In a paper in the Proceedings of the Royal Society for 1877, xxvi., 162, when describing a new method for determining the speed of machines, we pointed out that by the employment of a graduated drum rotating with a known velocity the true vibration number of a tuning-fork could be accurately determined. The following is an account of the apparatus employed, and subjoined are records of some experiments which have been made on tuning-forks with it, which, in view of the attention now being given to the subject, may prove of interest. One essential instrument proved to be a good time-measurer. It will be seen in the sequel that an electric current is required once a minute, and in the earlier experiments a two-day marine chronometer was employed, a key being depressed by hand at the end of each minute. So many difficulties, however, arose from its use that it was soon rejected and a clock substituted. Near the pendulum two springs were placed which, being pressed together at the end of each vibration, made a contact at every alternate second. About the 59 th second of each minute, a key was depressed by hand and held down until the clock completed the circuit. This, though a great improvement, was not entirely satisfactory, and endeavours had to be made to eliminate entirely all contacts made by hand. This was done by means of a compensated pendulum worked by electricity and connected with an electric clock The method of compensation was copied from that of a pendulum exhibited in the Loan Collection of Scientific Apparatus, as a model of the one belonging to the standard clock of the Royal Observatory a t Greenwich. Originally, the impulse was given by an electromagnet placed under the bob, the contact being made by a small trailing piece of steel, which, catching in a notch in a piece of steel below, depressed a spring at every alternate second. This method, which is frequently employed in small clocks, is generally arranged to give a powerful impulse to the pendulum, and this so much increases the arc of vibration that the trailing piece passes over the notch without again engaging in it until the arc has sufficiently diminished. Although such clocks are accurate enough for ordinary purposes, it is obvious that the method would be inadmissible in cases where the period of all vibrations must be the same. To ensure uniformity in this respect the battery power was diminished until the contact was made at each vibration, but after many trials the method was abandoned, for it was found that the friction between the steel trailing piece and the notched piece below was not constant, and, besides, the pendulum was often found to be swinging in an elliptic arc.