The magnetic needles employed in these experiments were cylinders of 0,16 inch diameter, and 2, 4 inches in length, pointed at the ends: they were suspended by a single silk fibre of rather more than five inches in length. The box in which they were inclosed, as a protection from the weather, was of wood, having at the bottom a graduated circle in ivory, rather exceeding in diameter the length of the needles, and over the centre of which the silk fibre was suspended. The bottom of the box being rendered horizontal by means of foot screws, and shown to be so by an unattached spirit level, the zeros of the circle were placed in the direction of the magnetic meridian, and a needle was suspended in a horizontal position. Another needle was then employed to draw it 50 or 60 degrees from its natural direction ; on the removal of which, the suspended needle resumed its direction in the ordinary process of vibration. The registry of the vibrations was commenced when the arc had diminished to 30°, and continued until it was reduced to below 5°: the method of registering the vibration will be best understood by a reference to the Tables at the close, and is too simple to require further explanation. The number of vibrations made by each needle between the arcs of 30° and 5° was usually from 300 to 400; and the time in which these were performed varied, in the different needles, from 12 to 16 minutes: the mean time of performing 100 vibrations between the specified arcs is the result deduced for each experiment. Four of the needles, Nos. IV, VIII, X, and XI, with an apparatus in duplicate, were sent to me in the summer of 1826 by Professor Hansteen of Christiania, to be employed in obtaining the comparative magnetic intensity in different parts of Great Britain. Shortly after their arrival, an opportunity occurred of sending two of the needles, Nos. IV and XI, with an apparatus, to Captain Basil Hall, in Edinburgh; by whom, assisted by Lieut. Robert Craigie, of the Royal Navy, the experiments numbered 12 to 16 in the subjoined tables were made, in February 1827; and the needles returned, so as to be included in the comparative experiments between Paris and London.