PERIODS OF ELECTRICAL VIBRATIONS. 203 
the wire is less in the circular form than when straight 
and the capacity is practically unaltered. 
A further decrease of inductance without appreciable 
change of capacity can be made by bending the wire form- 
ing the open circle into the shape of a narrow rectangle 
with anopenend. One would expect therefore, the period 
of vibration in sucha circuit to be somewhat less than 
that in an open circle of the same perimeter. That the 
periods of electrical vibration connected with such circuits 
are at least nearly equal, when the perimeters are the same, 
is shown by a result obtained by Sarasin and De la Rive’ 
in connection with their experiments with waves along 
wires. In these experiments it was found that the distance 
from the free ends of the wires to the first node was nearly 
equal to half the circumference of the resonator, and in 
such a case of parallel wires with free ends, the end section 
may be considered to correspond with an open rectangle. 
Macdonald’ in giving the distance to the first node from 
the ends of the wire as 0°192 makes the ratio of wave 
length to perimeter of open rectangle 2°60, or the period of 
vibration in such a circuit longer than in the case of an 
open circle of the same perimeter. Bumstead’ has investi- 
gated theoretically the reflection of electric waves at the 
free ends ofa parallel wire system. If lunderstand his result 
aright, it means that the distance from the free end of the 
wire to the first node is always less than a quarter the wave 
length along the wires by half the distance between them. 
This cannot be generally true. 
Kiebitz* has found the length of an open circle resonator 
when in tune witha straight rod oscillator. The rod being 
250 cms. long, 248 cms. was finally taken as the resonance 
’ Sarasin and De la Rive—Comptes Rendus, cx, 1890. 
* Macdonald —“ Electric Waves,” p. 121. 
3 Bumstead—Awm. Journ. Sci., xi1v., p. 359, 1902. 
* Kiebitz—Ann. der Physik., v., 4, p. 872, 1901. 
