The mortal remains of this Gallant and Illustrious Admiral were interred, May 29, in the Cimetiére de l' Est, or Eastern Division of the Great Cemetery of Pére la Chaise. The body was taken from his late residence in the Rue d'Aguisseau to the English Episcopal Church in the same street, followed by his relatives, William and Herbert Smith, Esquires, Nephews, Captain Arabin, and ---- St. Clair, Esquire, Sons-in-law of the deceased, with Vice Admiral Sir Charles Rowley, Bart. Lieut.-General Lord Aylmer, General Count Excelmans, Peer of France, and the French Admiral Bergeret, as supporters of the Pall, besides many of the principal English residents in Paris, among whom were several officers of high rank in the British Navy.--The introductory part of the service was performed in the Church by the Right Reverend Bishop Luscombe, and two assistants, and the body was then borne to the Cemetery, attended by a long cortége of mourning and private carriages. On the Coffin was placed the Hat, Sword, and Uniform of the deceased, and on a cushion his epaulettes and numerous orders. Over the foot of the coffin was spread the British Union Jack. At the conclusion of the burial service, which was most impressively read by Bishop Luscombe, three orations were delivered--the first by Monsieur Jullien, of Paris, who gave a short but comprehensive recapitulation of the services of Sir Sidney, from his first entering the British Navy at the age of 13, and also expatiated largely on his amiable and philanthrophic qualities. The next speaker, M. Caille, Advocate of the Cour Royale of Paris, after pronouncing a general panegyric on the character of the deceased as a warrior, proceeded to eulogise him for his active and generous exertion in promoting the objects of several philanthropic societies of which he was a member, and to which his advice, his practical and scientific acquirements, and his inventions, were so invaluable. Both speakers were loud in their praise of Sir Sidney, for his having been almost the first to interfere for the suppression of European slavery in Africa, and for his indefatigable and strenuous exertions in that humane cause. The third gentleman, M. Raoul, Advocat of the Court of Cassation, spoke in a similar strain of eulogium of the character of Sir Sidney as a citizen of the world, ever ready to aid the cause of humanity. No stronger testimony to his worth could, however, have been shewn, than to hear his eulogium pronounced solely by members of a Nation against which, in his career of arms, he had so successfully and gloriously fought. Sir Sidney Smith was Prince Magistral and Regent of the Order of the Temple, and a Member of the Legion of Honour. The following two Discourses pronounced upon the melancholy occasion, were, in the kindest and most handsome manner, contributed by M. Jullien, the learned author of many valuable works.--