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MATHEMATICS.

A Prize Queftion, by Mr. Timothy Dillon, Teacher of Mathe

matics, Poolbeg Sireet. (Re-proposed from our Magazine for December, 1807.) On a certain evening in the refraction and temperature of the year 1807, between the summer air in various regions : 10 account folftice, and the autumnal equi- for the descent of heavy bodies, nox, I amufed myself with reading and the propagation of found. an account of ærial excursions of A faithful account of those expesome of the moft famous æra. riments and discoveries, belides

auts, and having contemplared leveral other useful observations on the great difficulies ihey had tending to elucidate the true to encounter in navigating the philosophy of meteors, the ingethe different regions of the air, njous Garnerin intends to transand reflecting on the melancholy mit to the literari of Europe catastrophe of the celebrated Pi- early in the year of 180). 'I latre de Roziere and his unfortu. wifhed the ærial adventurer a nate companion Romaine, such a prosperous voyage, and Thorily train of ideas rushed upon my after the discharge of a gun an. mind, that upon my going to nounced his de pariure. fleep I had the following fingular Garnerin appeared fcated in a dream :

very magnificent car, fuperbly I thought I was conveyed ro a decorated, and finely illuminated genile eminence in the center of by a number of the most refplenan extensive plain in France, and nent lamps: his inicial alleut on looking around me, I beheld was inconceivably grand and lua valt concourse of people affem- blime, moving in an oblique di. bled at a distance from the place re&tion by now and equable da. whereon I food, and seeing a grets uniil he attained a certain a man passing by, I enquired ihe altiinde, he then ascended in the cause thereof: he informed me fame direction with an accele. that the renowned Garnerin was rared velocity, and having acgoing to make experiments in quired his greatest perpendicular meteorology, and that he had heighi, he became ftationary, and proposed to determine the true vertical to my firuation, at which height of the atmosphere, and time his twelve illuminared lamps demonstrate the fallacy of all for seemed condensed 10 onc, emis. mer calculations relating thereto: sing but a feeble solitary ray of to inveftigaie the true and ge. lighı. At this awful period the nuine caute of thunder and ligne admiring muliitude feli deeply ning : the generation of rain, hail interelled in Garrerin's faie; and snow : 10 explore the nature when he io diffipale their fears, of va pours, fogs and mifts : the applied a licnioroplonic tube to

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his mouth, and in a loud articulate Leinster's fons, loudly proclaim voice thus addressed them, “ I the honour of the firti pucki" foon ball see a glorious fight, He ceared. And nowo when ms Sol's upper limb has just appeared curiofily was raised to the highet in view.” In the short space of pitch, the shattered fragmenis of three minutes and an half, he a lamp fell at my feei, and in again declared "the Sun's lower 18" 22" afler a cannon's lour edge is in contact with the earn roar assailed my ears; amazed I tern limits of the horizon." Here looked up and saw the allonished a pause ensued, but no fooner xronaut wave a banner as a Gignal had the glorious lamp of day dif. of deep dismay. He then addressed fused iis irradiating beams, and me in those words:- Dilon tinged the western ocean, than farewell, I know your anxious the sagacious æronaut once more thoughis respefing the issue of proclaimed, : Far to the north this eventful hurling match, yet weft ward I see a verdant plain, I muft away, the threatened danwhose remoteft verge bounds my ger is great, another ball prohorizontal view, to which plain jected with such unerring ain thousands are now reforring, to might hurt deftruction on Garnebehold a momentous hurling rin, and crush his towering hopes match between two contending of future fame ; but' ere long I provinces in famed Hibernia's will direct my course to Slieubli. jne.

