NASHNILLE, Tenn., Saturday, Dec. 10, 1864. Nashville invested by a rebel army, and that army HOOD’s, is a queer record to make, in view of the marvelously successful and brilliant results of the past Summer’s campaign. Yet the redoubtable General, who fought at Atlanta and ran away from it with his army, has lived, by the process, to fight another day. And emulous, it may be, of the fame of SHERMAN, he has come to attempt the investing of a city on his own account, strong in the belief that he will capture it. A week has passed since his forces sat down before it. It has been a time of suspense, but of no serious fear or anxiety as to the result of anything HOOD might attempt against it. Today, even, the thunder of cannon from Union guns on the surrounding hill-tops has ceased to startle the most timid, and all prospect o’ a little excitement from an attack seems to have disappeared. The Question “Why don’t he come?” is getting superceded by the other — “Where is he gone?” But the town really has been invested. It may be still, though few persons seem to know anything positively about it — that is, whether HOOD, with his main army, is now lying just around the city, or is moving away from it, to try some less hopeless task. This latter is the prevailing opinion, among the uninitiated, at least. It will soon be known how well founded it is. But the week has been a lively one exceedingly. The telegraph has given your readers the “situation” here from day to day, and what matters of interest connected with the army proper have been unfolded. I may sketch a few things observed from my own standpoint, which may be supplementary information gathered from other sources, and have for some readers an interest of their own. The importance of Nashville to the Union, and the splendor of the prize to the rebels, if HOOD could by any means capture it, every reader sees at a glance, Enormous supplies for the army had been accumulating here for months. Immense store-houses filled with provisions, with grain and hay, large quantities of coal and wood, of quartermaster, commissary and medical stores, cars and locomotives by the hundred, with the multiform machinery, all on the grandest scale, designed and adapted to carry on the various work demanded by more than 1,200 miles of military railroad — all this was a part, and only a part, of the prize of Nashville taken. To take it, would be, moreover, to liberate Tennessee from hated Federal occupancy and rule, to rally to the rebel standard hosts of Tennesseans whom necessity had forced to swear loathed fealty to the stars and Stripes; to restore to their homes, and perhaps, families, many in the rebel ranks, long weary of banishment and of the field, and in fine, to raise the drooping spirits of the Confederacy by a conquest that would go far to make amends for all the disasters of the year’s campaign! With such motives urging HOOD and his army to take Nashville, who will wonder that people here, expected at least, a most desperate effort to take it? The effort was not made, only perhaps because prepared for so fully. After the severe fight at Franklin, on the 30th November, this preparation began in earnest. The city at once became a hive of buzzing and efficient industry. Not Dido’s “tolling Tyrians” as Father has from his cloud, saw them pushing forward their infant city, evinced more enterprise and activity. The employes of the Government swarmed everywhere. Every pick, spade, axe, shovel was brought into important requisition. Breast works were thrown up, earth forts constructed, with cannon looking out from them threateningly all along the approaches to the city. Nashville was girded’ with rifle-pits almost as rapidly as fairy Puck offered to “put a girdle reund about the earth.” From the reservoir, crowning an eminence on the southern bank of the Cumberland and straight across to Fort Nagley, half a mile off, the trenches took their stern way through the University grounds, through the gardens and yards of private mansions, through all obstructions that arose in their path. Multitudinous hands seemed to finish the work, almost as soon as it was begun. The forts and stockades already built, caught the spirit of energetic preparation for a sudden emergency. Those inadequately manned or supported, received a full supply of men for all their needs, while cannon, muskets, ammunition and other warlike material were arranged promptly where their aid was demanded. Outside the defences was much Government property, which the rebels would rejoice to seize upon if not secured. This was properly cared for. Immense droves of mules, many of the animals injured by hard service and released from work for a time to recruit, were driven from their suburban retreats through the town, and placed in secure corrals within the lines. Long trains of army wagons also passed through to the like place of safety. Single regiments, encampel two or three miles without the city, came into it, and were assigned to appropriate positions, with the main army which was now arriving. As the