Saml L Mitchill transmits to Mr Jefferson, in obedience to the Tammany Society of New york, an Address, which contains the respectful Sentiments of that respectable Body of Citizens toward the chief magistrate of the union. He also lays before the President, a letter from a Committee of that incorporated association to him, wherein an earnest Hope is expressed, that their Political Father may vouchsafe to become an Honorary Member of their patriotic band.—For the better understanding this business S. L. M. assures the President that the Tammany Society of Newyork consists of the vigorous part of the Republican Population, warmly attached to democratic principles, and uniformly friendly to the present administration of the National government.—Whatever notice shall be taken of their address and request, if forwarded to S L. M. will be duly sent to the Addressors at New york. In the mean time, he begs leave to renew the assurances of his most hearty respect.