others, because they are not innocent themselves. He is bound by gratitude to one man in this world; but that man, however differing from him in religious opinions, would scorn to impose upon him a yoke, which the principles of his head, or his heart, would ever reject. He knows not enough of any other man, between whom and Ormond he could institute a comparison. A man whose name he dare not mention; who, like Ormond, loves the good and honorable man of all persuasions, without being a bigot to any and who, scorning intrigues, and despising calumnia, tors, will capitulate only to the ad-. vantage of his country, and to the principles of his conviction." So much for the labours of Mr. O'Conor, and his two heroes, Ormond and Buckingham. The first the betrayer of his country, the latter an advocate for thinning our superabundant population. County of Tipperary, This County is one of the most fruitful in pasturage and cattle, of any, district in Europe; its inhabitants, are divided into separate castes. The people, i. . the labouring poor, and the cattle. The farmers are under the management of the magistrates, who are composed of landlords, ministers, and tythe proctors, that, inverting the order of nature, fatten brutes. and bunt men. The hog is domiciliated and the man is proscribed. The style is covered, and the cottage open. The minister of the gospel watches over the brute, as if the Saviour of the world died for the comfort of the stallion, and for the fecundity of the ewe. Farming is advanced by the increase of the brute creation, and the diminution of the human species, This system begets a jealousy, with the thinking brutes, who, in the spirit of pride and hunger, frequently dis pute their right to eat where they are doomed to starve. They fight the master to taste the steer, and so une qual does the hog and the lord sometimes appear in the contest, Lord Norbury is called in to settle the quarrel, and, as in such cases, where a sportsman is to decide, the is game preserved, and the poacher is punished. The father follows his son to the gibbet, in Tipperary, as regularly as he would a plough, if he was in America; this is named a spirit of improve ment, because it checks the growth of the superabundant population, advances the breed of cattle, by remov ing their enemies, and tranquillizes by making a desert, **། Walter Cox and the Attorney The Attorney General in his speech on my trial, stated or asserted that I. am the agent of a faction, meaning thereby, as meanings or inuudoes,, are allowed by law, that Walter Cox is the organ of a popish faction. With every deference to the character of the Attorney General, whose reputation for bonor and principle is indisputable, I can assure the public, though I am a papist, alias, an Irishman, I have no more attachment to a popish faction, nor to a popish syr cophant, than I have to any of the most orderly and lawful of my authorised oppressors, So far am I not the organ or the agent of any part of my aspersed countrymen, that I never, yet descended to seek any support personally or publicly, but the, spontaneous and casual protection my publication produced by its novelty and originality, The fact is that between the patronage of the enlight ened protestants, the curiosity of the. baser part of that respectable body, and the honest encouragement of my own whipped and hunted companions, I am enabled to publish a work, so extensive in circulation as not to be paralleled in the history of printing, since the introduction of that useful art into this unfortunate country. NEW NEW BOOKS, Just published by W. Cox, A An elegant History of British Prow- ་ The following INGENIOUS PROBLEM, exception, copied verbatim, from Mr. Sir, -- ̇to each of the two former, make h 2 × 4 + 2 a 2 x 2 + x 4 and a h4+ h2x2+x+ which are evidently square quantities, whatever may be the values of a hx, whether whole fracted, positive or negative, it there. fore only remains to make the sum of the two first h2Xa4-202x2+x4+a+ h?-2h2x2Xx4 a rational square; this expression, by combining the synoniimous terms, may be thus exhibited; a2+h?Xa2h2-4a2h2x2 + a2 +hx4 Now if a2+h2 be taken=m2 or which amounts to the same, if a and h be put for the legs of any ra. tional right angled triangle, whose hypothenusem, then by substituting m2 for a2+h2, our expression becomes m2 a2h 2—4a2h2x2+mx+=[]theseve ral terms whereof are evidently perfect squares we may therefore equate, the whole expression, to m2a2h2, in which 2ah case we find x=. or equate it m2x4 Q. F. D. 3, h=4; 117; hX : For example, take a m5, then a × 4h-m2 = 4aa-m=44 and Aahm=4X3X4X5 = 240, being the least roots possible, again take a= 5, h=12 and m =13, then a x 4h-m2 = 576-169X 5 2035, h×4aa-m2 = 12×100-169 =-828 and 4ahm = 3120, which are three other roots, whose squares will answer all the conditions of the question. It matters nothing if any of the roots have a negative sign, as it is too well known, even to beginners, that the square of a negative quantity, and all even powers thereof, will have an affirmative sign-and thus, by varying the sides of your assumed rational right angled triangle, an infinite number of answers may be obtained by this truly elegant and simple theorem. Whoever compares my method with Euler's or Bonnycastle's, will immediately perceive which to give a preference to Euler and Bonny castle's roots, obtained by a difficult process, and a variety of assumptions, bring out only one answer, namely, 528, 5796, 6325, for the roots. See Elemens d'Algebre, par M. EULER, tome 11. page 327, and BONNYCASTLE'S Algebra, edition, page 148. 