The ChhlleDgc of John 3forrissey to Figbt Tom Myer-Sceiic* at talon Coarse.We mentioned yesterday, in giving an accountuf the Race ol Union Course an Monday, tkat a challenge was given by John Mohribsey to Ton Hvkr, but that Hyer declined the conteBt.The way in which the challenge came about was as follows :At about o'clock, as Moriu9sey waa tonverslng with Jim Kerrioan and another friend, near Whitk'sbar, beneath the grand stand, he cugh a sight of Mr.HYER standing at the bar imbibing a toddy, and forthwith he stalked towards him, and entered Into canvorflft-tion. This movement collected a large and eager crowd, which liecoied intently to the dialogue. As the majority could hear only here and there a sentence, suchas 11 Take off your coat, and fight,” ** I want to fight you,” and 411 don't want to fight,” u You have money of mine,” *c., we append the dialogue as it wai spoken, nearly verbatim :Mr. Morrissey, on confronting Hybb, asked him ttbw ho did.Mr. HYER replied,44 How are you!”Mr. Morrissey—You hold Romo money which CirRls. Schaffer, of the Gem, bet upon my light wj Li YankeeSullivan. As I won that money, I want it, and have come to get it. And if you don't give it up now, 1 am on to fight you. Are you wellT Hyer—No, I am not well : 1 have a sore leg. T have no money belonging to yon, and shall not give you any.Morri.sney charged IIyer with having maltreated one of hie friends, whoso name we could not lourn, which he denied ; upon which ilio other reiterated thecharge, accompunying it with language more forciblethan polite. He added, ki But if you nro sick, and unable to light me, 1 don't want to take any advantage of you ; but whon you are well, I want to fight you, and you are the only man in thlH world 1 do want to tight-(Great excitement among the crowd.)Hyer—You are a professional fighter, are you not 7 Morbissey—1 am, and a d—d tough one too, though 1 do *ay it myself.Hyer—Well, I am not. If you wan- to fight, there are plenty of professional fighters around hero for you to have a set-to with.More issey—No ; 1 camo hereto fight you, and you are the only man I want to fight. If you will fight mo, you will very much oblige me-by taking off your coot, and stepping out here into the field and doing It. Hyeb—No, 1 don*t want to fight; 1 am not well. Morrissey—Then if yon are sick, I don’t want’,to lake eny advantage of you. Yon have a good mauy friends her© and elsewhere, who think you can beat me; but I don’t think you can fight so well os they say that you can. Now, I think I can whip you, and I would rather fight you now than take a glass of brandy,Hyer—There are plenty of fighters here ; I am not one. MqBJUsbey—No, G—dd-—n you\ like % good meny