cums lofiy mount, then bend my “ Thirty of Munfter's hrave way to Ofiory's delightful vales, and determined fons, arrayed in next trace the various windings caps of purest while, with manly of the rapid Nore, the copious fortitude, advance northeasterly Barrow, and the fertilizing Suir; towards the cenire of the green: this done, to Erin's verdant plains an equal number of Leinster's her hospitable shores, and io her hardy and intrepid youth, with faithful, brave and generous fons, a proud undaunced air, are seen I'll bid adieu." Here Garnerin in an oppofite direction, advanca ceased; then swift through yielding to the scene of action, those ing air directs his rapid flig's, and are arrayed in caps of golden hue. lands just owenty miles due north Marshalled by an illustrious chief of me. on either fide, with fern impa Ye aspiring Philomails of fait rience there matchless heroes a wait famed "Hibernia, you are per the fignal to begin the glorious quired, to determine the night conflict :-ardeni for glory, (the I took my ideal flight. 2. The ball being now thrown up,) chofe latitude of the place whereon I daring anii intrepid hurlers meet in dreadtul contact : quick as * The elevation of the cannon, er. thought, five of the yellow, and cecded the angle that Carnerio's lipe of as many of the whire, lie prostrare

decent made with the horizon by 3' 371

and half the former was double the sun on the embaceled plain. An Of

declination on laid day ; also the longis foropian of superior might has tudes of the ego places in France of ftruck the hall, ic Aies aloft in Ireland, are 1° 30' W. and ye so' W. air, triumphant louts of joy from respectively.

flood

food when viewing the lofty æro- brought out in numbers, with the naut. 3. The latitude of the analyrical investigation. hurling green. 4. The elevation Nore. Garnerin's ærial course, and borizontal range of the can. the position of the cannon, and non. 5. Garnerin's perpendicuo my fiuation on Gallia's plain, lar aliiiude, and distance from the are supposed io lie under the same hurling green when stationary, meridian, and his greatefi height 6. The difference of ihe times of coincided with the verrex of ihe fun rifing on the plain in Erin, curve described by the projected and that in Gallia; to be truly body.

SOLUTION.

By the Propofer Mr. Timothy Dillon, only,

Lut 1142 feet =R, 16'1=, 134400 (the feet in 20 miles) =d, 18" 22"" =g, the natural langeni of 3° 37'1 = m, and the langent of the angle Garnerin's line of delcent made with the horizon, put =k then m+x will expound the tangent of the elevation of she cannon,

1-mx and 1:1::*: dx = the greatest aliitude of the projected body; again per trigononeisy, and a well known property of the parabola,

...I— *:!— =half the cannons horizontal range,

m+* m +* X 20% hence the time that elapsed between firing the cannon and my hearing

h., 1--MX the report will be be expressed by ** a; but from the

m + xX2 d * do&rine of proje&iles y d*, will express the time the ball took to describe half the curve; which from the laws of falling bo. dies will allo represent the lime the fragmenis of the lamp werë do scending from the greatest height of the projection to the earth; there. fare from the nature of the question, and what we have premidea

Inx

n; squared, &c. and in numbers mt-x X 2 d x 7^; 'qu * -. 215** - 1.05243 - 2.08x2 + 10,26x = 9.4011; solved x = 1.0664 che natural tangent of 46° 50' 30", = the angle of Garnerin's line of descene, which added 10 3° 37' 30'', is 50° 28' the cannons elevation; shio las divided by 4 gives 12° 37 the funs declination, which answers 10 April the 24th, ihe night I look my imaginary Bigha.

Now let the fine and cofine of 77° 23' the suns polar diflance be put = a, and b; line and colines 90° 16' 30 the distance of the juns centre from the zenith when his upper limb appeared in view

c, and -d; coline 89° 40' 30" The diltance of his cedire from the sedith wben siten ; > h, and let coline 52' 30" (31 minuics) be

sm, then per spherics the coline of that arch of the ecliptic which the lun passed over while rifing will be expounded by mia? *-*b, which being a known quantity, pub =n, and the line of its complement = pi shen the fine of the angle included between the polar and the greater zenith difance will be truly expressed by h +**;

hence in an oblique spherical triangle, there are two fides and the contained angle given to find the colaiilude ; which is found to be 37° 40°; confequently the latitude of the place whereon I ftood when view. ing Garnerin is 43° 20', and the latitude of the hurling green 520 40'; the horizontal range of the cannon = 70.416 miles. Garnerin's greareft heighi = 21.33 and his distance from the hurling green = 412.7 miles; lastly the sun rose 10 minutes sooner, on the hurling green ihan on the plain in France.

