The Cabinet was in regular session to-day. Admiral Porter's Vicksburgh dispatch was received by Secretary Welles, and read to the President. The news immediately spread throughout the city, creating intense and joyous excitement. Flags were displayed from all the Departments, and crowds assembled with cheers. Secretary Stanton issued an order for a salute of one hundred guns.

The fall of Vicksburgh, conjointly with the Gettysburgh successes, is regarded as the turning point in the war. The President and high officials express a determination that the campaign shall not slacken off in consequences, but be carried on with renewed vigor. This sentiment is urged upon them by Messrs. Hamlin, Wilson, Chandler, Washburne and other prominent loyalists now in town.

The President gratulates himself on his inflexible resistance to the efforts once made to induce him to remove Gen. Grant. He always believed in Grant's genius and energy and is now rewarded for his decision in his favor. Hon. Elihu Washburne, Grant's nearest personal friend, who defended him last Winter In the House, is overjoyed at the result of the siege.

At 8 P. M., a crowd assembled in front of the National Hotel and marched up Pennsylvania avenue, headed by the Marine Band, to the executive Mansion, and serenaded, and enthusiastically cheered the President, with repeated cheers for Gens. Grant, Meade, Rosecrans, the Armies of the Union, etc. The President appeared at the window, amid loud cheers, and said

Fellow citizens: I am very glad indeed to see you tonight and yet I will not say I thank you for the call, but I do most sincerely thank Almighty God for the occasion on which you have called. (Cheers.) How long ago is it? 80 odd years, since on the 4th of July for the first time in the history of the world a nation by its representatives assembled and declared as a self-evident truth that all men are created equal. (Cheers.) That was the birthday of the United States of America. Since then the 4th of July has had several very peculiar recognitions. The two most distinguished men in the framing and support of the Declaration were Thomas Jefferson and John Adams, the one having framed it and the other sustained it the most forcibly in debate, the only two of the fifty-five who sustained it being elected President of the United States. Precisely fifty years after they put their hands to the paper, it pleased Almighty God to take both from this stage of action. This indeed was an extraordinary and remarkable event in our history. Another President five years after was called from the stage of existence on the same day and month of the year. And now on this last 4th of July, just passed, when we have a gigantic rebellion, at the bottom of which is an effort to overthrow the principle that all men are created equal, we have the surrender of a most powerful position and an army on that day (cheers), and not only have we gained a victory here, but in a succession of battles in Pennsylvania near to us. Through three days so rapidly fought that they might be called one great battle, on the 1st, 2d, and 3d of July, and on the 4th the cohorts of those who opposed the declaration that all men are equal, turned tail and ran. (Long continued cheers.) Gentlemen this is a glorious theme and the occasion for a speech, but I am prepared to make one mostly of the occasion. I would like to speak in terms of praise due to the many brave officers and soldiers who have fought in the cause of the Union and liberties of their country from the beginning of the war. These are trying occasions not only in success, but for the want of success. I dislike to mention the name of one single officer lest I might do wrong to those I might forget. The recent events bring up glorious names and particularly prominent ones, but these I will not mention. Having said this much I will now take the music.

At the close of the President's speech the crowd proceeded to the War Department and serenaded and cheered Mr. Stanton. The Secretary appeared on the steps and made a short, stirring speech. He said that something under two years ago, on receipt of an offer of conditional surrender from a rebel army, the General in command replied I propose to move immediately on your works." The same General again moved on the enemy's works, and the result is Vicksburgh. He paid many flattering compliments to Gen. Grant, also to Gen. Meade. He concluded with saying, "The same strategy, the same bravery, the same indomitable zeal, which have driven the enemy from the banks of the Mississippi, and the banks of the Susquehanna, will, in a very short period, drive every armed rebel from the field, and every Coppperhead to his den.

The Secretary next introduced Major-Gen. Hal-

leck, who was received with applause. He alluded to the time when he first took command of the Western army, two years ago. Since then Grant had been under his command. He had fought fifteen battles and won fifteen victories. He was in Vicksburgh on the Fourth, he will be in Port Hudson to-morrow or next day. {Renewed cheering.]

After Gen. Halleck finished speaking, he was suc- ceeded by Messrs. Wilkinson, Wilson and Wash- burne who gave an account of Gen. Grant's career; and the Jim Lane branch from the main crowd called on Mr. Seward, who spoke some minutes.

Mr. Seward said, that in his efforts to crush the re- bellion, he had abandoned party and friends, and had taken Andrew Johnson as his file tender. Speaking of his devotion to his country, he added that no human being could ever make him the recipient of any favor from the nation after the close of the rebellion. He had determined that, for one, he would not be swerved from his path by the lust for power, under which patriotism was so blighted.

REJOICING IN NEW-YORK.

Albany, T

uesday, July 7.

By order of the Adjutant-General, two salutes of thirty-four guns each were fired to-day—one in honor of our victory in Pennsylvania, and the other for the fall of Vicksburgh. To-night there is an impromptu demonstration by the citizens. Guns are exploding, bells ringing, and with music and fireworks, the demonstration will be kept up until a late hour by an immense gathering of both sexes.

Syracuse, T

uesday, July 7.

A grand impromptu celebration is taking place here, to-night, in honor of our victories. There is a mass-meeting in Hanover square. A salute of 100 guns is thundering. All the bells of the city are ringing. There is a parade by the Davis Guards, and fireworks, bonfires, and illuminations flame in all the principal streets. Such a scene of enthusiasm and rejoicing was never known.

Utica, T

uesday, July 7.

The fall of Vicksburgh has been celebrated here by the ringing of bells, firing of cannon, and every display of popular joy.

REJOICING IN NEW-JERSEY.

Burlington, T

uesday, July 7.

The glorious news of the surrender of Vicksburgh was received here amid the ringing of the church bells and a salute of one hundred guns. The most intense enthusiasm prevails. The Union League rooms and several private residences are illuminated.

REJOICING IN MASSACHUSETTS.

Boston, T

uesday, July 7.

The news of the surrender of Vicksburgh appeared to cause more joyous excitement in Boston than any previous event of the war. Bells were rung, cheers given, and congratulations exchanged generally.

At Newburyport the bells were rung, and a salute of one hundred guns fired.

Dispatches from many quarters describe similar demonstrations of joy and gratitude for the glorious result.

REJOICING IN PHILADELPHIA.

Philadelphia, T

uesday, July 7—2 P. M.

The State House bell is ringing a joyful peal over the capture of Vicksburgh.

All the fire-bells in the city are also now ringing, by direction of the Mayor, sent through the police telegraph.

Philadelphia, T

uesday, July 7.

The newspaper offices are illuminated this even- ing. The Ledger building has stars placed along the entire front. The North American has the word "Victory." The Bulletin and other offices are taste- fully decorated in honor of the victory. Numerous private dwellings and other edifices are illuminated.

REJOICING IN NEW-HAVEN.

New Haven, Conn., T

uesday, July 7.

There is great rejoicing in this city over the news of the capture of Vicksburgh.

A National salute is now being fired upon the Public Square by direction of the Mayor.