From The South-western Army

[We extract the following letter from the Rev. Mr. Day to W. S. Mayxard, Esq., of this city.] Jacksox, Teni)., Dec. 4, 18G2. Most of the army here, when I left, are now on the front in the advance, with Gen. Grant, sowe 15 or 20 miles below Holly Sprints, Our army ia duily on the advance and ihe enemy is steadily falling back towards Jackson, Miss., whero, it is thought, they will risk a general en gagenient. Our Mississippi flotilla, under Gen. McClernand, is nearly ready to start from Golumbus down the river towards its destination, supposed to be Yieksburg, at which point Gen. Grant will either meet our rivor army, or divert the rebel' fofce from that place by threirtening theai from tho rear, say from sonie point near Jackson, Mias. Such ia supposed to be the programme; although it ia only a supposition, as the government, very wisely, has learned to keep itfl own war-plun of operations, as well as all otlier Cubinot secrete. A great, tliough gradual, change of public sentiment, in favor of the Union, has been steadily manifesting itself in this part of Tennessee. Slave ownei'8 here all seem to adir;it that the ruin ol the nstitution 3 a foregone event in the future, and cifVso Houth Carolina for tho event so suro to come to pass more than they do the a.dïninistration. Could their cursea con demn South Carolina to the condiüon of the citiea of the plain,- Sodom, Admah and Zeboirn,- tho Palmetto State would, long ere this, have been a black, pitchy Iake, liko tho Dead Sea, instead of r.n abode for men and a place for plauting cotton aüd raising rico. L3C " '"0." D the L'wier of tliis city, adviscs the Republicana not to commit suicide by re-clecting Zack Cuan dler to the Senate, and nominates without naming, Dr. Tappan- though Buz Buggcsts that Gov. Fki.cii " received a numbcr of votes " at the timo uamcd - for that positiou, " '7!3'; hnsí-pokcn too late.