.433 IRISH REPRESENTATION. (Continued from our laft, page 352.) TERS BY JOHN CARTWRICHT, ESQ. TO LIEUT. COL. SHARMAN. SIR, Eld.d myfelf the honour to write to al meeting of the Irish parlia lization of commercial duties, &c. on abfentees, &c. tion of the late French duties, &c. gation of the British Admiralty 't, &c. Sorry to obferve the attention of any gentlemen who promoted the Dunng have held forth to their counMy che object is a proof of the foundThat attained, what elfe is wantdes all that citizens can with. a Bill of Rights, equalization of s of wholefome policy, before a conftitutional reprefentation, is to uits of liberty before you have The tree once planted, thefe, other bledlings, will be the fponTo extort from the fears of an mal parliament beneficial laws and Bus, were to waile that time in tutional parliament itself might be That alone is the prefent butinels of a thought ought the to bestow upon get. To magnify the importance gs, and if poffible to divide the feem to be the only fources to the enemies of your freedom. In , then, let the fagacity of Ireland h her virtue and her courage! D ages of adhering to the one object on meeting will be greater than ble. point, will produce celerity; will prove irrefiftiA handful of enterprifing men of addrefs may make their way in any direction, through millions intent on a diverfity of purfuits, leading them different ways; but what can penetrate or impede thofe millions, when condenfed to folidity by unity of object and unity of move ment! In ufing the word celerity, I have not meant to recommend any thing haily in the proceedings of Ireland. Haitinefs is only for thote who, through want of public virtue and well ordered power, are obliged to fnatch in a propitious mo ment at any nece Tary good. It is not fo with Ireland. On the first of all carthly concerns the may deliberate as becomes the importance of the occafion, and the dignity of human nature. Her councils may be the councils of men as free from fear as from a love of fervitude. Individuals in Ireland may bring forward motions for the annual fittings of a parliament, or for a more equal reprefentation of the people; but the ripened judgement of the community will require annual elections, as well as a reprefentation equal and univerfal; in fhort, a conftitutional pailiament, for none elfe deferves the name. Before I conclude, give me leave to fay, that, notwithstanding the apparent forgetfulness in this country at the prefent moment, of that parliamentary reform, which in many parts of it was of late fo ardently fought, I feel a strong perfuafion, that the will not be deaf to the patriot voice of her filter, Ireland. In my opinion, they are equally interested in each other's prof perity; in each other's freedom. An enslaved nation, in the hands of any government, is an engine of tyranny too dangerous to a free people under the fame government to be an object of indifference. As the freedom of GreatBritain could not be fecure were lieland completely enflaved; fo neither could there be fafety to the freedom of Ireland, although ever fo well eftablished within, while Great-Britain fhould remain without liberty. By means of a corrupt legislature, faction might fend its armies across the Irish channel, as it did across the Atlantic. With the greateft refpect, I have the honour to fubfcribe myfelt, Your well-wither, ed. Your force, directed to one Marnham, 31st Aug. 1783. LETTER II. which I yesterday did myfelf the addreifing to you, I ftated, in very , my ideas refpecting a reform in , and the means of effecting propose to fubmit to your confideconnected obfervations, in exMAG. June, 1784. BY DR. JE B B*. planation or confirmation of the opinions I have already advanced-trufting that your relpectable committee will receive with candour what I hall offer with integrity of purpofe. I am very fenfible that you have difficulties to ftruggle with peculiar to your country--others, 3 K For Dr. Jebb's first letter, lee Vol. I. p. 596. which which are common to both countries; but none, thank Heaven, which can be efteemed unfurmountable, when we reflect upon the part. The plan of univerfal reprefentation, by a new arrangement into diftrists, each district electing one member, is, I think, by far the moft prac ticable plan that can be propofed. The addrefs of the delegates of the Uliter regiment alerts, that the right of being governed only by laws of his own making is the birth-right of mana propofition equally true, whether the terms of it be applied to nations, or to the individuals of which they are compofed. Contented elections generally arife from difputes concerning qualifications; which can never be ftated in fo definite a manner, when any degree of property is eftablished as a requifite, as not to minifter matter for innumerable perjuries and endless altercations. It is impoflible to conceive that voters, in general, will put themfelves to the expence and trouble of travelling from one fide of an extenfive county to the other, to give their fuffrages, without fome compenfation. Laws to prevent bribery or corruption in fuch circumitances have