Death of Col. Lowe—Pursuit of the Retreating Rebels.

Pilot Knob, Oct. 22. [Special to the St. Louis Republican.]— From responsible parties who witnessed the light at Fredericton yesterday, we gather the following particulars

Col. Carlin, with parts of the Twenty first, Thirty third, and Thirty-eighth Illinois regiments, Eighth Wisconsin, Col. Bakers Indiana Cavalry, and Major Schofield’s battery, reached Fredericton at 9 o’clock in the morning, and at 1 o’clock P. M, was joined by the Eleventh, Seventeenth, and Twentieth Illinois, and 400 cavalry from Cape Girardeau. They then advanced in pursuit of the rebels under Jeff. Thompson and Col. Lowe, who had left the place 24 hours before, and were reported to be rapidly retreating south, but about a mile distant they discovered the entire force of the enemy drawn up in line of battle, partly posted in the open field and partly in the adjacent woods, with four iron 9 pounders well planted in their front. Major Schofield immediately opened fire, and at the fourth round silenced one of the rebel guns. The engagement then became general, and lasted about two hours, but after the first half hour the rebels left the Hold in disorder and took to the woods, closely followed by both our infantry and cavalry. Before leaving the field the rebel Colonel Lowe was shot in the head and instantly killed.