MATHEMATICS. A Prize Question, by Mr. TIMOTHY DILLON, Teacher of Mathematics, Poolbeg Street. (Re-propofed from our Magazine for December, 1807.) On a certain evening in the year 1807, between the fummer folftice, and the autumnal equinox, I amufed myself with reading an account of ærial excurfions of some of the moft famous æranauts, and having contemplated on the great difficulties they had to encounter in navigating the the different regions of the air, and reflecting on the melancholy eataftrophe of the celebrated Pilatre de Roziere and his unfortunate companion Romaine, fuch a train of ideas rushed upon my mind, that upon my going to fleep I had the following fingular dream: I thought I was conveyed to a gentle eminence in the center of an extenfive plain in France, and on looking around me, I beheld a vaft concourfe of people affembled at a distance from the place whereon I ftood, and feeing a a man paffing by, I enquired the caufe thereof: he informed me that the renowned Garnerin was going to make experiments in meteorology, and that he had propofed to determine the true height of the atmosphere, and demonftrate the fallacy of all former calculations relating thereto to inveftigate the true and genuine caule of thunder and light ning the generation of rain, hail and fnow to explore the nature of vapours, fogs and mifts: the : refraction and temperature of the air in various regions: to account for the defcent of heavy bodies, and the propagation of found. A faithful account of thofe ex periments and difcoveries, befides feveral other useful obfervations tending to elucidate the true philofophy of meteors, the ingenjous Garnerin intends_to_tranfmit to the literati of Europe early in the year of 1809. I wifhed the ærial adventurer a profperous voyage, and fhortly after the difcharge of a gun announced his departure. Garnerin appeared feated in a very magnificent car, fuperbly decorated, and finely illuminated by a number of the molt refplennent lamps: his initial aflent was inconceivably grand and fublime, moving in an oblique direction by flow and equable degrees until he attained a certain altitude, he then afcended in the fame direction with an accele rated velocity, and having acquired his greateft perpendicular height, he became stationary, and vertical to my fituation, at which time his twelve illuminated lampst feemed condenfed to onc, emit ting but a feeble folitary ray of light. At this awful period the admiring multitude felt deeply interefied in Garnerin's fate; when he to diffipate their fears, applied a femtorophonic tube to his his mouth, and in a loud articulate voice thus addreffed them, "I foon fhall fee a glorious fight, Sol's upper limb has juft appeared in view." In the fhort space of three minutes and an half, he again declared "the Sun's lower edge is in contact with the eaftern limits of the horizon." Here a pause enfued, but no fooner had the glorious lamp of day dif. fufed its irradiating beams, and tinged the western ocean, than the fagacious aronaut once more proclaimed, Far to the northweftward I fee a verdant plain, whofe remoteft verge bounds my horizontal view, to which plain thousands are now reforting, to behold a momentous hurling match between two contending provinces in famed Hibernia's Ifle. Thirty of Munter's brave and determined fons, arrayed in caps of pureft white, with manly fortitude, advance northeasterly towards the centre of the green: an equal number of Leinster's hardy and intrepid youth, with a proud undaunted air, are feen in an oppofite direction, advanc ing to the fcene of action, thofe are arrayed in caps of golden hue. Marthalled by an illuftrious chief on either fide, with fern impatience these matchless heroes a wait the fignal to begin the glorious conflict-ardent for glory, (the ball being now thrown up,) thofe daring and intrepid hurlers meet in dreadful contact: quick as thought, five of the yellow, and as many of the white, lie proftrare on the embattled plain. An OfAn Of foronian of fuperior might has ftruck the ball,-it flies aloft in air, triumphant houts of joy from 8 16 ronaut wave a banner as a fignal of deep difmay. He then addreffcd me in those words: Dillon farewell, I know your anxious thoughts refpeting the iffue of this eventful hurling match, yet I muft away, the threatened danger