Zz 
Electrical Vibrations associated with Simple Circuits. 639 
to perimeter of open rectangle 2°60, or the period of vibration 
in such a circuit longer than i in the case of an open circle of 
the same perimeter. Bumstead, in the Am. Journ. Sci. 
vol. xiv. p. 359 (1902), investigates theoretically the reflexion 
of electric waves at the free ends of a parallel] wire system. 
If I understand the 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 (Ann. der Physik, v. 4, p. 872, 1901) has found 
the length of an open circle resonator when in tune with a 
straight-r od oscillator. The rod being 250 ems. long, 248 ems. 
was finally taken as the resonance- length for the open circle, 
a result slightly different from that given above, where the 
distance between the ends of the resonator was much greater 
than in Kiebitz’s experiment. 
Sarasin & De la Rive, as the result of their final measure- 
ments*, give the wave- length of the vibration connected with 
open resonators, made of stout wire 1 em. in diameter, as 
600 ems. for an open circle 234 cms. in circumference, and 
400 ems. for one 156 cms. in circumference. This makes 
the wave-length 2°56 times the length of the circuit. 
Macdonald, ‘ Electric Waves,’ p. 111, in considering the 
question of stationar y waves in open circuits, calculates the 
wave-length for any resonator, and finds for the fundamental 
mode of vibration, No = 2°53/ where ij is the length of the 
circuit, a value in wonderful agreement with Sarasin & 
De la Rive’s conclusions. Appar ently , according to theory, 
the wave-length is independent, within wide limits, of the 
Hemeter of the wire of which:the resonator is made, in the 
ratio of wave-length to length of circuit independent of the 
size of the circle. 
By extrapolation (see fig. 2) the present experiments give, 
for a circle 200 cms. in cir reumference, the ratio of perimeter 
of rectangle to length of circuit 2°45. This is less than the 
ratio of wave-len oth to circumference as given above b 
Sarasin & De la Rive for asimilar-sized circle and as caleulated 
by Macdonald. In considering the difference it is necessary 
to remember that extra capacity effects at the ends of the 
resonator may not have been altogether negligible in Sarasin 
& De la Rive’s apparatus. On the other hand, the wave- 
length of the vibration connected with narrow "rectangular 
closed circuits, made of wire of finite thickness, may be a 
little longer than their perimeters. Again, the wave-length 
* Sarasin & De la Rive, C. &. vol. exv. p. 1280 (1892). 
