Z 
Electrical Vibrations associated with Simple Circuits. 637 
of the oscillation connected with a straight wire is much 
ereater than twice the length of the wire, a result opposed to 
Slaby’s conclusions and to Drude’s statement. 
For open circular resonators Sarasin and De la Rive * 
obtain results which are usually stated by saying that the wave- 
length of the free electrical oscillation connected with such 
circuits is equal to eight times the diameter of the circuit or 
to 2°55 times the wire-length. These results have been 
abundantly verified in a general sense, but it is doubtful if 
the statement is not too wide, as it takes no account of the 
diameter of the wire of which the resonator is made, nor of 
the shape or configuration of the ends of the circuit. 
Turpain, from observations published quite recentiy, arrives 
at a different conclusion. He has investigated the problem 
of the vibration connected with circular resonators in an 
ingenious manner, by inclosing them in exhausted glass tubes, 
and judging of the electrical state of the wires by the lumi- 
nosity produced in the rarefied gas. Turpain has published 
many accounts of his experiments, finally summarizing his 
work in the Journal de Physique, vol. x. p. 425 (1901). On 
p- 435 et sey. he describes experiments made with an open 
circular resonator and part of the inducing field inclosed in 
an exhausted vessel, and others where only the spark-gap 
was surrounded with rarefied gas. In both cases, it is stated 
that the resonator responds when one half the exciting wave- 
length is equal to the length of the resonator. Turpain 
considers it experimentally established that “the length of 
the wave of the electrical oscillation which excites a wire- 
formed resonator is equal (allowance being made for the 
micrometer perturbation) to double the length of the reso- 
nator.” That a perturbation set up at the spark-gap is not, 
however, responsible for any apparent discrepancy between 
theory and experiment, was shown by the work of Strind- 
berg t, who confirmed Sarasin & De la Rive’s results with a 
resonator in which no spark occurred. If Turpain has 
interpreted his experiments aright, his results must be con- 
sidered at variance with the great body of experimental 
evidence and with present theory. 
Drude (loc. cit. p. 380) gives the measures of the wave-length 
of the vibration connected with four open circles, three of them 
being supported by wooden cores and one being wholly sur- 
rounded by air. For the latter, the half wave-length is 
259 cms. when the length of the wire is 243 cms., the ratio 
* Sarasin & De la Rive, C. &. vol. cx. 1890, vol. exii. 1891, vol. exv. 
1892. 
+ Strindberg, C. &. vol. cxxii. p. 1403 (1896). 
