The most significant and most creditable celebration ever held in Washington has just transpired. A good ruler has been followed from his home to the Capitol by a grand cortege, worthy of the memory and of the nation's power. As description must do injustice to the extent of the display, so must criticism fail to sufficiently commend its perfect tastefulness, Rarely has a Republican assemblage been so orderly. The funeral of Mr. Lincoln is something to be remembered for a _cycle_. It caps all eulogy upon his life and services, and was, without exception, the most representative, spontaneous, and remarkable testimonial ever rendered to the remains of an American citizen. The night before the funeral showed the probable character of the cortege. At Willard's alone four hundred applications by telegraph for beds were refused. As many as six thousand persons spent Tuesday night in the streets, in depots and in outbuildings. The population of the city this morning was not far short of a hundred thousand, and of these as many at thirty thousand walked in procession with Mr. Lincoln's ashes. All orders of folks were at hand. The country adjacent sent in hay-wagons, donkey-carts, dearborns. All who could slip away from the army came to town, and every attainable section of the Union forwarded mourners. At no time in his life had Mr. Lincoln so many to throng about him as in this hour, when he is powerless to do any one a service. For once in history, office-seekers were disinterested, and contractors and hangers-on human. These came, for this time only, to the capital of the republic without an axe to grind or a curiosity to subserve; respect and grief were all their motive. This day was shown that the great public heart beats unselfish and reverent, even after a dynasty of plunder and war. The arrangements for the funeral were made by Mr. Harrington, Assistant-Secretary of the Treasury, who was beset by applicants for tickets. The number of these were reduced to six hundred, the clergy getting sixty and the press twenty. I was among the first to pass the White House guards and enter the building.