Another struggle letween the Iwo seclions of the Democratie party f this statfl has been had, and this time the Barnbnrners are yictorfc At the Byracuse Convention the Old Hunkers were in the ascendani and had every thing ti thÃ¼ir liking - made out its ticket whhh was defeated, the sima ns Henry (Jlay wns defenteil, for Ihe want of roles. ThDornburners were, however, in the majority in the Legislatore, nnd jusl before the a.ijnuri)ment ]at week of ;hat body, a caucus, in aceord.'inee with "Democratie usnges;" was held, nu Address nnd Resolulions were put furth, in wliich the incendiarisin" of VVilmot was endorse.! nnd spnt ahe..d as goud Demociaiic doctrine. Tliis l-.urts t!ie feelings of the OM IIiinkers,and is calling out the remainder of their pent up wrath. "No Union with Old Huiikers" seems to be a mottu ol the narnlmmers, and was siibstanlially so stated by Col. Young. The probabilitv is that two addresses wil bo pul forlh fmbodying the sentiments of the two scc'ions of tl. e party, and ihe leaders will go down to Ihe rank nnd file with them. At ihe lime of writing we have not ?een the OÃd Hunker Address,tut we are iold that it will be out with as many names ns Croswell, Stryker & Co. can get to it. That notable Roman, John Strvker, was on hand, nnd leut to the Editor of the Argns all the power of his exuerience in caucus management, but the RadicÃ¡is oul-managed them and were victorious. We give a few passnges from tlie Adrlress of the RadicÃ¡is, which by the way is the Addressof the party, since it is the nddress put forlh by n regularly called LegiÃ¼lative cnucus, in which boih sectionstook a part. Ofcourse, the Barnburners are all devotion to Mr. Polk's "conquer a peace" war, and go for territory as indemnity for the cost ofit. - But taking 11 for granted ihat there is tn be an accession of territory,they go on to siy, The conlemplated acquisition by our Government ofterritory in Mexico, and the actual occupa' ion thereof by our armies, have again forced this subject upon the attention ofCongress of 1846, the f'IIowing condition was nttached to ihe bilÃ to provide for, or facilÃtate the cession of, lerritory from Mexico - " Provided that in terri'ory thus to be ncquired," there shall be neilher slavey nor involuntary servitude, otherwise than in the punisliment of crimes, whereof ihe pnrly shall have been dulv convicted. This provisiÃ³n, ihough it failed in the SenatP, wbs adopted in the popular branch of the National Legisiatuie, by a vote which ncluded all the delÃ©gales of New York and of the mass of all of the free States. In contemplaron of this provisiÃ³n and of the action of Congress on it, in the succeeding session, your ropresentatives in this Legislatura adQpted the followiugresolution.s, by the nearly unanimous vote of both houses: Resolved, That f any territory is hereafter acquired by the United Siates, or annexed thereto, the act by which such territory is ncquiced or annexed, whatever such act may be, should containan unnlterahle fundamental articleor provisiÃ³n, wliereby slavery or involuntary servitude, except as a punishment for crime, shall be forever excluded from :he territory acquired or annexed. (We oniit all the resolutions but one, as tlie}' have previously appeared in our columns.) The instruction and request of the State Legislnture, thus uitered, wna obeyed nnd acceded to !y all the represetitative ol N. Y. in Cuugress, with but two e.ceptionj. To the doctrine thus avowed by the Lfgislaiure of this Stale, and Ihus with commendable fiJelity carried out by her representativos, her penale slill Ã¼rmly ndi.ere. Afier having seen the power of Congress, in ihe first days of the Constitution, wielded to remove Slavery from soil where it had already obtained a foothold, and at a later period recognising i but resisiine its progresa, they will not consent that it shall now become the nclive or passive agent, for the extensiÃ³n of this daneful Ã¯ristititution over territories where it has now no existenoe, and throughout which it has once been abolished. In this attitude this State has been t;u.-t:iined by the voice of ih State3 of Pennsylvania, Oliio, Michigan, New Htampsliire and Maine, expressed in their legislatures nna convenlions, and by the universa! sentiment. This determinaron of the Free States accompanied by the more stern andeffective reasoning of the ballot-box, may it is to be hoped reach, and arrest the attention at least of our Southern brethren, prompttd as it is by no unkind feeÃ¼ng to them but dictaied from a sene of ju-tice to the rights of the (ree laborers oithe South, as well as of the North, with whose interests the co-exis'ence of slavery Ls incom.iatble. The Address and Uesolutions, howevcr, are strongly tingeci wilh hypocrisy, ns ihe radicÃ¡is in thetn profess altaohment to Mr. Polk, and bestow fainl praise upor. his adininist-ation. Tliey cannot be sincera in ihis and still be opposed (o the grand object of his elevalion and the leading characieristic of his adm'nistration, wliich 3 the extensiÃ³n of slavery. They knoiv Mr. Polk was elected because he was more available in the South. They know ihat but for slavery and its 1 yi'.i we should liavo had no war with Mexico ; and that this war is waged for the purpo.