From the New Orleans Picaynne of Sunday.

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 ing with later advices fr'nn Vera Cruz. We are in debled Captain Patiers on for Vera Cruz dates o Ihe Huh insiInl-the schooner sailed on the l2tl, which is ten days iater than our previous ahsices.

 McI1co hds NOT decfaTed tpar againSf the U. States bu the official paper, Fl Diario del Gotierno uf the 3d inst. announces that is in possession of movements on the part of the Government of wnr like character, which Il is constrained ta withhold from the public, secreSy IS the soul of military ope- iatioHsj but that journal adds, that il that the speedy aud sucetsSfuI issue of these opaafons will eiieve lhe pnblic curiosity regard Io ihem

 The papers of the capital and of Vera Cruz are occupied almost exclusively with ihe subject of nexaIlon. There are not wanting those who insist that there IS no alternative left to Mexico to pre-. serve untarnshed her honor but war. The writers make the distinction that though, from the necessity of Ihe case, the acknowledgment of the ndepende nct ofrexas might not be incompatible with national honor, the annexation (dgrtgoeiOH) of that depart meni to d foreign country IS fragrant Outrage.- The logic of IhIs Is not obvious ii might be- They go 10 say that Il IS no longer an open ques tion; that however they may have been distracted by civil diSren ihe present government Is bound by the pledges ol peyIous administrations; and tha the protests against annexatIon, made many months since, should be followed up to avoid natlonai ht,n alon in the eyes of the world, and the proceeding. of the United States Congress. sanctioned by ,h, Executive be insisted upon as tacit declaratoH q war. The Mexican Congress has moi yet screwet up its courage 10 assume the responsibility 0t thi | position.

 l On the 3rd inst. Senor Cuevas, the Minister b Forpign Affairs, addressed to the Chambers a long and general memorial apperiaining tO his depart ment. We have not seen it but II is represented a, d cautious and guarded exposition of tle topics upol | which it touches but bI the liberal papers ii Is deemed enIrel, loo tame and pacific in it's tone, al though heargues that annexation should inesitabl, bring on war tle places strong apparent conf dence m the interference Of European pow CTS ! uh nI indS udeHf may, he trusts, oppose the further enargeun of States territory. The more high spirited editors buke him for these sentiments, and insist that nc people can maintain an honorable, distinct naisna existence when relying upon foreign powers for i', protection; that Mexico should appeal Ut once |, arms, trusting nothing to diplomacy, (which is F, swayed bs European instead oi American interests -and ,hat as her only hope ot resisting the ultI mate entire absorption ui her ierritery by tie An | glo. Saxuns, she should now take her stand aH, l fight, and If compelled to succumb at least do s with honor.

 | A large portion of the Secretary's yoluminou memorial is coupled with the presentation of ihe affairs oI the departments. They more interest ing to MeHicans than they conld be To our readers $ gSestions are madeiIn re- Il Io'the admnsirat oI O. different btarches of ihe public service which are said to show much sagdcity.

 The SigIO ol the 4tn nsi., contains a latter iron | Mir. Shannon io the Mexican Minister of Foreg Relations in reply to the official note of Senor Cue | between the two countries. This note, and d circu lar addressed hy the Mexican Cabinet to the Minls ter oi France, Spain and England, we laid before o, readers in Thursday's edition. We will no, give Mir. Shannon's reply which has under gone tw uanslati lis, first into apanish and now again n | Englisi-and also reJoinder from Senor Cuevas It appears to that Mir. shannon is not pun suing dignfed course, m pressing Il correspondence upo l the Mexican Guyeruaien after the publication of th documents. of which the following are ,he sequel:

 UNITED STATES LEGATIoN,1 | March 3Isi, lS+5

 The undersigned, Envo, Extraordinary, &c., 0 i the United States, has the honor oi acknow edgin the receipt of his Excellency's, SenOr Cutyas, Min ,sier of Foreign Relations, Gc note of he 28h 0 March, announcing that llie Congress of the United States has sanctioned the annexation of Texas to i | eirltoly; that ihe Mexican Minister al Washington had terminated his official relai ions, and protested agaius, the sni act of Ie Congress and Go, ernnen of the United States, and that d omaic ieiation between the two countries could not be continued. 1 The liberal and honorable sentiments eniertainr, by the actual Government of Mexico, had induced the un ersigned To hope that the differences whicl exist between the two Governments could be arranged amicably upoa terms just and honorable 10 both. ] would appear, however, from the note of his Exec lency Senor Cuevas, that Mexico declines To adjus these differences m this manner, and thus pl esers, 1 the peace 0t the TWO countries.

 | The undersigned can assure his Excellency. Seno Cuevas. that his Mir. Shannon's) Government en terlans the lvelies desire to cultivate amicahe lalog with that of Mexico; and here he will i'm prove tlIis opportunity 10 repeat that which he Ina | before communicated to the Government of Mexico to wit: that ihe United States has adopted the measure of annexation in any spirit oi hostility to- wards Mexico, and that the United Slaies | ious To settle all questions which may grow out Q ihis measure, including that of boundaries, in term | the most jtisl and liberal

 | Having offered the olive branch of peace, an, manifested a sincere desire to arrange these ques lions amIcaby and upon principles just and honura l ble to both Governments, the United States iay done whatever is in their power 10 preserve thu ! friendly relations between them, and il now remaIn for Mexico to decide whether they shall be continued whether lhe peace oi the two co, ries shall b. broken by conflict equally injurious io both, an' which give satisfaction only 10 the enemies | civil liberty and epublcan institutions.

 The undersigned will pass over in silence the charge nude against his Gov, rnnlen of having viola ted the treaty of friendship with Mexico Ih right of Texas to cede the whole or part of he terrtory 10 the Unitee States, and the right of th United States To accept such cession, have ulread been amply yindicaed repeatedly.

 The undersigned has received no ofhcial comnu nicalion as To ihe action of hls Government m re gard to the Annexation of Texas To the Union; ne .ertheess, he cann4t doubt, from the tenor Of hl personal spondence, that the measure has bee pas sed by Congress and approved by the President He expects daily despatches from his Government with special instructions upon this subject and be fore taking any further steps, has resolved 10 awai their arrival.

 The undersigned has the honor, &c.,,

 WILSON SHANNON, Minister, &c.