1. NEW THEOREMS. 5th See Bonnycastle's Algebra. Quest. 65, page 208 Let a, h, m, be the three sides of any rational right angled triangle whatever, then shall ah 4; am) 4; hm] 4 be three biquadrates, whose sum will always be a square number, whose root is universally represented by a4+a2h2+h4,query the demonstration 2. Again and. a+h a+h fractions, whose difference = the difference of their squares, and the sum of their squares, will always be a square number universally. Bonnycastle's Algebra, quest. 18, page 149. are two 3. Still retaining a, h, m as before, m4 I that. say will be always such 4a2h2 a square number, as being encreased and decreased by its root, shall in cach case make rational square numbers. Query the reason ? 2n+2 4. If v = 1-20+ v 2 then shall 1420v2 be always .and. 2 2 two such numbers, whose sum being encreased and decreased by their dif ference, and the difference of their square, the result shail in each case be rational squares. Bonnycastle's AL gebra, page 150. L Or thus universally. Square the sum of the legs of any rational right angled triangle, as also the the difference of the legs, and divide each square by double the square of the hypotheneuse, then these two fractions will be always such, that their sum increased and lessened by their difference, or difference of their squares, the result will always be a square number, i. e. retaining the foregoing notation, the fractions will be universally ath and a-h12 2m2 Query the reason? 2m2 5. Retaining the former notation, ah, am, hm, are the roots of three squares, the sum of whose squares shall be a square number universally. JOHN MORAN, Philomath and Land Surveyor. Mount Byrne Lodge, near Dundalk. 11th December, 1810. P. S. Having at an early period of my life, viz. at the age of sixteen, made the Algebra of Diophantus a particular part of my study, and at various times since, when the discharge of my public avocations, as professional land surveyor, allowed some intervals of leisure, I have assiduously cultivated this ingenious and intricate species of Algebra; many specimens of my improvements therein were published in the Diaries, these thirty years past; my researches always enabled me to arrive at the solutions of the most difficult problems, by assumptions, quite foreign to those made use of by that celebrated Author, or any of his commentators, who, except Euler alone, were nothing more than explanatory copies. If health and time permit, I intend (God willing,) submitting to the opinion of the public, the whole of my inventions on this subject, together with Kersep, Backet, Ozanam, and Euler's mode of treating indeterminate problems, of which due notice will be given in your miscellany and in the public papers. I am, &c. I. M. IMPORTANT EXTRACTS FROM NEWSPAPERS. Letters have been received from Birmingham by the Board of Saints, instituted for the conversion of the Irish. Those communications describe the flourishing state the Army and the Gospel have arrived at, by the decay of the workshops. It is reasonably conjectured, that not He less than four thousand preachers will be added to the Irish mission, in the short space of six weeks. Never was a better opportunity for the destruction of idolatry, since the invention of smoke jacks. Carnal occupations having ceased, the work of heavenly intercourse commences. that made candlesticks, is preparing to' manufacture Angels, and with the arms of the gospel, the hymn book, the Bible and stool, the Lancashire army is on the point of journeying on the Irish Crusade, to rescue the land of mutton from sedition and popery. IMPORTATION OF BIBLES. In the daily entries of the custom-house, we observed, in the last week, that Mr. Shaw, member for Dublin, imported two bales of Bibles. Our members of parliament pay more attention to our souls, than to our bodies. Under the name of Farming Societies, they improve our cattle, and in the character of Bible Societies, they would mend our minds. But we can assure the associated fraternities, however solicitous they may be to reconcile us to the church and the state, that the plans of conversion and loyalty they meditate,must make very little progress, in a country where eating is inaccessible, without the aid of felony. The Soliciter General, on the Trial of Mr. Cox, asserted, that he, Cox, was an agent, a pensioner of the French Emperor's. Though Mr. Solicitor and the Court thought very differently, yet the words had the effect of alarming an ignorant jury, Mr. Cox defies any person, in public or in private life, to quote any cir cumstance, before the unfortunate occasion of the late Trial, either in conversation or in print, that could be construed into an approbation of the conduct of the French Emperor. Mr. Cox has as just an abhorrence of despotism as ever Mr. Bushe had, and too highly values the