locked. Before fun-rife I re-meafured the radius, which required fome correction; the beam being of white fir, and the fcale of brafs, which probably contracted, while the beam remained unaltered: the other beam compaffes also required correction.' Mr. Bird then proceeds to explain the method more minutely by means of an accurate figure, for which the Reader muft have recourse to the work itself; but the following reafons why this kind of management has fucceeded better than any other yet known, muft not be omitted. • After I had found by experience, fays our Author, that the expanfion of the inftruments to be divided, occafioned by the increafing heat of the fun, or a contraction, by a decrease thereof, was the grand difficulty with which I had to ftruggle, efpecially when two or three hours were required to lay off the principal points; 1 immediately fet about contriving how to lay them off, in the leaft time poffible, i. e. before any expanfion, or contraction, could take place; and, as the heat of three or four perfons in the room may produce the fame effect as the fun, I never admit more than one, as an affiftant: neither muft any fire be fuffered in the room, till the principal points are done. The above being understood, it was easy to conceive, that, having all the chords before-mentioned computed, and meafured, the evening before they were to be laid off, I fhould be enabled to perform in a few minutes, what by trials would require fome hours; and, as too much caution cannot be used, it is proper to lay off the principal points before fun-rife, or elfe chufe a cloudy morning. The method of cutting the divifions, as described above, is to prevent any inequality that would arife from the expanfion of the beam compass by the heat of the hands, especially if the beam be of metalt wooden beams will also alter, probably from a fmall bending; but in this method, if the beam fhould alter of an inch, or more, it would not caufe any fenfible inequality. As the points of the nonius divifions, cannot be divided upon the nonius plate, without inconvenience, it is best to use the method defcribed in page [8], holding the beam compass a small while in the hand, previous to the cutting. The points being but few in number, the divifions may be cut, before any expanfion can sensibly take effect. 'Sextants, or octants, for obferving the distance of the moon from the fixed ftars, fhould be divided by the foregoing method, great accuracy being required. If, inftead of dividing fextants to every 20 upon the limb, as is commonly done, they fhould be divided to 15', a chord of 64° might be laid off, and divided by continual bfections: this would, in fome measure, crowd the limb with divifions; but it would shorten the nonius; for 15, inttead of 20, would fhew one minute. In dividing either arches or ftrait lines, a number (which will divide continually by 2) greater than is required upon the arc or line, is the best to begin with, and may be used in dividing a circle, by laying off the chord of the difference: fuppofe it was required to divide a circle into 54 equal parts, it would be 64-5410=102: 30'; the chord of which, laid off, must be added to 300°, and it will be 360° +10° : 30', to be divided into 64 equal parts, 54 of which will S 3 complete complete the circle.-If the arc of 10° 30′ be laid off from a dividing plate, it will answer the fame puip fe. Analagous to the foregoing method, my fcale of equal parts was divided. I took 12 of an inch in a beam compass, laid the scale which I took it from, the brafs scale to be divided, and the beam compafs, in a room facing the north, where they lay the whole night: early next mon ng, after correcting the lengths, the above were laid off three times (the orass being long enough to tike it is); then, having in other compatiys 256, 123, and 64, I bifected the three fpaces of 512 with all the expedition I could: having now only 6,4 inches in the laft bean compais, any partial or un qual expantion was not to be feared; therefore worked by continual bifections, tili 1 had done. The linear divifions were cut from the points, with a beam compafs, as before described. 101 "The nonius divifions of this fcile contain of an inch, which were divide into 100 in the following manner. As ico: 101: 256: 258,56 tenths of an inch, the integer in his cafe being. Suppole the cale to be numbered at every inch, from left to right; then exactly againft to the left of o. was made a fine point; from which was laid off 258,56 to the right hand.This was aken from a fcale three feet in Lengti, which was divided after the common method; but the error was fo fmall, as to vanish at the other extremity of the nonius, when divid d continually by 2. • Whoever undertakes to divide a fcale of the above kind, not being fu nifhed with one long enough to lay off 258.56 may take 25 from that Lefore him, to which he may add 8,56 taken from a diagonal scale, that may be made at a fmall expence. To prove