Electrical Vibrations associated with Simple Circuits. 641 
Pocklington (Proc. Camb. Phil. Soc. vol. ix. p. 324, 1897) 
has calculated theoretically the period of the free electrical 
vibration associated with a closed circular ring, and has 
arrived at the result that the wave-length is rather less than 
the circumference of the circle. Kiebitz’s experiment and 
the present investigation give a value rather greater than the 
circumference. The problem of the electrical oscillations 
connected with closed circuits is discussed generally by 
Macdonald (‘Electric Waves, p. 62), but calculations for 
special cases are not given. 
Diameter of the Wire forming the Circuits.—St. John, in 
experiments with waves along wires (Phil. Mag. vol. xxxviii. 
1894), for oscillations of the same period, obtains a 5 per 
cent. increase in the value of the wave-length along parallel 
copper wires as the diameter of the wires changes from 
0-04 em. to 0°12 cm. In St. John’s investigation, however, 
the problem is complicated by the presence of extra capacity at 
the ends of the circuit. No difference of period has been 
found in the present experiments between a rectangle made 
of thin brass wire 0°04 cm. in diameter and one of copper 
wire 0°33 cm. thick. An open circle was compared with 
the rectangles in turn, and was in tune with each of them 
when its circumference was 380 cms., the perimeter of each 
rectangle being 886 cms. and the width 30 cms. 
Permeability of the Medium surrounding the Circuits — With 
the rapid alternations of current used in these experiments, 
it is not to be expected that the permeability of the material 
of the circuit would have a considerable effect on the period 
of vibration (see St. John, loc. cit.). The permeability of the 
medium outside the wire, on the other hand, is of primary 
importance in this connexion. This may be readily shown 
by surrounding the middle portion of an open circuit, where 
the current is concentrated, when electrical oscillations take 
place in it, with fine, well-insulated iron filings, and comparing 
the period of vibration with that connected with the circuit in 
air. Inthe case tried, the central part of a straight copper wire 
0°33 cm. in diameter, covered with parattned paper, passed 
centrally through a glass tube 70 cms. long and 1 ecm. 
internal diameter, the tube being filled with parafiined iron 
filings. The wire under these circumstances when 345 cms. 
long had the same period of electrical vibration as a copper 
wire of the same gauge wholly in air 370 cms. long. 
Results of present Investigation. 
_ In the following Tables, under the headings “ perimeter of 
rectangle ”’ and “length of straight (or curved) wire,” the 
Phil. Mag. 8. 6. Vol. 7. No. 42. June 1904. ye. 
