The Report of Mr. Conrad, Secretary of war, is brief and clearly written. The whole number of men at present enrolled in the U. S. Army is 12,326, including officers. Of these, 7796 are under orders for Texas, New Mexico, California, and Oregon, thus leaving but 4530 in all the rest of the States and Territories. The Secretary, in view of the recent alarming incursions of the Indians, on the borders of Texas and New Mexico, urges an addition to the military establishment of the country. A history is given of the operations of infantry in New Mexico since last August. Mr. Conrad expresses the opinion, that the only description of troops to put an end to these savage forays, is cavalry. He says the Indians in that part of the country are excellent horsemen, and well skilled in the art of war. To extirpate them, he calls upon Congress to raise one or more regiments of mounted men. In this connection, moreover, he thinks that if the inhabitants of New Mexico were organized into a kind of protective militia of their own, much would be done to preserve the lives and property of those Territories, independently of Government relief. At all events the experiment, he says, is worth trying. The operations of that portion of the army employed in Oregon are next recapitulated, as are also those engaged in the recent troubles with the Indians in Florida. The Secretary entertains no apprehension of any farther disturbance there. A large portion of the troops are withdrawn from the State, but sufficient are left to meet any emergency which may possibly arise. The number of the Indians there, we are told, is very small, probably not more than one hundred, who, however, occasion annoyance to the whites; and these the most efficient measures will be taken to remove. It is recommended that a small force be sent against the Sioux tribe of Indians, in order to compel obedience to the Chippewa treaty, which they have broken, and which the United States is bound to see respected. He also refers to the reports of the officers appointed to examine the Pacific Coasts of the United States, in order to select suitable sites for fortifications and naval depots there. Captain Stansbury's Expedition to the Great Salt Lake, the Secretary says, is understood to be completed, and a report of his operations is supposed to be now on its way home. Other Expeditions, similar to this, are also referred to. The Secretary renews the recommendation of his predecessor for the formation of a retired list of officers of the Army. An asylum for disabled and destitute soldiers is also urged upon the attention of Congress. The financial estimates for this Department, for the ensuing year, do not appear quite so favorable as could be wished. The sum required for the next fiscal year will considerably exceed the aggregate for the current year—an increase caused, among other things, by the act of last Congress increasing the rank and file of all the companies serving on the Western frontier—paying nearly double all the officers and men in California and Oregon—and by increased expenditures in the Quartermaster's department. The Secretary points out several departments of the service where principles of economy may be introduced to advantage, and to them he calls the earnest and immediate attention of Congress.

The Report of Mr. Graham, Secretary of the Navy, is also brief, and gives an account of the six different squadrons into which the naval force in commission is divided. The Secretary remarks that occasional instances of British interference with vessels bearing our flag on the African coast have occurred, but that in each case explanations and apologies have been made to our officers on that station, and the reports thereof transmitted to the Government. The existing personnel of the Navy embraces 68 captains, 97 commanders, 327 lieutenants, 111 surgeons, 43 assistant surgeons, 64 pursers, 24 chaplains, 12 professors of mathematics, 11 masters in the line of promotion, 464 passed and other midshipmen, and 7500 petty officers, seamen, landsmen, boys, etc. The Secretary says that this system of officers is unshapely and disproportioned, there being great disparity between the head and the subordinate parts, and he recommends a great reduction in the three highest grades. The report discusses other questions respecting the organization and distribution of the service. The Secretary notices the improvements going on in the Navy Yards in New York and other places; states that he has invited proposals for the construction of a Dry Dock in the Pacific; says that the stores on hand in the various yards amount to $6,500,000. A reduction of the number of yards is discussed. The Secretary says that our flag has been respected on every sea, and that the interests of commerce have been secure under its protection. The Navy consists of 7 ships of the line, 1 razee, 12 frigates, 21 sloops of war, 4 brigs, 2 schooners, 6 steam frigates, 3 steamers of the first class, 6 steamers of less than first class, and 5 store ships. The ships in commission are one razee, 6 frigates, 15 sloops of war, 4 brigs, 2 schooners (coast survey), 2 steam frigates, 1 steamer of the first class, 3 less than first class, 3 ships of the line as receiving ships, 1 steamer do., and one sloop do. Four ships of the line and two frigates are on the stocks in process of construction, but the work suspended. Besides these, there are the mail steamships on the New York and Liverpool and New York and Chagres lines, liable to naval duty in case of necessity.

