50 Dr. A. Elsass on a new 
of the bob of a pendulum; then it is only necessary each time 
that it comes into the position a to give it a blow in the direc- 
tion ab. The motion will be sustained if the period T of the 
excitation is equal to the period of the oscillation. We see, 
however, that the motion of the pendulum may also be sus- 
tained by impulses of the periods 2T, 3T, &c.; for if the 
pendulum-bob is at a at the times 0, T, 2T, 37, &c., it is suffi- 
cient that it should receive an impulse in the direction ab at 
the instants T, 3T, 5T in order to replace the energy lost 
by friction. It is seen, however, that the amplitude of the 
pendulum-oscillations will be greatest for equality of periods, 
if the impulses are in all cases of equal intensity. 
From these considerations we should expect that, in the 
constrained vibrations of the thread, the mth partial vibration 
whose period T,, = =i is equal to the mth part of the period 
of the fundamental vibration, would appear if the period (T) 
of the excitation is equal to T,,, 2Tn, 3T,,, &c. The phenomena 
of oscillation, however, are not so complicated with the appa- 
ratus here described as might appear from this. A small wheel 
is fixed somewhat excentrically upon the axis of the, siren 
(fig. 2) (the excentricity amounts to about 0°5 millim.), and 
to the uprights carrying the wheelwork is fixed, by means of 
two screws, a support for a little bent lever, the conically- 
pointed axis of which rests in two steel screws passing through 
the support, and moves in it with 
a small amount of friction. The 
wheel itself and the supports for 
the lever are of cast brass. The 
lever (as shown in fig. 2) is ca- 
pable of motionin a vertical plane, 
presses with its vertical armagainst 
the excentric wheel, and has its 
horizontal arm attached to the 
stretched thread, which is hori- 
zontal and at right angles to the 
axis of the lever. The tension of 
the thread retains the lever in its 
position when the siren is at rest, 
and brings it back into its position 
of rest when the siren is sounding, 
and the revolving excentric wheel 
imparts to it periodically a small 
motion. It is not necessary, nor 
possible with a considerable ten- 
sion of the thread, that the lever should touch the wheel 
