DOUGLAS ON LINCOLN. – Mr. Douglas is reported as having recently said, in a speech at New Orleans that Mr. Lincoln, from what would be his helpless position as President, was rather to be pitied than feared. We are inclined to think so too, and that Mr. Douglas has occasion to congratulate himself that the late election has at least relived him of the cares and [burdens] of the White House, against all contingencies of the future, to the end of his natural life. When a man is done with this White House infatuation he becomes a philosopher, and Mr. Douglas beings to talk in that way. We next expect to hear that he is writing for the New York Ledger.