sacred character of the press, to, wish to see that press, that is yet allowed to linger in this country, in the hands of its most decided and relentless enemy. CATHOLIC LOYALTY. Though Catholic loyalty is much very suspected, yet it will be found, in many instances, of vital importance, that Catholies have evinced as decided enmity to French principles, and seditious insinuati ons, as any Williamite would. The Catholics of Bantry offered themselves, in 1796, to fight loche. The Catholic peer, Lord Fingal, at a meeting at Trim, voted thanks $ 2 to to Lord Wellington, in advance, for the great victory said Lord is to gain in Portugal, and the kindness the family of Talavera uniformly express for Catholic interests. On a late occasion, when Mr. WALTER Cox was tried for dreaming treasonably, a Catholic Citizen, who was on the Jury, › was so figeted into loyalty by the Attor ney General's picture of seditious slumbers, that he instantly and loyally joined with his brothers in a verdict of GUILTY.' Mr. Matthew Andoe, of High-street, woollen-draper, will always be an honor, and give a character to Catholicity and Juries. T 9 THE UNION. The present distracted state of this country, and the rapid appearance of decay which Dublin exhibits, deserted by our gentry, and crowded with an immense military force, contributes to bring the subject of the Union, and its fatal effects, under frequent discussion. While the contract that exists by the Union is so partially executed as it is at present, it will always be a serious subject of pain and irritation. An Union should be in its ope ration what the word means, a reciprocity of our favor, and who treat our indignation with contempt, that we are not entitled to any higher rank in the empire, than the provincial degradation we have been so recently reduced to. But, at this awful period, when the last retreat of any rational liberty in Europe, has to contend for its very existence with an armed world, England ought to be wise, where she ought to be just. She ought to see how unequal her physical force, her abridged trade and immense taxation, fit her for a contest with France, while one half of her dominions is kept in a ferment, worked into unmanageable agitation, by all the passions that animate the human mind. She ought to see, that the old fashioned manner of treating this country is not fitted for the present day. The Irish know their numbers, their services, and the important weight they may one day throw into the scale of Europe, to bear, with any appearance of reconciliation, a mode of treatment that exposes them to all the horrors of civil war, and all the injustice of commercial restrictions. Nothing short of perfect equality of rights and rank, can give weight or Sonterests, impartial in its inter- strength to the union of the two countries, équal through all its modifications. One country should not monopolize all the trade, nor consume all the provisions of both. London should not absorb all the wealth, by being exclusively -the residence of the Executive and the Legislature. The Duke of Richmond, more than thirty years ago, proposed a reasonable and unexceptionable plan of Union, which would have consolidated the empire, by reconciling the entire of the people; and were it carried then into effect, the empire, by being preserved. from internal jealousies, local interests, and religious vexations, would have no thing to fear at this day from the present ruler of Fance. This plan was, that the King and the Legislature should reside alternately in Dublin and London, which, at adopted, would have reconciled the Imost inveterate prejudices, and have sllenced, or have put to rest, every pretext that arises from a mode of government, which appears to be regulated by the ar rogance of a mistress, rather than what it ought to be, the equal affection of a sister. We know it would be a very difficult undertaking, to persuade the people of England, who are in the habit of hearing our complaints, without exciting in their minds one generous yaz or can stem the torrent that threatens to swallow them in the vortex of despotism, and the oblivion of slavery, but such a measure of new manners as will reconcile the Irish, by a fairer division of rights; and nothing would assure it more, than allowing Dublin, to enjoy alternately with London the right of having the seat of Government and the Legislature. MR. WALTER COX.· ́ On Monday, the 25th of February, Mr. Walter Cox was arraigned, before Lord, Norbury and Baron George, for publishing the same alleged libel, for which he was convicted on the 18th. On Tuesday morning the trial commenced, and after a long speech by the Attorney General, going into evidence, and a masterly address to the Jury by Mr. McNally, on the part of the traverser, Mr. Cox was again found guilty; but his Counsel, Messrs. O'Connell, MNally, Perzin, and Bethel, having detected an error in the indictment, a point of law was saved, which the Court allowed should be submitted to the opinion of the twelve Judges, before judgment could be given. The Judges, in consequence, met on Thursday, and agreed that the point saved was a legal objection. On Friday, larch the 1st, new bills of indictment were |