Independonce, Jnly 1G. Tho mail (rom New Mexico, witli dates to tho '2d inst., arrived thid evoning. The iiows from Santa Fe is of no importance. On the 8th ir.st., Mr. Thompson, who resides at Ash Creek, in the neighbor hood of Pa nee Fork discovered, aslie supposed, soino bufifaloes, orponies, ap. proacbing the ranch, and the man he had employed, wfaoso name waa John Cunningham, went out for the puipose of secing what thoy were. 31 r. Thompson soon alter heard a noise, and upon looking di?covered Cunningham running towarda the house pursuod by three indiana. The Indiana shot three arrows into him, and ju.st as he reaohed the house feil dead. Thompson ran tothehouso and firud three shots from a window at them, but without effect. Tho Indiana then closed upon the house and set firo to it. Thompson made bis ay out, and having two guns loadcd, firod on them ar.d made his esoape. As he was loaving be hoard tho report of a gun. Next day hc went back and found the dead body of a man by the name of Cliristian Krouso, who had been murdcred by the same Indians. The dead bodius were decently buried bv tho commanding officer at Pawnee Fork. The Indians took all the elotbing off tho dead men and calped them, Krouse had been in the erapioy of (J;ip. Scott, and was making his way to Missouri when killed. Thore is no news of any battle with indiana by the troops who aro in pursuit of ttiem. We had a fine rain here to'day.