what confequences they were to expect from any fuccefsful at tempt against the prefent eftablishment.' P. 23.

After thus begging the queftion, with respect to their inte. grity and their creed, the petitioners proceed humbly to pray what? Why, to fweep away at once the whole body of natutes enacted for the fecurity of the king's prerogative in ecclefiaftical concerns; to demolish, at once, the fyftem eftablifhed, on the king's fupremacy, in the external circumftances of the Church. We agree with the right reverend writer, that it is difficult which moft to admire, the want of moderation or the want of reafon in this requeft; and we alfo agree with his lordship in the perfuafion, that the day which fhall fee the petitioners enter the Houfe of Commons as legiflators, and at the fame time profeffed Catholics, will be the day from which we are to date the degradation of the Proteftant religion in the British empire. How unreafonable fuch a request is, is clearly demonftrated from hiflory, which teaches us that tefts and oaths conftitute no novelty in politics, and were fanctioned by thofe ufages of ancient nations which we are most accustomed to venerate. Confult the histo ries of Rome and Greece, of modern France, of America, all of which nations compelled their citizens, and do ftill compel them, to fwear they will fupport the conftitution to which they feverally belong. Having gone through all the claims and requests afferted in the petition, the bifhop comes to this unavoidable conclufion, that beyond the rights which the petitioners at this period enjoy, it is neither compatible with expediency, nor reconcileable with confcience, to make any addition. We are reminded of these facts, which can neither be palliated nor denied: the petitioners not only vilify the tranflation of the Holy Scriptures, ufed in our churches, but by vitiating the confecration of a metropolitan, at the beginning of the reformation, endeavour to defroy the foundation upon which the validity of our facerdotal func tions must reft. A popular tract pronounces this judgment of Catholics upon Proteftants:

"We are convinced that they are fchifmatics, by feparating

"

See A Difcourfe preached on June 7, 1716, in the vọlume of Difcourfes preached on feveral Occafions,' by Bp. Sherlock. Of whom, and Bp. Butler, it may be faid without fear of contradiction, that of all our English writers, few have equalled, one have excelled them, in clofe reasoning."

themselves

themfelves from the communion of the Church of Chrift; and beretics, by diffenting from her doctrine in many fubftantial arti cles; and confequently that they have no part in the Church of Christ, no lawful miffion, no fucceffion from the apostles, no authority at all to preach the word of God, or adminifter the facra. ments: in fine, no fhare in the promises of Chrift's heavenly kingdom (excepting the cafe of invincible ignorance), from which the Scripture in fo many places excludes heretics and fchifina tics." P. 39.

Abhorrence of the Proteftants is inculcated in another po pular tract, by appeal to the decifion of a pope; which deci. fion is,

"On no account go to the churches of heretics, or hear their fermors, or join in their rites, left you incur the wrath of God; for it is not lawful for you to do fuch things, without dishonour. ing God, and hurting your own fouls." P. 40.

The Rhemish translators of the Bible affirm,

"That in matters of religion, in praying, hearing their fermons, prefence at their fervice, partaking of their facraments, and all other communicating with them in fpiritual things, it is a great and damnable fin to deal with them." P. 40.

So much for the expediency of investing men who hold fuch opinions with political authority over us. What concience may be fuppofed to dictate, is fuggefted by a reference to the manuals and devotional prayers fanctioned by the Catholics, and fome of thefe prayers to our guardian angel, to the Virgin Mary, guardian angel and patron faint a prayer to St. Jofeph, &c. &c. Such prayers, to all the defcendants of the first fuffering reformers, require no comment. Let us he wife, from the experience of those who have gone before us; and, as far as in us lies, never give our conJent that greater encouragement fhould be conceded by the le giflature, to the adoption of Roman doctrines and Roman worship. Let us join with the excellent bishop in reverting to the "excruciating agonies of the protracted martyrdom of Hooper, prelate of this fame diocefe." At the fame time, let us unite in kindness and beneficence to every human being; but let us also with one heart and mind retain our affection to the Church of England firmu and unalterable.

ART

ART. IX. The Doctrine of Intereft and Annuities analytically investigated and explained: together with feveral ufeful Tables -connected with the Subject. By Francis Baily, of the StockExchange. 4to. pp. 144. 1 Plate. 10 Tables. Richardfon. 1808.

S our account of this book is late, we beg leave to state to our readers a few things which have confpired to make it fo. Firft, the perufal of mathematical books requires much more time than the perufal of books written on common fubjects. A perfon well fkilled in divinity, law, or phyfic, may in one day read many pages of a book written on either of thofe fubjects, and note the paffages where the author excels or is deficient; whereas an algebraic feries, expreffed in one line, may be the refult of several days labour, and may require as much time to ascertain whether it be true or falfe. Secondly, the work before us did not appear to be fuch as would prove very creditable to the author, or very ufeful to the public; and as he informed us, at the end of his preface, that it was the first part only of "a work which he had in view," we thought there would be no great harm done, either to him or the public, if this first part fhould lie by, on one of our back helves, till the fecond fhould appear: and we have fome doubts whether, if that part had not appeared, this might not have been forgotten.

