From the Memphis Appeal HIGHIY IMPORDA FROM MEXI
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The notes which are subjoined, from Gov. Shannon, our Minister to Mexico, and the Mexican Minister of Foreign Affairs, appear in the N. o. Picayune of the 29th ut., pre- ceded by the following brief review by the editors, of the previous action of the par ties. The negotiation has assumed a serious aspect, and we should not at all be surprised Ii rupture between the two nations ensued Our Government can do no less than instruct It's Representative to demand his passports:

 OUR RELATIONS WITH MEXICO.

 We have taken advantage of leisure hour 10 peruse the correspondence which has been carried on at Mexico between Governor Shannon and Senor Reion, the Mexican Min ister of Foreign Affairs, in regard to the n- vaslon of Texas. It is very evident that a crisis in the relations of the three countries In question, isnear at hand, unless perchance the civil dlssensions in which Mexico is now

 involved should terminate in the overthrow ot her present Government, or at least leave her Tn such state of exhaustion as to make any acton on her part utterly nugatory.

 The correspondence was opened by Gov. Shannon, in letter dated Oct. IA, written With clearness and vigor On the part of the Government of the United States, he enters hls formal protest against the invasion of Texas by Mexico, and then against the man. ner Tn which the invasion is ordered to be carried out. On the first point, he argues that Texas IS independent de facto and has been for eight years that she has been ac- knowledged as such by three of the great powers of the world and that, putting these considerations aside, she became indepen- dent when the constitution of 1924, under which she was separate and equal mem- Der ot the Confederation, was overthrown by force of arms. Upon that event, she fell back upon her original right distinct and independent State, and has ever since main- lalned her position against every effort of Mexico. She therefore has a right to treat Tor surrender of. territory to the United States, or annexation and ths United S.ssss