The Report of Mr. Hall, the Postmaster General, gives a gratifying picture of the operations of the Post Office Department. The number of mail routes within the United States at the close of the fiscal year in June last, not including California and Oregon, was 5590: the aggregate length of such routes was 178,672 miles, and the number of contractors employed thereon, 4,760. The annual transportation of the mails on these routes was 46,541,423 miles, at an annual cost of $2,724,436, making the average cost about five cents and eight and a half mills per mile. The increase in the number of inland mail routes during the year was 649; the increase in the length of mail routes was 10,969 miles; and the annual transportation of the year exceeded that of the previous year by 3,997,354 miles, at an increased cost of $342,440. There were, on the 30th of June last, five foreign mail routes, of the aggregate length of 15,079 miles, and the annual price of the transportation thereon, payable by this Department, was $264,506; being an increase of $8814 on the cost of the preceding year. The increase of our mail service for the last fiscal year, over the year preceding, was about 9.4 per cent., and the increase in the total cost was about 12.7 per cent. The number of Postmasters appointed during the year ending June 30, 1850, was 6518. Of that number 2600 were appointed to fill vacancies occasioned by resignations; 233 to fill vacancies occasioned by the decease of the previous incumbents; 562 on a change of the sites of the offices for which they were appointed; 1444 on the removal of their predecessors, and 1979 were appointed on the establishment of new offices. The whole number of post offices in the United States at the end of that year was 18,417. There were 1679 post offices established, and 309 discontinued during the year.

The gross revenue of the Department for the year was as follows:

From letter postage, including foreign postage, and stamps sold$4,575,663 86
From newspapers and pamphlets919,485 94
From fines38 00
From miscellaneous items3,048 66
From receipts on acc't of dead letters1,748 40
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$5,499,984 86
Appropriation for franked matter200,000 00
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Total$5,699,984 86
From this sum should be deducted the amount received during the year for British postages, which are payable to that Government, under the postal convention of December, 1848147,013 38
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Leaving for the gross revenue of the year$5,552,971 48
Total expenditures5,212,953 43
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Excess of receipts$340,018 05

The expenditures of the current year are estimated at $6,019,809, the increase consisting in the additional service provided for, and in the increased rates sometimes paid on the new contracts. No reliable estimate of receipts from postage for the year can be made. The increase for the year ending June 30, 1847, was 11.27 per cent.; that for the year ending June 30, 1848, only 7.43 per cent.; and that for the year ending June 30, 1849, 14.20 per cent.; being an average, for the three years, of 10.96 per cent.; and the increase for the year ending June 30, 1850, excluding the balance in favor of Great Britain was 14.62 per cent. It is believed that the increase for the current year will be at least 11 per cent. over the receipts of last year: and this will give an aggregate revenue of $6,166,616, an excess of $146,807 over the estimated expenditures. The conveyance of foreign correspondence has become an important branch of the service. The means provided are 16 large steamships in actual service, with four more to be added under existing contracts. Efforts are in progress to arrange with foreign countries for the interchange of mails and for the uninterrupted transit of our correspondence in the mails of those countries to the countries beyond. The mail service in California and Oregon is still in an unsettled state: some suggestions are made for improving its details. The Postmaster General recommends a considerable reduction in the rates of postage: he advises that the inland letter postage be reduced to three cents, the single letter, when pre-paid, and be fixed at the uniform rate of five cents when not pre-paid; and also, that the Postmaster General be required to reduce this pre-paid rate to two cents the single letter, whenever it shall be ascertained that the revenues of the Department, after the reductions now recommended, shall have exceeded its expenditures by more than five per cent. for two consecutive fiscal years. He also recommends that twenty cents the single letter, be charged on all correspondence to and from the Pacific coast, South America, the Eastern Continent and its islands, and points beyond either, and ten cents the single letter on all other sea-going letters, without the superaddition of inland postage; and that the provision which imposes an additional half cent postage upon newspapers, sent more than one hundred miles, and out of the State where they are mailed, be repealed, so as to leave the uniform inland postage on newspapers, sent to subscribers, from the office of publication, at one cent each. The postage upon pamphlets, periodicals, and other printed matter (except newspapers), Mr. Hall thinks, may be simplified and somewhat reduced, with advantage to the Department. Two cents for the pamphlet or periodical of the weight of two ounces or less, and one cent for every additional ounce or fraction of an ounce, is recommended as the inland rate upon all pamphlets, periodicals, and other printed matter; instead of the present rate of two and a half cents for the first ounce, and one cent for every additional ounce, or fraction of an ounce. For the sea-going charge on such matters, and on newspapers, twice the inland rate to and from the points to which it is proposed that the letter postage shall be ten cents, and four times the inland rate where the letter rate is twenty cents, is deemed a just and proper rate. The reductions recommended on printed matter are considerably less than those upon letters: and the reason of this is found in the fact that the rates of postage upon printed matter are now exceedingly low, when compared with the letter rates. The average postage on letters is estimated at about three dollars and sixteen cents per pound, and on newspapers or pamphlets at about sixteen cents per pound. After the reductions proposed, the average inland postage on letters will be about $2 50 per pound when not prepaid, and $1 50 per pound when pre-paid.

