"In conformity with public announcement, yesterday, at about half past 3 o'clock, the Honorable DANIEL WEBSTER arrived in this city in the steamboat Swan from Philadelphia. The intense desire on the part of the citizens to give a grateful reception to this great advocate of the constitution, set the whole city in motion towards the point of debarkation, for nearly an hour before the arrival of the distinguished visitor. At the moment when the steamboat reached the pier, the assemblage had attained that degree of density and anxiety to witness the landing, that it was feared serious consequences would result. At half past 3 o'clock Mr. Webster, accompanied by Philip Hone and David B. Ogden, landed from the boat amidst the deafening cheers and plaudits of the multitude, thrice repeated, and took his seat in an open barouche provided for the occasion. The procession, consisting of several hundred citizens upon horseback, a large train of carriages and citizens, formed upon State street, and after receiving their distinguished guest, proceeded with great order up Broadway to the apartments arranged for his reception at the American Hotel. The scene presented the most gratifying spectacle. Hundreds of citizens who had been opposed to Mr. Webster in politics, now that he appeared as a private individual, came forth to demonstrate their respect for his private worth and to express their approbation of his personal character; and thousands more who appreciated his principles and political integrity, crowded around to convince him of their personal attachment, and give evidence of their approval of his public acts. The wharves, the shipping, the housetops and windows, and the streets through which the procession passed, were thronged with citizens of every occupation and degree, and loud and continued cheers greeted the great statesman at every point. There was not a greater number at the reception of General Jackson in this city, with the exception of the military, nor a greater degree of enthusiasm manifested upon that occasion, than the arrival upon our shores of Daniel Webster. At 6 o'clock in the evening, the anxious multitude began to move towards Niblo's saloon, where Mr. Webster was to be addressed by the committee of citizens delegated for that purpose, and to which it was expected he would reply. A large body of officers were upon the ground to keep the assemblage within bounds, and at a quarter past six the doors were opened, when the saloon, garden, and avenues leading thereto were instantly crowded to overflowing.