On Monday, December the 29th, the Funeral Obsequies were performed. The following account of the imposing ceremonial is from the _Edinburgh Witness_. FUNERAL OF MR. HUGH MILLER. The mortal remains of this truly great man were consigned to the grave on Monday, amid the most marked demonstrations of sorrow on the part of the entire community. The private company, numbering about sixty individuals, met at Shrub Mount, the residence of the deceased at Portobello, about a quarter to one in the afternoon. Amongst those present were the Lord Provost of Edinburgh; A.M. Dunlop, Esq., M.P.; A. Black, Esq., M.P.; Professors Simpson, Balfour, and Fraser; Rev. Principal Cunningham; Professor James Buchanan; Rev. Drs. Guthrie, Candlish, Hanna, Bruce, Begg, Hetherington, and Wylie; Rev. Messrs. M'Kenzie of Dunfermline, Cameron and Hunter of Nagpoor; Maurice Lothian, Esq.; Geo. Dalziell, Esq., W.S.; W. Wood, Esq.; R. Paul, Esq.; Francis Russell, Esq., advocate; M. Torrance, Esq.; Dr. Russell; Dr. Geo. Bell; J.F. Macfarlan, Esq.; Archibald Gibson, Esq.; and Councillor Johnston. The devotional exercises were conducted by Dr. Guthrie, who was deeply affected during the prayer, and whose feelings at times threatened to overcome him. Thirteen two-horse mourning coaches were here in waiting to convey the company to the place of sepulture in the Grange Cemetery, preceded by the hearse, which had four horses. The melancholy event, as might have been expected, cast a gloom over the whole of Portobello; and the Provost and Magistrates, anticipating the general feeling of the inhabitants, to whom Mr. Miller had endeared himself by his genius and the modesty of his demeanor, and also by the readiness which he ever displayed to contribute to their intellectual elevation, by taking part in several courses of popular lectures in the town, recommended the closing of the different shops,--a request which was at once readily complied with. Another striking proof of the general desire to pay the last tribute of respect to the remains of the deceased, was furnished by the circumstance that upwards of one hundred gentlemen, many of whom had, so recently as the previous Tuesday, listened to the reading of one of the ablest of his lectures, by the Rev. Mr. Wight, the Congregational minister, met at half-past twelve in the Free Church, in order to accompany the funeral, either on foot or in carriages, to the burial place,--a distance of about four miles. After a short, impressive religious service, conducted by the Rev. Mr. Philip and the Rev. Mr. Wight, they proceeded to join the private company, who had by this time taken their places in the mourning carriages, on their way to Edinburgh.