PERIODS OF ELECTRICAL VIBRATIONS. 201 
with such circuits is equal to eight times the diameter of 
the circuits, 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 recently, 
arrives at a different conclusion. He has investigated the 
problem of the vibration connected with circular resonators 
in an ingenious manner, by enclosing them in exhausted 
glass tubes, and judging of the electrical state of the wires 
by the luminosity produced in the rarefied gas. Turpain 
has published many accounts of his experiences, finally 
summarising his work in the Journal de Physique, Vol. x., 
p- 425, 1901. On pp. 435 et seq., he describes experiments 
made with an open circular resonator and part of the in- 
ducing field enclosed 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 estab- 
lished that ‘* the length of the wave of the electric oscil- 
lation which excites a given wire formed resonator is equal 
(allowance being made for the micrometer perturbation) to 
double the length of the resonator.’’ 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 Strindberg’ who confirmed Sarasin 
and De la Rive’s results with a resonator in which no sparks 
occurred. li Turpain has interpreted his experiments 
aright his results must be considered at variance with the 
+ Strindberg—Comptus Rendus, cxx11., p. 1403, 1896. 
N—Sept. 2, 1903. 
