Agreeably to public advertisement, the discussion betwixt Mr. GEORGE THOMPSON and the REV. R. J. BRECKINRIDGE, was opened Monday evening, June 13. By half-past six, the hour fixed on by the Committee, Dr. Wardlaw's Chapel contained 1,200 individuals, the number agreed upon by both parties. A great number could not gain admittance, in consequence of the tickets allotted, being bought up on Saturday. On the entrance of the two antagonists, accompanied by the Committee, the audience warmly cheered them. By appointment of the Committee-- * * * * * REV. DR. WARDLAW took the Chair. Having thanked the Committee for the honor they had conferred on him, and which, he trusted, would meet with the concurrence of the meeting, he said he had accepted the honorable post with the utmost confidence in the forbearance and propriety of conduct of the two gentlemen--or antagonists, should he call them? who were to address the meeting; and also, with the most perfect confidence in the good conduct and sense of propriety possessed by the meeting. Had he not possessed such confidence, he would never have thought of undertaking the present task. Had he imagined that the present meeting would give way to similar expressions of feeling as had taken place within these walls on some former occasions, he would at once have declined the task, as one for which he was totally unfit,--he was not fit to manage storms. The parties on the present occasion were different from those to whom they had listened at the time to which he referred. One of them, it was true, was the same, and his character all of them knew. They knew his sentiments, his zeal, his eloquence, his devotedness to the great cause of which he was the fearless advocate. In reference to his opponent, on the present occasion, he would not dishonor that gentleman by naming him along with an individual who had stood before them formerly in opposition to their eloquent friend. He felt it to be his duty to introduce to them his friend--for he was allowed to call him so--the Rev. Mr. Breckinridge. That gentleman had come to this country, the accredited agent from the Presbyterian church--a large and influential body of Christians in America, to the congregational union of England and Wales. It was proper that he should state to the meeting that Mr. Breckinridge was no advocate of slavery--that he believed it to be opposed to the letter and spirit of the gospel, and as a proof how far he was in earnest in his professions in this matter, he had freely parted with a patrimonial estate so far as it consisted of slaves. (Cheers.) Having stated this, it might be further necessary that he should mention what gave rise to the present meeting. They were all aware, then, he said, that since his return from America, Mr. George Thompson had been lecturing in various parts of the kingdom. In the course of his labors he was accused of having