Indian Wars-- Rumors have been circulated of a defeat by the Indians in Missouri of the troops under Gen Gaines. The following letter from the General himself furnishes the latest and most authentic account of the operations in that quarter.

Extract of a letter from Gen. E. P. Gaines, dated Rock Island 20th June, 1831.

'I have visited the Rock River villages with a view to ascertain in the localities and as far as possible the disposition of the Indians. They confirmed me in the opinion I had previously formed, that whatever may be their feelings of hostility, they are resolved to abstain from the use of their tomahawks and fire arms except in self defence. But few of their warriors were to be seen-their women and children and their old men appeared anxious, and at first somewhat confused, but none attempted to run off. Having previously notified their chiefs that I would have nothing more to say to them, unless they should desire to inform me of their intention to move forthwith, as I had directed them; I did not speak to them, though within fifty yards of many of them. I had with me on board the steam boat some artillery and two companies of Infantry. Their village is immediately on Rock River ' so situated that I could from the steam boat destroy all their bark houses (the only kind of houses they have) in a few minutes, with the force now with me-probably without the loss of a man. But I am resolved to abstain from firing a shot without some bloodshed, or some manifest attempt to shed blood, on the part of the Indians. I have already induced nearly one third of them to cross the Mississippi to their own land. The residue, however, say, as the friendly chiefs report, that they never will move, and what is very uncommon, their women urge their hostile husbands to fight rather than to move and thus to abandon their homes. Should the appearance of Governor Reynolds' mounted men fail to move them--their chiefs will then be arrested and kept in confinement until disposed of by the civil authorities, and the others will be landed on the opposite bank of the Mississippi and notified that if they return they will be punished. The reports of other tribes having engaged to assist this band in defending themselves against us, are entitled to but little credit. Several other tribes, such as the Winnebagoes, Pottawattomies, and Kickapoos, have been invited by these Sacks to assist them, but I cannot positively ascertain that more than two hundred have actually joined, and it is very doubtful whether these will remain true to their offending allies. I was assured by Gov. Reynolds in his last letter that he would be here on the 19th or 20th. I therefore look for him momently.'