1905.] Measurement of the Length of Long Electric Waves, etc. 495 



If W is the velocity of the wave along the helix and A is the wave- 

 length of the stationary wave, as measured on the helix, and * the 

 frequency of the oscillations, then W = rcA. If C is the capacity and 

 L the inductance in the oscillatory circuit formed with the condenser 

 of unknown capacity and^ariable inductance, then the frequency in 

 this circuit is n = l/2:r ,J QL 



Also if c and I are the capacity and inductance per unit of length of 

 the long helix, we have W = I/ Jd. Therefore 



A 



or 



FIG. 5. 



Hence, since A can be measured, and the oscillation constant of the 

 helix per unit of length ,Jd is known, we have the oscillation constant 

 of the exciting circuit, and therefore of the closed circuit wave-meter in 

 any position when it is adjusted to agree with that circuit. Otherwise, if 

 we have the means at hand, the oscillation constant of the instrument can 

 be determined for various positions of the slider by simply measuring 

 the capacity (C) of the condenser and inductance (L) of the helix which 

 are effective in that position, and calculating the value of v CL for 

 various positions of the outer or inner jacket, according to the form of 

 instrument used. The instrument can have its scale marked to show 

 directly either oscillation constants (0) or frequencies (n), or aerial 

 wave lengths (A) in metres or feet. The instrument is not only useful 

 for quantitative work in connection with Hertzian-wave telegraphy, but 



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