is great, another ball pro jected with fuch unerring aim might hurl deftruction on Garnerin, and cruth his towering hopes of future fame; but ere lang I will direct my courfe to Slieublicums lofty mount, then bend my way to Offory's delightful vales, next trace the various windings of the rapid Nore, the copious Barrow, and the fertilizing Suir; this done, to Erin's verdant plains her hofpitable fhores, and to her faithful, brave and generous fons, I'll bid adieu." Here Garnerin ceafed; then fwift through yielding air directs his rapid flight, and lands just twenty miles due north of me. Ye afpiring Philomaths of fait famed Hibernia, you are required, to determine the night I took my ideal flight. 2. The latitude of the place whereon I The elevation of the cannon, exceeded the angle that Garnerin's line of decent made with the horizon by 3° 37′ and half the former was double the funs declination on faid day; alio the longi tudes of the two places in France and Ireland, are 1° 30' W. and 7° 50' W. refpectively. food flood when viewing the lofty aeronaut. 3. The latitude of the hurling green. 4. The elevation and horizontal range of the cannon. 5. Garnerin's perpendicular altitude, and diftance from the hurling green when stationary. 6. The difference of the times of fun rifing on the plain in Erin, and that in Gallia; to be truly brought out in numbers, with the analytical inveftigation. Note. Garnerin's ærial courfe, the pofition of the cannon, and my fituation on Gallia's plain, are fuppofed to lie under the fame meridian, and his greatest height coincided with the vertex of the curve defcribed by the projected body. SOLUTION. By the Propofer Mr. TIMOTHY DILLON, only. LET 1142 feet ẹ, 16′4 = b. 134400 (the feet in 20 miles) =¿, 18" 22" g, the natural tangent of 3° 37', and the tangent of the angle Garnerin's line of defcent made with the horizon, put = then + will expound the tangent of the elevation of the cannon, and 1: dx: dx the greateft altitude of the projected body; again per trigonometry, and a well known property of the parabola, : I --- mx Į - mx : m+x m+xx2dx hence the time that elapfed between firing the cannon and my hearing m+xX24x a; but from the doctrine of projectiles 4*, Vaz, will exprefs the time the ball b took to describe half the curve; which from the laws of falling bodies will alto reprefent the time the fragments of the lamp were de fcending from the greateft height of the projection to the earth; there fore from the nature of the queftion, and what we have premileg گیر x = 1- nx a; fquared, &c. and in numbers x +g 9.4011; folved 1.0664 the natural tangent of 46° 50' 30", the angle of Garnerin's line of defcent, which added to 3° 37' 30", is 50° 28' the cannons elevation; this laft divided by 4 gives 12° 37 the funs declination, which answers to April the 24th, the night I took my imaginary flight. Now let the fine and cofine of 77° 23' the funs polar diflance be puta, and b; fine and cofines 90° 16' 30 the diftance of the funs centre from the zenith when his upper limb appeared in view c, and―d; cofine 89° 40' 30" the distance of his centre from the zenith when rifen; = h, and let cofine 52′ 30′′ (31⁄2 minutes) be ➡m, thes per fpherics the cofine of that arch of the ecliptic which the fun paffed over while rifing will be expounded by ma2 2, which being a known quantity, puo n, and the fine of its complement p; then the fine of the angle included between the polar and the greater zenith diftance will be truly expreffed by h+nd; = ср hence in an oblique spherical triangle, there are two fides and the contained angle given to find the colatitude; which is found to be 37° 40'; confequently the latitude of the place whereon I ftood when viewing Garnerin is 48° 20', and the latitude of the hurling green 520 40'; the horizontal range of the cannon 70.416 miles. Garnerin's greatest height: 21.33 and his diftance from the hurling green 412.7 miles; laftly the fun rofe 103 minutes fooner on the hurling green than on the plain in France. Dr. MILNER. This Right Reverend Englishman continues to agitate the publie mind, and infult the Irish understanding, by his enigmatical productions. He has iffued ancther of them, dated November 13, at Wolverhamton. His difappointment at the decifion of our Bishops is manifeft through the whole of this impertinent production. He is not very fparing of attributing this act of the Prelacy, to the powerful influence of a party of men in Dublin, whom he accufes of difloyalty, and who take pains to prevent a good underfanding between the Catholic Clergy and the Government. This infamous and malignant infinuation, bears with it fuch an evident character of falfhood, that the fimpleft man in fociety, muft fee that the English miffionary is more influenced by politics than religion. What good understanding has thefe men (whom he mentions) a.prevented?