Dr. MILNER.

This Right Reverend English- Majesty's minifters and the Irish man continues to agitale the pub- Catholics, on a better fooling tban lie mind, and insuli the Irish un- at present, and if any mistake er. derlianding, by his enigmatical ifts, it cannot originare with any productions. He has issued ano- set of Irish Catholics. The opither of them, dared November 13, nions of Lord Redesdale, and of at Wolverhamton. His disap- Dr. Duigenan, tend more to depointment at the decision of our tach the Catholics from the Go. Bishops is manifest through the vernment, than any act which ibe whole of this imperiinent produc- learned Doctor can quote from tion. He is noi very sparing of the conduct of any Irish Catholic. attributing this act of the Prelacy, In addision to the libel on the 10 the powerful influence of a par-Catholic laity, he has the affrosty of men in Dublin, whom hetery to infinuate, that the Bishops accuses of disloyalıy, and who take would have acceded to the Veto, pains to prevent a good under- if they were not intimidated by a Manding between the Catholic powerful party." This we conClergy and the Government, fider as an aggravation of his unThis infamous and malignant in- ' precedented intrusion on the effinuation, bears with is such an fairs of a people, whose condition evident character of fallhood, that religion or interests, were never the simplest man in society, muft / in the most diftant manner, subfee that the English miffionary is mitted either to his management more influenced by politics than or advice. Thus disclaiming, as religion, . .

we do, any of the services of this What good understanding has reverend writer, we requeft, if he These men (whom he mentions) values the tranquillity of the Coa.prevenied ?-We do not remember tholic Church in Ireland, he will

under ftanding between bis confine his labours to the fervices

of

of his own countrymen ;- as we That this bafe accusation serve know, that if our Prelates were ed up so folemnly to the public, fo corrupt or weak; as to be cod in all the cánt of paragraph wriducted into so traitorbus a measure ters, is as unfounded as it is 35 that of the thaking off the wicked, is obvious to any person authority of the holy See, they who understands the process used, would be abandoned by their by potter makers and barm ma: flock, and another Hierarchy and kers; for it is the porter brewers a more faithful though humble barm, deserves the character, that Priesthood would be chosen by the editor attempts to affix to the them; and thus at one spirited bakers barm.' lesson, demonstrate their unpe The porter brewers, if men rilable attachment to the head of who exclude corn, in the making the Church; by whose Apoftolic of drink, can be juftly called so, inftruAions, through the medium are notoriously known 10 ufé of a learned and martyred Pred every substitute for grain, that the lacy, the Irish had preserved with mineral or vegetable kingdom purity and unity, ihe religion of can produce, and all the fa&ticias their ancectors.

rus ones, that ihe art of chemistry has yet given to the world.

The faccharine sweetness of

malt; is imitated by strong ina .ON THE MAUFACTURE OF fufions of liquorice root, and hopi BAKER'S BARM.

are banilhed in a considerable des A Morning Paper, that fre- gree, for quaffia, a bitter wood quenıly boafts of the liberty of imported from America, coriana the press, affecting a high degree der feeds, cochylus, cranberries, of indignation against the Mafter and juniper berries, are used in Bakers, has been pleated to try, great quantities, according to the and convidt the unfortunate men skill and avidity of the operator, for another offence.

copperas finely pulverized, is dirThis liberal Editor, so profuse solved in the porier while in the of his praises of the liberty of vat, to give that fine yellow froste the press, becomes judge and ju- ibat appears on the quart, which ty in this case, by accusing the the public mistake for the rich Bakers "r" having eftablished generous produce of malt. The manufactories of a deleserious brown colour which the porrer kind of barm, to the exclusion wears, is given by a colouring of porter brewers wholesome b.arm, made by violently boiling molasses and the confequent injury of and water together, and frequenttheir fellow citizens."

ly checking the conflicting ma· This is not a new plan for ex® serials by lumps of salied butter. citing popular fury against ba- The Barm inade in such netari. kers, it is a plain call upon his ous manufactories, which the imperial majesty the mob, 10 pu- hired news-maker, is pleased to nila the culprits a la Paris. call wholesome, is certainly not

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