the expedience of the above methods of dividing aftronomical inftruments, &c. I need only to mention the following particulars, taken from the Nautical Almanac for this prefent year 1767, page 152. : "Mr. Mayer made his obferv tions with his fix foot mural arch, from the year 1755 to the time of his deceafe: with it he fettled the mean obliquity of the ecliptic, to the beginning of the year 1756, at 23° 28′ 16′′; which Dr. Bradley fettled by his obfervations, made in the years 1750 and 1751, at 23° : 28′ : 18′′. The difference is agreeable to what ought to aile from the gradual diminution of the obliquity of the ecliptic, at the rate of about a fecond in a year," &c. That two different obfervers. with inftruments of different radii, and in different parts of Europe, fhould fo nearly agree, is matter of no mall aftonishment; and fufficiently proves, that a mean of feveral onfervations, made by good obfervers with accurate in Iruments, properly adjusted, will always lead us either to the truth itfelf, or extremely near to it.' Such is the method ufed by this ingenious mechanic in dividing attronomical inftruments, and fuch are the reafons upon which it is founded. Experience has already demonftrated the utility of the inftruments made by Mr Bird; and there is reaon to hope that other ma hematical inftrument-makers will profit hom the inftructions given in this performance. B. An An Apology for the Catholics of Great Britain and Ireland, humbiy offered to the Confideration of the King's Most Excellent Majesty, and both Houses of Parliament. 12mo. 2s. 6d. Peat. 1768. WE have many instances in our own, and every other language, of words which have, in a series of years, been so perverted from their original meaning, as to stand for the direct contrary to what they at firft fignified. Catholic is one of this fort. According to its etymology it fignifies univerfal, or whole By the catholic church, therefore, was formerly meant, the univerfal or whole church of Christ. Must we not, then, be greatly forp ifed that any 'one fect, and especially the molt confined and narrow-minded fect that ever appeared amongit Chriftians, fhould i ave the infolence to affume this name to themselves, exclufive of all others: yet this the gentlemen of Rome have done, without blushing At the time of the reformation they were not displeafed to be called pupils, that is, perfons profeffing, and adhering to, the religion of the pope but that name becoming odious amongst us, by their plots, their maffacres, and horrid attempts to overturn the reformed religion, they though: fit to change it for that of Rom on car shies: but this appearing to be gros nonfenfe, and a downright contrádiction, they now denote them'elves, and would have us to call them, plain catholics. As this then is the fame feet which was formerly known under the other recited names, we must remember that papifts and catholics are now made to fignify the fame perfons. The Author of this Apology cannot help acknowledging in his preface, that there are certain reafons for fuppofing them obnoxious to the prefent establishment in church and ftate; and therefore fome perfons may be inclined to periecute them.' But to prevent this, he has u dertaken to ftate the care of the catholics in the British dominions; and this he has done, he fays, in fo fair and impartial a manner, and with fo much fincerity and truth, and without the feafl aifu fe, that he fatters himfelf, every difpaflionate profeftant will entertain more favourable fentiments of them.' How he has executed this defign will appear in reviewing his work. His first chapter is, Of perfecution in general; and at the head of this he quotes John xvi. 1, 2, 3, 4. He begins with fome very proper ob ervations upon perfecution, pticularly that which the primitive Chriftians fuffered from the Jees: but he tys. If the gofpirculcates that we fhould confider all mankind as our neighbours; that a fiendly difpofition should mani eft itself in the whole conduct of our lives, that fraternal charity fhould be, as it were, the moving force of our Ctions; and that univerfal benevolence fhould conftantly inspire our hearts with the warmest affection for the welfare of our fellowcreatures; there will be no room left for imagining, that to chaften with the rod of perfecution is doing God fervice, much lefs, that it can be juftified in his fight.' And a little after he fays, It is impoffible for a man to be a good orthodox Christian from mere compulfion. You must correct his heart, or convince his understanding. Tortures may extort a confeffion from his lips, but how is his mind difpofed? Has he that has undertaken to reclaim him from error, or to make him return to the ways of righteousness, prayed that the divine illumination might reft upon his foul?