always hitherto been evaded, and thus have increated the evils they were intended to remedy. Laws enacted to prevent the candidate from bearing the expences of an elector, inha biting the extremity of Yorkshire, to the place of election, will either be eluded, or operate as a disfranchisement. The utmost exertion of human intellect cannot invent a method of taking the fuffrages of an extenfive county, which will not be liable to ftrong objections. If you increafe the number of county members, the difficulties are increafed: a divifion of the larger counties into districts appears therefore neceffary, whatever be the plan of reform you fhall think proper to adopt with refpect to the qualification of the voters. If a lefs extenfive plan than what has been hinted be adopted, it will be prudent to leave the matter open for pofterity to improve upon it, if they judge proper. We know not what is really impracticable before trial-we have feen what Ireland has effected in lefs than four years. The objections to the plan of the Duke of Richmond and Major Cartwright, and the apprehenfions which many entertain of danger, from admitting Roman Catholics to the entire rights of citizenship, may appear fearcely worthy of a moment's confideration at no very diftant period. Unanimity is certainly very defirable-but there are two forts of unanimity: one of which confifts in blindly following the dictates of a few; the other is the refult of calm and difpaffionate enquiry into the real relations of things. I allow, on one fide, that it would be imprudent to aim at establishing more than what will meet with general concurrence: on the other, I maintain, that many prefent prejudices may naturally be expected to give way, when a fair appeal is made to the understandings of men, and truth is held forth to public view, by characters who juttly poffefs the confidence of the people. The generous fentiments of the Uliter volunteers refpecting religious toleration diffuled themfelves with rapidity inconceivable through the breafts of millions; and, I truft, that many of them will live to fee their fair example followed by more thần hart the Duto can world. I will only fur ther obferve upon this point, that unlefs en be done to render the true intereft of the com predominant in the Houfe of Commons THING IS DONE. It appears to me, that you will lead they in the great point of parliamentary reforma Next to yourfelves Scotland appears moft in neft. It is, therefore, on many actouds, o with you may be able to effect your par Your fuccefs will greatly facilitate the e ment of a fimilar reform in this kingin troft, that our committees will emulate you nerofity and candour, and by inviting a tivating a free and open correfpondence themselves of whatever light the frien berty in Scotland and Ireland may be fuggeft. I have fent inclofed two of addreffes, with a refolution of our focie conftitutional information at the head May the fpirit they breathe contribute the rekindling of that flame of liberty once was wont to burn with to bright in the breafts of Englishmen. I have alfo taken the liberty to inclof port of the Westminster Sub-committ 1pecting an annual, equal, and univeral fentation of the Commons of England addrefs to the freeholders of Middle fome other tracts, which state with ments than I can urge the objections extenfive plans that have been proped kingdom. Among thefe, the letter of ley to the Rev. Mr. Wyvill, refpecting expediency of adding an hundred cou bers, appears well worthy of peruial. I attended clofely to the debates of liament, when Mr. Grattan and Mr. first propofed their motions in the Hou mons. I faw the force of influence, fpaired. The volunteer fpirit arole, and was emancipated from its chains! A liament may contain a greater numbe friends to freedom; but an incurable herent in its conftitution. If it be le liament to form a plan, the fcheme fallibly be defeated. The aristocratic united with the regal, like a blight from will affuredly blaft every hope of harvet you retain the matter in your own ha cannot fail of effecting, under Provide permanent falvation of your country. enfuing meeting it may be agreed how exercife of the right of luttrage should general outline of a plan may be dra divifion of the counties into untrictsfranchifement of fome boroughs, and ferring the right of electing members populous townihips may be propoled molt material regulations reipecting t of the fuffrages of the electors pointed & an adjourned meeting, you will be able how far parliament has complied with of the people. The refolves and intra your conttituents will give fufficient we authority to your proceedings, atfuch 4 Once more requesting your favoura gence, and with my heartiest good waha fucccfs of a measure, in the event of caufe of public virtue, of civil and reli berty, is to deeply intereiled, I remain, At Brighthelmflen, x4/6 Aug. 1783. LETTER FROM LIEUTENANT-COLONEL SHARMAN TO DR. JEBB. R, S chairman of the Ulfter Committee of Correfpondence, I am directed to return ur warment thanks for your very obliging eful communications on the fubject of a mentary reform, to