[From (he .Mis-ioari Republican.1THE WAR IN WESTERN ARKANSAS.Tho Armr of (lie Frontier 'Water line I r IKorasH m tbe Arkansas Ulver•-■Tile Trip Over Boston axoun-(uins—•Defenses in front of Van B»»-ren—-Brilliant Camirr Charfc—Ocrupaiion of tlie Cltf^tcnmbodts Taken—Two Day* ilicro anil there* about*—Exprei«lon« of Union Sentiment—Brilliant Close of General Ilium** Campaign—matters and Things*—Prices and Prospects In Van Btireti) Ac., Ac.Van Buhkn, Ark., Dec. 30, 18G2.It is doubtless some time since your correspondence has been dated from this place.— I'liat such is now the case, is owing to the occupation of this country’ by the Army of the Frontier. The main incidents of this brilliant and successful movement—the forced march from Cave HiJJ—the passage of Boston Mountains—the capture of the outposts, defenses and defenders of Van Boren—the terrible and exciting cavalry charge in two columns along twelve miles of road to the city—the stars and strips again waving from the Liberty Polo i*i the public square—the capture of the steamboats, and thcsu salient points, arc doubtless before you. The details are what you want.Thursday which was Christmas, we had orders to be ready to march Saturday, the 28th, with six days’ rations, and a jieck ofcorn to each horse. ' What the secret design of Gen. Blunt, was, nobody knew. The general impression was that the army was to move Kastwanlly, where forage was more abundant.And so successfully was the secret kept, that far in the Boston Mountains high officers in the army were looking for the forks in the road that would head from Cane Hill to White Kiver. They were soon undeceived. The road led up and down rocky hills, through gorges of immense length; along mountain sides, whore toppling crags hang above, and.rattling cascades disturb the silence below; across mountain torrents, icy cold and waist deep ; hut no halt or rest till the mountains were left behind us, and the broad valley of the Arkansas lay spread before us.' This was at the juncture with the “Wire road,*’so called—the old stage route via of Fayetteville to Fort Smith. Sunday morning, ■ the 28tli, at five o'clock, we were again on the march, the columns of General Herron and General Blunt having united. The cavalry, three thousand strong, was in the advance, with several mountain howitzers; then followed the artillery,in the rear. About tenthe infantry beingmeat seemed on foot. The infantry thronged the roads leading from the city, and the artillery limbered up and drove away. The cavalry was sad tiled‘but remained m the streets till dark, when they were again ordered to quarters, to he ready for the inarch at day. light. The captured rebel train and all the wagons that could be procured, were loaded with the most valuable stores, the boats at the levee were dismantled, and .at 8 o’clock the flames, kindled under Gen. Blunt’s orders by Stockton’s battery men, consumed them. Wo now learn that, the line of march is the back track, and at ten this morning we are. to start on the winding way and recross the Boston mountains.It is well ascertained that all of Hindman’s army except a small portion, have gone down the river, on the other side, and are 65 miles below. Their stores at Fort Smith, they entirely destroyed. Xo demonstration was made by our army on Fort Smith. Gunboats are needed for tbe purpose of thoroughly taking and holding such places as this,1 especially where rivers are to be crossed in the face of strong enemies well posted at advantageous points.The same accounts of Ilindmand’s cruelty and unpopularity are told here that are current everywhere, lie has ordered to be shot thirteen men for telling this truth, that he left his dead unburied at Prairie Grove He has been shot at by his own men often. Ilis body guard is a full regiment, yet he lives in constant dread for his life. Gen. Sle.n (killed at Prairie Grove,) was buried here with great ceremonies. Our appearance was a perfect surprise to everybody, the first notice being from the retreating enemy, in their flight through the city. The blacks swarmed around our camps, their mouths distended, and the ivory showing like a row of piano keys .on each countenance. As our columns are marching out, they fall in the rear, on foot, in old break down carts, and in every sort of conveyance. which they can press iulo service.The market prices hero show the distress caused by the war. Coffee is absolutely not to’be had ; flour is $15 n hundred : salt is $25 a bushel; whisky is $50 !•» $30 a gallon : calico is $4 a yard; women’s shoes are $13. and I men’s boots $50 a pair. wood i- $10 to $12a cord ; tea is $12 a pound, and butter $2.— From this specimen you can judet* the cost »•: a decent livelihood. There is no gold and .-.liver to be bail. Confederate note-, Arkansas State warrants and dim plasters form the currency.Among the boat- burned were tho Van Bu-: Irt c1 1