GOOD NEWS*FROM .TIIE NORTH WESTERN ARMY THE ENEMV REPULSED,[A dispatch of prior date to the following' supposed to contain tlie earlier ti-unsactiona of the siege, has not yet reacted the Department of War, as will appear from passages of General IlurriBOn’s letter ]Copy of a dispatch from Major Qencrat William H. Har bison, to the Secret my at Wart dated.Head Quarters. Lower Sandusky, May 13th 1813. Sir—Having ascertained that the me. my (Inpians as well at British) had entirely abandoned the neighborhood of the Rvpids, 1 left the conVmand of Camp Meigs with Gen Clay and came here last night. It is with the greatest satisfaction, I inforih von, *ir, that I have evtry reason to believe' that the loss of the Kentucky troops in ki'L on the north side of the river does not ex* ceed fifty. On the 10th and 11 inst. I eoused the ground which was the scene of , the action and its environs to be carefully «} examined, and after the most diligent « 1 search 43 bodies only of our men weke discovered--amongst thtm was the leader of the detachment Col. Dudley. No othejr officers of note fell in the action. 1 have strong reason to believe that a considerable number of the Kentuckians effected their retreat up the river to Fort Winchester General Proctor did not furnish me with a retnrn of the prisoners in his possession, although repeatedly promised, IBs retreat was a precipitate as it could properly be*, leaving a number of cannon hall, j* new elegant sling carriage for cannon, and mher valuable articles. The night before his departure two persons that were employed In the British Gun Boats (Americansin birth) deserted to us. The information they gave me was very interesting—H ey ?.ty that the Indians, of which tfc e we/e from 1600 to 2000, left the British the day before their departure in a high state of dissatisfaction, fr m the great loss which they had sustained in tho several engagements of the 5th, and the failure of the British its accomplishing their promise of taking the post at the Rapids. From the account given by these men, my opinion fa confirmed of the great superiority of the enemy which were defeated by our troops in two •allies madeonthe 3th inst* That led by Col. Miller did not exceed 350 men, and it is very certain that they defeated 200 British Regulars, 150 militia, and 4 or JDO Indians. That American Regulars (although they were raw recruits) and such men as com. pose the Pittsburg, Penn, and Petersburg, Va. Volunteers, shou d behave Well, is not to be wondered at—but that a company of millitia should maintain ita ground against four times its numbers, as did Capt. Sebres of the Kentucky, is tru y astonishing. These brave fellows were at length however entirely surrounded by Indians, and would have been onterely cut off, but for the gallantry of Lt. Gwynne of the 19th Regiment, who, with part of Captain Elliott's campany, charging the enemy and released the Kentuckians. I inclose you a list of the killed and wounded dur ng the whole eiege. It is considerably largor than I had supposed it would be whtn I last wrote to you —but it is satisfactory to know that they did not bleed uselessly— but in the course of successful exertions. The return d.*s not embrace those who fell on the N. VV. side of the Miami.You will also receive herewith a monthly return of the troops at Camp Meigs (or the last month ; the communication with the other post* being cut off, the returns wero not received. A copy of Grn. Clay’s report to me of the manner ef his executing my orders for the attach on the enemies' batteries, is likewise forwarded, by which it will be seen that my intentions were perfectly understood, and the great facil ty with which they might have been executed is apparent to every individual who witnessed the scene. Indeed the cannon might have been spiked, the carriages cut to pieces, the magazine destroyed and the retreat effected to the boates without the loss cf a man,as none were killed in taking the batteries, so complete was the surprize.