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

In the mean time the poor brother, fimple as he was, conceiving that the bleffed Virgin's voice was no other than that of the fub-prior, began to fufpect the fraud. On this it was thought proper to difpatch him by poifon; and, at his receiving the communion, they gave him a hoft fprinkled with fublimate corrofive; but the acridity made him caft it out of his mouth; immediately the monks feized him, and bound him as a facrilegious perfon. To fave his life, the poor creature promised that he would never reveal the fecret, and confirmed his promife on another hoft; but fome time after, finding means to make his escape, he went, and, on oath, made a depofition of the whole affair before the Magiftrates. The procefs lafted two years, and terminated in the burning of four Dominicans before one of the gates of Berne, on the first of May 1509, O. S. the fentence being pronounced by a bishop delegated from Rome.'

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An eafy Introduction to the Theory and Practice of Mechanics; containing 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 Compofition and Revolution of Forces. By Samuel Clarke. 4to. 6s. Nourfe.

W

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 effects impoffible to be equalled by the faint attempts of human fagacity. We should, however, labour to imitate Nature as far as the limited faculties of our mind will admit, and, confequently, endeavour to found the feveral arts and fciences on as few principles as poffible. This is what our Author has attempted in the work before us, with regard to Mechanics. He has founded the whole on one general principle, namely, that The Center of Gravity of a body, or the common Center of Gravity of a fyftem of bodies, will, when the bodies are at reft, be in the loweft place poffible. A principle fo evident in itself, and fo plainly pointed out by Nature, that it is amazing, how it could have fo long escaped the notice of Max thematicians.

Our Author, after premifing two useful Lemmas, proceeds to the folution of a great variety of curious and important problems, without having recourfe to any other principle than that already mentioned, the lowest defcent of the common Center of gravity of a fyftem of bodies. And it is very pleafing to obferve, through the whole course of these investigations, the conclufions exactly coincide with those given by Sir Ifaac Newton, Bernoulli, Parent, Varignon, and others, in their folutions to the fame kind of problems, derived from the refolution and compofition of forces: at the fame time Mr. Clark's operations are attended with lefs apparatus, and performed with much greater facility. The Reader will find inftances of this kind in pages 7, 9, 23, 29, and that remarkable one, page 84, relating to the inveftigation of Roberval's balance.

But conciseness and facility are not the only advantages that flow from this fertile principle: the ingenious Author has given folutions to several problems, where recourse cannot be had to the compofition and divifion of forces, tho' eafily investigated by the general principle made ufe of throughout the whole work. Inftances 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 defirous of being acquainted with the theory and practice of Mechanics; as it contains the common properties of heavy bodies fuftained on inclined planes, those of the several forts of levers, the fcrew, 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 propofed arch: all clearly inveftigated by one general method, and rendered as eafy to be understood, as the nature of the fubject will admit.

At the end of the folution to the feventeenth problem, where it is required to determine the pofition of a beam when fuftained at rest between two inclined planes, Mr. Clark is of opinion, that Mr. Emerfon's folution to a problem of the fame kind, page 71, of the fecond edition of his treatife on Mechanics, is not univerfally true, holding good only in fuch particular cafes wherein the quantities p and q in the expreffion for the fine of the angle SOC, (fee the figure in Clark's treatife, page 36) entirely vanish. We muft indeed, confefs, that what Mr. Emerfon afferts, namely, "that it will be exactly the fame thing "whether the beam be fupported by two planes, after the man66 ner defcribed in the problem, or by two ftrings faftened to "the ends of the beam, and acting in perpendicular directions "to thofe planes refpectively," is a property we do not remember to have met with in any other book of Mechanics.

By

[blocks in formation]

m.

pam2 + nr

✓ p2a2 m2 + m2\?

'p2 a2 m2 + r2 — pam2 + nr2
p2 a2 m2 + r2,

rx√p2a2 m2 + r2

223

rl

p2 a2 m2 + r2 m2)?

: from hence we get the fine

that of the angle

also the fine of the angle O B C

gle OCB =

p2 a2 m2 p2a2 m2 + r2 and B OC make two right-angles, it follows, that the fine of either will be the fame; but, by the elements of plane Trigonometry, the fine of the angle B OC will be expreffed by the fine of the angle OBC X fin. ang. EBC + fin. ang. EBC X fin. ang. OCB; which muft, if Mr. Emerfon be right, be equal to the fine of the angle BO C. This, algebraically expreffed, gives

and the fine of the an

Now fince the angles BES

4

· pam2 + nr2 + pam× pam2 + nr p2 a2 m2 + y2

Here p and q may be varied at pleasure; but whether this equation can hold true universally, we fubmit to the confideration of our mathematical Readers.the above remarks would not be difagreeable to the curious, as -We were perfuaded that it is of importance to Mechanics that it be decided on one fide or the other.

B.

MONTHLY CATALOGUE,

For SEPTEMBER, 1764.
RELIGIOUS and CONTROVERSIAL.

