Why should the House of Representatives desire to encroach on the other departments of the Government? Their rightful powers are ample for every legitimate purpose. They are the impeaching body. In their legislative capacity it is their most wise and wholesome prerogative to institute rigid examinations into the manner in which all departments of the Government are conducted, with a view to reform abuses, to promote economy, and to improve every branch of the administration. Should they find reason to believe, in the course of their examinations, that any grave offence had been committed by the President or any officer of the Government, rendering it proper, in their judgment, to resort to impeachment, their course would be plain. They would then transfer the question from their legislative to their accusatory jurisdiction, and take care that in all the preliminary judicial proceedings, preparatory to the vote of articles of impeachment, the accused should enjoy the benefit of cross-examining the witnesses, and all the other safeguards with which the Constitution surrounds every American citizen. If, in a legislative investigation, it should appear that the public interest required the removal of any officer of the Government, no President has ever existed who, after giving him a fair hearing, would hesitate to apply the remedy. This I take to be the ancient and well-established practice. An adherence to it will best promote the harmony and the dignity of the intercourse between the coördinate branches of the Government, and render us all more respectable both in the eyes of our own countrymen and of foreign nations. JAMES BUCHANAN. WASHINGTON, June 22, 1860. This last message was referred to a select committee, with instructions to report at the next session. But no report was ever made, and legislative action on the doings of the “Covode Committee” thus came to an end. But in the country the materials for calumniating the President continued to be used as they were originally designed to be. It will be interesting to know something more of the feelings of Mr. Buchanan on the subject, as expressed in a private letter to the editor and proprietor of a great New York journal. [TO JAMES GORDON BENNETT, ESQ.] (Private and Confidential.) WASHINGTON, June 18th, 1860. MR DEAR SIR:—