-In short, no facrifice is acceptable to God, but that which is perfectly voluntary; and if we serve him truly and unfeignedly, we must serve him with a love of choice and a love of reafon." Nothing can be more like a true Christian than this. But, foon after, we fee what it all ends in, by a diftinction which the Author makes, of a religious and a political perfecution. Religious perfecution, he fays, is influenced by the notion of doing God fervice; and political perfecution feems to have in view, not fo much the intention of doing God service, as being of fervice to the ftate. Every government has adopted a favourite fyftem of religion, and wishes that all its members would indifcriminately conform to it, in order to promote the purposes of unanimity, a thing very defirable in a well policed ftate. Hence the civil power friendly confpires with thofe to whom they have delegated the ecclefiaftical power, to cherish and maintain in permanency this favourite religious fyftem. The latter are to take care that no attempt is formed which has a tendency to its abolition, either by the introduction of a new one, or by altering any material point with ftrange gloffes and interpretations. The former, upon a report made of the delinquent's offence, with the circumstances aggravating or extenuating it, proceed to inflict on him fuch pains and penalties, as the laws have, in such case, provided.' In this paragraph is the whole mystery of popish perfecution contained. The church never inflicts corporal punifhment on heretics. It only determines who are fuch; and the civil magistrate inflicts the punishment; because, forsooth, these heretics must be called criminals against the state. Bleffed effect of alliance between church and ftate! How dexterously does the church thus clear herself of the charge of perfecution, and throw it entirely upon the civil magiftrate for putting her own decrees in execution. But the Apologist has not acted like a thorough honeft witnefs in this cafe: for, though he has told us fo much of the truth as is abundantly fufficient to alarm all proteftants, yet he has not told the whole truth. We must therefore make up, in fome meafure, what he has been defective in. The ! The third general council of Lateran under Pope Alexander III. the fourth general council of Lateran under Innocent III. and the general council of Conftance, decree that the goods of heretics fhall be confifcated. They decree that the temporal lords, being required by the inquifitors, archbishops, bishops, &c. fhall, within their jurifdictions, without delay, imprison heretics, and cause them to be kept in close cuftody, by putting them into fetters and iron chains, till the church hath paffed fentence upon them. They decree that the fecular powers, what office foever they enjoy, fhall be admonished, and, if need be, compelled, by ecclefiaftical cenfure, that, as they defire to be reputed Chriftians, fo they will take an oath for the defence of the faith, and that they will honeftly endeavour, with their whole power, to exterminate all heretics, condemned by the church, out of their territories. And it is declared that if any temporal dord fhall neglect to act after this manner, that he fhall forfeit all right to his dominion and lands, and the fame fhall be given to fomebody that will. And it is to be obferved, that both the councils of Conftance and Bafil do reckon this Lateran among those councils which all their popes must fwear to maintain to the leaft tittle, and to defend, even to blood. And the council of Trent has not only declared it to be a general council, but alfo affirms its definition to be the voice of the whole church. The general council of Conftance decrees that all heretics, all followers and defenders of them, or partakers with them, tho' they fhine in the dignity of patriarchs, archbishops, bishops, kings, queens, dukes, or any other ecclefiaftical or mundane title, fhall be pronounced excommunicate in the presence of the people every Sunday and holiday: and that the archbishops, bifhops, and inquifitors, fhall diligently enquire concerning them who hold, approve, defend, or receive fuch herefies or errors, as they before had mentioned, of what dignity, ftate, pre eminence, degree, order, or condition foever they are: and if they be found guilty or intamed, by their authority, fhall proceed against them by the punishments of excommunication, fufpenfion, interdict; as alfo of deprivation of their dignities, offices and benefices ecclefiaftical, and alfo of their fecular dignities and honours; and by any other penalties, fentences, ecclefiaftical cenfures, ways or manners which they fhall judge expedient, even by taking and imprisoning their perfons, and executing upon them any corporal punishments with which heretics ufe to be punished, according to the canonical fanctions. And now what becomes of the Apologist's ingenious diftinction between religious and political perfecution! To excufe the church, and throw the blame on the magiftrate, is altogether as abfurd, as for a man accused of stabbing another to the heart, to alledge, in his excufe, that it was not he that committed the |