The exploring expedition sailed from Norfolk on the 19th of August last, and information has been received of its safe arrival at the island of Madeira. The best spirit animates the officers and crews, and there is every reason to anticipate from its efforts results beneficial to commerce and honorable to the nation.

It will also be seen that no reduction of the force now in commission is contemplated. The unsettled state of a portion of South America renders it indispensable that our commerce should receive protection in that quarter; the vast and increasing interests embarked in the trade of the Indian and China seas, in the whale fisheries of the Pacific Ocean, and in the Gulf of Mexico require equal attention to their safety, and a small squadron may be employed to great advantage on our Atlantic coast in meeting sudden demands for the reenforcement of other stations, in aiding merchant vessels in distress, in affording active service to an additional number of officers, and in visiting the different ports of the United States, an accurate knowledge of which is obviously of the highest importance.

The attention of Congress is respectfully called to that portion of the report recommending an increase in the number of smaller vessels, and to other suggestions contained in that document. The rapid increase and wide expansion of our commerce, which is every day seeking new avenues of profitable adventure; the absolute necessity of a naval force for its protection precisely in the degree of its extension; a due regard to the national rights and honor; the recollection of its former exploits, and the anticipation of its future triumphs whenever opportunity presents itself, which we may rightfully indulge from the experience of the past--all seem to point to the Navy as a most efficient arm of our national defense and a proper object of legislative encouragement.

The progress and condition of the Post-Office Department will be seen by reference to the report of the Postmaster-General. The extent of post-roads covered by mail contracts is stated to be 134,818 miles, and the annual transportation upon them 34,580,202 miles. The number of post-offices in the United States is 12,553, and rapidly increasing. The gross revenue for the year ending on the 30th day of June last was $4,262,145; the accruing expenditures, $4,680,068; excess of expenditures, $417,923. This has been made up out of the surplus previously on hand. The cash on hand on the 1st instant was $314,068. The revenue for the year ending June 30, 1838, was $161,540 more than that for the year ending June 30, 1837. The expenditures of the Department had been graduated upon the anticipation of a largely increased revenue. A moderate curtailment of mail service consequently became necessary, and has been effected, to shield the Department against the danger of embarrassment. Its revenue is now improving, and it will soon resume its onward course in the march of improvement.

Your particular attention is requested to so much of the Postmaster-Generals report as relates to the transportation of the mails upon railroads. The laws on that subject do not seem adequate to secure that service, now become almost essential to the public interests, and at the same time protect the Department from combinations and unreasonable demands.

Nor can I too earnestly request your attention to the necessity of providing a more secure building for this Department. The danger of destruction to which its important books and papers are continually exposed, as well from the highly combustible character of the building occupied as from that of others in the vicinity, calls loudly for prompt action.

Your attention is again earnestly invited to the suggestions and recommendations submitted at the last session in respect to the District of Columbia.

I feel it my duty also to bring to your notice certain proceedings at law which have recently been prosecuted in this District in the name of the United States, on the relation of Messrs. Stockton & Stokes, of the State of Maryland, against the Postmaster-General, and which have resulted in the payment of money out of the National Treasury, for the first time since the establishment of the Government, by judicial compulsion exercised by the common-law writ of mandamus issued by the circuit court of this District.

The facts of the case and the grounds of the proceedings will be found fully stated in the report of the decision, and any additional information which you may desire will be supplied by the proper Department. No interference in the particular case is contemplated. The money has been paid, the claims of the prosecutors have been satisfied, and the whole subject, so far as they are concerned, is finally disposed of; but it is on the supposition that the case may be regarded as an authoritative exposition of the law as it now stands that I have thought it necessary to present it to your consideration.

The object of the application to the circuit court was to compel the Postmaster-General to carry into effect an award made by the Solicitor of the Treasury, under a special act of Congress for the settlement of certain claims of the relators on the Post-Office Department, which award the Postmaster-General declined to execute in full until he should receive further legislative direction on the subject. If the duty imposed on the Postmaster-General by that law was to be regarded as one of an official nature, belonging to his office as a branch of the executive, then it is obvious that the constitutional competency of the judiciary to direct and control him in its discharge was necessarily drawn in question; and if the duty so imposed on the Postmaster-General was to be considered as merely ministerial, and not executive, it yet remained to be shown that the circuit court of this District had authority to interfere by mandamus, such a power having never before been asserted or claimed by that court. With a view to the settlement of these important questions, the judgment of the circuit court was carried by a writ of error to the Supreme Court of the United States. In the opinion of that tribunal the duty imposed on the Postmaster-General was not an official executive duty, but one of a merely ministerial nature. The grave constitutional questions which had been discussed were therefore excluded from the decision of the case, the court, indeed, expressly admitting that with powers and duties properly belonging to the executive no other department can interfere by the writ of mandamus; and the question therefore resolved itself into this: Has Congress conferred upon the circuit court of this District the power to issue such a writ to an officer of the General Government commanding him to perform a ministerial act? A majority of the court have decided that it has, but have rounded their decision upon a process of reasoning which in my judgment renders further legislative provision indispensable to the public interests and the equal administration of justice.