The Democratic National Convention, for the nomination of candidates for the coming canvass, met at Baltimore on the 1st of June, and was organized by the election of Hon. JOHN W. DAVIS, of Indiana, President. The number of delegates present was 288, and a rule was adopted requiring a vote of two-thirds (192) for a nomination. Unsuccessful ballotings were had for four days, and it was not until the forty-ninth ballot that General FRANKLIN PIERCE, of New Hampshire, received the nomination. Upon the forty-eighth ballot he received 55 votes, the remainder being divided among Messrs. Cass, Buchanan, Douglass, and Marcy:--upon the next trial he received 282 votes. Hon. WILLIAM R. KING, of Alabama, was then nominated for Vice President. A series of resolutions was adopted, rehearsing the leading principles of the Democratic party, and declaring resistance to "all attempts at renewing in Congress, or out of it, the agitation of the slavery question under whatever shape or color the attempt may be made"--and also a determination to "abide by, and adhere to, a faithful execution of the acts known as the Compromise measures settled by the last Congress--the act reclaiming fugitives from service or labor included." The Convention adjourned on the 5th. Mr. Webster, being upon a brief visit to his place of residence, accepted an invitation of the citizens of Boston to meet them at Faneuil Hall, on the 22d of May, when he made a brief address. He spoke of the pleasure which it always gave him to meet the people of Boston--of the astonishing progress and prosperity of that city, and of the many motives her citizens had to labor strenuously for her advancement. He spoke also of the general nature and functions of government, and of the many causes which the people of this country have to reverence and cherish the institutions bequeathed to them by their fathers.