troops of Gen. THOMAS came in, they took their designated posts, pitching chiefly on the eminences, which run all around the city, and from all of which batteries were frowning. It was a picturesque and striking spectacle to see these hills lit up by night with countless camp fires, while the roar of cannon, heard once or twice within the week, all night at intervals, was relieved by the frequent sharp crack of the picket rifles; for the rebel lines were, in a short time, erected over against our own, and not only picket firing, but brisk skirmishing, heard distinctly in the city, has been for a week an almost daily occurrence. With the bustle and noise incidental to these movements, there has been little confusion or excitement, and less fear. I have not found the first man or we man yet that showed signs of alarm at the approach of the rebels or at the prospect of a successful assault by HOOD. Every one seems calmly confident of the safety of the place, and without uneasiness as to the result of the situation. Skirmishing between the lines is frequent. On Wednesday our skirmishers were advanced in considerable numbers, and over, a wide circuit, to discover the actual strength and position. A strong line started directly in front of the University grounds, advancing in plain sight of us, for more than half a mile, between the Lebanon and Murfreesboro pikes, till it drew the rebels’ fire. For half an hour the rattle of musketry was so sharp that one might fancy a pretty serious engagement going on. Our line fell back gradually, the rebels proving themselves to be in force at that point. The damage done to private property between the lines is estimated as high already as half a million of dollars. Several fine dwellings have been shelled and burned. The Orphan Asylum still stands, but its fencing and barns have disappeared. The house of Mrs. A.V. BROWN, widow of the late Postmaster-General, situated three miles from the city on the Franklin pike, has become the headquarters of Gen. CHEATHAM, the family having sought an asylum several days ago at a friend’s house within our lines. This house, a fine mansion of the olden time, and famous for the free hearted hospitality of its recent occupants, is reported shelled and demolished. Suburban Nashville is noted for its elegant residences; those lying along the Franklin pike being specially attractive. Should HOOD be really determined to tarry where he is, till forced away, as he doubtless will be presently, or should he undertake an assault upon the city in earnest, the record of devastation will find a terrible addition to what the rebellion has already written up, against this once beautiful place. One of the present serious effects of the city’s being encircled by the rebel army, is the cutting off the market supply from the surrounding country. This, during the Summer and Fall, had been considerable, the various articles furnished by the farmers, particularly vegetables, not bearing a higher price than in the Western markets. The prices have already begun to run up, with the prospect of swift, advance, unless the proper relief comes. This will appear from a recent order of the Provost-Marshal, Capt. BROOKE, fixing the following schedule of prices, all parties to be punished who transcend the prescribed Standard: “Wood $15 ??? cord; beef 20c. ??? ???utton 18c.; Irish potatoes $3 ??? bushel; sweet potatoes $4 ??? bushel; turnips $2 50 ??? bushel; cabbages 50c. ??? head; butter 80c. ??? lb.; onions $4 ??? bushel; flour $15 ??? barrel; milk 15c. ??? quart.” Some of these prices seem moderate enough for the times. But without this military order, the prices would have doubled for most of these articles, and a large number of the population must have suffered distress, as many no doubt do even now. There is an immense population, requiring to be fed here the present Winter. What with hosts of contrabands, refugees and people whom the war has deprived of all employment, sweeping them clean of their worldly effects, subsistence would be hard enough under the most favorable circumstances. HOOD and his army fixed here will prove an added ingredient of terrible bitterness to their cup. This cup, however, they may not be forced much longer to drink. The battle of Franklin, fought on the 30th ult., proves to have resulted in heavier loss to our troops than at the first reports. It appears now that our whole loss in killed and wounded amounts to 2.165, and of this number 110 were officers. It was a terrific conflict truly, as all reports concur in representing it. Great as our loss was, it was but one-third that of the rebels, whose fierce charges on our open field were again and again repulsed. A large number of our wounded were but slightly wounded, and will soon be fit to return to duty. Of the officers, fifty-two have come in to the officers’ hospital here, but one of whom. Major R.S. BOWEN. One Hundreth I???inois Volunteers, has died. A list of those wounded here I append for insertion, if the requisite room can be found for it in your columns. C.V.S.