The reduction recommended will probably reduce the revenue of the Department for the first three or four years; but at the end of that period its revenues under the reduced rates will probably again equal its expenditures. To meet the temporary deficiency, additional appropriations from the Treasury will probably be required unless Congress should abolish the franking privilege, which is held to be the privilege of the constituent rather than of the representative. It is recommended, however, that if the franking privilege, and the privilege now accorded to newspaper proprietors of receiving exchange newspapers free of postage, be continued, the expense be paid out of the public Treasury. The present laws provide for a semi-monthly mail from New York and New Orleans to Chagres, and for only a monthly mail from that point to San Francisco. The defect has been partially supplied by an arrangement with the mail contractors, but the action of Congress on the subject is still required.

The report of Mr. Stuart, Secretary of the Department of the Interior, presents a variety of interesting information concerning the various subjects which come under his supervision. The expenses of the department for the year have been $5,403,372; those for the next year are estimated at $7,132,043. The report enters at some length into an explanation of the various items of this increase. The whole number of persons on the pension rolls of the United States is 19,758; the whole number who have drawn pensions during the first two quarters of the present year is 13,079. The whole amount expended for pensions during the year is estimated at $1,400,000. The number of land warrants issued for Revolutionary service is 12,588; and for the war of 1812, 28,978. The number of claims presented for service in the Mexican war is 81,373, and for scrip in lieu of land, 3332, making a total of 84,705. The number of claimants under the general Bounty Land Law of the last session of Congress is estimated at 250,000. The sales of Public Lands during the first three quarters of 1850 have amounted to 869,082 acres; the amount sold in 1849 was 1,329,902. The amount located by Mexican bounty land warrants during three quarters of the present year was 1,520,120, against 3,405,520, during the whole of last year. The aggregate amount disposed of in three quarters of 1850 was 2,815,366—in 1849 it was 5,184,410. The revenue derived from the sale of public lands has averaged about a million and a quarter of dollars per annum, for the last fifty years, above all expenses. The extension of our Land System over our possessions on the Pacific is strongly urged; and a commission is suggested to adjudicate on all questions of disputed titles to land in California. Mr. Stuart recommends the sale of the mineral lands, in fee simple to the highest bidder at public auction—in lots small enough to afford persons in moderate circumstances the opportunity of being bidders. The annexation of Texas and our treaty with Mexico, have added about 124,000 Indians to our population; many of them are fierce in their disposition and predatory in their habits. Further legislation for the protection of our people from them has become necessary. The Secretary urges the necessity of a highway to the Pacific; whether a railway, a plank road, or a turnpike would be most expedient, he says, can only be determined after a careful survey of the country and its resources shall have been made. He suggests the propriety of authorizing an immediate survey. The establishment of an Agricultural Bureau is urged, and statements are made of the steps taken in securing the census returns.

