In compliance with an act of the last session a Territorial Government has been established in Florida on the principles of our system. By this act the inhabitants are secured in the full enjoyment of their rights and liberties, and to admission into the Union, with equal participation in the Government with the original States on the conditions heretofore prescribed to other Territories. By a clause in the 9th article of the treaty with Spain, by which that Territory was ceded to the United States, it is stipulated that satisfaction shall be made for the injuries, if any, which by process of law shall be established to have been suffered by the Spanish officers and individual Spanish inhabitants by the late operations of our troops in Florida. No provision having yet been made to carry that stipulation into effect, it is submitted to the consideration of Congress whether it will not be proper to vest the competent power in the district court at Pensacola, or in some tribunal to be specially organized for the purpose.

The fiscal operations of the year have been more successful than had been anticipated at the commencement of the last session of Congress.

The receipts into the Treasury during the three first quarters of the year have exceeded the sum of $14.745 millions. The payments made at the Treasury during the same period have exceeded $12.279 millions, leaving the Treasury on the 30th day of September last, including $1,168,592.24 which were in the Treasury on the first day of January last, a sum exceeding $4.128 millions.

Besides discharging all demands for the current service of the year, including the interest and reimbursement of the public debt, the 6% stock of 1796, amounting to $80,000, has been redeemed. It is estimated that, after defraying the current expenses of the present quarter and redeeming the $2 millions of 6% stock of 1820, there will remain in the Treasury on the first of January next nearly $3 millions. It is estimated that the gross amount of duties which have been secured from the first of January to the 30th of September last has exceeded $19.5 millions, and the amount for the whole year will probably not fall short of $23 millions.

Of the actual force in service under the present military establishment, the posts at which it is stationed, and the condition of each post, a report from the Secretary of War which is now communicated will give a distinct idea. By like reports the state of the Academy at West Point will be seen, as will be the progress which has been made on the fortifications along the coast and at the national armories and arsenals.

The organization of the several corps composing the Army is such as to admit its expansion to a great extent in case of emergency, the officers carrying with them all the light which they possess to the new corps to which they might be appointed.

With the organization of the staff there is equal cause to be satisfied. By the concentration of every branch with its chief in this city, in the presence of the Department, and with a grade in the chief military station to keep alive and cherish a military spirit, the greatest promptitude in the execution of orders, with the greatest economy and efficiency, are secured. The same view is taken of the Military Academy. Good order is preserved in it, and the youth are well instructed in every science connected with the great objects of the institution. They are also well trained and disciplined in the practical parts of the profession. It has been always found difficult to control the ardor inseparable from that early age in such manner as to give it a proper direction. The rights of manhood are too often claimed prematurely, in pressing which too far the respect which is due to age and the obedience necessary to a course of study and instruction in every such institution are sometimes lost sight of. The great object to be accomplished is the restraint of that ardor by such wise regulations and Government as, by directing all the energies of the youthful mind to the attainment of useful knowledge, will keep it within a just subordination and at the same time elevate it to the highest purposes. This object seems to be essentially obtained in this institution, and with great advantage to the Union.

The Military Academy forms the basis, in regard to science, on which the military establishment rests. It furnishes annually, after due examination and on the report of the academic staff, many well-informed youths to fill the vacancies which occur in the several corps of the Army, while others who retire to private life carry with them such attainments as, under the right reserved to the several States to appoint the officers and to train the militia, will enable them, by affording a wider field for selection, to promote the great object of the power vested in Congress of providing for the organizing, arming, and disciplining the militia. Thus by the mutual and harmonious cooperation of the two governments in the execution of a power divided between them, an object always to be cherished, the attainment of a great result, on which our liberties may depend, can not fail to be secured. I have to add that in proportion as our regular force is small should the instruction and discipline of the militia, the great resource on which we rely, be pushed to the utmost extent that circumstances will admit.

A report from the Secretary of the Navy will communicate the progress which has been made in the construction of vessels of war, with other interesting details respecting the actual state of the affairs of that Department. It has been found necessary for the protection of our commerce to maintain the usual squadrons on the Mediterranean, the Pacific, and along the Atlantic coast, extending the cruises of the latter into the West Indies, where piracy, organized into a system, has preyed on the commerce of every country trading thither. A cruise has also been maintained on the coast of Africa, when the season would permit, for the suppression of the slave trade, and orders have been given to the commanders of all our public ships to seize our own vessels, should they find any engaging in that trade, and to bring them in for adjudication.

In the West Indies piracy is of recent date, which may explain the cause why other powers have not combined against it. By the documents communicated it will be seen that the efforts of the United States to suppress it have had a very salutary effect. The benevolent provision of the act under which the protection has been extended alike to the commerce of other nations can not fail to be duly appreciated by them.