, &c. together with a compleat theory of arches of equal libration, and an exact determination of the thickness of the piers, necefsary to sustain in equilibrio the parts of any proposed arch : all clearly investigated by one general method, and rendered as eafy to be understood, as the nature of the subject will admit.

At the end of the folution to the seventeenth problem, where it is required to determine the position of a beam when suftained at rest between two inclined planes, Mr. Clark is of opinion, that Mr. Emerson's solution to a problem of the same kind, page 71, of the second edition of his treatise on Mechanics, is not universally true, holding good only in such particular cases wherein the quantities p and q in the expression for the fine of the angle SoC, (see the figure in Clark's treatise, page 36) entirely vanish. We must indeed, confess, that what Mr. Emerson asserts, namely, “ that it will be exactly the same thing “ whether the beam be supported by two planes, after the man

ner described in the problem, or by two strings fastened to “ the ends of the beam, and acting in perpendicular directions “ to those planes respectively,” is a property we do not remember to have met with in any other book of Mechanics.

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By Mr. Clark's solution we have x =

v pia’m+ + r2 m2 Ipam? + url and EC=

from hence we get the fine p’a'm+ + pre ma

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2

of the angle EBC=

a'm trzis that of the angle pam? t nr ECB = ✓ pra’m2 + gaz

also the fine of the angle O BC peam2 + y2 — pamto not, and the fine of the an

pe am2 + r? gle O CB=

pa a' m

Now since the angles B ES. pa m + r? and B O C make two right-angles, it follows, that the fine of either will be the same; but, by the elements of plane Trigonometry, the fine of the angle B O C will be expressed by the fine of the angle OBCX fin. ang. E B C + fin. ang. EBC X fin. ang. O CB; which must, if Mr. Emerson be right, be equal to the fine of the angle B O C. This, algebraically expressed, gives rx V p?a? m2 + y2 — pam+ nr2 + pam x pam+ nr

p2 a2 m2 + 2 Here p and q may be varied at pleasure ; but whether this equation can hold true universally, we submit to the consideration of our mathematical Readers. We were persuaded that the above remarks would not be disagreeable to the curious, as it is of importance to Mechanics that it be decided on one side or the other.

B.

m.

MONTHLY CATALOGUE,

For SEPTEMBER, 1764.

RELIGIOUS and CONTROVERSIAL. Art. 1. A Scripture Account of the Faith and Practice of Christians :

Confifting of numerous Collections of Texts of Scripture, upon the fundry Articles of revealed Religion, reduced into distinct Sections ; such as, Threatnings and Promises, Rewards, Punishments, Examples, &c. for enforcing the Practice of Gospel Righteousness, and restraining from Sin by Gospel Motives; being an Improve

ment

E

ment upon every Thing of the Kind hitherta published; &c. &c. By the Rev. Hugh Gaston. 8vo. 6s. Becket.

VERY work that tends to facilitate the knowlege of Scrip

ture, and to render the important truths contained in it familiar to the mind, is entitled to a candid and favourable reception from every serious Reader. We need say nothing, therefore, in regard to the design of Mr. Gaston's performance : the method in which he proceeds is as follows:

The several articles of revealed religion are ranged under diftin& heads or chapters. The fubje&t of each chapter is only mentioned at the beginning of it; and the scripture account of the subject is afterwards given at large, in a numerous collection of express and pertinent texts of Scripture, with which the chapter is filled up. Care is taken to insert every article of revealed religion, and every express and perti. nent text upon every one, in order to make it full and compleat. "The several different words by which any article of religion is expressed in she Bible, are exhibited under distinct sections, and these sečtions are filled

up

with those places in the Bible where the word occurs upon that fubject, and produced mostly in the order in which they lie in the Bible ; so that the work, in some measure, anfwers the ends of both a Common-place Book and Concordance upon the articles of religion.—Every doctrine or duty of revealed religion is laid down first, and the motives to che belief or practice of them, are made so many diftin& fections in the chapter, and generally come under the heads of threatening, promifes, examples, &c. So much is transcribed of the places quoted, as expreffes the principal part of the text, and is fufficient to direct the Reader to the places to be consulted at large in the Bible upon the fube ject; more would have needlessly swelled the size of the book, and not have left fufficient room for inserting every pertinent text upon every subject.