Several of the State Legislatures are now in session, or have been during the past month. In several of them action has been taken upon the general question of Slavery. In Vermont a bill was passed for the protection of persons who may be claimed within that state as fugitive slaves. This bill provides (1.) That it shall be the duty of the State's attorneys within the several counties "to use all lawful means to protect, defend, and cause to be discharged" every person arrested or claimed as a fugitive slave; (2.) The application of any State's attorney in due form shall be sufficient authority for any one of the Judges of the Supreme Court, or any Circuit Judge, to authorize the issuing a writ of habeas corpus, which shall be made returnable to the supreme or county court when in session, and in vacation before any of the judges aforesaid; (3.) That it shall be the duty of all judicial and executive officers in the State, whenever they shall have reason to believe that any inhabitant of the State is about to be arrested as a fugitive slave, to give notice thereof to the State's attorneys in their respective counties; (4.) That whenever the writ of habeas corpus is granted in vacation, if upon the hearing of the same before any of the judges, the person arrested and claimed as a fugitive slave shall not be discharged, he shall be entitled to an appeal to the next stated term of the county court, on furnishing such bail and within such time as the judge granting the writ shall deem reasonable and proper; (5.) That the court to which such appeal is taken, or any other court to which a writ of habeas corpus in behalf of any such alleged fugitive slave is made returnable, shall, on application, allow and direct a trial by jury on all questions of fact in issue between the parties, and the costs thereof shall be chargeable to the State. The bill passed both branches of the Legislature with very little discussion, and was approved by the Governor, Nov. 13, 1850.

The Virginia Legislature assembled on the 2d of December. The Message of Governor Floyd closes with some emphatic comments on the Compromise measures of Congress. The action of the last session on the subject, the Governor says, has placed the Union in the most momentous and difficult crisis through which it has ever passed. Some of its enactments have produced a feeling of deep and bitter dissatisfaction at the South; while the law for the recovery of fugitive slaves has been met with a reception at the North little, if at all, short of open rebellion and utter defiance. This state of things, the Governor says, has grown out of an "unwarrantable interference on the part of Congress with the subject of slavery, and is another proof of the great danger which must ever follow any attempt on the part of that body to transcend the clear, well-defined limits set by the Constitution to govern and control their action." The action of Congress, it is held, has been grossly injurious to the South, for of the whole domain acquired from Mexico, not a foot is left, worth having, for the occupation of the slaveholder. Nothing ought to reconcile the South to this action, but the hope that it may settle forever all agitation of the question of slavery. But if peace and quiet can be thereby restored, if the Constitution can be respected and the Union maintained, these sacrifices, great as they are, may well be regarded as light in comparison with the objects attained. But should this expectation prove fallacious, and the slavery agitation be renewed, it will furnish, the Governor says, "proof, convincing and conclusive, of that fixed and settled hostility to slavery on the part of the North which should and will satisfy every reasonable man that peace between us is impossible; and then a necessity stronger than all law, the necessity of self-preservation, will demand at our hands a separation from those who use the relationship of brotherhood only for the purpose of inflicting upon us the worst acts of malignant hostility." The supineness of the South upon this subject is very warmly censured, and the hostility evinced in the Northern States toward the fugitive slave law is referred to as among the indications that peace and harmony have not been restored. Virginia, and all the slaveholding states, he thinks, "can and ought, calmly and explicitly to declare that the repeal of the fugitive slave law, or any essential modification of it, is a virtual repeal of the Union. The faithful execution of the law is the only means now left by which the Union can be preserved with honor to ourselves and peace to the country. Such a declaration on the part of the South will give strength and great moral weight to the conservative patriots at the North, now struggling for the Constitution and the supremacy of the laws, who are, in truth, fighting the battle of the Union, in the bosom of the non-slaveholding States. If, however, no consideration of prudence or patriotism can restrain the majority from the non-slaveholding States in their headlong career of usurpation and wrong, and should they repeal or essentially modify the fugitive slave law, the most prompt and decisive action 'will be required at your hands'. In either event, I would earnestly recommend that a Convention of the people be called at once to take into consideration the mode and measure of redress, as well as the means of providing for our future security and peace."