—we do not remember understanding between his Majefty's minifters and the Irish Catholics, on a better footing than at prefent, and if any mistake exifts, it cannot originate with any fet of Irish Catholics. The opinions of Lord Redesdale, and of Dr. Duigenan, tend more to detach the Catholics from the Government, than any act which the learned Doctor can quote from the conduct of any Irith Catholic. In addition to the libel on the Catholic laity, he has the affrostery to infinuate, that the Bishops would have acceded to the Veto, if they were not intimidated by a powerful party." This we confider as an aggravation of his unprecedented intrufion on the ef fairs of a people, whose condition religion or interefts, were never in the most diftant manner, fubmitted either to his management or advice. Thus difclaiming, as we do, any of the fervices of this reverend writer, we request, if he values the tranquillity of the Ctholic Church in Ireland, he will confine his labours to the fervices of of his own countrymen ; as we know, that if our Prelates were fo corrupt or weak, as to be conducted into fo traitorous a measure as that of the thaking off the authority of the holy See, they would be abandoned by their flock, and another Hierarchy and a more faithful though humble Priesthood would be chofen by them; and thus at one fpirited leffon, demonftrate their unperishable attachment to the head of the Church, by whofe Apoftolic inftructions, through the medium of a learned and martyred Pre lacy, the Irish had preferved with purity and unity, the religion of their ancectors. ON THE MAUFACTURE OF BAKER'S BARM. A Morning Paper, that frequently boafts of the liberty of the prefs, affecting a high degree of indignation against the Mafter Bakers, has been pleated to try, and convict the unfortunate men for another offence. This liberal Editor, so profuse of his praifes of the liberty of the prefs, becomes judge and ju ry in this cafe. by accufing the Bakers having eftablished manufactories of a deleterious kind of barm, to the exclufion of porter brewers wholesome barm, and the confequent injury of their fellow citizens." This is not a new plan for exciting popular fury againft bakers, it is a plain call upon his imperial majefty the mob, to punifh the culprits a la Paris. 3 X That this bafe accufation ferv. ed up fo folemnly to the public, in all the cant of paragraph writers, is as unfounded as it is wicked, is obvious to any perfon who understands the process used, by porter makers and barm ma kers; for it is the porter brewers barm, deferves the character, that the editor attempts to affix to the bakers barm. The porter brewers, if men who exclude corn, in the making of drink, can be juftly called fo, are notorioufly known to use every fubftitute for grain, that the mineral or vegetable kingdom can produce, and all the factitious ones, that the art of chemistry has yet given to the world. The facchatine fweetness of malt, is imitated by ftrong infufions of liquorice root, and hops are banished in a confiderable de gree, for quaffia, gree, for quaffia, a bitter wood imported from America, coriander feeds, cochylus, cranberries, and juniper berries, are ufed in great quantities, according to the kill and avidity of the operator, copperas finely pulverized, is dif folved in the porter while in the vat, to give that fine yellow froth that appears on the quart, which the public mistake for the rich generous produce of malt. The brown colour which the porter wears, is given by a colouring made by violently boiling molaffes and water together, and frequently checking the conflicting maerials by lumps of falted butter. The Barm made in fuch netarious manufactories, which the hired news-maker, is pleafed to call wholesome, is certainly not ufed |