R
Art. 2. The indispenfible Duty of frequenting the public Worship of

God, and the Behaviour required therein. By Thomas Talbot,
D.D. Rector of the Parishes of Ullingswick and Little
Cowatn, in Herefordshire. 12mo, 6d, Buckland.

The subject of this small treatise is certainly of the utmost import. ance, both to the happiness of individuals, the peace and comfort of families, and the welfare of society in general. "Without public wor, thip, even the practice of moral virtue cannot be duly supported amongit mankind, nor encouraged and enforced by such motives as are fufficient to balance those powerful temptations to vice, with which every age, and every nation, so plentifuily abound.

We do not remember to have seen any performance upon this fubject so well calculated to do good, as chat now before us. It is written with great plainness and perfpicuity; with candour and judgment: the seriOus Christian, of every denomination, will peruse it with pleasure.

R Art. 3. An Admonition to the younger Clergy; fewing the Expedi

ency of Propriety, Temperance, Afiduity, and Candour,, 8vo, is, Rivington,

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A very

1 By M. Watkinson, a phart

A very candid and fenfible admonition ; containing many things that deserve the serious attention of the Clergy, both young and old.

R Art. 4. A Treatise upon the Life of Faith. By William Ro

maine, M. A. Lecturer of St. Dunstan's in the West. 12mo. 2 s.

Worrall. There is a certain class of Readers which, no doubt, will look upon this as a sweet treatif, a comfortable treatise, a precious treatise, a joulreviving, foul-refreshing treatise, &c. &c. To us it appears a filly treatise, a Aupid treatise, a nonsenfical treatife, a fanatical treatise, &c. &c.

R Art.5. Busy-Bodies anatomized; or a succinet Description of one

of the most mischievous Characters of the present' Age. With a prefatory Address to the Public. By James How, N. A. Rector of St. Margaret's Lothbury, London, Author of The Reformed Prodigal. 8vo. Is. Dilly, &c.

We have here two sensible and well-meant Discourses against Gossiping, which, the Author says, is now grown one of the moit fashionable and reigning vices in the kingdom.

Ru Art. 6. A Letter to the Rev. Mr. Samuel Pike, occasioned by his very

unfair and partial Publication of one to the Author, without any notice of his Reply to the surne ; with some Remarks on his Four Sermons on the Nature and Evidence of Saving Faith. By T. Whitewood. 8vo. 6d. Keith, &c.

We have, with great patience, perused both Mr. Pike's publication, and these remarks on is; and, on the whole, it is our opinion, that if these spiritual Champions would amicably sit down together, over a moderate bowl of good wholesome rum and water, without any acid, but as much sugar as they will, it would be the most efficacious expediens they could have recourse to, for putting an end to this unpleasant and unprofitable controversy. Art. 7. Comfort to the afflicted, under every Distress. With suit

able Devotions. By William Dodd, M. A. Prebendary of Brecon, and Chaplain to the Lord Bishop of St. Davids. 8vo. 55. Dilly

Chiefly compiled, as the Author ingenuously professes, from old Bi. fhop Hall's Balm of Gilead, and Grosvenor's Holy Mourner. The generality of this kind of compositions are, by some, confidered as a Tort of religious quackery; but we think there are in these forms, a vá. riety of wholesome, tho' not elegant, prescriptions, and many useful medicines for fickly minds. Art. 8. A Defence of the Observations on the Charter and Conduct

of the Society for the Propagation of the Gospel in foreign Parts, against an anonymous Pamphlet fally entitled, A candid Exa

mination of Dr. Mayhew's Observations, &c. By Jonathan Rev. Sep. 1764.

Q

Mayhew,

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