lt;jol. uarrara,—in an men.Buch was the dashing energy of the pursuit, that, not withe tending the rebels had thirty six hours the start, they were over* taken four miles north of Somerset.Qen. Carter, in command of 800 mounted men had reached Buok Creek, twelve miles from Somerset, when General Gilmore retched him with hist body guard and the 7th Ohio Cavalry, increasing the number to 1,200, with whioh they double-quicked until within reaoh of the enemy’s re£ guard. The skirmishing then commenoed, Generals Gilmore and Carter with Wool-foid and the body guard in the advanoe. As often as the rebels made a stand they were dislodged with shell. 'Within twelve miles of Somerset, at Dutton’s Hill, in a very strong position, the rebels drew up in foroe and planted their batteries; and here, about 12 o’elook, oommenoed the real battle. Oar line of battle was drawn up, with the bat* teries in the center, supported by the 7th Cavalry—Rankle, with a detachment of the 44th and 45th on the left, and Wool* ford’s on the right. The preliminary artillery fight lasted one and a half hours, and resulted in the dismounting of three of their guns.