Ã¯e of exiending glavery. To praise him, theref re, is (o endorse the vpry thing which has made him notable; luid to oppose him in his extension-of'?' ' Ã" ' oppOW hÃ¯ni in the jrand objecl orhis elevnlion to power. - ' This i iiconsistency of the radicÃ¡is - an neonsibtency by wliich thev are made on tho one liand tu stnnd by James K. Polk, and 'jn the other to be arrayed against the : crowning nel of his ndrnfriislratioh - is lo be uocounted for on ihe ground of yolicij. It s n-'t popular to Opose the war, so they oppose ihe object of it. Besides ilipy are in for James K. Polk by their previous acts - by their votes nnd the rndorsenient of the niliatorv steps of the war - and it requiivs so i.e moral courage ajid some reul contrilion, now to stand up erect in oosition to the murderous crusade nguinsi Mexico. But llieir professions of regard tu Mr. Polk and their endorsement of the war will on))1 act on the masses. They cannot secure for the Wilinut men the good will of ;he Piesidetit, his smilfs or his patronng1, so long as their influence is employed in extending fiecdom over soil which t' e slave power is seeking t curse with slavery. Th:s manner of suppoiting the Presiden reminds one of the aid which conserva tism brought to tl;e support of MÃ¡rtir Van Duren when itarrayed Iself n hos'J lity to liis measures ! From such suppor no doubt Van Buren prayed to be deliver ed, and from the "aid and comfori" o the VVilinot men we think Mr. Polk wil derive no great satisfaclion. One thing is certain, the O!d Hunkers are greatlv pained bÃ©cause they cannot br ing out the Radicnls direct ngainst the President, anc agninst the war; fur th-n they coqli claim all the patriotism and have all the offices. From the Resolutions, we copy two one on Slavery, and one suggestive o valuable reform in the matter of Execu tive patronage : Resolved, That the patronage of the. general govornment has grown lo propor tions so vast, peivading and complicnted as to endanger the freedom of election;md the purity of the public press, anc should therefore be subjected to tlie seve rest proceÃs of retrenchment and reform Resolved) That all impututions upon the Democracy of this state, come from what quarter they may, that its patriotic mnsses are in favor of the extensiÃ³n o slavery into territories now free, are bok nventions of open adversaries or secre foes; that we regard such extensiÃ³n a derogatury to the principies of natura justice, subversive of the riglits and inter estsof the free laboring classes of all the states and at war wilh the poÃ¼cy establish ed by the fathers of the Republic, in the ordinance of 1787, for the governmen of tlie norlhwestern terrilory ; a policy the wisdom of which has been proved anc illustrated by ihe unprecedented grtwtl and prosperity of the noble states non of the Ohio river, and by the intelligence patrioÃ¼sm and energy of their jopula tion. Let the Censtitution of the Unite Siates be so amended as to make the grea proportion of the offices-of-appointmen elective, and the motives to servility ant doughfaceism would be removed. A slaveholding President has incalculabl power in the patronage whicli his offic confeis ; and from this power great na tinnal time-serving parties derive the ele rnent of adhesiÃ³n and perpetuity. Office by the thousand are to bedispensed on th issue of the Presidential conflict; and fo this cause tens of thousands of eager effic expeclants are raised up to canvass for Presidential aspirant. And on all nearl balanced questions of public importance ilie President can buy up Congressme enough to turn the scale. We certainly go for this branch of ccnstitutional reform with all the zeal of a Barnburner. There is another point on whieh th RadicÃ¡is and Ã¼lu Hunkers are at issue that is, on the monner of electing dele gales to the National Convention. The RadicÃ¡is art fiar eleciing ota State Con vention assembled for that purpose ; aii( the Oonservatives at the Syracuse Con vention adopted ihe district syslem - ndop led it, ihe RadicÃ¡is siy, without instruc tion from the nmsses who alone have ihe power lo set aside an eslablished usnge of the party. The Radical members o1 the Legiblature have. therefbre, called a Siaie Convention to be held in this city on the 16ih of February, to elect delÃ©gales to the National Convention. - Whether the OÃd Hunkers will come into t as a legitÃmate Democratie State Convention is doubiful. They probably will not, for the reason, first, that to do so would be a virtual acknowledgement of 'rregularity in the adoption of the district syslem at the Syracuse Convention ; and second, because they have not numerical sirength sufÃ¯Ã¯cient to carry the Convention. So at the next great National gathering of the party will have two se'.ts of delegates from the Empire Siatedemanding sents, and asking the endorsement of the National Conveniion. And then sighis wÃ¼l be seen, and the concentrated Democratie wisdom of the Nation will be brought to Vear to manage the impracticables andstill pacify Old Hunkerisrn. P. S. The OÃd Hunker Address was published in the Argns last Salurday with the Ã±ames of 28 members of the Legislnture appended to il. The Radical Address had 37 names. Simultaneotisly with the appearance of the Hunker Address appeared in the Argus a ca!l for a Democratie State Convention, to be held :n Albany on the 26th of Janunry, and signed by the State Committee appoinled by the Syracuse Convention. So tbe party bas two State Conventions in prospect, onc called Uy ihe RadicÃ¡is to be held in ihiscily tlie ICth of February, and the other by ihe Hunkers in Albaoy in January. Thus divicled we can see no wnj' of uiiii'iig tlie sunderel frag'npnts bul bv the nomination of llenry Llay.