.i;v York, May 21. - Tho followüig Í8 the official noticc to Mr. Grooley of tho Liberal Re'pubhcan noruinatión : Oixcixxatt, May '3. lii'Ait Snt - Tho Xatioual Convention of the Liberal ltcpublicang of the Unit:d States lmv instracted tbs andersigned, tho Preaideht, Vioe-President and Hecrotarios of tho Oouvention, to ini'orm you that you have been nominated as the candidato of tho Libera] Republioans for bh Presidenoy of tho United States. Wo alo aubmit to you the address and resolutiona unanimoosly adopted by the Convention. Bo pleased to siguify tousyour acceptnnce ot' the platform und noinination, and boliuvo us, Very truly your, C. 8CHÜBZ, President, GEO. W. JULIÁN, Viee-President, Wk. E. MoLE j JNO. G. DAVIDSÜN, -Secretarios. ,1. H MIODES, ) Ilon. Hornee Grceley, New York City. Tiio l'ollowing is Mr. Greoluy's reply : New Youk, May 20. GEinXEMÈH - I have ohosen nut to acknowledgo your letter of tho 3d inst. until I eoulil luiiiu how tho work of your ronviüition was received in all parts of out great country, and judge whothor that Work was approvüd and ratifled by the mtiss tf our follow citizcus. Thoirroroonse lias from day to day reacbed me tlmmgh tclegrnms, letters and comments of Journaliste independent of official patronago and indifferent to the smiles and frowns of power. Tho number and character of tho unconstrained, unpurchased and unsolicitod utterances satisfy me that tho movomont wliioh found expression at Cincinnati has received the stamp of publio approval and been hailed by a majoiity of our countrymon as a harbingor of a botter day for the llcpublic. I do not misintorpret tliis npproval as espocially complimentary to mysolf, nor oven to tho chivalroüsand justlyestoemed gen tleman with whose name I thank your Convention for associating mine. I receive and woloomo it as a spontaneous and desorved tributo to that admirable platform of principies, wherein your Convention so tcrsely, so lucidly, so forcibly sets forth tlio convictions whicb. iinpelled and thoso purposos which guided its courso - a platform which, casting bohini] it the wreek and rubbish of worn out o intentions, of bygone fends, embodifis in fit and fcw words the needs and aspirations of to-day. Though thousands. stand rearly to condo'.nn your every act, hardly a syllablo o) criticism or cavil has beiüi aimed at your Ilatform, of which the substanco may bo fairly epitomized aR follows : First, alj political rights and frauchises which huvi been acquired throiigh our lato bloody convulsión mut and shail bo guarauteed, maintained, enjoyed and rospected evermoro ; second, all political rights and franchisos whioh liiivy been lost through thai convnlsiou should and must bo promptly restored and ro-established, so tliat thcif sball be henceforth no prosoribcd clase and no disfranehised casto withiu tho Umita of our Union, whose lonp: estrangod people hall reunito and fraterniza upon tbo broad basis of universal amnesty with ïinpartial sufFrago ; ihircL, that subject to our solemn constitiitional obligaÖon to maintain the equal rights of al] citizens our policy should aim nt loca' self-government, and not centralization that tho oivil authority should be su premo over the military : tbat the writ o: habea eorptts should bo joalously uplieh as ti safeguard of personal freedom ; that tlio individual citizen should enjoy thi largeat liberty consistent wifli public ordpr, and that there shall bü no Federa! subdivisión of the intentál policy of the soveral States and municipalities, bui that each shall bo left froe to onforue the rights and promote the wcll being of its inhabitauts by such means as the judgment8 of its o wn poople shall prescribe fowrth, there shall be a real and not nierely assimilated reform in t'io' civil Lía;vjf.i siüiii; tnaVfno cniof disponser of its vas offieiü.1 patriotism shaU be ehièlded from the main temptátion to U3o his power selfishly by a rule forbidding anc precluding lus re-election ; Jif't, V.iai the rttising of revenuc, whethor by tarif jr Qtherwiso, shall bo recogniaod and treutcd as the jx;ople's immediate busito be shaped and directod by them tjjrough their reprosentatives in Con. whose aotion thereon the Presideui must neither overrulo by his veto, attompt to díctate, nor presume to p !y bostowing ofïieo only on thoatí wiici agree with him or withdrawing it those who do not ; sicth, that the public must l-.e Bacredly reserve pation and ocquisition by oultivjitors, and not sqnandered on the projectors oí railroads, for whioh our people have no present need, and the premature coiiytrnction of which is plungins uu into doeper and deoperabyss i of foraign iiidebtedness ; ., that the achievomont of these grand purpoecs of universal boneficence Landsought at the hands of all who approve thara, irrespectivo of past affiliations; cig'ilh, that the public i'aith must at nll hazards be maintained and the national credit preserved ; nintk, that the patriotío devotednoss and inestimable services of our féllow oitizona who as soldiers or sailors upheld the flag and maintained the unity ot' the Republio shail ever bo gratcfully remembered and honorably requited. These propositions, so ably and forcibly presenta! in the platform of your Convention, have alroady fixed the at tention and comruanded the assent of a large number of our oountrymen, who jusiiy fulopt thcin, as I. di, is tiu; basis oí u i rué beiielieent natioual Constitución, of a rem oval from jealousies, strifes and hates which have po longer an adequate motive, or even plausible pretext, into an a tmosphere of peace, f raternity and mutual good will. In vain do tho drill sergeants of tho docayiug órganizations Bourish menaciagly their trunoheons and angrily insi.st that the files shall bo nlosed and straightened. In vain do the whippers-in of partios onco vital, becauso rooted in tho vital deeds of tho hour, protest iststraying and bolting, denounco men in no wise their inferiors as traitors and renega les, aud threaten them with infamy and ruin. I uu confident that tho Amerioan people have already mado your cause their own, fully resolved that their brave hearts. and strong anus shall bear it on to triumph. In the fnith and with tho distinct undorstanding that if I 1 .shaU be tho President, not of a party, but of tho wholo poople, I accept your nomination, in tho conlident trust that the masses of our cóuntrymen, North and South, are enger to clasp hands aeross tlui bloody chasm which has too long divided them, forgotting that they have been ouomies in thu joyful oonsoious bhat thoy are und must hencuforth remain brethren. i Yours, gratefully, (Signed) ÏIOÜACK GBEELEY. Tollón. Cari Sehurz, President; Hon. . W. Julián, Vioe-Presidsnt, and Í Messrs. Win. E. MoXiean, Jno. G. ' son, and J. H. lihodcs, .Soeretaries of ( the National Convention of tho ' al Bepublioans of the United Status.