The fo'.lowing letter, which is from the i. O. Picayune, gives fuller information if the new revolution : Pcnsacola, Jan. 31, 1846. The Somers arriyed from Vera Cruz o-day. Sho brings ndvices from Vera uz of the 30th Janunry, nnd as late as ho 17th from the city of Mexico. Lt. White, of the Somers, wu.sbearer of desmtches to our Ministor in Mexico, and eft the capital in company with Mr. Sliiell on the 17th of January. The President's message was eonvey?d to Mexico by Mr. White about th 12th of January, and was immediately translated in the principal journals without comment of any kind. Information was receivcd by privato ttdvicÃ¨s from Mexico, the day aftor Mr. White left, that Gen. Arista had arrived at San Luis Potosi and declared in favor of the former order of things, and invited all to join him in putting down the revolutionists and those who would destroy the peace of the country. lt was added that Arista had takon Tampico, and levied an additional duty of 62 cents to support his troops. This intelligfince is without doubt authentic. Gen. Arista's disaffection toward Paredeawas very clearly indicated in his official letteis of the 24lh of December, publishcd on the 8th January in Mexico. Sinco then, various official declarations from the northern departments have been pubÃ¼shed, indicatinga determined opposition to the r6volutionary movements of Paredes. The Santa Anna party is growing stronger every day in Vera Cruz. It is confidently asserted thnt if he were to make his appearance at any time, he would be supported by an imjnediate pronuncinmento. It is thought that the revolutionary government will not, therefore, venture to wenken their force on the seaboardby scnding any military or naval detachmenls against the rebellious Yucatanos, Information has been receired from nine departments, whose garrison and military posts have declared in favor of Gen. Paredes, viz : - San Luis PotosÃ, Mexico, Vera Cruz, Guanajuato, Oaxaca, Jalisco, Queretaro, Michoacan and Puebla. The revolutionists had nowhere met with any armed resistance, andtheboast of Paredes, in his inaugural address to tho republic, was fully supported, M that his enter prise had not cost the nation a drop of blood nor a single sigh." Information had been received in Mexico that the French government had disavowed the course pursued by Baron Aloye do Cyprey.