F0 and F being the values of the force at the beginning and at the end of the time, t. The above formula is independent of the choice of units. If we wish t to be expressed in seconds, we must give ρ the corresponding value (ρ = 1.058 × 10-16). If we take ρ as a unit we make ρ = 1, and we find the absolute value of the time by the expression:
(lS) / (8πe s) log hyp(F0/F)
We remark that this expression of time contains only abstract numbers, being independent of the choice of the units of length and force. S and e denote surface and the thickness of the condenser; s and l the section and the length of a column of mercury of the resistance, R. This form of apparatus enables us practically to measure the notable values of t only if the value of the resistance, R, is enormous, the arrangement described in the text has not the same inconvenience.
NEW METHOD OF MAINTAINING THE VIBRATION OF A PENDULUM.
A recent number of the Comptes Rendus contains a note by M.J. Carpentier describing a method of maintaining the vibrations of a pendulum by means of electricity, which differs from previous devices of the same character in that the impulse given to the pendulum at each vibration is independent of the strength of the current employed, and that the pendulum itself is entirely free, save at the point of suspension. The vibrations are maintained, not by direct impulsion, but by a slight horizontal displacement of the point of suspension in alternate directions.
This, as M. Carpentier observes, is the method which we naturally adopt in order to maintain the amplitude of swing of a heavy body suspended from a cord held in the hand. The required movement of the point of suspension is effected by means of a polarized relay, through the coils of which the current is periodically reversed by the action of the pendulum, in a manner which will presently be explained. The armature of the relay oscillates between two stops whose distance apart is capable of fine adjustment.
It is clear, therefore, that the impulse is independent of the strength of the current in the relay, provided that the armature is brought up to the stop on either side. The reversal of the current is effected by means of a small magnet carried by the bob of the pendulum, and which as it passes underneath the point of suspension is brought close to a soft iron armature, which has the form of an arc of a circle described about the point of suspension. This armature is pivoted at its center, and thus executes vibrations synchronously with those of the pendulum. These vibrations are adjusted to a very narrow range, but are sufficient to close the contacts of a commutator which reverses the current at each semi-vibration of the pendulum.
The beauty and ingenuity of this device will readily be appreciated.