Art. 1. A Scripture Account of the Faith and Practice of Chriftians:
Confifting of numerous Collections of Texts of Scripture, upon the
fundry Articles of revealed Religion, reduced into diftin&t Sections ;
fuch as, Threatnings and Promifes, Rewards, Punishments, Ex-
amples, &c. for enforcing the Practice of Gofpel Righteousness,
and reftraining from Sin by Gospel Motives; being an Improve-

ment

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

VERY work that tends to facilitate the knowlege of Scripture, and to render the important truths contained in it familiar to the mind, is entitled to a candid and favourable reception from every ferious Reader. We need fay nothing, therefore, in regard to the defign of Mr. Gafton'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 fubject of each chapter is only mentioned at the beginning of it; and the fcripture account of the fubject is afterwards given at large, in a numerous collection of exprefs and pertinent texts of Scripture, with which the chapter is filled up. Care is taken to infert every article of revealed religion, and every exprefs and pertinent text upon every one, in order to make it full and compleat. The feveral different words by which any article of religion is expreffed in the Bible, are exhibited under diftinct fections, and these fections are filled up with thofe places in the Bible where the word occurs upon that fubject, and produced moftly in the order in which they lie in the Bible; fo that the work, in fome 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 the belief or practice of them, are made fo many diftin&t fections in the chapter, and generally come under the heads of threatening, promifes, examples, &c. So much is tranfcribed of the places quoted, as expreffes the principal part of the text, and is fufficient to direct the Reader to the places to be confulted at large in the Bible upon the fubject; more would have needlefsly fwelled the fize of the book, and not have left fufficient room for inferting every pertinent text upon every fubject.

R

Art. 2. The indifpenfible Duty of frequenting the public Worship of
God, and the Behaviour required therein. By Thomas Talbot,
D. D. Rector of the Parishes of Ullingfwick and Little
Cowath, in Herefordshire.
12mo. 6d. Buckland.

The fubject of this fmall treatife is certainly of the utmost import ance, both to the happiness of individuals, the peace and comfort of families, and the welfare of fociety in general. Without public wor ship, even the practice of moral virtue cannot be duly fupported amongst mankind, nor encouraged and enforced by fuch motives as are fufficient to balance thofe powerful temptations to vice, with which every age, and every nation, fo plentifully abound.

We do not remember to have feen any performance upon this fubject fo well calculated to do good, as that now before us. It is written with great plainnefs and perfpicuity; with candour and judgment: the ferious Chriftian, of every denomination, will perufe it with pleasure.

R

Art. 3. An Admonition to the younger Clergy; fhewing the Expediency of Propriety, Temperance, Affiduity, and Candour, 8yo, ^ 15. Rivington.

A very

1

↑ By Mr Wäkinson, of Chart

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

R

Art. 4. A Treatife upon the Life of Faith. By William Romaine, M. A. Lecturer of St. Dunstan's in the Weft. 12mo. 2S. Worrall.

There is a certain clafs of Readers which, no doubt, will look upon this as a Sweet treatise, a comfortable treatise, a precious treatise, a foulreviving, foul-refreshing treatise, &c. &c. To us it appears a filly treatife, a fupid treatise, a nonfenfical treatife, a fanatical treatise, &c. &c. R

Art

·5. Bufy-Bodies anatomized; or a fuccinct Defcription of one of the most mifchievous Characters of the prefent Age. With a prefatory Addrefs to the Public. By James How, M. A. Rector of St. Margaret's Lothbury, London, Author of The Reformed Prodigal. 8vo. 1s. Dilly, &c.

We have here two fenfible and well-meant Difcourfes against Goffiping, which, the Author fays, is now grown one of the most fashionable and reigning vices in the kingdom.

R Art. 6. A Letter to the Rev. Mr. Samuel Pike, occafioned by his very unfair and partial Publication of one to the Author, without any notice of his Reply to the fame; with fome 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, perufed both Mr. Pike's publication, and these remarks on it; and, on the whole, it is our opinion, that if thefe fpiritual Champions would amicably fit down together, over a moderate bowl of good wholefome rum and water, without any acid, but as much fugar as they will, it would be the most efficacious expedient they could have recourse to, for putting an end to this unpleasant and unprofitable controversy.

"

Art. 7. Comfort to the afflicted, under every Diftrefs. With fuitable Devotions. By William Dodd, M. A. Prebendary of Brecon, and Chaplain to the Lord Bishop of St. Davids. 8vo. 5s. Dilly.

Chiefly compiled, as the Author ingenuously profeffes, from old Bifhop Hall's Balm of Gilead, and Grofvenor's Holy Mourner. The generality of this kind of compofitions are, by fome, confidered as a fort of religious quackery; but we think there are in these forms, a våriety of wholesome, tho' not elegant, prefcriptions, and many useful medicines for fickly minds.

Art. 8. A Defence of the Obfervations on the Charter and Conduct of the Society for the Propagation of the Gofpel in foreign Parts, against an anonymous Pamphlet falfly entitled, A candid Examination of Dr. Mayhew's Obfervations, &c. By Jonathan REV. Sep. 1764.

Q

Mayhew,

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