Sir WM THOMSON acknowledged in cordial terms the hearty welcome expressed in this address. The Association, he continued, when it commenced the experiment of being a peripatetic Association for the advancement of science, made an experiment which many considered of a doubtful character. It was urged that although zeal for a new thing might carry the Association on for a few years successfully, the success would cease with the novelty. This prophecy had not been fulfilled. On the contrary, the experiment had been crowned with brilliant success. He did not think the founders of the Association, fifty-two years ago, when they drew up the wise plan and regulations of the society which have since continued in force almost without change, imagined, for a moment, the possibility of a meeting being held on this side of the Atlantic. (Applause) Their meeting here was strictly within the letter of the law and wholly in accordance with the spirit by which the British Association was directed, and that was to carry through the British Empire any advancement in science that could be promoted by the existence of the Association. At the outset, when the body was formed, some fifty years ago, the mathematical section, of which he was now president, held that it was impossible for a steamboat to cross the Atlantic. As president of that section, he ought to be ashamed that it had adopted such a conclusion. The business of the Association was to advance science and never to stand still. Many misgivings had been felt as to the success of the experiment of visiting this side of the water, but none were felt as to the kindness with which they would be received. Nobody doubted that the warmest welcome would be given by their countrymen on this side, and none knew better how to give a warm welcome. With respect to his own feelings, he felt most deeply the privilege and honour of filling the position be held, but it was accompanied with one regret and that was the absence of Professor Cayley, who would have been in his place had not circumstances compelled him to remain on the other side. He concluded by again expressing his warm thanks and those of the Association for the magnificent welcome given them. Lord RAYLEIGH, as president-elect, joined in the expression of thanks for the hearty welcome. We all, he said, felt great interest in visiting, many of us for the first time, this extensive and diversified land, which has become the borne of so many of our fellow countrymen. Before the day is out I am afraid the tones of my voice will have become only too familiar to you, and I will therefore say nothing more than that we most cordially reciprocate the sentiments expressed in the address presented to us.