allure you, that we the most grateful fenfe of your kind , and of the great trouble you have on this occafion, and to enclofe you a copy refolves of the Provincial Affembly of acknowledgements had been fooner made, the multiplicity of bufinefs which dethis committee, both antecedent and ent to the meeting at Dungannon, very engroffed our time; this feeming neglect yo your good nature to excufe. provinces of Leinster and Connaught have ady called general meetings on the fame fubMaker had in part declared before; and doubt will now join the reft. You er, that in the public refolves of Ulfter, bar confined ourselves to fuch general prinand objects as we were convinced would mamity both in this and the other pro- the specific mode of reform the might differ; different opinions might arien amongst ourselves; our plan of rethe outlines of which I annex) is, there1bmitted to the grand National Convenwhat they fhall agree upon, the kingdom , I dare fay, will acquiefce in, and fupwith their united powers; and against that fitance will be vain. pro the courfe of our deliberations the utmolt ion was paid to the opinions and commuof all our illuftrious and much respectdpondents; we could not, however, in point apply them to the fituation of this Mon; and where we find great and good Aequally zealous in the caufe, differ with it to the mode, our only choice was to adopt which feemed to us moft applicable to the ry we live in. r counties, towns, and parishes are now up the fubject, and calling public meetto declare their acceffion to the Dungannon ses, and to inftruct their reprefentatives on Eject of a parliamentary reform. We earwith to fee the good people of Great-Bri forward in the promotion of the fame tant object, convinced that the united efof the fifter nations must prove irresistible, Ian, with the utmost respect, Sir, Your most obedient humble fervant, febb, Parliament-freet. 435 Lijburn, 08. 11, 1783. a Parliamentary Reform, Heads of a plan of propofed by the Ulfter Committee of Correfpondence to the Provincial Affembly of Volunteers, and by them referred to the Grand National Convention. ANNUAL parliaments-election by ballot. Mean, decayed, or depopulated boroughs to be deprived. The diminution of members thereby occafioned to be fupplied by giving reprefentatives to fuch confiderable towns as are not now reprefented, and by increafing the number of reprefentatives for counties, cities, and great towns. QUALIFICATION. In counties, every proteftant male (ideots, criminals, &c. excepted) having inhabited twelve months, and for that time poffeiled freehold worth forty fhillings per annum clear, or any kind of property to the value of 2cl. over and above legal debts, to be an elector.-In cities and towns the fame qualifications as in counties to entitle a perfon to vote-alto living in a house for which he pays 51. yearly rent, or more-no menial fervants, however, to vote, either in county, city, or town, unless a householder, paying taxes. Every perfon offering to vote (if required by any candidate or elector) to be obliged to wear to his qualification, and that he will vote for fuch candidate or candidates as he believes most likely to fupport the liberties of the people in parliament--and alfo to take the path against bribery. All votes once given to fand unimpeachable, but any elector fwearing falfely, and thereof convicted by verdict of a jury, to forfeit 201. to the profecutor, lofe his franchise for ever, and fuffer the punishment allotted for perthereof convicted by verdict of a jury, difabiliofficer make a falfe return, and jury. If any ties, heavy penalties, and a new election to take place. Every member returned, before taking his feat, befides the prefent oaths, to fwear that he, nor no perion for him, at his coit or knowledge, has, directly or indirectly, bribed any elector to vote for him. A reasonable compenfation to be made to the patrons of disfranchifed boroughs, alfo to thofe of fuch as from having the elective fuffrage vefted in a few fhall become free citics or boroughs, at the national expence. Extenfion of fuffrage to fuch defcription of Roman Catholics as the National Convention may deem proper objects of that great truit. Elections to be held on fame day in the different baronies, halt baronies, or parishes, fo as to finish in one, or in a very few days. Total exclufion of penfioners and placemen, fave that the Lord-Lieutenant may appoint any of the public officers of the crown, not exceeding fix at any one time, to fit, debate, and explain the public bufinefs, but not to vote. (To be concluded in our next.) 436 ANSWERS TO MATHEMATICAL QUESTIONS, Thomas Mofs, the propofer of that question: Of all triangles that can be infcribed in a given circle, the equilateral ove will have both the greatest area and the greateft perimeter. DEMONSTRATION. Draw any other chord DE parallel to AB, and draw CD and CE; from middle of the chord CE, and perpendicular thereto, draw GF, meeting the phery of the circle in F, and draw CF and EF; moreover draw DH parallel to Then, becaufe (by hyp.) DE is parallel to AB the fide of the equilateral tria it is