Science is to art what the great fly-wheel and governor of a steam-engine are to the working part of the machinery--it guides, regulates, and controls the whole. Science and art are inseparably connected; like the Siamese Twins, they cannot be separated without producing the death of both. How, then, are we to regard the superb specimens of natural history, which the liberality, the munificence; and the wisdom of our State have collected at the Capitol? They are the elements from which we can here determine all that belongs to the Natural History of our State; and may we not indulge the hope, that science and genius will come here, and, striking them with a magic wand, cause the true practical to spring into immortal life? Remarks were also uttered by Prof. CHESTER DEWEY, President ANDERSON, and Rev. Dr. COX. And thus ended the Inauguration of the State Geological Hall. We turn to the Observatory, in regular order of succession. INAUGURATION OF DUDLEY OBSERVATORY. The Inauguration of the Dudley Observatory took place under the same tent which was appropriated to the dedication of the Geological Hall, and on the day following that event. An immense audience was assembled, drawn by the announcement of Mr. EVERETT'S Oration. At a little past three o'clock the procession of _savans_ arrived from the Assembly Chamber, escorted by the Burgesses Corps. Directly in front of the speaker's stand sat Mrs. DUDLEY, the venerable lady to whose munificence the world is indebted for this Observatory. She was dressed in an antique, olive-colored silk, with a figure of a lighter color, a heavy, red broché shawl, and her bonnet, cap, &c., after the strictest style of the old school. Her presence added a new point of interest. Prayer having been uttered by Rev. Dr. SPRAGUE, of Albany, THOMAS W. OLCOTT, Esq., introduced to the audience Ex-Governor WASHINGTON HUNT, who spoke briefly in honor of the memory of CHARLES E. DUDLEY, whose widow has founded and in part endowed this Observatory with a liberality so remarkable. Remarks were offered by Dr. B. A. GOULD and Prof. A. D. BACHE, and Judge HARRIS read the following letter from Mrs. DUDLEY, announcing another munificent donation in aid of the new Observatory--$50,000, in addition to the $25,000 which had been already expended in the construction of the building. The letter was received with shouts of applause, Prof. AGASSIZ rising and leading the vast assemblage in three vehement cheers in honor of Mrs. DUDLEY! ALBANY, Thursday, Aug. 14, 1856. _To the Trustees of the Dudley Observatory:_