Professor Carlini was engaged, in the summer of 1821, in concert with Professor Plana, in determining the amplitude of the celestial arc between the Hospice on Mont Cenis and the Observatory at Milan, by means of fire-signals made on the Roche Melon, and observed simultaneously at Milan and at a temporary observatory established at the Hospice. Whilst thus engaged, Professor Carlini, being stationary for several days on Mont Cenis, and obliged to have time very accurately determined, for the purpose of comparing with the observatory at Milan, availed himself of the opportunity to employ a pendulum apparatus of the same general nature as that used by M. Biot at Paris, which had been prepared at Milan some years before, under the direction of a commission of weights and measures, with the view of determining the value of the divisions of the national linear scale. As this apparatus differed in some few particulars from the original employed in France, we shall briefly notice the differences, presuming our readers to be acquainted with the apparatus of MM. Borda and Biot. 1. In the Milan apparatus, by means of two microscopes furnished with wire micrometers, the length of the pendulum [p156] may be measured without touching it; without approaching it; without even opening the case which contains it. The measure is obtained by bringing the wires in contact with the images of the knife-edge suspension, and of the upper and lower borders alternately of the platinum disk suspended to the thread: thus preventing the risk of deranging the equilibrium, and avoiding the effect which the heat of the body might have on the dilatable metallic thread. 2. The half sum of the distances taken between the suspension, and the upper and lower edges of the disk, gives the distance of the centre of the disk itself; without measuring its diameter with a compass, an operation exceedingly difficult to execute with the necessary precision. By this apparatus of microscopes the length may be measured at pleasure, even during the time of oscillation; and being attached to the wall, instead of supported by the floor, the risk of derangement by the tread of the observer is avoided. 3. The pendulum, and the clock by which its oscillations are measured, were not, as usually, near together and resting on the same base, but were perfectly separated. The coincidences of the oscillations were observed, by bringing the image of the pendulum of the clock, reflected by means of an oblique mirror, in contact with the image of the simple pendulum seen direct through a telescope. By this modification the risk of the mutual influence of the pendulum and the clock is avoided. 4. The disk was attached to the thread by means of knots in the thread itself; avoiding the correction for the small cup usually employed for that purpose.