278 Electrical Vibrations associated with Conducting Rods. 
are very rapidly damped ; and in fact theoretical considera- 
tions based on experiment indicate that the rate of damping 
of the free vibrations of longest period associated with a 
terminated straight wire is not very far removed from the 
order of magnitude of the known result for a spherical 
vibrator. 
The experiments of Sarasin and de la Rive, referred to 
above, show that the period of the waves to which a termi- 
nated straight wire resonates is approximately that of a 
nearly closed ring resonator of the same length. Prof. 
Pollock’s experiments* show that when a ring resonator is 
opened out the free period at first diminishes, but that, after 
it has been opened out a certain amount, further straightening 
of the wire does not alter the free period. Thus, for a wire 
152 ems. long bent into a ring resonator the wave-length 
was found to be 404 cms., and when it was straightened out 
the wave-length diminished to 387 cms., remaining at this 
length when the wire was farther straightened out; so that 
it may be concluded that the ratio of the wave-length of the 
free oscillations of longest period associated with a straight 
wire 152 cms. long to the w ave-length of the oscillations to 
which it resonates is 387/404. Now, if we may compare 
with a simple vibrating system, whose equation of motion is 
2+ Que+Ka=0, 
the period 207/P1 of the oscillations to which it resonates is 
given by p?=«—2yu*, and the free period 2/p) by 
Pose —p. Hence, if A, ard Ay, are the corresponding 
wave-lengths, 
that is 
No /Ay = VAC! — 1/47°n*), 
where n is the number of vibrations executed before the 
amplitude falls to 1/e of its value. Taking \/A,=387/404 
the value of 7 is °55, and it may be inferred that this repre- 
sents roughly the rate at which free oscillations associated 
with a terminated straight wire 152 ems. long decay. 
* Phil. Mag, June 1904. 