Confidering the feveral treatifes of algebra now extant, in which the doctrine of intereft and annuities is well explained, we did not fee any neceffity for a new treatise on that fubject; and if we could fuppofe that Mr. Smart's Tables of Intereft, Discount, and Annuities, (by which the labour of fuch computations is much facilitated,) were become fo fcarce, that a new edition of them was greatly wanted, we fhould not expect to fee them reprinted with all their imperfections on their head," as Mr. Baily declares * they are, but a new impreflion, in which all their former errors were corrected. This, however, was a task which Mr. B. as he tells us t, had "neither time nor inclination" to perform. What then, it may be afked, was his design ?— Obviously, to make a book :—a book, of which we have the unpleasant tafk to make a report.

That Mr. Baily's acquifition in algebra was fufficient for the undertaking, appears in the work; and, had he likewife

Preface, p. vii.

+ Ibidem.

poffeffed

poffeffed the requifite qualifications of a good author, it would have been free from the faults which we have ob→ ferved in it, the principal of which we shall briefly specify.

In various parts of this work the author has expreffed himself in an arrogant tone, which cannot fail of difpleafing modeft ears.

His ftyle, which is verbofe, is often inaccurate, and fometimes obfcure. Allude is a word of very frequent occurrence in this work, and, befides its common acceptation, has others which we never before obferved in any good author, "Alluded to," with Mr. B. fometimes ftands for " exprefsly referred to," and fometimes even for "defcribed," as in 88. Deduce, and determine, feem alfo to be great favourites with him: the latter of which words he fometimes ufes when an operation in common arithmetic is meant, when the word compute would found better in our ears; and the former is used to signify that a theorem is deduced from itself, in 95, 108, and 111.

19

In 87 Mr. B. talks of "a quantity affected with n, inftead of a quantity raifed to the power n." In § 174, he talks of "inverting a feries" by Sir Ifaac Newton's mcthod, inflead of "reverting" it: and in the fame fection, contrary to the general ufage of the ableft mathematicians both in this ifland and on the continent, he calls that an "exponential," which is "a given quantity raifed to a given power." Now the learned Euler, in his Introductio in Analyfin Infinitorum, (a work to which Mr. B. with more oftentation than judgment, appeals on another occafion,) Tom. i. 96, defines Quantitates exponentiales" to be " poteftates quarum exponens ipfe eft quantitas variabilis."

Confufion of terms tends to confufion of ideas; and whether this fault in the work now before us arose from a fcanty knowledge of the English language, or, what is worfe, from an affectation of novelty, it deferves reprehenfion and we cannot but remark, that this fault in the English ftyle very ill comports with the affected ufe which Mr. B. has made of the Greek letters, which were not at all neceflary on the occafion, the Italic letters of the alphabet being in number more than fufficient, as may be seen in the writings of Halley, Ward, Simpfon, Robertson, and Maferes, on the fame fubject; from the writings of the laft mentioned of which authors, Mr. B. has taken no fmall part of the materials of the book now before us.

Nor does Mr. B.'s fkill in logic feem to be much better than his knowledge of language. In p. viii of his preface, speaking of Dr. Price's labours on the fubject of Interest and

Annuities,

Annuities, he fays, they "are entitled to the highest respect and commendation." He then mentions fome of the Doctor's theorems, grounded upon a new hypothefis, (an hypothefis not well fupported by reason, nor ufed by any able mathematician before that time,) which were published in the Philof. Tranf. for 1775. And in the very next paragraph he tells us, that

"M. D'Alembert," (a very eminent French mathematician,) "in his memoir Sur les Annuités, inferted in the eighth volume of his Opufcules Mathematiques (1780), has entered into an in. veftigation of this very fubject; and in which he fupports the principles laid down by all former authors, in oppofition to this new hypothefis."

Q. Does Mr. B. mean to bring this as a proof that the Doctor's theorems, grounded on this new hypothefis," are entitled to the highest respect and commendation?" Something more of this kind might be found, but we pass by it.

The parts of this work alfo fhould, according to the rules of method, have been difpofed fomewhat differently from what they are. For inflance, the chapter on the Equation of Payments fhould have been placed immediately after that on Difcount, with which it is by its nature nearly connected; whereas they are now feparated by the intervention of thirteen other chapters: and if Compound Intereft be allowed in the one, it ought to be allowed in the other; and then neither of those chapters ought to occupy the place now given to it.

To a defect in method may alfo be afcribed Mr. B.'s ftrange way of referring his reader from one part of the book to another, and fometimes without fatisfactory information. For inftance, in 126, the reader is referred for a demonstration of the value of a series to § 72; in § 72 he is referred to a note in § 58; and when he looks into that note, he ftill finds no demonftration, but is again referred to five different books there named, and is further informed, that such a demonstration may be found in moft treatises of algebra. If Euclid had treated his readers in this manner, we believe his Elements of Geometry would not have been preferved to the prefent time.

Nor is the mathematical fkill which we find in this work fuch as the author's pompous difplay of great reading might have led us to expect, had we not been old enough to know, that Fronti nulla fides. In 22, Mr. B. fays, "when m is infinite, the quantities m, m-1, m−2, m−3, &c. become feverally equal to m." This we deny; and we contend,

that