A correspondent of the St. Louis Rcpubhcan, wriling frofn Washington, lias tlie following : "Gen Dix has been instructed to close the negotiation pending with the Souttiorn Confoderauy for a mutual exebaoge of pii-sonor?, npon torens not vet ruado public, but understood to be based upon the Brittsh cartel oí 1814 - man for man, rank for Tank, or in proportion, and the roleased prisoners to be uoder no rostraint in taking up arms tigain. ■'Tliis is tlio first timo the Southern Oonfederaöy has boon honored by a pen and ink recognition from this oor respondent; and hia escuso for thta flagrant violution ol tho letter' and spil it in which the war is wuged by the govornment is doemed excusable Irom tho faut tho name Jeff. Davis claims for his dominions i.i betwjen lioro and Richmond, on the subject of exchange of prisoners. It is said the liicliinondit.es insiatod that the tornfoolery ol' denying them recognition as belligerents should cease, and it may now be considereü to have ceased in the future. The Richmond papers say thatthey have enongh prisonere on hand to exchange all in our posession, with suveral thousand to spare. This may ba so, but in the absence of official figures it may be safe to say Ihey ought to conie out buhiudhaud iu the swapping off. It is certaib tliey took between seven and cight thousand fi-om Gen. McClellan, which, added to fifteen hundred at J3u!l Run acd Ball's Uluff. toeother. tbreo thousand five bundred at Shiloh, and two thousand during Jackon's raid in tha ralley, will foot lip on their side the number of fiiteen thousand to offset öur hauls at Docelson, Roanoko Island, No. 10. and Carinth, whiuh, estimated by the official reporta, should rea:h over twonty-five thousand. It may be bero remarked that the returns of tho War Department of the actual number oFprisoner8 now in our pos-'sfion, Bbow that tho reports of tho n umbera taken have been exaggeratcd, and in Bpito of iho popular belief that we have a largo preponderence in numbors, it may be íotind a close ehave to release all our soldiere in tho Souüi without baggibg mere rebels.