GENERAL ATKINSON'S REPORT. HEADQUARTERS FIRST ARTILLERY CORPS, NORTH-WESTERN ARMY, Prairie du Chiens, Aug. 25, 1832. SIR:--I have the honor to report to you that I crossed the Ouisconsin on the 27th and 28th ultimo, with a select body of troops, consisting of the regulars under Colonel Taylor, four hundred in number, part of Henry's, Posey's and Alexander's brigades, amounting in all to 1,300 men, and immediately fell upon the trail of the enemy, and pursued it by a forced march, through a mountainous and difficult country, till the morning of the 2d inst., when we came up with his main body on the left bank of the Mississippi, nearly opposite the mouth of the Ioway, which we attacked, defeated and dispensed, with a loss on his part of about a hundred and fifty men killed, thirty men, women and children taken prisoners--the precise number could not be ascertained, as the greater potion was slain after being forced into the river. Our loss in killed and wounded, which is stated below, is very small in comparison with the enemy, which may be attributed to the enemy's being forced from his position by a rapid charge the commencement, and throughout the engagement the remnant of the enemy, cut up and disheartened, crossed to the opposite side of the river, and had fled into the interior, with a view, it is supposed, of joining Keokuk and Wapello's bands of Sacs and Foxes. The horses of the volunteer troops being exhausted by long marches, and the regular troops without shoes, it was not thought advisable to continue the pursuit; indeed, a stop to the further effusion of blood seemed to be called for, till it might be ascertained if the enemy would surrender. It is ascertained from our prisoners that the enemy lost in the battle of the Ouisconsin sixty-eight killed and a very large number wounded; his whole loss does not fall short of three hundred. After the battle on the Ouisconsin, those of the enemy's women and children, and some who were dismounted, attempted to make their escape by descending that river, but judicious measures being taken by Captain Loomis and Lieutenant Street, Indian Agent, thirty-two women and children and four men have been captured, and some fifteen men killed by the detachment under Lieutenant Ritner. The day after the battle on the river, I fell down with the regular troops to this place by water, and the wounded men will join us to-day. It is now my purpose to direct, Keokuk to demand a surrender of the remaining principal men of the hostile party, which, from the large number of women and children we hold prisoners, I have every reason to believe will be compiled with. Should it not, they should be pursued and subdued, a step Major-General Scott will take upon his arrival.