evident that DCE is an ifofceles triangle, which triangle (by Thee. 6. Simpson's Geo. 2d edit.) is manifeftly greater than any other that can pet conftituted upon the chord DE, and infcribed in the fame circle: and (by Ea 3.) the triangle EFC is alfo an ifofceles one; and, therefore, by the aforelan rem of Simpton, greater than the ifofceles triangle DCE; that is ¦ EC x greater ECXDH. C G Now, if any other chord be fuppofed to be drawn parallel to the chord AB, either above or below it, and an ifofceles triangle be formed by drawing lines (as above) from the point C to the extremes of fuch parallel chord, it will evidently appear, by the fame kind of reafoning, that greater triangles than the ifofceles triangle, fo formed, can be always infcribed in the circle, and conftituted upon one of the equal fides of the faid ifofceles triangle; but when the faid fuppofed chord, inftead of being parallel to AB, coincides with that line, no greater triangle than ABC can poffibly be conftituted on BC (or AB) and infcribed in the fame circle; whence, because the triangle ABC may be affumed in any other pofition of the circle, and the very fame method of reafoning be ftill applied, it is therefore manifeft, that of all triangles infcribed in the fame cird equilateral one will contain the greatest area. A H 14 Again, it is exceedingly easy to prove, geometrically, that the perimeter ifofteles triangle in the preceding fig. is greater than any other triangle that ca conftituted upon the chord DE, and inferibed in the fame circle; and, ter it evidently follows, that the perimeter of the ifofceles triangle EFC is greater the perimeter of the ifofceles triangle EDC; that is, EF+FC+EC is greates ED+DC+EC. Now, if any other chord be fuppofed to be drawn parallel t line AB, either above or below it, and an ifofceles triangle be formed by dis lines (as above-mentioned) from C to the extremes of that parallel chord, it evidently appear, by reasoning in the very fame manner as above, that of angles may be conftituted upon one of the equal fides of the faid ifofceles tr and infcribed in the fame circle, whofe perimeters are each of them greater that of the faid ifofceles triangle. But, when the faid fuppofed chord is cons to coincide with AB, and the triangle (ABC) is formed by drawing lines t Cas aforefaid, no triangle whatever, by the fame method of reafoning, ca conftituted (and infcribed in the circle AFCB) upon one of the equal fides c faid triangle (which now becomes equilateral) that can have a greater pe... *This follows as a cor. to a theorem which is very eafy to demonftrate, and which felf-evident; viz. Of all triangles having the fame bafe and equal vertical angles, that which i feeles one will have the fam of the other two fides the greatest, 437 that of the faid triangle; and, fince the triangle ABC may be affumed in any Er pofition of the circle, and the very fame method of reafoning ftill holds good, erefore, follows, that of all triangles infcribed in a given circle, the equilateral i have the greatest perimeter. Q. E. D. e. By a fimilar method of reafoning, and the addition of one other circum. ce, it may be proved, that of all triangles that can be infcribed in a given cir the equilateral one will alfo contain the greateft infcribed circle. -End, May 16th, 1784. THOMAS MOSS, QUESTION (I. Feb.) answered by Mr. E. L. DUFFAUT, of the Rev. Mr. James's Academy, at Greenwich. CONSTRUCTION. tABVC reprefent the given elliptic I which BT, CT, is the femie, and VT the femi-tranfverfe * Draw TS perpendicular to produce it to K, fo that TS may be equal to TV2. On TK the circle TKP, and produce to meet the circumference again in Draw PR, through T; and, paral5through any point (as C) draw CvD, and it will either be or the fegment of one. DEMONSTRATION. B R S D A V K P construction; therefore, RTXTP is alfo equal to TV2. Again, because fmilarity of the triangles A/D and ATR, A/C and ATP, Atv and ATV, AT Di: TR::C: TP :: tv : TV; therefore, Dt: TR :: tv: TV; alfo TP tv: EV: but the rectangles under the correfponding lines of two proportionals are themfelves proportionals; confequently, DtxtC: TRX TV, and as the confequents are here equal, the antecedents must be fo fe; that is, DtxtC=tv2: the fection CD is therefore a circle. Q. E. D. Ficus anfwers to this question were alfo received from Mr. W. Richards and James Webb. QUESTION (II. Feb.) anfwered by Mr. W. RICHARDS, of Chacewater, near Truro, in Cornwall. EZP reprefent the meridian of en, P the pole, Z the zenith, EC quinoctial, Aa the parallel of deBen defcribed by Aldebaran, A the on of that ftar when it changes its 15'in a minute of time, and a tion when the change in azimuth man. It has been demonftrated writers on fluxions that the fluxion tangle at P is to the fluxion of the at Z, as rad. x fin. ZA is to fin. Z P 3 X coline A: now it is well known that the cofine A is equal to the ZPXR-cof.ZA xco.PAXR ún. ZA x fin. PA ; and this value being fubftituted in the preceding Wegy, we have flux. of P: flux, of Z :: fin. 2 ZA: fin. ZP x R cof. ZA X A. Putting, therefore, unity for Rs for the cos. ZP,fine of 51° 32'; d for |