CHARLESTON, S.C. June 3.- Southern Indians.- The Cherokee Council assembled at Red Hill, on the 13th ult. to take into consideration the propriety of accepting the offer of the General Government, recently made them for their claims to lands on this side of the Mississippi, was generally attended on the part of the intelligent portion of the people, and very numerously attended by the common Indians. They remained in Council several days, upon this all important subject, and have at length dispersed without agreeing to the liberal proposition of the United States Government, which should have been by all means so very desirable to them. This result is attributed, by the Auraria (Geo.) Herald, from which these particulars are taken, to a Chief named John Ross, who, it would appear, possesses much influence over the Indians, and is very unfavorable to the General Government, and to the people of Georgia in particular. Many of the most enlightened Chiefs are said to have advocated the acceptance of the proposition, and it is to be regretted that the 'Sons of the Forest' should have suffered themselves to be swayed by one who had more probably acted from personal motives, rather than the advantage of those whom he was advising.

The Milledgeville Federal Union states that the Indians have only postponed making a treaty, until the meeting of Congress, and to prevent any unnecessary delay after that time, an exploring party is to visit the Arkansas country during the present summer, and remarks, we 'believe that our Indian controversies are rapidly approaching an harmonious and satisfactory close.'___ Nat. Banner.