PIGEON HILL.--Famous as the scene of a skirmish between the British Regulars and Volunteers and the Fenian bandits, who attempted to invade Canada during the past summer. The following gives honor to whom honor is due, and is written by a gentleman who can be relied on: “If any evidence were required, more than we possess, of the essentially weak and contemptible character of the Fenian organization, the circumstances attending the operations of Her Majesty’s forces and our own volunteers on Saturday, June 9th, in the neighborhood of Pigeon Hill, would furnish it. As one who accompanied that expedition, and had an opportunity of observing all that passed, I shall be happy to furnish you with a few details. I arrived at St. Armand’s Station between 11 and 12 o’clock, just at the moment that two waggons from Pigeon Hill arrived, bringing five Fenian prisoners, who had been taken that morning by different parties, whose names I need not mention, as I cannot give all with accuracy. I must confess that my astonishment was great when I saw them. Three were little scamps--such as one sees about the streets of all great cities, as news-boys, &c. One was a tolerably stout, resolute looking-fellow, the other a mild-looking young man, much better dressed, who, I am sorry to say, stated himself to have been born in Yorkshire, though hailing from Montpelier, Vt. Shortly after they were lodged in the guard-house, another prisoner, an able-bodied hard-looking customer, about 28 or 30 years of age, was brought in. He had a tremendous black eye, which he told me he received in a brawl with his own companions the night previous. Leaving these in the custody of the St. Armand volunteers, the column of attack started for Pigeon Hill about 2 P.M. The Granby and Waterloo volunteers, commanded by Captain Millar, formed the advance guard, being followed by two 12-pounder Armstrong guns of Captain Balfour’s battery, with their complements of artillerymen, commanded by Captain Phipps, R.A. These were followed by two companies of the Rifle Brigade, under Major Nixon, who, I understand, commanded the whole column, and two companies of the 25th regiment--another company of that regiment forming the rear guard. Between the main body and the rear guard, the supply waggon and a farmer’s waggon, carrying the Surgeon’s apparatus and medical comforts, were placed.