371 
1907-8.] Note on Electrical Resistance of Spark Gaps. 
solder at T. FH and DK are the leads to the galvanometer. When the 
current passed from A to B, the junction T heated and a current passed in 
the galvanometer circuit. 
The resonator was thus a long narrow rectangle, the length of which 
could be varied from 58 to 100 eras, by sliding the rods inside the tubes 
The self-inductance of the resonator was found to he strictly proportional 
to its length. The latter was read off on a scale. 
© 
The procedure was as follows : — When the induction coil was started it 
charged the condenser. The latter then discharged itself through the spark 
gap in a train of diminishing oscillations and induced oscillations in the 
resonator. These heated the thermo-couple and produced a deflection on 
the galvanometer scale. This deflection was proportional to the mean 
square of the induced current. The self-inductance — i.e. the length — of 
the resonator was altered until this deflection was a maximum. The 
resonator was then in resonance with the oscillator. The deflection of the 
galvanometer was then read for different lengths on both sides of resonance, 
and deflection plotted against length gave the “ resonance curve.” 
If J m denotes the maximum value of the deflection, a m the corresponding 
length of the rectangle, J the value of the deflection for another length, 
a m zLSa where See is small in comparison with a m , then Drude has shown * 
that 
where y x and y 2 are respectively the logarithmic decrements of the 
vibrations in the oscillator and the resonator, the logarithmic decrement 
being defined as the natural logarithm of the ratio of two successive 
oscillations in the same direction. 
where R denotes the resistance, C the capacity, and L the self-inductance 
in the circuit. Drude’s formula is derived on the suppositions (1) that the 
magnetic coupling of the two circuits is weak ; (2) that the resistance of 
the spark gap is constant ; and (3) that the oscillator condenser is not 
charged again until it has been completely discharged. In other words, 
there are no partial oscillations in the secondary of the induction coil. 
The second supposition is open to serious objections. Still it is obvious 
that y 1 + y 2 measures the flatness of the resonance curve, and that from 
general considerations the less the vibrations in the oscillator are damped, 
the sharper and better defined the resonance curve must be. 
* Ann. d. Phys., xv., 1904, p. 709. 
